ACHIEVING A LONG - LIVED CHARGE - SEPARATED FE(II) CHROMOPHORE: INSIGHTS INTO THE ROLE OF REORGANIZATION ENERGY ON THE ULTRAFAST PHOTOPHYSICAL PROCESSES OF D 6 POLYPYRIDYL COMPLEXES By Monica Catherine Carey A D ISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Chemistry Doctor of Philosophy 2018 ABSTRACT ACHIEVING A LONG - LIVED CHARGE - SEPARATED FE(II) CHROMOPHORE: INSIGHTS INTO THE ROLE OF REORGANIZATION ENER GY ON THE ULTRAFAST PHOTOPHYSICAL PROCESSES OF D 6 POLYPYRIDYL COMPLEXES By Monica Catherine Carey Photoredox catalysis reactions are ubiquitous in nature. These processes require a long - lived charge - separated state that is ideally suited for redox - based chemistry and pho tovoltaic applications. Many common chromophores used in these systems are ruthenium(II) - based, but the low earth abundance of this metal make s it non - viable for large - scale applications in the long - term. The first row congener of Ru(II) is iron(II), but its decreased ligand field strength relative to the second row transition metal causes the metal - to - ligand charge transfer (MLCT) excited state to be de popul ated on an ultrafast timescale, deactivating into metal - centered ligand field (LF) excited states that are inefficient for photovoltaic applications. The aim of this work is to understand the funda mental differences in the photophysical processes of Ru(II) and Fe(II) analogues. Three strategies can be envisioned for prolonging the MLCT lifetime in Fe(II) complexes: (1) p rohibiting the vibrational modes associated with the MLCT LF transition with synthetic mo difications to the ligand, (2) i ncreasing the ligand field strength to tu ne the LF and MLCT states such that the potential energy surface diagram for Fe(II) re sembles that of Ru(II), or (3) extending conjugation within the ligand away from the metal center, thereby decoupling the MLCT and LF excited states. Any one of these app roaches will inherent ly affect the reorganization energy, or the amount of energy required for the reactants to undergo vibrational and nuclear motions in order to achieve the geometry of the products without any electron transfer or electronic state cross ing occurring. Variable - temperature transient absorption (VT - TA) spectroscopy i s a methodology that has been developed to initially study the ground state recovery (GSR) processes of some low - spin Fe(II) polypyridyl complexes. Arrhenius parameters for this class of compounds are found experimentally for the first time and from these data, s emi - classical Marcus theory analysis is performed , allowing for inner - sphere (i.e., complex - only) reorganization energies to be found for each. The H ab 4 / ratio is determined to be different between bis - tridentate and tris - bidentate species, which is postulated to imply a difference in nuclear coordinate for the relaxation process . The VT - TA methodology is also applied to a bis - tridentate compound for which GSR is both nearly barrierless and nearly at the crossing - point of the 5 T 2 / 3 T 1 as the lowest - energy excited state . The outer - sphere reorganization energy is adju sted through the use of counteranions and solvents in an attempt to tune the barrierless nature of the complex. T he identity of the solvent did appear to affect the reorganization energy and the inverted region may have been accessed . The solvation dynamics of the vibrational cooling process in a Ru(II) chromophore were studied as a function of excitation wavelength in a series of alcohol and nitrile solvents . A dual solvation mechanism was observed depending on the amount of excess energy given to the system. T hrough the use of a sterically - encumbered analogue, t he large aryl rotation in the MLCT excited state was determined to be the relevant nuclear coordinate in the vibrational cooling process as it related to the solvation. The Fe(II) analogue of this complex has also been prepared and st udied in order to draw direct comparisons of the photophysical processes of these two related systems . These analogues are based on li gands with extended conjugation. In order to study the effects of delocalization on the excited state lifetime, o ther comp ounds of this type have been prepared and preliminary measurements of the MLCT lifetimes indicate that increasing delocalization away from the Fe(II) center lengthens the charge - separated lifetime, which is an important first s tep in achieving long - lived charge transfer states for this class of compounds iv This work is dedicated to the girls and women who are told that they Prove them wrong. v ACKNOWLEDGMENTS Although I am the one receiving the degree and honorific, this disse rtation was the work of so many: I could never have achieved this on my own, and I owe so much to those who shared their experience and knowledge, as well as to those who stood by my side during this process. To Jim, for believing in me and my work, for guiding and supporting me, and for your eternal interest and e nthusiasm in my research and career. To my family, for listening to me and being nothing but s upportive over these six years. To Bob Rasico, Glenn Wesley, Richard Staples, and Dan Holmes, for being so generous with your time and help. To my committee for t heir continued guidance and support. To my friends, for being wonderful people I knew I could count on. To the McCusker group, for all the help you provided with my science . And finally, to Mr. Spahr, Mr. Sharp, and Dr. Marsh, for inspiring my interests an d believing in my abilities. vi TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ .......................... x LIST OF FIGURES ................................ ................................ ................................ ..................... xiii LIST OF SCHEMES ................................ ................................ ................................ .................. xxix KEY TO ABBREVIATIONS ................................ ................................ ................................ .. xxxiii CHAPTER 1. ENDEAVORING TO ACHIEVE EFFICIENT IRON(II) DYES FOR SOLAR ENERGY CONVERSION APPLICATIONS ................................ ................................ ................ 1 1. The Global Energy Crisis ................................ ................................ ................................ .... 1 2. Dye - Sensitized Photovoltaic Devices ................................ ................................ ................. 7 3. Adapting Iron For Redox Applications ................................ ................................ ............. 14 3.1 Fundamental Disadvantages to Using Low - Spin Fe(II) ................................ ....... 15 3.2 Strategies to Lengthen the MLCT Lifetime in Fe(II) Chromophores ................... 20 3.2.1 Inverting the MLCT and Ligand Field Excited State Energetics ................... 20 3.2.2 Disrupting the MLCT Manifold Deactivation Nuclear Coordinate ................ 23 3.2.3 Extending the Delocalization in the MLCT Excited States ............................ 25 4. The Critical Role of Reorganization Energy ................................ ................................ .... 28 4.1 Methods for Determining Energetic Parameters ................................ ................... 30 5. Nonradiative Decay Theory ................................ ................................ .............................. 35 6. Concluding Comments ................................ ................................ ................................ ...... 45 REFERENCES ................................ ................................ ................................ ............................. 48 CHAPTER 2. VARIABLE - TEMPERATURE ULTRAFAST SPECTROSCOPY YIELDS INSIGHT INTO RELAXATION PATHWAYS OF FE(II) POLYPYRIDYL COMPLEXES ... 60 1. Introduction ................................ ................................ ................................ ....................... 60 2. Experimen tal ................................ ................................ ................................ ..................... 63 2.1 Materials and Synthesis ................................ ................................ ........................ 63 2.1.1 General ................................ ................................ ................................ ............ 63 2.1.2 Characterization of Free Ligands and Complexes ................................ .......... 64 2.1.3 Crystal Structure Determination ................................ ................................ ..... 65 2.2 Ultrafast Transient Absorption Spectroscopy ................................ ....................... 66 2.3 Variable - Temperature Measurements ................................ ................................ ... 67 3. Results and Discussion ................................ ................................ ................................ ..... 68 3.1 Characterization ................................ ................................ ................................ .... 68 3.1.1 Ground State Absorption Spectra ................................ ................................ ... 68 3.2 Crystal Structures ................................ ................................ ................................ .. 69 3.3 Challenges of Variable - Temperature Ultrafast Spectroscopy .............................. 72 3.3.1 Pulse Broadening Calculations ................................ ................................ ....... 75 3.3.2 Water Content of Acetonitrile ................................ ................................ ......... 76 3.4 3 ] 2+ Series ................................ ... 78 3.4.1 Effect of Diethyl Ether in Lattice on Lifetime of Complexes. ....................... 88 3.5 Arrhenius and Marcus Parameters of [Fe(terpy) 2 ] 2+ ................................ ............. 91 vii 3.5.1 The Ligand Field Strength of [Fe(terpy) 2 ] 2+ ................................ ................... 96 4. Future Works and Conclusions ................................ ................................ ....................... 101 4. 1 5 T 2 Excited State Energetics Determined by Photoredox Methods .................... 102 4.2 Direct Quantification of Driving Force by Photoacoustic Spectroscopy ............ 1 05 REFERENCES ................................ ................................ ................................ ........................... 109 CHAPTER 3. THE INFLUENCE OF OUTER - SPHERE REORGANIZATION ENERGY ON A BARRIERLESS REACTION IN THE EXCITED STATE DYNAMICS OF AN OCTAHEDRAL IRON(II) POLYPYRIDYL COMPLEX ................................ ........................ 116 1. Introduction ................................ ................................ ................................ ..................... 116 2. Experimental ................................ ................................ ................................ ................... 119 2.1 Materials and Synthesis ................................ ................................ ...................... 119 2.1.1 General ................................ ................................ ................................ .......... 119 2.1.2 Characterization ................................ ................................ ............................ 120 2.2 Ultrafast Transient Absorption Spectroscopy ................................ ..................... 121 2.2.1 Variable - Temperature Measurements ................................ ........................... 121 2.2.2 MLCT Lifetime Measurements ................................ ................................ .... 121 3. Results and Discussion ................................ ................................ ................................ ... 123 3.1 Characterization ................................ ................................ ................................ .. 123 3.1.1 X - Ray Crystallography ................................ ................................ ................. 123 3.1.2 Ground State Absorption Spectra ................................ ................................ . 125 3.2 Measuring Outer - Sphere Reorganization Energy ................................ ............... 127 3.2.1 [Fe(dcpp) 2 ](PF 6 ) 2 ................................ ................................ .......................... 127 3.2.2 The Role of the Counteranion ................................ ................................ ....... 134 3.2.3 Solvent Effects ................................ ................................ .............................. 139 3.2.4 Calculations of Marcus Parameters ................................ .............................. 146 3.3 The Effect of Excitation Energy ................................ ................................ ......... 148 3.3.1 Ground State Recovery ................................ ................................ ................. 148 3.3.2 MLCT Lifetimes ................................ ................................ ........................... 152 3.4 Additional Peculiarities: [Fe(dcpp) 2 ] 2+ in Dichloromethane .............................. 157 4. Future Works and Conclusions ................................ ................................ ....................... 161 REFERENCES ................................ ................................ ................................ ........................... 165 CHAPTER 4. DUAL SOLVATION MECHANISM IN RU(II) POLYPYRIDYL COMPLEX DRIVEN BY EXCITATION ENERGY ................................ ................................ .................... 172 1. Introduction ................................ ................................ ................................ ..................... 172 2. Experimental ................................ ................................ ................................ ................... 178 2.1 Materia ls and Synthesis ................................ ................................ ...................... 178 2.1.1 General ................................ ................................ ................................ .......... 178 2.1.2 X - Ray Crystallography ................................ ................................ ................. 180 2.2 Density Functional Theory Calculations ................................ ............................ 181 2.3 Steady State and Time - Resolved Spectroscopy ................................ .................. 182 2.3.1 Steady - State Absorption and Emission Spectroscopy ................................ .. 182 2.3.2 Nanosecond Transient Absorption and Emission Spectroscopy .................. 183 2.3.3 Ultrafast Transient Absorption Spectroscopy ................................ ............... 184 3. Results ................................ ................................ ................................ ............................. 186 3.1 Synthesis ................................ ................................ ................................ ............. 186 viii 3.1.1 [Ru(dpb) 3 ](BAr F ) 2 ................................ ................................ ......................... 186 3.1.2 [Ru(dmesb) 3 ](BAr F ) 2 ................................ ................................ .................... 186 3. 2 X - Ray Crystallographic Data ................................ ................................ .............. 192 3.3 Role of Solvent on the Ground State Absorption Properties of [Ru(dpb) 3 ] 2+ ..... 196 3.4 Vibrational Cooling Dynamics in [Ru(dpb) 3 ] 2+ ................................ .................. 202 3.4.1 Ultrafast Kinetics Measured in Alcohol Solvents ................................ ......... 202 3.4.2 Ultrafast Kinetics Measured in Nitrile Solvents ................................ ........... 205 4. Discussion ................................ ................................ ................................ ....................... 207 4.1 Dual Solvation Mechanism ................................ ................................ ................. 207 4.1.1 Anomalous Trend in the Shorter Kinetic Component ................................ .. 215 4.2 [Ru(dmesb) 3 ] 2+ : Determining the Nuclear Coordinate of Vibrational Cooling .. 217 4.3 Further Understanding of [Ru(dpb) 3 ] 2+ ................................ ............................... 224 4.3.1 Ground State Recovery ................................ ................................ ................. 224 4.3.2 1 3 MLCT Intersystem Crossing ................................ ....................... 234 5. Future Works and Conclusions ................................ ................................ ....................... 249 REFERENCES ................................ ................................ ................................ ........................... 252 CHAPTER 5. INCREASED CHARGE SEPARATION DISTANCE VIA EXTENDED LIGAND DELOCALIZATION AS A STRATEGY TO LENGTHEN THE MLCT LIFETIME IN FE(II) POLYPYRIDYL COMPLEXES ................................ ................................ ................ 259 1. Introduction ................................ ................................ ................................ ..................... 259 2. Experimental ................................ ................................ ................................ ................... 261 2.1 Materia ls and Synthesis ................................ ................................ ...................... 261 2.1.1 General ................................ ................................ ................................ .......... 261 2.1.2 Characterization of Free Ligands and Complexes ................................ ........ 263 2.1.3 Crystal Structure Determination ................................ ................................ ... 263 2.2 Ultrafast Transient Absorption Spectroscopy ................................ ..................... 264 3. Results and Discussion ................................ ................................ ................................ ... 264 3.1 [Fe(dpb) 3 ](PF 6 ) 2 ................................ ................................ ................................ . 264 3.1.1 Synthesis ................................ ................................ ................................ ....... 264 3.1.2 Crystal Structure Data ................................ ................................ ................... 270 3.1.3 Extinction Coefficient ................................ ................................ ................... 272 3.1.4 Ultrafast Spectroscopy Results ................................ ................................ ..... 276 3.2 Extending Delocalization By Synthetic Modification of the Ligand .................. 282 3.2.1 Increased Conjuga tion Around the Metal Center ................................ ......... 282 3.2.2 Extending Delocalization Away from the Fe(II) Center ............................... 288 4. Future Works and Conclusions ................................ ................................ ....................... 296 4.1 Results from Extended Delocalization Studies ................................ ................... 296 4.2 Proposed Future Complexes ................................ ................................ ............... 298 4.3 The Future of the Quest for Long - Lived MLCT Lifetime in Fe(II) Complexes 304 4.3.1 Altering the Nuclear Coordinate ................................ ................................ ... 305 4.3.2 Inverting the MLCT and LF Manifolds ................................ ........................ 306 4.3.3 Increasing Charge - Separated Distance via Deloc alization ........................... 308 4.4 Fe(II) and Ru(II) Complexes as Analogues ................................ ........................ 310 REFERENCES ................................ ................................ ................................ ........................... 314 APPENDICES ................................ ................................ ................................ ............................ 321 ix APPENDIX A. ADDITIONAL VARIABLE - TEMPERATURE RESULTS ...................... 322 REFERENCES ................................ ................................ ................................ ..................... 349 APPENDIX B. ULTR AFAST PULSE DURATION DETERMINATION ......................... 351 REFERENCES ................................ ................................ ................................ ..................... 38 8 APPENDIX C. MARCUS ANALYSIS ................................ ................................ ............... 391 REFERENCES ................................ ................................ ................................ ..................... 415 APPENDIX D. CART ESIAN COORDINATES USED IN TIME - DEPENDENT DENSITY FUNCTIONAL THEORY CALCULATIONS ................................ ................................ .... 418 APPENDIX E. DATA PROCESSING AND ANALYSIS ................................ .................. 435 REFERENCES ................................ ................................ ................................ ..................... 501 APPENDIX F. VARIABLE - TEMPERATURE SET - UP ................................ .................... 504 REFERENCES ................................ ................................ ................................ ..................... 526 x LIST OF TABLES Table 2.1. Bond distances and angles from X - ray crystallographic data for all four complexes. 72 Table 2.2. Summary of the lifetime of the complexes at room temperature and 235 K, and the Arrhenius values found from the variable - temperature experiments. ................................ .......... 80 Table 2.3. E lectrochemical potentials for the Fe(II/III) oxidation and the corresponding Marcus parameters of the four complexes. ................................ ................................ ................................ 87 Table 2. 4. Force constant analysis of [Fe(bpy) 3 ] 2+ and [Fe(terpy) 2 ] 2+ . ................................ ........ 99 Table 3.1. Single crystal X - ray data comparison between the PF 6 - and BF 4 - salts of [Fe(dcpp) 2 ] 2+ . ................................ ................................ ................................ ................................ ..................... 124 Table 3.2. Arrhenius and Marcus parameter values of [Fe(dcpp) 2 ] 2+ relative to [Fe(bpy) 3 ] 2+ and [Fe(terpy) 2 ] 2+ . ................................ ................................ ................................ .............................. 133 Table 3.3. Arrhenius and Marcus parameters of [Fe(dcpp) 2 ] 2+ with varying counteranions. .... 137 Table 3.4. Summary of VT - TA data and Arrhenius parameters of [Fe(dcpp) 2 ](BAr F ) 2 in the four different solvents. ................................ ................................ ................................ ........................ 143 Table 3.5. Comparison of Marcus parameters of [Fe(dcpp) 2 ](BAr F ) 2 in the four solvents. ...... 144 Table 3.6. Difference in reorganization energy of [Fe(dcpp) 2 ] 2+ in different counteranions and solvents relative to BAr F - in MeCN. ................................ ................................ ........................... 145 Table 3.7. Marcus values calculated from a constant reorganization energy. ........................... 147 Table 3.8. Marcus values calculated from a constant electronic coupling matrix element. ....... 148 Table 3.9. Summary of parameters measured and calculated from VT - TA of [Fe(dcpp) 2 ] 2+ as a function of excitation wavelength. ................................ ................................ .............................. 151 Table 4.1. X - ray crystallographic data of [Ru(dpb) 3 ](PF 6 ) 2 compared to the dmesb and bpy analogues. ................................ ................................ ................................ ................................ .... 194 Table 4.2. Summary of the MLCT maxima of the ground state absorption spectra of [Ru(dpb) 3 ](BAr F ) 2 in the solvents used in the transient absorption spectroscopy measurements. ................................ ................................ ................................ ................................ ..................... 201 Table 4.3. Vibrational cooling time constants for [Ru(dpb) 3 ](BAr F ) 2 in the alcohol solvents of ................................ .................. 203 Table 4.4. Vibrational cooling tim e constants for [Ru(dpb) 3 ](BAr F ) 2 in the nitrile solvents with ................................ .................. 206 xi Table 4.5. 1 VC versus viscosity ( and average solvation time, , 13 using eqn. (4.3). ................................ ................................ ................................ ......................... 212 Table 4.6. vibrational cooling transient absorption data for [Ru(dpb) 3 ] 2+ in alcoh ol and nitrile solvents. .. 216 Table 4.7. Short - 1 ) of [Ru(dpb) 3 ](BAr F ) 2 as a function of solvent and excitation wavelength. ................................ ................................ ................................ ................ 217 Table 4.8. Summary of the short - time kinetics observed upon probing at 5 30 nm in [Ru(dmesb) 3 ] 2+ . ................................ ................................ ................................ ........................... 221 Table 4.9. Quantum yield data and experimental setups for [Ru(bpy) 3 ] 2+ and [Ru(dpb) 3 ] 2+ . .... 236 Table 4.10. em abs ) lifetimes, and the radiative (k r ) and nonradiative (k nr ) rates of [Ru(dpb) 3 ](BAr F ) 2 in MeOH and 1 - OctOH as a function of excitation wavelength. ................................ ................................ .............................. 239 Table 4.11. Quantum yield of deaerated [Ru(dpb) 3 ](BAr F ) 2 as a function of solvent and excitation wavelength relative to air - free [Ru(bpy) 3 ](PF 6 ) 2 in MeCN. ................................ ...... 241 Table 5.1. Single crystal X - ray data of [Fe(dpb) 3 ](PF 6 ) 2 and [Ru(dpb) 3 ](PF 6 ) 2 . ....................... 271 Table 5.2. Kinetic parameters of the Fe(II) complexes studied to determine the effect of extended delocalization on the rate of MLCT deactivation. ................................ ....................... 278 Table A.1. Summary of lifetimes and Arrhenius parameters of the ground state recovery dynamics in [Fe(bpy) 3 ]Cl 2 in various solvents. ................................ ................................ .......... 330 Table A.2. Marcus parameters for ground state recovery of [Fe(bpy) 3 ]Cl 2 in various solvents. 330 Table A.3. Summary of lifetimes and Arrhenius values of [Fe(dcpp) 2 ] 2+ in acetone. ............... 336 Table A.4. Marcus parameters for [Fe(dcpp) 2 ] 2+ in acetone. ................................ ..................... 336 Table A.5. Summary of lifetimes and Arrhenius values of [Fe(dtbb) 3 ] 2+ in three different solvents. ................................ ................................ ................................ ................................ ...... 348 Table A.6. Marcus parameters of [Fe(dtbb) 3 ] 2+ in various solvents. ................................ ......... 348 Table B.1. Summary of signal - to - probe ) from OKE data in 1 - exc probe = 530 nm, as a function of the pump/probe power ratio. ................................ ................................ ................................ ................................ ..................... 363 Table B.2. Summary of the cross - correlation results with and without the analyzing polarizer probe ). ................................ ..................... 371 Table B.3. Summary of one - color studies for acetonitrile, including the cross - correlations with and without the analyzing polarizer, OKE - determined pulse durations. ................................ .... 375 xii Table B.4. Summary of pulse durations by OKE as optics are removed and reangled after the sample for the data shown in Fig. B.23. ................................ ................................ ..................... 385 Table C.1. a ................................ ........... 401 Table C.2. H ab 4 ab .................. 407 Table C.3. Marcus parameters calculated for four Fe(II) polypyridyl complexes using an ................................ ................................ ..... 410 Table C.4. Marcus parameters calculated for four Fe(II) polypyridyl complexes using an ................................ ................................ ..... 411 Table C.5. Marcus parameters calculated for four Fe(II) polypyridyl complexes using an ................................ ................................ ................................ ..................... 412 Table C.6. Marcus parameters calculated for four Fe(II) polypyridyl complexes using an assumed value of H ab . ................................ ................................ ................................ ................. 413 Table E.1. Fit parameters for Gaussian deconvolution in Igor by both version 1.4 and 2. ....... 449 Table F.1. Summary of pulse characterization data as a function of temperature. .................... 518 xiii LIST OF FIGURES Figure 1.1. (a) Two - dimensional full spectral data of the optical Kerr effect induced between the pump and probe pulses when both are 550 nm. (b) If the data are plotted for one specific probe wavelength versus the time delay, a kinetic trace can be collected. (c) Th e data can also be plotted against the probe wavelength, providing a one - dimensional full spectral trace. .............. 33 Figure 2.1. Ground s tate absorption spectra of the four Fe(II) polypyridyl complexes: [Fe(bpy) 3 ](PF 6 ) 2 in red, [Fe(dmb) 3 ](PF 6 ) 2 in green, [Fe(dtbb) 3 ](PF 6 ) 2 in blue, and [Fe(terpy) 2 ](PF 6 ) 2 in purple. All spectra are normalized to 0.7 AU at 490 nm (~20400 cm - 1 ). See text for de tails. ................................ ................................ ................................ .............................. 69 Figure 2.2. X - ray crystal structure of [Fe(dmb) 3 ](PF 6 ) 2 , with solvent molecules and counteranions omitted for clarity. Crystals grown and solved by S. L. Adelman. ....................... 71 Figure 2.3. X - ray structure of [Fe(terpy) 2 ](PF 6 ) 2 , with solvent molecules and counteranions omitted for clarity. Crystals grown and solved by S. L. Adelman. ................................ ............... 71 Figure 2.4. Calculated effects of group velo city delay (GVD) or dispersion on an ultrafast laser pulse. The red trace shows an input pulse that does not traverse through media and is therefore equivalent to its output pulse. In green is the calculated duration of a pulse at 490 nm propagating throug h 12 mm of fused silica. The dashed line denotes 150 fs, which is the pulse duration used in the work reported here. ................................ ................................ ...................... 76 Figure 2.5. 1 H NMR of CD 3 CN blank. Assignments can be found in the text. ........................... 77 Figure 2.6. 1 H NMR spe ctrum of HPLC - grade acetonitrile in CD 3 CN. Assignments can be found in the text. ................................ ................................ ................................ ................................ ...... 78 Figure 2.7. Variable - temperature lifetimes of [Fe(bpy) 3 ] 2+ upon excitation at 490 nm and probing at 530 nm. At room temperature (red), the lifetime of the complex is 1.05 ± 0.02 ns. This lengthens with decreasing temperature to 235 K (purple), at which point the lifetime is 1.52 ± 0.03 ns. ................................ ................................ ................................ ................................ .......... 79 Figure 2.8. Arrhenius plot for [Fe(bpy) 3 ] 2+ showing average ln(k nr ) as a function of inverse temperature from variable - temperature lifetimes. The data fit very well (R 2 = 0.98) to a single mode, for which the barrierless rate is 230 ± 20 ps - 1 , and the activation energy is 310 ± 15 cm - 1 . ................................ ................................ ................................ ................................ ....................... 80 Figure 2.9. Ground state recovery lifetimes of [Fe(dmb) 3 ] 2+ as a function of temperature. Excitation was performed at 490 nm, and the probe was 530 nm. ................................ ............... 82 Figure 2.10. Ground state recovery lifetimes of [Fe(dtbb) 3 ] 2+ as a function of temperature. Excitation was performed at 490 nm, and the probe was 530 nm. ................................ ............... 82 Figure 2.11. Arrhenius plot of the averaged [Fe(dmb) 3 ] 2+ variable - temperature data. The xiv preexponential factor, A, was found to be 240 ± 20 ps - 1 , with the activation energy being 345 ± 10 cm - 1 . The data fit well (R 2 = 0.97) to a single mode. ................................ ............................... 83 Figure 2.12. Arrhenius plot of the averaged [Fe(dtbb) 3 ] 2+ variable - temperature data. The preexponential factor, A, was found to be 230 ± 15 ps - 1 , with the activation energy being 315 ± 15 cm - 1 . The data fit well (R 2 = 0.99) to a single mode. ................................ ............................... 83 Figure 2.13. Ground state recovery lifetimes of [Fe(bpy) 3 ] 2+ doped with 125 mol equiv. of diethyl ether, as a function of temperature. Excitation was performed at 490 nm, and the probe was 530 nm. Lifetimes at the various temperatures are within error of those reporte d for the sample without diethyl ether. ................................ ................................ ................................ ........ 90 Figure 2.14. Arrhenius plot of the averaged variable - temperature data of [Fe(bpy) 3 ] 2+ doped with 125 mol equiv. of diethyl ether. The preexponential factor, A, was found to be 225 ± 20 ps - 1 , with the activation energy being 310 ± 15 cm - 1 . These values are in excellent agreement with the Arrhenius factors found for the undoped [Fe(bpy) 3 ] 2+ s ample. The data fit well (R 2 = 0.99) to a single mode. ................................ ................................ ................................ ................................ .. 91 Figure 2.15. Ground state recovery lifetimes of [Fe(terpy) 3 ] 2+ as a func tion of temperature. Excitation was performed at 490 nm, and the probe was 530 nm. Because of the delay stage used in this experiment, at no temperature does the molecule recover the ground state fully (i.e. the signal returns to zero). This effect is only worsened at cold temperatures, to such an extent that the signal appears to be linear. These issues give rise to the increase in uncertainty on the lifetimes and subsequently calculated values. ................................ ................................ .............. 94 Figure 2.16. Arrhenius plot of the averaged [Fe(terpy) 2 ] 2+ variable - temperature data. The preexponential factor, A, was found to be 150 ± 55 ps - 1 , with the activation energy being 755 ± 70 cm - 1 . The data fit well (R 2 = 0.96) to a single mode. ................................ ............................... 95 Figure 2.17. Overlay of the variable - temperature ultrafast transient absorption spectra for [Fe(bpy) 3 ] 2+ 2 ] 2+ ( -- ). The traces indicate the temperature of the sample, red being 292 K to purple being 235 K. The left axis shows the scale for the [Fe(bpy) 3 ] 2+ , whereas [Fe(terpy) 2 ] 2+ is plotted against the right axis. ................................ ................................ .............. 95 Figure 2.18. Comparison of the Arrhenius plots for the four complexes. The data are displayed as diamonds, and the straight line is the fit of the data: [Fe(bpy) 3 ] 2+ in red, [Fe(dmb) 3 ] 2+ in orange, [Fe(dtbb) 3 ] 2+ in green, and [Fe(terpy) 2 ] 2+ in blue. ................................ ............................ 96 Figure 2.19. Potential energy surfaces calculated from harmonic oscillators for [Fe(bpy) 3 ](PF 6 ) 2 in Me CN. The blue traces represent the 1 A 1 ground state, whereas the red curves are the 5 T 2 excited states. The activation and reorganization energies are given (see text and Table 2.4 for more details). ................................ ................................ ................................ ............................... 100 Figure 2.20. Potential energy surfaces calculated from harmonic oscillators for [Fe(terpy) 2 ](PF 6 ) 2 in MeCN. The blue traces represent the 1 A 1 ground state, whereas the red curves are the 5 T 2 excited states. The activation and reorganization energies are given (see text and Table 2.4 for more details). ................................ ................................ ................................ .. 101 xv Figure 3.1. Ground state absorption spectra of [Fe(dcpp) 2 ] 2+ salts, normalized to the MLCT maximum: BF 4 - at 607 nm (purple), PF 6 - at 605 nm (red), and BAr F - at 606 nm (green). ......... 126 Figure 3.2. Ground state absorption spectra of [Fe(dcpp) 2 ](BAr F ) 2 in EtOAc (red), acetone (green), MeCN (blue), and PC (purple). The spectra are normalized to the MLCT maximum. 127 Figure 3.3. Re presentative variable - temperature lifetimes of [Fe(dcpp) 2 ](PF 6 ) 2 in MeCN. Excitation occurred at 490 nm, and a 540 nm probe was used. At room temperature (red) the lifetime of the complex is 290 ± 5 ps, and at 235 K (not shown) the average lifetime is 340 ± 10 ps. ................................ ................................ ................................ ................................ ................ 129 Figure 3.4. Arrhenius plot for average variable - temperature data of [Fe(dcpp) 2 ](PF 6 ) 2 in MeCN. From these data, the barrierless rate is 165 ± 15 ps - 1 , and the activation energy is 115 ± 15 cm - 1 . The correlation was modest, with R 2 = 0.738. ................................ ................................ ............ 129 Figure 3.5. Representative variable - temperature lifetimes of [Fe(dcpp) 2 ](BF 4 ) 2 in MeCN. Excitation occurred at 490 nm, and a 540 nm probe was used. At room te mperature (red) the lifetime of the complex is 295 ± 5 ps, and at 235 K (purple) the average lifetime is 325 ± 10 ps. ................................ ................................ ................................ ................................ ..................... 136 Figure 3 .6. Representative variable - temperature lifetimes of [Fe(dcpp) 2 ](BAr F ) 2 in MeCN. Excitation occurred at 490 nm, and a 540 nm probe was used. At room temperature (red) the lifetime of the complex is 285 ± 5 ps, and at 235 K (not shown) the average lifetime is 315 ± 5 ps. ................................ ................................ ................................ ................................ ................ 136 Figure 3.7. Overlaid Arrhenius plot for average variable - temperature data of [Fe(dcpp) 2 ](PF 6 ) 2 (red), [Fe(dcpp) 2 ](BF 4 ) 2 (green), and [Fe(dcpp) 2 ](BAr F ) 2 (blue) in MeCN. The Arrhenius values from these plots can be found in Table 3.3. The correlations were modest, with R 2 for the PF 6 - salt being 0.738, 0.580 for the BF 4 - salt, and 0.884 for the BAr F - compound. ........................... 137 Figure 3.8. Representative varia ble - temperature lifetimes of [Fe(dcpp) 2 ](BAr F ) 2 in EtOAc. Excitation occurred at 490 nm, and a 540 nm probe was used. At room temperature (red) the lifetime of the complex is 265 ± 5 ps, and at 235 K (cyan) the average lifetime is 275 ± 10 ps. 141 Figure 3.9. Representative variable - temperature lifetimes of [Fe(dcpp) 2 ](BAr F ) 2 in acetone. Excitation occurred at 490 nm, and a 540 nm probe was used. At room temperature (red) the lifetime of the complex is 240 ± 5 ps, and at 235 K (cyan) the average lifetime is 255 ± 10 ps. 141 Figure 3.10. Representative variable - temperature lifetimes of [Fe(dcpp) 2 ](BAr F ) 2 in PC. Excitation occurred at 490 nm, and a 540 nm probe was used. At room temperature (red) the life time of the complex is 245 ± 5 ps, and at 235 K (not shown) the average lifetime is 255 ± 10 ps. ................................ ................................ ................................ ................................ ................ 142 Figure 3.11. Overlaid Arrhen ius plot for average variable - temperature data of [Fe(dcpp) 2 ](BAr F ) 2 in EtOAc (red), acetone (green), MeCN (blue), and PC (purple). The Arrhenius values from these plots can be found in Table 3.4. The correlations were modest to poor, with R 2 for the EtOAc data being 0.737, 0.821 for acetone, 0.884 for MeCN, and 0.077 for the PC data. ................................ ................................ ................................ ................................ . 143 xvi Figure 3.12. Gaussian deconvolution of the ground state absorption spectrum of [Fe(dcpp) 2 ](PF 6 ) 2 in MeCN. The experimental data are the blue diamonds, the calculated Gaussian bands are the black lines (offset for clarity), and the convolved fit is the red trace. ... 150 Figure 3.13. Single - wavelength kinetics of [Fe(dcpp) 2 ](PF 6 ) 2 in MeCN, pumped at 490 nm and probed at 540 nm. The kinetics measured (black diamonds) are those of the deactivation out of the MLCT manifold into the LF manifold and correspond to a MLCT lifetime (red trace) of 35 ± 5 fs. The solvent (red diamonds) data are shown for reference. ................................ ................. 154 Figure 3.14. Single - wavelength kinetics of [Fe(dcpp) 2 ](PF 6 ) 2 in MeCN, pumped at 610 nm and probed at 540 nm. The kinetics measured (black diamonds) are those of the deact ivation out of the MLCT manifold into the LF manifold and correspond to a MLCT lifetime (red trace) of 120 ± 20 fs. A portion of the data at 375 - 475 fs is omitted for clarity due to oscillations of unknown origin. The solvent (red diamonds) data are shown for reference. ................................ ............. 155 Figure 3.15. Timed ground state absorption study of [Fe(dcpp) 2 ](BAr F ) 2 in THF. ................... 157 Figure 3.16. Ground state absorption spectra of [Fe(dcpp) 2 ](BAr F ) 2 in MeCN (green) and DCM (blue). ................................ ................................ ................................ ................................ .......... 159 Figure 3.17. Ground state recovery lifetime of [Fe(dcpp) 2 ](BAr F ) 2 in DCM (black diamonds) upon excitation at 490 nm and probing at 540 nm. The fit (red trace) showed a lifetime of 470 ± 10 ps. ................................ ................................ ................................ ................................ ........... 160 Figure 3.18. MLCT kinetics of [Fe(dcpp) 2 ](BAr F ) 2 in DCM measured at 540 nm upon excitation at 620 nm. The data (black diamonds) displayed vibrational coherenc e caused by the solvent interacting with a very temporally short pump pulse. The fit (red trace) gave a MLCT lifetime of 180 ± 55 fs. ................................ ................................ ................................ ................................ . 160 Figure 3.19. 1 H NMR of [Fe(dcpp) 2 ](BAr F ) 2 in (CD 3 ) 2 CO (bottom, red) and doped with a small amount of undeuterated DCM (top, green). Assignments can be found in the text. .................. 161 Figure 4.1. 1 H NMR spectrum of [Ru(dmesb) 3 ]Cl 2 reaction mixture in CD 3 CN. While many of the main features can be assigned to the desired homoleptic complex (see text for assignments), some features clearly belong to an oxidized and/or heteroleptic complex, as evidenced by the shifts ~10.1 ppm. ................................ ................................ ................................ ......................... 188 Figure 4.2. Electrospray ionization mass spectrum of [Ru(dmesb) 3 ] 2+ in positive mode. (Top) Calculated spectrum for the [M] 2+ ion. (Bottom) Experimental spectrum for the [M] 2+ ion. The repeating unit is attributed to the oxidation of the methyl substituent s in the mesityl moiety to aldehydes. ................................ ................................ ................................ ................................ .... 19 1 Figure 4.3. 1 H NMR spectrum of the [Ru(dmesb) 3 ](BAr F ) 2 sample used to collect the mass s pectrometry data in Fig. 4.2. No evidence of an aryl - aldehyde is present, as indicated by the featureless area around 10 ppm. ................................ ................................ ................................ .. 192 Figure 4.4. The X - ray crystal structure of [Ru(dpb) 3 ](PF 6 ) 2 . The counteranions and solvent are omitted for clarity. ................................ ................................ ................................ ...................... 194 xvii Figure 4.5. (Left) Ground state absorption spectrum of [Ru(dpb) 3 ](BAr F ) 2 in MeOH. (Right) Differential absorption spectrum of [Ru(dpb) 3 ](BAr F ) 2 in MeOH of the thermalized 3 MLCT excited state. See text for assignments. ................................ ................................ ....................... 197 Figure 4.6. Steady state absorption spectrum (black diamonds) of [Ru(dpb) 3 ](BAr F ) 2 in MeOH. Gaussian deconvolution of this region revealed seven separate bands (red traces) were required to reconstruct the spectrum (blue trace). ................................ ................................ ..................... 199 Figure 4.7. Ground state absorption spectra of [Ru(dpb) 3 ](BAr F ) 2 in the solvents used in the ultrafast transient absorption experiments. The spectra are normalized to the maximum of the lowest energy MLCT band. [Ru(dpb) 3 ] 2+ is modestl y solvatochromic. ................................ ..... 200 Figure 4.8. Overlay of the vibrational cooling dynamics of [Ru(dpb) 3 ](BAr F ) 2 in MeOH (red diamonds) and 1 - Oc tOH (purple diamonds) upon excitation at 480 nm. The final 30 data points VC in MeOH (black trace) is 1.5 ± 0.3 ps, which is significantly lengthen ed in 1 - OctOH (red trace) to 17.1 ± 2.6 ps. ................................ ................................ ............................. 204 Figure 4.9. Vibrational cooling kinetics of [Ru(dpb) 3 ](BAr F ) 2 in the nitrile solvents (diamonds) with their fits (traces) upon excitation at 480 nm: MeCN (red) = 1.5 ± 0.3 ps, PrCN (green) = 1.7 ± 0.5 ps, BuCN (blue) = 2.3 ± 1.4 ps, and HexCN (purple) = 5.8 ± 1.6 ps. ............................... 206 Figure 4.10. Correlation of the vibrational cooling time constant to the solvent polarity as a exc = 400 nm (purple) fit with R 2 exc = 480 nm (blue) fit with R 2 exc = 550 nm (green) fit with R 2 = 0.80. ................................ ............... 208 Figure 4.11. Correlation of the vibratio nal cooling time constant to the solvent polarizability as a exc = 400 nm (purple) fit with R 2 exc = 480 nm (blue) fit with R 2 exc = 550 nm (green) fit with R 2 = 0.52. No value of n , and therefore R( n ), could be found for 1 - HexOH, 1 - OctOH, or HexCN. ................................ ........................ 209 Figure 4.12. Correlation of vibrat ional cooling time constant of [Ru(dpb) 3 ](BAr F ) 2 with solvent exc = 400 nm are shown in exc exc = 550 nm are in green. ................................ ................... 211 Figure 4.13. Vibrational cooling time constant of [Ru(dpb) 3 ](BAr F ) 2 versus the average exc = 400 nm exc exc = 550 nm (green). ................................ ......................... 211 Figure 4.14. Ground state absorption spectra of [Ru(bpy) 3 ] 2+ (black), [Ru(dpb) 3 ] 2+ (blue), and [Ru(dmesb) 3 ] 2+ (yellow) in MeCN, normalized to the maximum of the lowest energy 1 MLCT transition. The two MLC excited state: 286 and 450 nm in [Ru(bpy) 3 ] 2+ , 292 and 459 in [Ru(dmesb) 3 ] 2+ , and 310 and 475 nm in [Ru(dpb) 3 ] 2+ . ................................ ................................ ................................ ..................... 219 Figure 4.15. Vibrational cooling dynamics in [Ru(dmesb) 3 ](BAr F ) 2 in 1 - OctOH at 532 nm upon excitation at 480 nm. The data (black diamonds) appear to rise slowly with a multiexponential fit (red trace) that was greater than the delay of the stage. ................................ .............................. 220 xviii Figure 4.16. Vibrational cooling dynamics of [Ru(dmesb) 3 ](BAr F ) 2 in MeCN upon excitation at 480 nm with probing at 530 nm. Initially the amplitude of the signal is relatively high but decays with bi exponential kinetics to a long - lived signal. ................................ ................................ ..... 223 Figure 4.17. Ground state absorption spectra of [Ru(dmesb) 3 ] 2+ normalized to the maximum of the lowest - energy MLCT band. The data presented are of the complex in MeOH (blue), 1 - OctOH (red), and MeCN (green). ................................ ................................ ............................... 223 Figure 4.18. Overlay of the experimentally - determined ground state absorption spectrum of [Ru(dpb) 3 ] 2+ in MeCN (black trace) with the singlet (blue triangles) and triplet (red circles) transitions from time - dependent DFT calc ulations. ................................ ................................ .... 225 Figure 4.19. Orbital pictures of [Ru(dpb) 3 ] 2+ transitions as calculated from TD - DFT. The 400 nm absorption is a sing 49% probability. The 550 nm absorption is a triplet transition found at 551.71 nm with f = 0 fou probabilities, respectively. The bottom two 480 nm absorptions are singlet transitions found at es, respectively. ................................ ................................ ................................ ................................ 227 Figure 4.20. Overlay of the experimentally - determined ground state absorption spectrum of [Ru(dmesb) 3 ] 2+ in MeCN (black trace) with the singlet (blue triangles) and triplet (red circles) transitions from time - dependent DFT calculations. ................................ ................................ .... 228 Figure 4.21. Orbital pictures of [Ru(dmesb) 3 ] 2+ transitions as calculated from TD - DFT. The 400 37% probability. The 480 nm absorption is a singlet transition found at 467.67 nm with f = ................................ ................. 230 Figure 4.22. Steady state emission spectra of [Ru(dpb) 3 ](BAr F ) 2 exc = 340 nm (red), 470 nm (orange), and 550 nm (yellow), and in 1 - exc = 340 nm (gr een), 470 nm (blue), and 550 nm (purple). The emission spectra showed no dependence on excitation wavelength; the maximum in MeOH is 630 nm and is 640 nm in 1 - OctOH. ............................ 232 Figure 4.23. Overlay of the steady state absorption (red trace) and emission (blue trace) of [Ru(dpb) 3 ](BAr F ) 2 in 1 - OctOH. The lowest energy MLCT transition and the emission maxima are normalized to each other. ................................ ................................ ................................ ...... 233 Figure 4.24. Overlay of the ground state absorption (red, left axis) and excitation emission (blue, right axis) spectra of [Ru(dpb) 3 ](BAr F ) 2 in MeOH. The spectra match moderately well for ~340 - 550 nm, indicating the phosphorescence process from the 3 MLCT is well - behaved (see text for more details). ................................ ................................ ................................ ............................... 234 Figure 4.25. Quantum yields measured for deaerated [Ru(dpb) 3 ](BAr F ) 2 in MeOH (red diamonds) and 1 - OctOH (b lue diamonds) depicting the excitation wavelength dependence, particularly in 1 - OctOH. These are shown in comparison to the quantum yield of air - free xix [Ru(bpy) 3 ](PF 6 ) 2 in MeCN which displays no excitation wavelength dependence. .................. 240 Figure 4.26. Excitation wavelength - dependent quantum yields of deaerated [Ru(dpb) 3 ](BAr F ) 2 in MeCN (red diamonds) and BuCN (blue - diamonds) as compared to the quantum yield of deaerated [Ru(bpy) 3 ](PF 6 ) 2 in MeCN (black diamonds) that is independent of the excitation wavelength. ................................ ................................ ................................ ................................ . 242 Figure 4.27. Overlay of the ground state absorption spectrum (blue trace, left axis) of [Ru(dpb) 3 ](BAr F ) 2 in 1 - OctOH with the excitation wavelength - dependent deaerated quantum yield (red diamond s, right axis). There is a modest agreement between the trends of both. ...... 243 Figure 5.1. Steady state absorption spectrum of [Fe(dp b) 3 ](PF 6 ) 2 in acetonitrile (black) prior to recrystallization. After ~24 h, the solution was observed to go colorless (red). This indicated ligand dissociation from the metal center, but also suggests decomposition of the ligand itself, as the spectrum does not matc h that of the free dpb ligand (blue). ................................ ................. 266 Figure 5.2. 1 H NMR spectrum of [Fe(dpb) 3 ](PF 6 ) 2 in (CD 3 ) 2 CO. This product was first recrystallized and used for single crystal X - ray diffraction studies, and then redissolved for this spectrum. The main product, as well as the free ligand and bis - ligated complex are present. ... 268 Figure 5.3. Single crystal X - ray structure of [Fe(dpb) 3 ](PF 6 ) 2 . The protons, counterions, and solvent are omitted for clarity. ................................ ................................ ................................ .... 271 Figure 5.4. Ground state absorption spectrum of [Fe(dpb) 3 ](PF 6 ) 2 in MeCN, with molar extinction coefficients. ................................ ................................ ................................ ................ 273 Figure 5.5. Comparison of the steady - state absorption spectra of [Fe(dpb) 3 ] 2+ (red) and [Fe(bpy) 3 ] 2+ (blue). ................................ ................................ ................................ ..................... 273 Figure 5.6. Overlay of the ground state absorption spectra of [Fe(dpb) 3 ] 2+ (purple), [Ru(dpb) 3 ] 2+ (red), [Zn(dpb) 3 ] 2+ (blue), and the free dpb ligand (black). The spectra are normalized to the maximum of the dpb - - ................................ ................................ ............. 275 Figure 5 .7. Ground state recovery dynamics of [Fe(dpb) 3 ](PF 6 ) 2 in MeOH (black diamonds) measured by probing at 540 nm after exciting at 490 nm. The fit (red trace) gives a lifetime of 760 ± 10 ps. ................................ ................................ ................................ ................................ . 277 Figure 5.8. Presumed MLCT decay of [Fe(dpb) 3 ](PF 6 ) 2 in MeOH upon excitation at 490 nm and probing at 690 nm. The data (black diamonds) show a positive feature that in Fe(II) complexes is indic ative of MLCT absorption. The lifetime (red trace) was found to be 160 ± 20 fs. ............. 277 Figure 5.9. Ground state recovery lifetime of [Fe(dpb) 3 ](PF 6 ) 2 in MeOH as a function of temperature. Excitation occurred at 490 nm with probing at 540 nm. ................................ ....... 280 Figure 5.10. Arrhenius plot of the variable - temperature lifetimes of [Fe(dpb) 3 ](PF 6 ) 2 in MeOH, as shown in Fig. 5.9. From these data an activation energy of 260 ± 10 cm - 1 is found, as well as a barrierless rate of 205 ± 10 ps - 1 . The data fit well to a single mode, with R 2 = 0.996. ............... 281 xx Figure 5.11. Overlay ground state absorption spectra of [Fe(dqp) 2 ](PF 6 ) 2 (black) a nd [Fe(qphen) 2 ](PF 6 ) 2 (red). ................................ ................................ ................................ ............. 284 Figure 5.12. Ground state recovery of [Fe(dqp) 2 ](PF 6 ) 2 in MeCN, upon excitation at 570 nm and probing at 480 nm. The data (black diamonds) fit well to a lifet ime of 4.29 ± 0.03 ns (red trace). ................................ ................................ ................................ ................................ ..................... 285 Figure 5.13. The MLCT deactivation of [Fe(dqp) 2 ](PF 6 ) 2 in MeCN (black diamonds) fit to sin gle exponential kinetics (red trace) with a 145 ± 10 fs lifetime. The solvent data (blue diamonds) are shown for comparison. ................................ ................................ ........................ 286 Figure 5.14. Ground state recovery lifetime of [Fe(qphen) 2 ](PF 6 ) 2 in MeCN (black diamonds). Excitation occurred at 570 nm and probing at 480 nm. The data fit well to a single exponential (red trace) with a lifetime of 3.16 ± 0.03 ns. ................................ ................................ ............... 287 Figure 5.15. MLCT deactivation of [Fe(qphen) 2 ](PF 6 ) 2 in MeCN (black diamonds) fit to a lifetime of 170 ± 40 fs (red trace). The data were collected at 660 nm upon 570 nm excitation. The solvent trace (blue diamon ds) is given for reference. ................................ .......................... 288 Figure 5.16. Comparison of the ground state absorption spectra of [Fe(dmib) 3 ](PF 6 ) 2 (black) and [F e(caab) 3 ](PF 6 ) 2 (red). ................................ ................................ ................................ ............... 291 Figure 5.17. Ground state recovery dynamics (black diamonds) of [Fe(dmib) 3 ](PF 6 ) 2 in MeCN. The complex was excited at 570 nm and probed at 510 nm. The data were fit with a single exponential (red trace) with a lifetime of 0.94 ± 0.01 ns. ................................ ........................... 293 Figure 5.18. MLCT kinetics (black diamonds, lower) measured for [Fe(dmib) 3 ](PF 6 ) 2 in MeCN upon excitation at 570 nm and probing at 650 nm. The data required a double exponential (red trace) for an adequate fit, with two lifetimes of 45 ± 10 fs and 900 ± 400 fs. Because the data did not fit the second exponential very well, the residuals are plotted (black diamonds, upper) along with the solvent trace (red dia monds) for reference. ................................ ................................ .. 294 Figure 5.19. Ground state recovery measurement of [Fe(caab) 3 ](PF 6 ) 2 in MeCN (black diamonds). These data were collected at 550 nm with 605 nm excitation. The lifetime (red trace) was found to be 0.79 ± 0.01 ns. ................................ ................................ ................................ .. 295 Figure 5.20. Overlay of the steady - state absorption spectra of [Fe(terpy) 2 ] 2+ (black) and [Fe(tpvpvp) 2 ] 2+ (red). ................................ ................................ ................................ .................. 304 Figure A.1. Representati ve ground state recovery data as a function of temperature of [Fe(bpy) 3 ]Cl 2 in MeCN. Excitation occurred at 490 nm and probing at 530 nm. ...................... 323 Figure A.2. Arrhenius plot of VT - TA data of [Fe(bpy) 3 ]Cl 2 in MeCN. The fit (black trace) of these data (red diamonds) gave an activation energy of 320 ± 25 cm - 1 and a preexponential factor of 220 ± 25 ps - 1 . The data fit well to a single - mode wi th R 2 = 0.947. ................................ ........ 323 Figure A.3. Representative ground state recovery data as a function of temperature of [Fe(bpy) 3 ]Cl 2 in MeOH. Excitation occurred at 490 nm and probing at 530 nm. ...................... 325 xxi Figure A.4. Arrhenius plot of VT - TA data of [Fe(bpy) 3 ]Cl 2 in MeCN. The fit (black trace) of these data (red diamonds) gave an activation energy of 250 ± 25 cm - 1 and a preexponential factor of 250 ± 25 ps - 1 . The data fit well to a single - mode with R 2 = 0.968. ................................ ........ 325 Figure A.5. Ground state recovery data as a function of temperature of [Fe(bpy) 3 ]Cl 2 in acetone. Excitation occurred at 490 nm and probing at 530 nm. ................................ .............................. 326 Figure A.6. Arrhenius plot of VT - TA data of [Fe(bpy) 3 ]Cl 2 in acetone, collected once. The fit (black trace) of these data (red diamonds) gave an E a of 295 ± 1 0 cm - 1 and A = 255 ± 20 ps - 1 . The data fit well to a single - mode with R 2 = 0.989. ................................ ................................ ... 327 Figure A.7. Representative ground state reco very data as a function of temperature of [Fe(bpy) 3 ]Cl 2 in acetone. Excitation occurred at 490 nm and probing at 520 nm. The kinetics were not significantly different when probed at 530 nm. ................................ ........................... 328 Figure A.8. Arrhenius plot of VT - TA data of [Fe(bpy) 3 ]Cl 2 in acetone. These data were only collected once. The fit (black trace) of these data (red diamonds) gave an activation energy of 175 ± 30 cm - 1 and a preexponential factor of 295 ± 40 ps - 1 . The data fit modestly to a single - mode with R 2 = 0.804. ................................ ................................ ................................ ................ 329 Figure A.9. Representative VT - TA data of the ground state recovery of [Fe(dcpp) 2 ](BF 4 ) 2 in exc probe = 540 nm. ................................ ................................ 333 Figure A.10. Arrhenius plot of all the VT - TA data collected of [Fe(dcpp) 2 ](BF 4 ) 2 in acetone. From this plot, E a = 50 ± 10 cm - 1 and A = 190 ± 10 ps - 1 . The data were found to fit modestly to a single mode with R 2 = 0.747. ................................ ................................ ................................ ...... 333 Figure A.11. Representative VT - TA data of [Fe(dcpp) 2 ](PF 6 ) 2 in acetone at 540 nm when excited at 490 nm. ................................ ................................ ................................ ...................... 334 Figure A.12. Arrhenius plot of all the data collected by VT - TA of [Fe(dcpp) 2 ](PF 6 ) 2 in acetone. From this fit, the activation energy was found to be 50 ± 10 c m - 1 and the frequency factor is 190 ± 10 ps - 1 . The data fit modestly to a single mode with R 2 = 0.816. ................................ ............ 335 Figure A.13. Room temperature ground state recovery dynamics of [Fe(dvpp) 2 ](PF 6 ) 2 in MeCN. The data (black diamonds) fit well to a single exponential (red trace), as determined by the residuals (black trace, above) centered a round 0. These data have been collected multiple times and the error propagated to determine a lifetime of 1.06 ± 0.03 ns. ................................ ........... 338 Fi gure A.14. Representative VT - TA data of [Fe(dvpp) 2 ](PF 6 ) 2 in MeCN upon excitation at 480 nm and probing at 530 nm. ................................ ................................ ................................ ......... 339 Figure A.1 5. Arrhenius plot for [Fe(dvpp) 2 ](PF 6 ) 2 in MeCN. Fitting these data yielded E a = 310 ± 40 cm - 1 and A = 265 ± 40 ps - 1 . The data fit modestly to a single mode with R 2 = 0.885. ....... 340 Figure A.16. Representative variable - temperature data of [Fe(dtbb) 3 ]Br 2 in MeOH. Excitation occurred at 550 nm, with probing at 490 nm. ................................ ................................ ............. 342 xxii Figure A.17. Arrhenius plot of all the data of [Fe(dtbb) 3 ]Br 2 in MeOH. This fit gives an activation energy of 325 ± 20 cm - 1 and a barrierless rate o f 225 ± 30 ps - 1 . These data fit well to a single Arrhenius mode with R 2 = 0.971. ................................ ................................ ..................... 343 Figure A.18. Representative data of the vari able - temperature ground state recovery dynamics of [Fe(dtbb) 3 ]Br 2 in 1 - BuOH upon excitation at 550 nm and probing at 500 nm. The dynamics did not change significantly when probed at 490 nm, as is expected of ground state recovery. ...... 344 Figure A.19. Arrhenius plot of the ground state recovery lifetimes of [Fe(dtbb) 3 ]Br 2 in 1 - BuOH. The data (red diamonds) are no t represented well by the fit (black trace, lower) as determined by the residuals (black trace, upper). This is likely due to the water content of 1 - BuOH (see text for details). ................................ ................................ ................................ ................................ ........ 345 Figure A.20. Arrhenius fit of the temperature - dependent lifetimes of [Fe(dtbb) 3 ]Br 2 in 1 - BuOH. The data (red diamonds) are fit (black trace, lower) best when excluding the lowest three temperatures, as in dicated by the residuals (black trace, upper). This fit yields an E a = 330 ± 15 cm - 1 and A = 255 ± 20 ps - 1 . ................................ ................................ ................................ ......... 346 Figure B.1. Single - wavelength kinetics of acetonitrile upon excitation at 550 nm and probing at 530 nm. The resultant cross - correlation can be used to identify the IRF of the system, or one - half the time from when signal begins to appear until it returns to baseline. From t he inset, the IRF for this experiment is 135 fs. ................................ ................................ ................................ ............ 358 Figure B.2. OKE spectrum of methanol (black diamonds) upon excitation at 550 nm and probing at 530 nm. The data can be fit with a Gaussian curve (red trace) t o yield pulse durations of the pump or probe pulses. ................................ ................................ ................................ ................. 359 Figure B.3. OKE spectrum of acetonitrile (black diamonds) upon excitatio n at 550 nm and probing at 530 nm. Although the main signal is fit well with a Gaussian (red trace), there is an exponential decay at positive times. ................................ ................................ ........................... 361 Figure B.4. Cross - correlation spectra of ethanol in a one - (blue) and two - color (red) experiment. In each the pump was 490 nm, and the probe for the two - color experiment was 530 nm. Both yielded an IRF of 145 fs. ................................ ................................ ................................ ............. 365 Figure B.5. exc probe = 530 nm in both methanol (black diamonds) and ethanol (red diamonds). When fit w ith a Gaussian, the pulse durations in methanol (black trace) and ethanol (red trace) may be found. ................................ .................... 366 Figure B.6. Cross - correlations found in methanol (black) and ethanol (red) in a two - color setup utilizing a 490 nm pump and 530 nm probe. The IRF was found in each solvent, being 125 fs in methanol, and 145 fs in ethanol. ................................ ................................ ................................ . 366 Figure B.7. Cross - correlation spectra in a series of 1 - alcohol s: methanol (blue), ethanol (green), 1 - butanol (orange), and 1 - octanol (purple). The pump and probe wavelengths used for this two - color experiment were 490 and 530 nm, respectively. ................................ ............................... 367 Figure B.8. One - color cross - exc probe = 600 xxiii nm with the analyzing polarizer in place. The effective probe wavelength measured was scanned over t he bandwidth of the probe (579 - 617 nm) through the use of a monochromator. Care was taken to ensure I 0 was the same for every probe wavelength. ................................ .................... 369 Figure B.9. One - color cross - exc probe = 600 nm without the analyzing polarizer in place. The effective probe wavelength measured was scanned over the bandwidth of the probe (579 - 617 nm) through the use of a monochromator. Care was taken to ensure I 0 was the same for every probe wavelength. ................................ .... 370 Figure B.10. Cross - correlation spectra in acetonitrile adjusting the use of entrance and exit slits with the monochromator: both slits in (blue), only exit slits in (red), only entrance slits in (green), no slits (purple), and the removal of the monochromator entirely (orange). Excitation occurred at 600 nm with probing at 480 nm. No analyzing polarizer was used to collect these da ta. ................................ ................................ ................................ ................................ ............. 372 Figure B.11. Cross - correlation spectra in acetonitrile adjusting the use of entrance and exit slits with the monochromator : both slits in (blue), only exit slits in (red), only entrance slits in (green), no slits (purple), and the removal of the monochromator entirely (orange). Excitation occurred at 600 nm with probing at 480 nm. The analyzing polarizer was used to collect t hese data. ................................ ................................ ................................ ................................ ............. 373 Figure B.12. OKE spectra in acetonitrile adjusting the use of entrance and exit slits with the monochromator: both slits in (blue), only exit slits in (red), only entrance slits in (green), no slits (purple), and the removal of the monochromator entirely (orange). Excitation occurred at 600 nm with probing at 480 nm. No analyzing polarizer was used to collect these da ta. ....................... 374 Figure B.13. Full spectral cross - correlation data collected in acetonitrile. The pump and probe wavelengths were 600 nm in this one - color setup. No analyzing polarizer or monochromator was used to collect these data. ................................ ................................ ................................ ............ 376 Figure B.14. Full spectral cross - correlation data collected in acetonitrile. The pump and probe wavelengths were 600 nm in this one - color setup. No monochromator was used to co llect these data, but the analyzing polarizer was in place after the sample. ................................ ................. 377 Figure B.15. Full spectral OKE data collected in acetonitrile. The pump and probe wavelengths were 600 nm in this one - color setup. No monochromator was used to collect these data. ........ 378 Figure B.16. trace of the pump and probe within the acetonitrile solvent during the OKE event. The setup was a one - color experiment, with the pump and probe being 60 0 nm. ................................ ............. 378 Figure B.17. Taken from Fig. B.15, these are the kinetic traces of the pump and probe within the acetonitrile sample dur ing the OKE event for the probe wavelengths of 560 (blue) and 620 (red) nm. The setup was a one - color experiment, with the pump and probe being 600 nm. .............. 379 Figure B.18. Full spectrum of a one - color OKE experiment in 1 - OctOH, for which the pump and probe wavelengths are 550 nm. ................................ ................................ ................................ .. 380 xxiv Figure B.19. Full spectrum of a two - color OKE experiment in 1 - OctOH, for which the pump wavelength is 550 nm, and the probe is 530 nm. ................................ ................................ ........ 381 Figure B.20. Full spectrum of a two - color cross - correlation in 1 - exc = 550 nm probe = 530. ................................ ................................ ................................ .......................... 382 Figure B.21. Single - wavelength kinetics abstracted from the full spectrum in Fig. B.20. When probing at two different wavelengths, 495 nm (blue) and 535 nm (r ed), in the same spectrum, a similar IRF is observed despite having opposite signals. ................................ ........................... 382 Figure B.22. Full spectral data from Fig. B.20 represented in a two - dimensional fashion. Here, a two - color cross - correlation is collected in 1 - exc probe = 530. ................................ ................................ ................................ ................................ ..................... 383 Figure B.23. OKE traces that were collected in ethanol in a two - color setup, in which a pump of 490 nm and a probe of 530 nm were used. The pump pulse duration was known from the one - color experiment, a pulse = 138 fs, pulse = 97 fs, and further reangling other optics produces pulse = 86 fs. ................................ ................................ ................................ ................................ 385 Figure C.1. Two sets of variable - temperature transient absorption data collected on the ground state recovery process of [Fe(bpy) 3 ](PF 6 ) 2 in MeCN. Excitation occurred at 490 nm with probin g at 530 nm. One set is represented with a solid line, and the other with a dashed line. Even without normalization, both sets overlay well indicating good reproducibility. ........................ 399 Figure C.2. Arrhenius plots for the data (red diamonds) shown in Fig. C.1 with the fits being the black trace. (Left) Data set 1 with R 2 = 0.961, E a = 309 ± 19 cm - 1 , and A = 233 ± 24 ps - 1 . (Right) Data set 2 with R 2 = 0.993, E a = 309 ± 8 cm - 1 , and A = 229 ± 10 ps - 1 . Both data sets are in good agreement with each other. ................................ ................................ ................................ ......... 399 Figure C.3. Arrhenius plot fitting the combined total data from Fig. C.1 with the data in red diamonds and the fit being the black trace. This fit gives R 2 = 0.975, E a = 309 ± 10 cm - 1 , and A = 230 ± 13 ps - 1 . ................................ ................................ ................................ ............................... 400 Figure C.4. Arrhenius plot fitting the data from Fig. C.1 when averaged at each temperature point, with the data in red diamonds and fit being the black trace. This fit gives R 2 = 0.980, E a = 308 ± 14 cm - 1 , and A = 232 ± 18 p s - 1 . ................................ ................................ ........................ 400 Figure E.1. Example of data (red diamonds) fit in Igor Pro 8 with a monoexponential function with an x - offset (black tra ce). The constants are provided in a box on the graph, and residuals are displayed as black diamonds above. The solvent scan (black diamonds, below) is provided for reference. The cursors can be seen in the gray box below the graph. In the residuals an osc illation is visible, particular before ~6 ps. This indicates that another exponential may be required to fit the data well. (Data shown are of the complex CRT - S3 - exc probe = 620 nm.) ................................ ................................ ................................ ................................ ............. 437 Figure E.2. Data of CRT - S3 - 173 in MeCN (red diamonds) fit in IgorPro with a double exponential function with an x - offset (black trace). The residuals (black diamonds, above) are xxv represent the solvent trace, for reference. ................................ ................................ ................... 438 Figure E.3. (Left) The absorption spectrum of [Ru(dpb) 3 ](PF 6 ) 2 in MeCN plotted against energy. (Right) The multipeak fitting panel for version 1.4 in Igor. ................................ ....................... 443 Figure E.4. Ground state absorption spectrum (black diamonds) of [Ru(dpb) 3 ](PF 6 ) 2 in MeCN. Igor initially finds four main Gaussians (red traces) but when summed together (blue trace), the spectr um is clearly not well - represented. ................................ ................................ .................... 444 Figure E.5. Steady state absorption spectrum (black diamonds) of [Ru(dpb) 3 ](PF 6 ) 2 in MeCN reconstructed (blue trace) by Gaussian deconvolution. Seven bands were required to fit these data. ................................ ................................ ................................ ................................ ............. 445 Figure E.6. (Left) Ground state absorption data of [Ru(dpb) 3 ](PF 6 ) 2 in MeCN. (Right) Multipeak fitting dialog box for version 2 in Igor. ................................ ................................ ....................... 446 Figure E.7. Multipeak Gaussian fitting of the absorption spectrum of [Ru(dpb) 3 ](PF 6 ) 2 in MeCN using version 2 of the software. The original data are held in the middle panel (black diamonds) along with the summatio n of Gaussians (blue trace) that is composed of the individual Gaussians calculated in the bottom panel. Above is shown the residuals. ................................ .................. 447 Figure E.8. Ground state absorption spectrum of [Ru(dpb) 3 ](PF 6 ) 2 in MeCN (black diamonds) overlaid with the convolved Gaussian fit (blue trace) in the center panel made up of the sum of the individual curves in the lower panel. The residuals (upp er panel) are evenly dispersed around which is to be expected (see text for details). Seven Gaussians were required to reconstruct these data. ................................ ................................ ................................ ................................ ............. 448 Figure E.9. positive feature and dark blue is a negative feature. The center of the signal is taken to be time - actually spreads from - 0.4 ps at the bluest wavelengths to nearly 0.3 ps at ~550 nm. ................................ .............................. 456 Figure E.10. Plot of the time and wavele ngth points (black diamonds) from the full spectral solvent scan fitted with a double exponential (red trace) that is used for the chirp correction. .. 456 Figure E.11. Full spectral solvent trace after the chirp correction has been applied. Here, the chirp - correction is evident in t he smearing of the pixels, which is why it is important to collect extra time points before and after the signal. ................................ ................................ .............. 457 Figure E.12. Full spectral data of [Ru(dpb) 3 ](PF 6 ) 2 in EtOH. These data have been chirp - = 0. ................................ ................................ ................................ ................................ .............. 457 Figure E.13. The data plotted in Fig. E.9 but recast in a different color scheme and modulated so the positive and negative color scales were roughly equal. T his helps increase the contrast. The xxvi black line in the center of the yellow signal helps guide the eye and is user - drawn. ................. 459 Figu re E.14. Raw full spectra data of [Ru(dpb) 3 ] 2+ in EtOH when pumped at 480 nm. Before time - zero (red and orange traces), no real signal is observed due to the probe hitting the sample before the pump can excite it. After time - zero, the long - lived transient grows in resulting in the ................................ .......... 473 Figure E.15. The first spectra l component, U 1 , of [Ru(dpb) 3 ] 2+ in EtOH (S 1 = 16.5). This trace represents the long - lived transient for this complex. ................................ ................................ .. 474 Figure E.16. The first kinetic component, V 1 , of [Ru(dpb) 3 ] 2+ in EtOH (S 1 = 16.5). This trace represents the temporal behavior of U 1 , and shows a single picosecond grow - in followed by a long (>40 ps) static signal. ................................ ................................ ................................ .......... 474 Figure E.17. The recombined spectra for the first spectral and kinetic components, A 1 . While these data do generally describe the full d ata set, there are obviously more features that must be included. ................................ ................................ ................................ ................................ ...... 475 Figure E.18. The second spectral component, U 2 , of [Ru(dpb) 3 ] 2+ in EtOH (S 2 = 2.6) is shown in green compared to the first (in red). This trace is predominantly ESA at higher energy and is - * absorption of the reduced dpb ligand. ................................ ......... 476 Figure E.19. The second kinetic component, V 2 , of [Ru(dpb) 3 ] 2+ in EtOH (S 2 = 2.6) is shown in green compared to the first (in red). This trace shows only a large spike centered around time - zero, imp lying the spectral features associated with it (U 2 ) are very short - lived (i.e., k r . Indeed, Meyer found that ln(k nr ) vs. E em yielded a linear correlation in alcoholic solvents; interestingly, water was found to deviate substantially from the line. 38 The temperature dependence observed in k nr can be explained by the ligand field strength 13 of Ru(II) polypyridyls. In this class of compo unds, the ligand field strength is great enough that only low - spin complexes are observed, and the 3 T 1 is invariably the lowest energy ligand field excited state, 27 as indicated by the d 6 Tanabe - Sugano diagram. 39 The ligand field (LF) states, however, are nearly degenerate with the MLCT manifold ( Scheme 1.1 ), and in some cases are actually energetically below that manifold as is obse rved with [Ru(terpy) 2 ] 2+ , in which terpy is the - terpyridine ligand. 26,27, 40,41 In some instances, then, thermal energy may allow population of the 3 T 1 ligand field state, which thus reduces k r the 3 MLCT state formation. Higher - lying LF states are often associated with ligand dissociation and may therefore also reduce k nr by inadvertently undergoing photochemistry. Caspar and Meyer theorized that the solvent effects observed in [Ru(bpy) 3 ] 2+ were likely linked to photodissociation of the ligand, with subsequent solvent coordination occurring, thereby affecting the observed rates of ground state recovery. 38 The photophysics and photo chemistry of Ru(II) polypyridyls have long dominated photovoltaic research, 24,25, 42 and have recently come to define the field of photoredox catalysis. 43 - 45 This is in large p art due to the long - lived charge transfer excited state present in [Ru(bpy) 3 ] 2+ and its analogues. The appendage of an anchoring group such as a carboxylic acid allows for chemisorption to a semiconductor. In fact, the two most commonly referenced and stud ied dyes are N3 and N719, [Ru II - dicarboxy - - bipyridine) 2 (isothiocyanate) 2 ] in which the carboxylic acid is protonated for N3 but tetra butylammonium ions replace protons in N719. 42 Upon excitation, the electron promoted fr om the Ru(II) center to the bipyridyl ligand may be transferred to the semiconductor surface, then diffuse through the semiconductor nanoparticles to the back electrode in order to produce a current. Interfacial electron transfer from the chromophore to th e semiconductor, also known as injection, is a multiexponential process that typically occurs on the 14 order of femtoseconds to picoseconds. It is critical, then, that the excited state lifetime of the dye outlast the injection rate for a moderately efficien t cell. As of August 2018, the highest efficiency certified dye - sensitized solar cell utilizes a Ru(II) sensitizer to achieve 11.9% power conversion efficiency under one sun illumination (AM 1.5 G, 1000 Wm - 2 ). 46,47 When used as a photocatalyst for redox - based reactions, the excited electron of the Ru(II) complex may oxidatively or reductively react with a second species to initiate the catalytic cycle. These reactions are typically bimolecular and therefore the MLCT excited state of the ruthenium - based catalyst must live longer than the rate of diffusion, which occurs on the order of nanoseconds and is solvent - dependent. 43 For these, and many analogous photovoltaic processes, the limiting s tep is the lifetime of the charge - separated excited state. When the MLCT is the lowest - lying excited electronic state, it frequently relaxes on the order of hundreds of nanoseconds to microseconds. It is easy to understand, then, why Ru(II) polypyridyl - bas ed chromophores with their long - lived charge - separated excited states, visible absorption profile with relatively high extinction coefficients, and synthetic tunability are so highly studied in the areas requiring photo - initiated reactions. 3. Adapting Ir on For Redox Applications The case for ruthenium chromophores is strong but falls apart when dissecting long - term and scaled viability. While the catalyst is not the greatest material cost of a DSSC, the price of ruthenium is of some concern. The current c ost of ruthenium is nearly 8200 USD/kg, 48 which will obviously translate to starting material costs for cell fabrication. More importantly, however, is the driving force for the cost: elemental abundance. It is currently estimate d that ruthenium is the sixth 49 If Ru - based photovoltaics were to be scaled for global use, all of the ruthenium would be entirely used up within years. Because 15 the find more efficient methods of harvesting solar energy, it would be all too counterproductive then to work solely on ruthenium - based devices. Analogous compo unds must be found and developed to have competing, if not improved, efficiencies. Coupled to their increased abundance, these materials would also be more cost - effective, allowing for large - scale manufacturing and greater access for people of all income l evels, and thus a reduced dependence on carbon - emitting and other limited natural resources. Many groups have already begun to tackle this problem. Indeed, work done on zinc(II) phthalocyanines 50 and sterically rigid Cu(I) dyes 51 show enormous promise. Alternatively, organic dyes have also been studied, removing the concern for metal choice, but having the disadvantageous side effect of reduced synthetic tunability. 52 Ideally, the wealth of knowledge that has been gained from the work done on Ru(II) dyes could be incorporated into new chromophores prepared from more abundant materials. This would keep the chemistry and photophysical processes from being so unrecognizable as to e ssentially be resetting the entire field of photovoltaics back to zero. The metal of choice, then, is iron. Iron is the first - row transition metal congener of ruthenium, maintaining the d 6 electronic configuration provided both are in the 2+ oxidation stat e. It is not uncommon for Fe(II) polypyridyls to be studied, including [Fe(bpy) 3 ] 2+ , as direct analogues of the Ru(II) compounds. Most relevant, though, is the abundance of iron in imated to be the fourth most abundant element, drastically improving the cost efficiency and scalability of iron - based solar cells. 3.1 Fundamental Disadvantages to Using Low - Spin Fe(II) Despite the incredible salesmanship above, it should be apparent tha t there are inherent 16 pitfalls to using Fe(II) polypyridyl chromophores for photon - to - current conversion processes. The use of an iron sensitizer has been reported previously in a DSSC setup. 53 - di - H 2 carbox y - - bipyridine) 2 (CN) 2 ] prepared by Ferrere and Gregg was found to perform with only 0.10% efficiency. While the conditions for the device were not optimized in this study, low - spin Fe(II) polypyridyl dyes are, typically, approximately 1 - 2 orders of magn itude less efficient than their Ru(II) counterparts. 54 Ultimately, the poor performance of iron dyes is owed to the smaller ionic radius of Fe(II) relative to Ru(II). As a first row transition metal, the orbital overlap achieve d between the metal and ligand is much less than in analogous second row elements. This greatly reduces the ligand field strength of iron dyes. When the photophysics of this class of compounds was first being intensely studied in the 1970s and 1980s, the n ature of the lowest energy excited state was not immediately apparent. The ground state absorption spectra for Fe(II) polypyridyls are generally red - shifted relative to their Ru(II) analogues, but still display MLCT transitions in the visible region. Low - s pin Fe(II) complexes, as a rule, though, do not emit. 33 , 55 Electronic excited state spectra were collected to compare these two metal - centered systems, and where Ru(II) displayed state, no such positive band was observed in Fe(II) chromophores. 34, 56,57 This was the very first evidence of the attenuated ligand field strength in iron - based dyes relative to the ruthenium analogues, such that the lowest energy excited stat e was actually LF and not MLCT in nature. Furthermore, due to the extremely short (i.e., sub - nanosecond) lifetime of Fe(II) chromophores, it was further concluded that the ground and lowest energy excited states in the iron - based complexes were likely to b e coupled. The energetic difference between the ground state and the 3 MLCT state in Ru(II) dyes is large, and the molecular geometries are very similar, such that these potential 17 energy surfaces are nested, lengthening the lifetimes to be on the order of m icroseconds. 55 Over the course of nearly 25 years, researchers slowly transitioned from claiming the lowest energy excited state was 1 LF or 3 LF to citing either a 3 LF or 5 LF state. 56,58 - 62 The exact spi n could not be distinguished for these Fe(II) compounds, until nearly simultaneously, work by Hauser, 63 and McCusker et al. 57 finally identified the 5 T 2 as the lowest energy excited state. By the early 1990s, iron had been found to be fundamentally different from ruthenium in terms of its photophysics. While the complexes themselves may appear similar, following excitation, [Ru(bpy) 3 ] 2+ forms a MLCT excited state with a microsecond lifetime, wherea s [Fe(bpy) 3 ] 2+ displays a ligand field excited state that is three orders of magnitude shorter in lifetime. Not only is a LF state metal - centered, making it a worse candidate for charge - transfer processes than MLCT states, but it is also lower in energy th an the charge separated states, thus reducing the driving force for electron transfer and specifically with regards to DSSCs resulting in weaker overlap with the conduction band of titanium dioxide, TiO 2 . 53,54 That being said , the ground state absorption spectrum of [Fe(bpy) 3 ] 2+ does display a signature MLCT band in the visible region, and the iron - based Ferrere dye was capable of producing an amount of photocurrent, albeit one - tenth that of an average Ru - based DSSC device. 53 As the photophysics are not so altered in moving from ruthenium to iron that the MLCT excited states are entirely lost, the question then is why do the MLCT excited states only minimally participate in electron injection? This question could only begin t o be answered with the advent of femtosecond laser spectroscopy. The first report of a sub - nanosecond MLCT deactivation timescale came when the formation of the 5 T 2 was found to be complete within ~700 fs. 57 Nearly a decade later , this rate was narrowed down even further in an Fe(II) hexadentate complex, for which depopulation of the MLCT manifold was described as occurring in a sub - 100 fs manner by transient absorption 18 spectroscopy. 64 This lifetime has now been generally verified in a variety of Fe(II) polypyridyl complexes, though is more frequently reported as a ~130 fs specifically in [Fe(bpy) 3 ] 2+ . 65 - 68 This ultrafast deactivation from the charge - separated excited explains t he poor performance of Fe(II) polypyridyl - based dyes in DSSCs. Over time, much of the photophysical cycle of [Fe(bpy) 3 ] 2+ has been determined through a wide variety of spectroscopic techniques ( Scheme 1.3 ). Visible excitation of [Fe(bpy) 3 ] 2+ prepares a 1 MLCT excited state that undergoes sub - 30 fs ISC into the 3 MLCT. 65, 69 The MLCT manifold is depopulated in ~130 fs and ultimately results in the formation of the 5 T 2 lowest en ergy excited state with unity quantum yield. 61 The 5 T 2 electronic configuration is (t 2g ) 4 (e g *) 2 and therefore produces a 0.2 Å (or 10%) bond elongation in the excited state relative to the 1 A 1 ground state, which is (t 2g ) 6 (e g *) 0 . 70 While this quintet excited state is known, the pathway from the 3 MLCT is hotly contested in the Fe(II) community. Ultrafast X - ray absorption near edge structure 65 and X - ray fluorescence 66 spectroscopies were performed and yielded similar results but vastly different interpretations. For the latter set of data, spectral and kinetic modeling confirmed that a 3 T intermediate needed to be included to fit the data. 66 The relaxation pathway was found to be 1 3 3 5 T 2 . The intermediate was determined to only be transiently populated. In the case of the X - ray absorption study, the data were observed to plateau around 250 fs. 65 The authors note that these kinetics could be fit with a sub - 60 fs component if a singlet or triplet intermediate were introduced, but they deemed this lifetime to be unreasonable considering the high frequency nature of the vibrational modes at thes e positions on the potential energy surfaces; the relaxation pathway in this case was 1 3 5 T 2 . 65 Some ab initio computational work has been done in an attempt to address this question, and found that the 5 T 2 state crosses to the MLCT manifold near the lowest energy vibrational mode of the charge transfer 19 states. 71 These results, while not definitive, appear to at least provide a pathway in which direct 5 T 2 interconversion might occur. Scheme 1.3. Potential energy surfaces for [Fe(bpy) 3 ] 2+ along the Fe - N bond distance nuclear coordinate. Visible excitation prepares the 1 MLCT excited state, followed by sub - 30 fs intersystem crossing to the 3 MLCT. The MLCT manifold is depopulated in approx imately 130 fs and may transiently populate the 3 T ligand field state during deactivation to the lowest energy excited state, the 5 T 2 . Ground state recovery occurs to the 1 A 1 on the order of 1 ns, depending on solvent. 20 From the 5 T 2 , ground state recovery t o the 1 A 1 occurs on the hundreds of picosecond to nanosecond timescale . This lifetime is found to be highly dependent on both the ligand and solvent environment. 72,73 Although MLCT excited states are inherently influenced by the nature of the solvent, as described for Ru(II) complexes above, the sub - 150 fs lifetime is not long enough to fully allow solvent reorientation to the instantaneous dipole moment of the chromophore. Any solvent effects, then, must be a result of the LF sta tes. It is not intuitive that metal - centered excited states would display lifetimes with as strong a dependence on solvent as the charge - transfer excited states in Ru(II) - based chromophores. Just as is true for [Ru(bpy) 3 ] 2+ , water is especially noted to be an outlier. 72,73 These effects have generally been postulated as being related to the volume expansion for the 1 A 1 5 T 2 transition, as well as the excited state being more prone to solvent - aided stabilization relative to the grou nd state. 73 3.2 Strategies to Lengthen the MLCT Lifetime in Fe(II) Chromophores It is clear that the photophysical processes of analogous Fe(II) and Ru(II) polypyridyl complexes are comparable in many ways. They have MLCT transitions that absorb light in the visible region. The 1 3 MLCT intersystem crossing occurs in ~30 fs due to the heavy metal centers. The lowest - energy excited state in each complex is formed with near unity quantum yield, and ground state recovery from that state is highly solvent - dependent. But despite all their similarities, Fe(II) - based dyes convert photons t o electricity with 1 / 10 1 / 100 the efficiency of their Ru(II) congeners. Based on Schemes 1.1 and 1.3 , then, three possible strategies can be envisioned in which to increase the MLCT lifetime for these Fe(II) complexes. 3.2.1 Inverting the MLCT and Ligand Field Excited State Energetics The most simplistic method for lengthening the charge transfer lifetime in Fe(II) polypyridyls is by increasing the ligand field strength of the chromophores; in p rinciple, this will 21 raise the LF states to lie energetically above the MLCT manifold and effectively make the excited electronic picture for Fe(II) dyes the same as the Ru(II) analogues. On paper, this should be relatively straightforward. However, pushing the LF manifold above the MLCT states would require much greater ligand field strength, particularly for a first row transition metal complex. From the Tanabe - Sugano d 6 diagram of a generic octahedral complex with a d 6 electron configuration, 39 the ligand field strength would need to increase not just to the 5 T 2 / 3 T 1 crossing point such that the lowest energy ligand field excited state is the 3 T 1 , but likely well beyond that point. For many decades, the only first row transition m etal compound with a lowest energy 3 T 1 excited state was [Co(CN) 6 ] 3 - , as reported by Miskowski and coworkers. 74 Cyano - ligands are commonly employed in the endeavor to increase ligand field strength due to their standing in the sp ectrochemical series. Very recently, [Fe(bpy)(CN) 4 ] 2 - was studied by combined ultrafast X - ray fluorescence and absorption spectroscopies. 75 The effect of solvatochromism due to the cyano ligands played a critical role in the ultr afast dynamics of the chromophore. In water, the same sub - 100 fs MLCT deactivation is observed, but relaxation proceeds to the 3 T 1 ligand field state, rather than the typical 5 T 2 . When the complex is dissolved in weaker Lewis acids such as acetonitrile or dimethyl sulfoxide, however, the MLCT excited state is observed to be the lowest energy excited state with a single picosecond lifetime, meaning the ligand field manifold has been energetically promoted so deactivation is unfeasible. This compound, then, h as achieved the desired goal of a lowest - energy MLCT excited state, although the dynamics are highly sensitive to the nature of the solvent. The addition of electron - - positions of the bpy ligand, for example, might be e xpected to reduce electron density in the Fe - N bond, thereby increasing the ligand field strength. Computational work by Ashley and Jakubikova on this very premise 22 seems to indicate this strategy will not be effective. 76 - 3 ] 2+ complexes, the Fe(II/III) oxidation potential (which gives a measure of the energetics of the t 2g set of orbitals) spanned 2.07 V, whereas the free energy between the 1 A 1 and 5 T 2 ligand field states varied no more than 0.29 V. These results imply that while the t 2g orbitals may be greatly stabilized - donor or - withdrawing agent, respectively, the e g * orbitals are likewise being affected such that the overall driving forc e for the compounds are unchanged. However, this picture changes when studying the bis(tridentate) [Fe(terpy) 2 ] 2+ complex. 77 For this work, the position of substitution on the peripheral pyridyl rings was varied with different co - donating groups is estimated to red - shifts the absorption profile while increasing the MLCT character of the lowest energy excited - carboxylic acid - - di(2,3 ,4 - triaminothiophene)) 2 ] 2+ is predicted to increase the ligand field manifold to lie energetically above the charge transfer states. It is therefore difficult to say with any certainty whether an inversion of LF and MLCT manifolds is possible in Fe(II) pol ypyridyls. Due to the ease of synthetic modification, terpy - based Fe(II) complexes are also highl y studied. Work done by Jamula et al. showed that by increasing the octahedral symmetry about the metal center for a terpy - type ligand system through the appe nding of carbonyl linkers, a greater ligand field strength could be achieved. 78 Although the 3 T 1 state was not achieved, [Fe(dcpp) 2 ] 2+ (dcpp = 2,6 - di(2 - carboxypyridyl)pyridine) is one polypyridyl that came incredibly close. The l igand structure proved to significantly stabilize the t 2g orbitals of Fe(II), as evidenced by its electrochemical properties, resulting in a very red - shifted absorption spectrum. Unfortunately, the ground state recovery lifetime has been reduced by nearly a factor of four relative to [Fe(bpy) 3 ] 2+ to 280 ± 10 ps, that has subsequently been assigned as coming from the 5 T 2 excited state via 23 ultrafast X - ray spectroscopy. 79 In a slightly different vein, Fe(II) carbene chemistry has se en a resurgence as of late due to the promising results yielded initially by Liu and coworkers. 80 Here, complexes with the N - heterocyclic carbene (NHC) ligands are afforded a 9 ps lifetime out of the 3 MLCT excited state despite h aving a ligand field - based lowest energy excited state a remarkable result owed to the - donating ability of these C - donor ligands. This effect is further observed in the relatively short Fe - C bond distance (~0.13 Å). Calculations on injectio n from this complex with an appended carboxylic acid linker into a semiconductor improved the efficiency of injection, particularly from the lower - lying 3 MLCT excited state. 81 Despite this marked improvement in MLCT lifetime in an Fe(II) chromophore and computational results, application of these NHCs with a carboxylate anchoring group displayed very poor performance in a DSSC device. 82 While the effi ciency for the Ferrere cell (using a dye with a sub - 200 fs MLCT state lifetime) was 0.10%, a two - order of magnitude decrease in the MLCT deactivation rate (i.e., 16 ps MLCT lifetime) only improved the efficiency to 0.13%. Since the initial report by Liu et al., newer Fe(II) carbene complexes have continued to be designed and prepared, 83,84 with one in particular having since yielded a 528 ps lifetime believed to be from the MLCT manifold. 85 This field is yet in its infancy but appears to show the most potential for achieving Ru(II) - like photophysics. The question at hand, however, is whether the strategy to increase ligand field strength in order to elongate the MLCT lifetime is viable for Fe(II) polypyri dyl complexes. 3.2.2 Disrupting the MLCT Manifold Deactivation Nuclear Coordinate The first strategy described above is a question of electronics; an alternative approach aims instead at disrupting the relaxation pathway of interest along the nuclear coor dinate. This method would require precise knowledge of the vibrational modes responsible and/or participating in the 24 ultrafast deactivation from the MLCT manifold into the 5 T 2 state. With this information in hand, targeted synthetic modifications may be ma de to the ligand scaffolding to inhibit these motions, 86 thereby increasing the barrier to LF relaxation and extending the MLCT lifetime. This method has been performed previously within the McCusker research group 87,88 on another first row transition metal complex, Cr III (acac) 3 , for which acac is the acetylacetonate ligand. Ultrafast transient absorption spectroscopy found intersystem crossing from the Franck - Condon to the lowest - energy excited state to occur in a sub - 100 fs fashion. From combinatorial vibrational coherence and computational data, a vibrational mode corresponding to the Cr - O bond lengthening and large amplitude acac backbone motion was identified as the major nuclear motion occurring dur ing ISC. In an attempt to elongate the ISC process, prohibition of this ligand stretching mode was targeted and t - butyl substituents were added to the outermost carbon atoms on the acac ligand. This addition sterically hindered the large amplitude motions, which resulted in a reduced rate of intersystem crossing by more than an order of magnitude, proving the viability of this strategy. Theoretical work has also been performed on [Fe(bpy) 3 ] 2+ in an attempt to identify the tion. 89 Ray - Dutt, classic Bailar, and a distorted or - Dutt and dancing Bailar twists were found to be lower in energy, thus likely linked to intersystem crossing. This has been experimentally observed by Stock et al., who studied an Fe(II) spin - crossover (SCO) complex with a tripod - like geometry. 90 Through ultrafast X - ray and magnetic measurements in conjunction with calculations, trigonal twis ting was identified as the nuclear coordinate associated with the quintet - to - singlet conversion. A dual Bailar twisting and breathing mode was found to be hindered by the stereochemistry of the ligand, providing a ~33 kJ/mol barrier to the reaction, which is consistent with the results from Jakubikova. 89 25 It is difficult at this juncture, however, to know how interconnected the vibrational 5 T 2 1 A 1 relaxation processes are. Some clues are provided by the low - spin [Fe(tren(py) 3 )] 2+ complex, for which tren(py) 3 = tris( N - (2 - pyridylmethyl) - 2 - iminoethyl)amine. Methyl groups may be substituted systematically onto the 6 - position of the pyridyl ring, affording SCO complexes upon the addition of either one or two methyl groups, and a high - spin complex for the fully methylated version. 91,92 Not only are these methyls electron - donating so as to reduce the ligand field strength of the complex, but they also serve to sterically prohibit g ood orbital overlap between the metal and ligands. 93 Even the fully protonated compound has a relatively long 5 T 2 state lifetime for a low - spin Fe(II) polypyridyl complex: approximately 60 ns in acetonitrile. 92 It is evident that the cage - like structure surrounding the metal center hinders the torsional motions that facilitate ground state conversion has been measured by femtosecond transient absorption, 65 picosecond soft X - ray, 93 and femtosecond stimulated Raman scattering spectroscopies; 94 all three were consistent with each other, in which they found time constants of sub - 100 fs, 85 ± 75 fs, and 190 ± 50 fs, respectively. It is clear that the steric encumbrance hindering torsion along the 5 T 2 1 A 1 coordinate does not signi ficantly lengthen the MLCT lifetime in [Fe(tren(py) 3 )] 2+ relative to [Fe(bpy) 3 ] 2+ . It is probable that this process does not access the same vibrational modes as the MLCT deactivation, reinforcing the need for intimate knowledge of these specific reaction coordinates. 3.2.3 Extending the Delocalization in the MLCT Excited States Like the previous two strategies, the final method that is envisioned to increase the lifetime of the MLCT states in Fe(II) polypyridyls has been somewhat explored in the literatur e, but not to nearly the same extent. Recall that upon excitation, the MLCT state is formed and typically lasts for less than 130 fs. Despite being a charge - separated state, the distance between the oxidized 26 Fe(III) center and the reduced bipyridine ligand is not overly large. The addition of conjugated substituents could serve to increase the distance between the excited electron and the metal; if the distance grows large enough, the electron may lose memory of its starting position and remain on the ligan d for a longer period of time, thereby extending the lifetime of the MLCT state. And indeed, many phenyl - substituted Fe(II) complexes have been synthesized with bpy, terpy, and phenanthroline backbones, 95 - 98 in which these compou nds displayed a red - shifted MLCT excited state by ground state absorption spectroscopy relative to the parent complex. By increasing the delocalization of the MLCT excited state, the phenyl moieties actually reduce the distortion of the excited state relat ive to the ground state, such that these potential energy surfaces are nested. 99 This serves to increase the observed lifetime while increasing the quantum yield of emission as vibronic coupling between the lowest energy excited state and the 1 A 1 ground state is reduced and thereby decreases k nr - diphenyl - - bipyridine) 3 ] 2+ by Damrauer and coworkers, 99 - para - tolyl - terpy complexes of ruthenium and osmiu m. 4 0 In a series of complexes with systematically increasing units of delocalization, the lifetimes of Ru(II) terpy - like compounds were studied. 100 As previously mentioned, the bis - tridentate nature of terpyridine reduces the ligand field strength of [Ru(terpy) 2 ] 2+ such that its lowest energy excited state is actually the 3 T 1 state and has a lifetime on the order of 250 ps. 4 1 In this work, phenylene and vinylene linkers were appended to [Ru(terpy) 2 ] 2+ - based trimers. The excited state lifetime increased to 10 ns when a phenylene - vinylene - phenylene linker between terpyridines on adjacent - posi tion of the terpy backbone and increased again to 320 ns with an additional phenylene - vinylene linkage in the ligand before the terpyridine backbone. That is a more than 1000 - fold increase in excited state lifetime through the simple addition of 27 conjugated substituents. The authors went on to synthesize a Ru/Fe/Ru linear trimer in which each metal was coordinated to two terpyridine ligands with the Ru atoms flanking Fe. The terpy units were bridged via a vinylene linker such that the overall structure (from left to right) would be: terpy - Ru - terpy - phenylene - vinylene - phenylene - terpy - Fe - terpy - phenylene - vinylenephenylene - terpy - Ru - terpy. The MLCT absorptions specific to the Fe(II) metal center were able to be spectroscopically identified, and excitation into this band yielded a 275 ns lifetime with no observable ultrafast deactivation to a lower - lying LF state. Without further characterization by methods such as spectroelectrochemistry, however, it is difficult to know if the extended delocalization alone increase d the Fe(II) MLCT lifetime, or if the Ru(II) atoms played a role. Analogous work done on a strictly Fe(II) monomer or trimer could be more compelling. While not exactly the same, a cyclic Fe(II) terpy - based trimer complex was prepared with a series of conj ugated linkages. 101 The linkers of interest that were used were acetylene, phenylene, and a 1,4 - di - acetylene - 2,5 - di - dodecamethoxy - - position of the terpyridine backbone. In every comple x, an ultrafast component was observed with a time constant on the order of ~100 fs, which is consistent with the MLCT deactivation lifetime of the monomeric [Fe(terpy) 2 ] 2+ complex. 102 However, upon excitation into the terpy - bas - * absorption at 330 nm and probing on the red side of the 1 MLCT 1 A 1 absorption at 675 nm, a long - lived (ps) excited state absorption feature is observed. At this pump - probe combination, it is highly likely that the single picosecond lifetime is indic ative of the MLCT manifold. Again, these results are difficult to fully interpret considering the trimeric nature of the complex, but all these data together appear to indicate that extended delocalization may serve increase the MLCT lifetime in Fe(II) chr omophores. 28 4. The Critical Role of Reorganization Energy Any one of the proposed methods outlined above for lengthening the MLCT lifetime will impart substantial geometric distortions in the resultant Fe(II) chromophore relative to the more commonly stud ied complexes. These distortions are likely to translate to the excited states of the compounds as well, especially when one considers the ~0.2 Å Fe - N bond elongation that occurs concomitantly with 1 A 1 5 T 2 interconversion. 7 0 It is not only imperative then to understand the energetic effects that these alterations will have on the photophysical dynamics, but also the nuclear coordinates being accessed at each step along the relaxation pathway. While synthetic modifications may lengthen the MLCT lifetime along one coordinate, a new excited state crossing could then arise along a separate mode that had been previously unimportant. It is therefore critical that the energetics and vibrational modes of these complexes are constantly assessed and reassessed with each subsequent ligand alteration. Fortunately, the nonradiative kinetics associated with Fe(II) chromophores can be described by semi - classical Marcus theory, 103 eqn. (1.2) : (1.2) Here, k nr The coupling between electronic states is given by H ab , a nd the driving force between the states of energy required for the reactants to transform into the products without undergoing any electron transfer process. 22 This transformation requires vibrational motion of the complex and is therefore measure of the relationship between the rate of the rea function in the exponential product of eqn. (1.2) 29 defined as the Marcus normal region in which an increase in driving force will result in an increase in k nr decrease in the observed rate, which is kno wn as the Marcus inverted region. 22, 103,104 These three regions are displayed in Scheme 1.4 . Finally, the reorganization energy is comprised of two components: inner - spher is ) and outer - os is is specific to the vibrational modes and os is dependent on the environment surrounding the complex of interest. The outer - sphere component, then, can provide insight into the specific solute - solvent interactions that accompany excited state processes. The application of this form of Marcus theory to nonradiative decay will be further described (vide infra), but for the time being, it is apparent that a substantial amount of inf ormation can be derived from this equation. When combined with vibrational and structural experimental data and computational analysis, a much more thorough understanding of the molecular - level relaxation process in these Fe(II) complexes may be garnered. 30 Scheme 1.4. free energy between the reactant and product potential energy surfaces. The normal region (red) is increases, a maximum rate of reaction is achieved for 4.1 Methods for Determining Energe tic Parameters The most straightforward method for determining Marcus parameters and their relationship to one another is through the use of variable - temperature (VT) time - resolved measurements. In this way, k nr may be determined as a function of T. Anothe r simpler way of expressing eqn. (1.2) is by the Arrhenius equation, from which Marcus theory was based on: (1.3) in which A is the frequency factor, E a is the activation energy, and k B stant. The frequency factor encompasses the preexponential term in eqn. (1.2) and describes the rate of 31 the reaction in the absence of a barrier. Linearizing eqn. (1.3) allows for explicit values of A a nd E a to be found for a set of relaxation rates over some temperature range. These terms will be specific to the complex of interest, the relaxation process being investigated, and the experimental conditions under which the system is analyzed. The questio n therefore becomes one of how to go about measuring k nr . Traditionally this is done either by time - resolved emission 105 or transient absorption (TA) spectroscopy. 21 In the case of Fe(II) chromophores, emission does not occur and the processes of interest are on the sub - nanosecond timescale in the Fe(II) polypyridyl complexes we are proposing to study. And although ultrafast VT - TA setups have been described previously, they have largely been used in the realms of photosynthesis 106 and physics. 107 Previously, picosecond VT - TA anisotropy spectroscopy has been employed to study the temperature dependence of interligand electron transfer in [Ru(bpy) 3 ] 2+ by Malone and Kelley. 108 However, for various technical reasons, ultrafast VT - TA has not been applied to transition metal complexes in solution before. TA spectroscopy represents a pump - probe technique in which the pump pulse is used to create an initial excited state, and then the probe pulse creates a second absorption event which will monitor the subsequent kinetics. 109 These two pulses are delayed with respect to one another, thereby generating a time - resolved profile of the excited dynamics of the complex being studied. If the probe pulse reaches the sample before the pump, no signal will be observed. It is only upon excitation by the pump pulse that the temporal evolution may be monitored by the probe pulse. As the laser systems used to collect the data in this dissertation have been described extensively by others previously, 110,111 a lengthy review of them will not be provided here. Additionally, a complete descripti on of TA setups in general is given in an excellent review by Megerle and coworkers that inspired much of the experimental design used within this work. 112 32 This experiment may be performed in one of two regimes that reflect how the sample is probed: as a full spectrum or at a single wavelength ( Fig. 1. 1 ). Full spectral data are the excited state equivalent of a UV - Vis, or ground state absorption spectrum, at selected time delays in which a white light wavelength. They provide a complete picture of the excited state dynamics over the probe window. To fully understand which processes are being monitored, it is necessary to collect both ground state absorption and full spectra data. The former allows for identification of the state that is initially prepared by the pump pulse; the latter is used to determine the excited state process being measured. Unfortunately, what a ful l spectral measurement provides in spectral resolution it loses in temporal resolution; it is therefore common to select a probe wavelength of interest in order to en the pump and probe pulse and allow for precise characterization of the kinetic profile. The addition of an optical cryostat in the sample position allows for temperature - dependent nonradiative lifetimes of Fe(II) chromophores to be measured, providing a method for both Arrhenius and Marcus analyses to be performed on the photophysical processes of this class of compounds. 33 Figure 1. 1 . (a) Two - dimensional full spectral data of the optical Kerr effect induced between the pump an d probe pulses when both are 550 nm. (b) If the data are plotted for one specific probe wavelength versus the time delay, a kinetic trace can be collected. (c) The data can also be plotted against the probe wavelength, providing a one - dimensional full spec tral trace. Due to the nonemissive, metal - centered nature of the ligand field states that dominate Fe(II) photophysics, accurate thermodynamic information on these excited states is hard to come by. Some of the best and only estimates of the 5 T 2 / 1 A 1 driving force associated with the relaxation from the 5 T 2 state to the 1 A 1 come from the SCO community. These are compounds in which the B T) such that the excited state can be accessed by changes in temperature, pressure, or via light absorption. 57 , 92 VT lifetimes may yield 34 the specific driving force is grea tly reduced relative to prototypical Fe(II) polypyridyl complexes, it is believed that many of the same vibrational modes will be accessed for a low - spin and SCO compound of similar ligand scaffolding. Calculations can then be performed on a series of anal 113 providing an initial understanding of the crucial nuclear coordinates involved in the relaxation of Fe(II) compounds. A final tool to be used in the development of methodol ogies for studying Fe(II) polypyridyl photophysics is, surprisingly, Ru(II) compounds. As already described, the excited state processes undergone in this class of complexes is much simpler due to the higher energy ligand field manifold relative to the MLC conversion, information regarding the charge transfer excited states is critical, and more easily garnered from Ru(II) analogues. Experimental methodologies may be developed on these simpler compoun ds, and then used more rigorously to study the Fe(II) compounds of interest. Moreover, Ru(II) polypyridyls are not restricted to analysis by TA studies only. The presence of luminescent states also allows for steady state and time - resolved emission spectro scopies to be performed, as well as quantum yield determination. All of these data together tell a more complete story of the MLCT manifold in these d 6 compounds. coord inate of interest. For various technical and computation reasons, this coordinate cannot be measured directly. Unfortunately, the data presented in this dissertation do not directly measure the MLCT deactivation coordinate by VT - TA. When variable - temperatu re measurements are being discussed with respect to Fe(II) complexes, unless otherwise noted, the ground state recovery process is being investigated. Eventually, these data can be used in conjunction Ru(II) analogues, 1 A 1 n uclear coordinate. It is through the combined usage of all 35 of these methods and computation work that the fundamental photophysics of Fe(II) polypyridyls can be better understood. 5. Nonradiative Decay Theory As mentioned above, semi - classical Marcus theory is adept at describing the nonradiative ground state recovery dynamics in Fe(II) complexes and has been successfully applied previously. 104, 114 This ma y seem counterintuitive, particularly to those who associate Marcus theory solely with electron transfer. True, this model was developed to describe bimolecular self - exchange electron transfer reactions in solution, 115 - 117 howev er, this theory has evolved over time and can be used to describe other phenomena, 22 such as intramolecular nonradiative decay. In some regards, this may not be surprising. Metal - to - ligand charge transfer, for example, may be a n onradiative process that accompanies electron transfer between two species that are physically separated from one another (albeit linked covalently) in a unimolecular fashion. The theory applies just as well to a ligand field state interconversion, as is o bserved in SCO complexes, or the ground state recovery of low - spin Fe(II) polypyridyls. Marcus theory is simply a classical treatment of a reaction rate describing electronic states and need not be applied to electron transfer from one physical location to another, be it inter - or intra - molecularly. Rule which describes the nonradiative rate of a transition between two states with two different electronic configurations. 117 It is defined as: (1.4) Here, the rate of the transition (k) from the initial state (a) to the final state (b) is a function of the Hamiltonian matrix element describing the electronic communication bet ween the two states (H ab ), 36 and the density of states - weighted Franck - 118 in an attempt to more accurately define the temperature dependence of reaction rates. At warmer temperatures, a linear dependence exists between ln(k) and T - 1 . Upon reaching low temperatures however, experimental reaction rates are observed to level off, that is, they become temperature - independent. This has been identified as electron tunneling, in which vibrational wavefunction overlap between the two electronic states allows for vertical energy transfer beneath the barrier. In this way, a reaction may o ccur even without the thermal energy typically required to surmount the free energy of activation. Classical intramolecular electron transfer treatments only predict the trend seen for warmer temperatures as tunneling is not allowed by this theory. The der ivation of the semi - classical and quantum mechanical theories has been described in great detail elsewhere. 117 Since all of the kinetics depicted in this dissertation occur in the high - temperature region, at which these models c onverge to one temperature - dependent picture, only the details for the classical Marcus theory and its expressions will be examined here. decay theory, it also takes th e form that broadly describes each of the theories that will be elaborated on hereafter. Namely, a reaction rate is comprised of the product of a nuclear factor and an electronic one. In eqn. (1.4) , the electronic component is H a b , the electronic coupling matrix element. The Franck - Condon factor incorporates the nuclear part of the equation. This separation of electronic and nuclear factors is a consequence of the Born - Oppenheimer approximation, in which electronic motion is insta ntaneous with respect to nuclear motion due to the size of the respective particles. We take first the electronic factor, which Marcus derived from transition state or activated 37 complex theory. Much of the subsequent discussion is taken from Barbara, Meye r, and Ratner. 22 This model follows reactants (R) transforming into products (P) via an intermediate (I), or transition state ( Scheme 1.5 ). The reaction is assumed to occur solely along one nuclear c oordinate, and the potential energy surfaces used to describe the reactants and products are harmonic oscillators, such that the potential energy surfaces may be described by: (1.5a) (1.5b) for which the potential energy f being the force constant, Q being the distance along some nuclear coordinate, and Q 0 being the position of the minimum of the well. Transition state theory also makes use of adiabatic p otential energy surfaces. Adiabaticity refers to the degree to which electronic states are coupled. If the k B T, then very weak communication occurs between the two states, and they are referred to as nonadiab atic: the potential energy surfaces are only weakly interacting and population transfer is unlikely. If H ab = 0, then the surfaces are diabatic k B T, the states are r eferred to as adiabatic , or highly coupled. This results in an avoided crossing of the two states ( Scheme 1.5 ), which dramatically increases the transition probability. Adiabaticity also requires that if a transition proceeds from one surface to the next, the reverse reaction may not occur. The reaction barrier can be described in many ways, including the Eyring equation or collision theory, but is often expressed as the Arrhenius equation , eqn. (1.3) . Again, the frequency factor, A, envelops the electronic piece of the function, whereas the exponential describes the nuclear motion. In fact, for the reactants to reach the transit ion state as the free energy of activation, or E a ( Scheme 1.5 ). 38 Scheme 1.5. Reaction coordinate depicting the components of transition state theory. The potential energy surfaces are assumed to be harmonic oscillators, and the reaction proceeds from the reactant (R) centered around Q 0 (R) to the product (P) parabola at Q 0 (P) with no back reaction being possible due to the adiabaticity of the states. This adiabatic nature also presents as an avoided crossing, in which H ab is sufficiently large that the two states are highly coupled and form an intermediate (V I ) transition state. The a shows the energy requirement for surmounting the barrier from the reactant state. The transition state drawn in Scheme 1.5 in the case of ground state recovery for Fe(II) pol ypyridyls actually represents a higher - lying 3 LF excited state. The 5 T 2 1 A 1 transition is doubly spin - - order interaction between these two states. 39 A second - order spin - orbit coupling interaction must be invo ked, whereby the 5 T 2 and 3 T 1 states interact, as do the 3 T 1 and 1 A 1 states with some spin - 114 This may be shown as: (1.6a) (1.6a) The second - order spin - orbit coupling allows the reaction to proceed despite the first - order coupling between the reactant and product states being nearly diabatic. Despite having many degrees of freedom, transition state theory relies on the assumption that the active nucl ear coordinate is isolatable from all others, simplifying the picture to one vibrational mode. Ultimately, this has the result of taking multidimensional potential energy surfaces and reducing them to nothing more than parabolas. The reaction above can be redrawn (as in Scheme 1.6 energy surfaces. This is possible if the entropic contributions for the reaction are assumed to be zero (which is unlike ly for 5 T 2 1 A 1 - N being on the order of 0.2 Å but will difference between V R and V P at their equilibrium positions: (1.7) in which Q B is the nuclear position of the barrier. From its definition, the reorganization energy can be mathematically expressed as (1.8) which shows the parabolic nature of this constant. Similarly, the free energy of activation can be translated into potential energy surfaces by the relationship E a = V R [Q B ] - V R [Q 0 (R)]. This quantity is a measure of the energy difference of the barrier at Q B and the reactants at Q 0 (R): 40 (1.9) From eqn. (1.7) , Q B may be found algebraically in terms of Q 0 (R) and Q 0 (P) based on the fact that V R [Q B (R)] = V P [Q B (P)], such that (1.10) Substitution of this expression for Q B eqn. (1.8) into eqn. (1.9) yields (1.11) in which the activation energy is expressed in terms of reorganization energy and driving force. In this way, these thermodynamic and electronic parameters may be accurately used to describe the potential energy surfaces involved in an electronic transition ( Scheme 1.6 ). Furthermore, eqn. (1.11) directly equates the Arrhenius a nd Marcus theories. Eqn. (1.3) may then be understood as: (1.12) 41 Scheme 1.6. Potential energy surfaces for an electronic transition from the reactants (V R ) to the products (V P ) along some re action coordinate, Q. The position of the barrier is given by Q B . For simplicity, diabatic curves are shown, and as such H ab , or the coupling between electronic states, would be approximately 0 cm - 1 . The activation energy (E a ) is given by the energy difference energy required for the atoms in the reactants to re arrange to resemble the atoms in the products, without any surface crossing occurring. The electronic term may now be taken into consideration and will be guided by a discussion from DeVault. 117 By Arrhenius theory, the frequen cy factor is the rate of the reaction in the limit 42 E a = 0. This term can be treated as a probability of the passage from reactants to products via Q B using the Landau - Zener Quantum Mechanical formulation. The probability, P ab , is described as (1.13) for which v is the velocity of the system as it passes along the nuclear coordinate through the surfaces at Q B . The displacement amplitude , X, of the oscillation in the reactant state may be expressed by (1.14) Taken from the classical expression for an oscillating system, E represents the total energy of the is convenient here to denote the displacement between the minimum of the reactant surface Q 0 (R) and the barrier Q B as Q . The velocity, v, of the system as it passes through Q is thus (1.15) of the intersecting parabolas at Q B from Scheme 1.5 : (1.16a) such that (1.16b) eqn. (1.8) , this may be rewritten a s (1.16 c) The expressions for the velocity and change in slope for the reactants and products are then substituted into eqn. (1.13) , giving the rate of the reaction, eqn . (1.17) . 43 (1.17a) (1.17b) It is clear from eqn. (1.17) that the rate of the transition is given by the frequency at which the transition state is passed through, as governed by the probability of the transition pop ulating the product surface. The average rate of passage from the reactant surface to that of the products may be found over a Boltzmann distribution of energies such that (1.18a) (1.18b) From here, terms may be reduced and the preexponential factor from eqn. (1.18b) is used in combination with the exponential term determined from eqn. (1.11) to result in the semi - classical Marcus expression for nonradiative decay, as originally introduced in eqn. (1.2) . This derivation may be performed via alternate methods, 119 but the result will ultimately be the same. The application of quantum mechanics to Marcus theory allows for the vibrational overlap that participates in electronic transitions to be accounted for, while still taking advantage of the Marcus relationship b etween the activation energy, driving force, and reorganization energy. Finally, a further note on the Marcus reorganization energy is required. As discussed - sphere and outer - sphere componen ts, relating to the intramolecular vibrations and the surrounding medium of the the Stokes shift, as one - half of the energy difference between corresponding absorption and emission maxima. Alternatively, in the self - exchange reactions that came to define Marcus 44 electron transfer theory, the reorganization energy is defined as four times the activation energy. 22 oth the preexponential and exponential factors in the nonradiative decay expression, it encompasses both nuclear and electronic components. In some ways, it is the best i s can be related to the degree of nuclear distortion between the reactant and product states: (1.19a) for (1.19b) In eqn. (1.19) , S is known as the Huang - Rhys factor. The calculation of S is limited to a single nuclear c oordinate. To a first approximation, however, S may be a powerful indicator of how two i represents the structural changes undergone as the reaction proceeds from reactants throu gh the transition state to the products. o s , this parameter may depict specific solvent - solute interactions. Classically, Marcus defined this term according to a dielectric continuum model: 116 (1.20) This model is based on two spherical species, the donor and acceptor, surrounded by a medium donor and acceptor are r D and r A , respecti vely. R represents the distance between the centers of the two species. The final term is for the modeling of the solvent, for which and 0 are the optical and static dielectric constants, respectively. Unfortunately, eqn. (1. 20) is not applicable to the systems that will be studied here due to the assumptions it is built on: namely, that electron transfer is occurring, that it be between two particles, that those particles are spherical, and that solvent medium is well - described by a bulk function. The semi - classical Marcus expression for nonradiative decay has been derived and shown 45 to be applicable to the ligand field transitions that will be studied in this work. From this equation in conjunction with VT - TA measurements, the c energetic difference between the 5 T 2 and 1 A 1 states may begin to be estimated. The electronic coupling constant, H ab , for these two states is likely to be very near to 0 cm - 1 due to the doubly spin - forbidden natu re of the transition. That being said, H ab has previously been estimated to be on the order of 170 cm - 1 . 104, 114 These measurements may provide some insight into the true magnitude of the coupling betw een these states. And most importantly, inner - and outer - sphere reorganization energy contributions may be determined, providing crucial insight into the vibrational modes that participate in the MLCT deactivation process into lower - lying ligand field stat es. Based on the information provided by VT - TA and Marcus theory, significant progress may be made in extending the charge transfer lifetime in Fe(II) polypyridyls, thereby improving the outlook for these chromophores in the realm of photovoltaic applicati ons. 6. Concluding Comments This dissertation is a compilation of the work performed over six years in an attempt to better understand the fundamental photophysical processes of low - spin Fe(II) polypyridyl complexes. It serves to expand the wealth of know ledge available on this class of compounds and attempts to provoke ideas for future studies. The ultimate goal of this research is to extend the MLCT lifetime of Fe(II) complexes in a knowable and reproducible manner. In some regards, this was achieved. Pe rhaps more importantly, this work sought to understand on a molecular level the effect that the metal, ligand backbone, substituents, counteranions, solvent, and excitation energy have on complexes of this type in an effort to truly define the multicompone nt parameter that is Marcus reorganization energy. 46 Chapter 2 describes the ultrafast VT - TA methodology that was designed and implemented so as to perform Arrhenius and Marcus analyses on Fe(II) chromophores. A family of [Fe(bpy ) 3 ] 2+ - type compounds are studied and compared to [Fe(terpy) 2 ] 2+ , resulting in reaction barriers being reported for these complexes for the first time. In Chapter 3 is a second variable - temperature study, in this case of [Fe(dcpp ) 2 ] 2+ . The ground state recovery process in this compound is found to be nearly barrierless, the first to be reported. The nature of these dynamics allow for the fine - tuning of that barrier by external perturbations, such as via a change in counteranion an d solvent. Chapter 4 takes a departure from iron - based chromophores but continues the work begun in Chapter 3 with a thorough study of the effects of solvent and excitation energy on the excited state evolution of a Ru(II) polypyridyl system. These outer - sphere components drive the photophysics observed for this complex and provide insight into MLCT - based dynamics. Finally, Chapter 5 draws a direct comparison between Fe(II) and Ru(II) photophysical processes with the iron analogue of the compound studied in Chapter 4 being prepared and analyzed. These results also serve as a conduit to the research of the effects of extended delocalization on the M LCT lifetime in Fe(II) chromophores. The data and interpretations provided in this dissertation offer a more thorough understanding of some prototypical Fe(II) complexes, as well as a few that are relatively under - studied. Three strategies are provided an d explored in an attempt to increase the charge transfer lifetime of this class of compounds. As is true with the implementation of renewable energy sources to solve the global energy crisis, it will not be one approach that solves the problem, but an amal gamation of all these methods. In this way, the MLCT lifetime may actually be lengthened such that these chromophores are comparable with their second row congeners, thereby providing a path to a high - efficiency, Fe(II) - based photovoltaic device and greatl y improving the global 47 energy outlook. 48 REFERENCES 49 REFERENCES 1 . Cook, J. Oreskes, N.; Doran, P. T.; Anderegg, W. R. L.; Verheggen, B.; Maibach, E. W.; Carlton, J. S.; Lewandowsky, S.; Skuce, A. G.; Green, S. 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S.; Chuan, Y. - T.; Li, S.; Newkome, G. R. ; Goodson, T. Ultrafast Time - Resolved Spectroscopy of Self - Assembled Cyclic Fe(II) - Bisterpyridine Complexes. J. Phys. Chem. B 58 2010 , 114 , 11731 - 11736; DOI: 10.1021/jp104836k . 102 . Brown, A. M. Excited - State Dynamics of Iron(II) - Based Charge - Transfer Chromophores. Ph.D. Thesis, Michigan State University, East Lansing, MI, 2011. 103 . Marcus, R. A.; S utin, N. Electron Transfers in Chemistry and Biology. Biochim. Biophys. Acta 1985 , 811 , 265 - 322; DOI: 10.1016/0304 - 4173(85)90014 - X . 104 . Sutin, N. Nuclear, Electronic, and F requency Factors in Electron - Transfer Reactions. Acc. Chem. Res. 1982 , 15 , 275 - 282; DOI: 10.1021/ar00081a002 . 105 . Claude, J. P.; Meyer, T. J. Temperature Dependence of Nonradiative Decay. J. Phys. Chem. 1995 , 99 , 51 - 54; DOI: 10.1021/j100001a010 . 106 . Huber, H.; Meyer, M.; Scheer, H.; Zinth, W.; Wachtveitl, J. 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Understanding the Interplay Between Geometry and Ultrafast Dynamics in Ligand Field Excited States of Inorganic Chromophores. Ph.D. Thesis, Mi chigan State University, East Lansing, MI, 2015. 11 1. Miller, J. N. Ultrafast Dynamics of Iron(II) - Based Complexes in Solution and Semiconductor - Chromophore Assemblies. Ph.D. Thesis, Michigan State University, East Lansing, MI, 2018. 112 . Megerle, U.; Pugl iesi, L.; Schriever, C.; Sailer, C.F.; Riedle, E. Sub - 50 fs Broadband Absorption Spectroscopy with Tunable Excitation: Putting the Analysis of Ultrafast Molecular Dynamics on Solid Ground. Appl. Phys. B 2009 , 96 , 215 - 231; DOI: 10.1007/s00340 - 009 - 3610 - 0 . 113 . A delman, S. L.; Jakubikova, E. U npublished results. 114 . Buhks, E.; Navon, G.; Bixon, M.; Jortner, J. Spin Conversion Processes in Solutions. J. Am. Chem. Soc. 1980 , 102 , 2918 - 2 923; DOI: 10.1021/ja00529a009 . 59 115 . Marcus, R. A. On the Theory of Oxidation - Reduction Reactions Involving Electron Transfer. I. J. Chem. Phys. 1956 , 24 , 966 - 978; DOI: 10.1063/1.1742723 . 116 . Marcus, R. A. On the Theory of Electron Transfe r Reactions. VI. Unified Treatment for Homogeneous and Electrode Reactions. J. Chem. Phys. 1965 , 43 , 679 - 701; DOI: 10.1063/1.1696792 . 117 . DeVault, D. Quantum - Mechanical Tunnelling in Biological Systems , 2 nd ed.; Cambridge University Press: New York, 1984, and references therein. 118 . Jortner, J. Temperature Dependent Activation Energy for Electron Transfer Between Biological Molecules. J. Chem. Phys. 1976 , 64 , 4860 - ; DOI: 10.1063/1.432142 . 119 . Schrauben, J. N. Electronic Structure and Excited State Dynamics of Chromium(III) Complexes. Ph.D. Thesis, Michigan State University, East Lansing, MI, 2010. 60 CHAPTER 2. VARIABLE - TEMPERATURE ULTRAFAS T SPECTROSCOPY YIELDS INSIGHT INTO RELAXAT ION PATHWAYS OF FE(I I) POLYPYRIDYL COMPL EXES 1. Introduction For over half a century, [Fe(bpy) 3 ] 2+ - bipyridine) has been the benchmark for an array of iron(II) complexes. 1 - 16 Among its attributes, [Fe(bpy) 3 ] 2+ is one of the most well - studied and well - understood of the first - row transition metal complexes and provid es a good fundamental handle for d 6 photophysics. For this chromophore, and for nearly all Fe(II) polypyridyls, absorption of visible light excites the low - spin 1 A 1 ground state into the singlet metal - to - ligand charge transfer (MLCT) state, whereupon ultra fast intersystem crossing to the 3 MLCT occurs in ~20 fs. 1 Deactivation out of the MLCT manifold occurs in <100 fs 2 with unit efficiency 3 via a ligand field manifold, sampling a 3 T state, 4 into the lowest energy excited state, the 5 T 2 . 5 Ground state recovery from this ligand field state occurs on the order of 1 ns 6 and is dependent on the nature of the solvent. 7 Despite our knowledge of these photophysical processes, there remain a number of unanswered fundamental questions about this model complex. For instance, although attempts have been made to estimate the zero - point lowest energy excited state ( 1 A 1 / 5 T 2 ), a range of values spanning nearly one eV (i.e. 2000 - 9000 cm - 1 ) exists in the literature. 8 - 10, 17,18 complexes is that the 5 T 2 1 A 1 transition is doubly spin - - electron process, and does not emit; therefore there is no immediately apparent way to experimentally determine this energy. Consequently, other fundamental energetic parameters are unknown with regard to the ground state recovery of [Fe(bpy) 3 ] 2+ . Values for the Marcus reorganization energy oupling of the two electronic states (H ab ) for Fe(II) 61 polypyridyl complexes have been estimated, but not directly measured. For example, Sutin uses the lifetime of [Fe(bpy) 3 ] 2+ along with modified electron - - 7300 cm - 1 0, and H ab = 20 - 200 cm - 1 . 8 Likewise, using energy gap theory, Jortner approximated the electronic coupling constant from the Fe(II) free ion and found it to be 170 cm - 1 . 17,18 Hauser et al . studied [Fe(b py) 3 ] 2+ doped into a Zn(II) lattice by variable - temperature time - resolved absorption spectroscopy. 10 ab value, they determined the activation energy (E a ) of ground state recovery to be 364 cm - 1 for a zero - point energy difference of - 2000 cm - 1 . These values are some of the best, and only, indicators for energetic parameters of the electronic states available in the literature, yet they are merely estimates and lack experimental verification. To g ain a better grasp on these energetic parameters, many have taken advantage of Fe(II) spin - crossover complexes, 9, 19 - 21 in which the excited state is in a thermal equilibrium with the ground state. For t his type of system, variable - temperature magnetic susceptibility measurements of values exist in the literature for a whole host of complexes with varying deg rees of similarity to the Fe(II) polypyridyl complexes of interest here. 19,20 As part of a study on a series of spin - crossover complexes, Conti et al . studied a low - spin Fe(II) complex with a relatively long - lived excited state b y variable - temperature nanosecond transient absorption spectroscopy. 21 Unlike other reports at the time, their data produced an electronic coupling constant on the order of single wavenumbers. That being said, [Fe(bpy) 3 ] 2+ , with a zero - point energy difference substantially greater than k B T, is not spin - crossover rendering these methods inaccessible. energetic parameters are technically within r each, namely the activation energy and the frequency factor, or the rate in the absence of the barrier. The most direct method of determining activation 62 energy is through the use of Arrhenius behavior, where measuring the rate of reaction as a function of temperature yields both E a and the frequency factor. Although it is a very obvious solution, variable - temperature transient absorption spectroscopy is not a widely employed technique; when performed on the ultrafast timescale, it is even less commonly empl oyed. 22 One substantive reason for this is broadening of ultrafast pulses caused by the glass introduced from the optical cryostat necessary to control the temperature in these experiments. Advantageously, the lifetimes of the fo ur Fe(II) complexes studied here are on the order of nanoseconds, allowing for the utilization of relatively longer pulses (~150 fs), minimizing the effects of broadening. For the first time, variable - temperature ultrafast transient absorption spectroscopy is performed on [Fe(bpy) 3 ] 2+ is - di - substituted bipyridine compounds ( Scheme 2. 1 ). Comparisons between this family and a terpyridyl iron(II) system allows for deeper understanding of intrinsic differences between the complexes. Through this method, Arrhenius parameters are determined for each complex, and essential electronic values can begin to be found and interpreted. We believe that with our specific experimental s etup, this technique becomes an incredibly powerful tool in the study of fundamental energetic parameters of Fe(II) complexes. 63 Scheme 2. 1. 3 ] 2+ family, in which R = H is [Fe(bpy) 3 ] 2+ , R = Me is [Fe(dmb) 3 ] 2+ , and R = t Bu is [Fe(dtbb) 3 ] 2+ . Right: [Fe(terpy) 2 ] 2+ . 2. Experimental 2.1 Materials and Synthesis 2.1.1 General - bipyridine) iron(II) hexafluorophosphate, [Fe(bpy) 3 ](PF 6 ) 2 ; - dimethyl - - bipyridine) iron(II) hexafluorophosphate, [Fe(dmb) 3 ](PF 6 ) 2 - di - tert - butyl - - bipyridine) iron(II) hexafluorophosphate, [Fe(dtbb) 3 ](PF 6 ) 2 - terpyridine) iron(II) hexafluorophosphate, [Fe(terpy) 2 ](PF 6 ) 2 . They were prepared according to previously reported procedures. 11 - 13 1 H NMR spectra were collected on a Bruker 500 MHz NMR spectrometer. Electrospray - ionization mass - spectrometry (ESI - MS) was performed on a Waters Xevo G2 - XS Quad rupole Time - of - Flight spectrometer in positive mode. NMR and mass spectra were collected and analyzed by S. L. Adelman. HPLC grade acetonitrile was purchased from Sigma - Aldrich and used as received. Ground state absorption 64 spectra were collected with a Var ian (now Agilent) Cary 50 UV - Vis spectrophotometer. Electrochemical data were collected by S. L. Adelman using a CH Instruments Model CHI620D electrochemical workstation under inert atmosphere in an argon - filled glove box. A standard three - electrode setup was used to obtain Fe(II/III) potentials with differential pulse voltammetry and cyclic voltammetry in acetonitrile with 0.1 M TBAPF 6 using a Pt working electrode and a Ag reference electrode. TBAPF 6 was purchased from Oakwood Chemical Company and recrystallized from ethanol twice before use. All potentials are referenced internally to Fc/Fc + . [Fe(dmb) 3 ](PF 6 ) 2 was recrystallized by vap or diffusion of diethyl ether into methanol, while [Fe(terpy) 2 ](PF 6 ) 2 was recrystallized by vapor diffusion of diethyl ether into acetonitrile. In both cases, the single crystals were mounted in paratone oil and transferred to the cold nitrogen gas stream of the diffractometer for data collection. Single crystal X - ray diffraction was collected on suitable crystals mounted on a Bruker APEX - II CCD diffractometer with CuK radiation at the Center for Crystallographic Research at Michigan State University. The crystal structures were solved by S. L. Adelman. 2.1.2 Characterization of Free Ligands and Complexes - bipyridine (bpy) 1 H NMR (500 MHz, [d 6 - 4.65 Hz), 8.48 (dt, 1 H, J = 1.08, 7.96 Hz), 7.92 (ddd, 1 H, J = 1.8, 7.64 Hz), 7.41 (ddd, 1 H, 1.23, 2.72, 6.1 Hz)]. - dimethyl - - bipyridine (dmb) 1 H NMR (500 MHz, [d 6 - = 4.72 Hz), 8.30 (m, 1 H), 7.23 (m, 1 H), 2.44 (s, 3 H)]. - di - tert - butyl - - bipyridine (dtbb) 1 H NMR (500 MHz , [d 6 - H, J = 0.77, 5.23 Hz), 8.54 (dd, 1 H, J = 0.75, 2.0 Hz), 7.44 (dd, 1 H, J = 2.03, 5.14 Hz)]. 65 - bipyridine) iron(II) hexafluorophosphate [Fe(bpy) 3 ](PF 6 ) 2 1 H NMR (500 MHz, [d 6 - Hz), 8.27 (t, 1 H, J = 7.84 Hz), 7.74 (d, 1 H, J = 5.61 Hz), 7.59 (t, 1 H, J = 6.79 Hz)]. ESI - MS (m/z): [C 30 H 24 N 6 Fe] 2+ calcd. 262.07; found 262.06. - dimethyl - - bipyridine) iron(II) hexafluorophosphate [Fe(dmb) 3 ](PF 6 ) 2 1 H NMR (500 MHz, [d 6 - aceto 5.82), 2.58 (s, 3 H)]. ESI - MS (m/z): [C 36 H 36 N 6 Fe] 2+ calcd. 304.12; found 304.10. - di - tert - butyl - - bipyridine) iron(II) hexafluorophosphate [Fe(dtbb) 3 ](PF 6 ) 2 1 H NMR (500 M Hz, [d 6 - 1 H, J = 5.93 Hz), 1.40 (s, 9 H). ESI - MS (m/z): [C 36 H 36 N 6 Fe] 2+ calcd. 430.26; found 430.28. - terpyridine) iron(II) hexafluorophosphate [Fe(terpy) 2 ](PF 6 ) 2 1 H NMR (500 MHz, [d 6 - 0.6, 2.11, 8.07 Hz), 8.05 (td, 2 H, J = 1.48, 7.72 Hz), 7.44 (ddd, 2 H, J = 0.6, 2.3, 5.74 Hz), 7.25 (ddd, 2 H, J = 0.6, 1.32, 6.54 Hz). ESI - MS ( m/z): [C 30 H 22 N 6 Fe] 2+ calcd. 261.06; found 261.04. 2.1.3 Crystal Structure Determination [Fe(dmb) 3 ](PF 6 ) 2 crystal data: C 40 H 45 F 12 FeN 6 OP 2 , M r = 971.61, triclinic, a = 8.6648(2) Å, b = 14.3856(3) Å, c = 17.4683(4) Å, T= 173 K, space group P - 1 (No. 2), Z = 2, 25863 reflections measured, 7808 unique (Rint = 0.1207), which were used in all calculations. The final wR(F2) was 0.0625 (all data). CCDC 1810752. [Fe(terpy) 2 ](PF 6 ) 2 crystal data: C 34 H 28 F 12 FeN 8 P 2 , M r = 894.43, tetragonal, a = 12.3462(2) Å, b = 12.3462(2 ) Å, c = 48.9067(9) Å, T = 173 K, space group P4 1 (no. 76), Z = 8, 26729 reflections measured, 11934 unique (Rint = 0.0446), which were used in all calculations. The final wR(F2) was 0.1140 (all data). CCDC 1810753. 66 2.2 Ultrafast Transient Absorption Spectroscopy Ultrafast transient absorption (TA) spectroscopy measurements were carried out as previously described, 23 with the following modifications: The Ti:sapphire oscillator (Coherent Mira 900) is now pumped by a diode - pumped solid state laser (Coherent Verdi V6) operating at 5.0 W. The output from the regenerative amplifier (Positive Light Spitfire) is split 70:30 to the pump and probe lines, respectively. The pump wavelength is tunable in the visible region by u se of an optical parametric amplifier (Light Conversion TOPAS), the output of which is double - passed by retroreflectors mounted on a 1.2 m delay stage (Aerotech) controlled by Soloist CP software. This set - up affords 13 ns of delay between the pump and pro be pulses, a necessity when collecting ground state recovery dynamics of Fe(II) polypyridyl complexes. The detection scheme utilizes ~10 nm UV/Vis bandpass notch filters (Thorlabs) to select the probe wavelength of 530 nm that was desired from the white li ght continuum, which is then focused onto a Si amplified photodiode (Thorlabs). collected in the linear regime. The ground state absorbance for each of the samples was approximately 0.7 in a 1 - cm sample cryogenic cuvette (FireFlySci) at 490 nm, the excitation wavelength, and no spectral changes were observed after the variable - temperature experiments were complete. Pulse characterization is performed within the cryo stat by optical Kerr effect (OKE) measurements made in acetonitrile, yielding approximately 160 fs pulses. Cross - correlation performed in acetonitrile gives an instrument response function better than 300 fs. The spectra shown here are an average of approx imately 10 scans, with no single scan giving a fit that is a statistical outlier. Monoexponential and Arrhenius fits to the data were performed with Igor Pro (v. 6.37) software. All error reported was propagated across multiple data sets. 67 2.3 Variable - Temp erature Measurements In order to obtain spectra at a continuum of temperatures, an optical Dewar (Janis Research SuperTran - VP 100) was implemented, with capabilities of maintaining temperatures <2 - 325 K. Initially, a turbomolecular pumping station (Pfeiffe r Vacuum HiCube 80 Eco) brings the pressure of the outer jacket of the cryostat to 10 - 6 mbar, thereby producing an insulating atmosphere. A liquid nitrogen storage Dewar (International Cryogenics, Inc.) is connected to the cryostat with a transfer line (Ja nis Research) that remains in place throughout data collection for minimal cryogen loss. The continuous - flow setup also allows for the cryostat to remain stationary throughout data collection, thereby minimizing changes in the pump/probe overlap within the sample. The temperature of the sample within the cryostat is monitored (Lake Shore Cryotronics) by two sensors placed above and below the sample mount. The average of these two temperatures is assumed to be the sample temperature, affording better than ±2 K certainty. A schematic of the variable - temperature ultrafast set - up can be seen in Scheme 2. 2 . No stabilization time was necessary as data collection is on the order of one hour, more than sufficient for the sample temperat ure to equilibrate. 68 Scheme 2. 2. Schematic overview of the variable - temperature apparatus used within the standard ultrafast transient absorption setup. Arrows demonstrate the direction of the air flow; for example, the turbomolecular pump pulls vacuum on the outer jacket, whereas the cooled nitrogen flows into the inner jacket of the cryostat. 3. Results and Discussion 3.1 Characterization 3.1.1 Ground State Absorption Spectra The same pump probe cross - section was used to study each of the complexes. Specifically, all four compounds were excited at 490 nm and probing at 530 nm. An overlay of the ground state absorption spectra for the four complexes can be seen in Fig. 2. 1 . The spectra have been normalized to the excitation energy for an absorbance of 0.7, as is used for these experiments. All 3 ] 2+ complexes have very similar spectra, with the typical MLCT band shape centered aroun d ca. 500 nm. In the case of [Fe(bpy) 3 ] 2+ , the manifold is narrower, with the red edge being blue - shifted relative to the other two complexes. At the probe wavelength, the 69 absorbance for [Fe(bpy) 3 ] 2+ is 0.74 AU and is 0.8 for [Fe(dmb) 3 ] 2+ and [Fe(dtbb) 3 ] 2+ . [Fe(terpy) 2 ] 2+ , however, is another case, entirely. The entire MLCT manifold is red - shifted compared to the bpy - based family. It also displays much sharper features. Because of these factors, the absorbance at the probe wavelength is 1. 0 AU. For all of these complexes, the rather high absorption at the probe energy serves to decrease the detected signal by way of reducing the amount of light transmitted through the sample. All kinetics were checked for linearity, however, and signal was optimized by focusing the pump and probe as tightly as possible within the sample. Figure 2. 1 . Ground state absorption spectra of the four Fe(II) polypyridyl complexes: [Fe(bpy) 3 ](PF 6 ) 2 in red, [Fe(dmb) 3 ](PF 6 ) 2 in green, [Fe(dtbb) 3 ](PF 6 ) 2 in blue, and [ Fe(terpy) 2 ](PF 6 ) 2 in purple. All spectra are normalized to 0.7 AU at 490 nm (~20400 cm - 1 ). See text for details. 3.2 Crystal Structures Single - crystal X - ray structures have not been previously reported for either 70 [Fe(dmb) 3 ](PF 6 ) 2 or [Fe(terpy) 2 ](PF 6 ) 2 . The structure of [Fe(dmb) 3 ](PF 6 ) 2 can be found in Fig. 2. 2 , and [Fe(terpy) 2 ](PF 6 ) 2 in Fig. 2. 3 . The Fe - N bond distances given in Table 2. 1 are typical for low - spin Fe(II) complexes, as expected. [Fe(terpy) 2 ](PF 6 ) 2 deviates the most from octahedral symmetry of all four complexes, with cis N - Fe - N angles spanning 80.82 - 99.97º. Significant distortion is also observed in the Fe - N bond distances, in which the axial bonds are ~1.88 Å whereas approximately 1.97 Å bond lengths are seen for the equatorial N - Fe bonds. Compared to the trans N - Fe - N an gles 3 ](PF 6 ) 2 family, those for [Fe(terpy) 2 ](PF 6 ) 2 are 167.75 ± 9.60º, supporting the descent in symmetry from octahedral. This is to be expected, however, due to the tridentate nature of the ligand, which more strained than its bidentate analogues. 3 ](PF 6 ) 2 family, [Fe(dmb) 3 ](PF 6 ) 2 is the lowest in symmetry, with [Fe(bpy) 3 ](PF 6 ) 2 being the highest. This is evidenced by the greater variance in cis N - Fe - N angles for the methylated com plex. To gauge the electron - donating ability of the R groups in the substituted bpy family, two parameters are closely examined: 1) the Fe - N distances, and 2) the C - C bond distance connecting the R group to the bipyridine backbone. In the first case, the F e - N bond increases for the complexes as dtbb < dmb < bpy; secondly, the C - C bond is longer in the case of [Fe(dtbb) 3 ](PF 6 ) 2 . These two pieces of data indicate that the t butyl group is less electron - donating than the methyl group. Although the structures re ported herein are of the ground state geometries, knowledge of the effects of the ligands on the iron center inform the understanding of the ligand field strength and is therefore relevant to discussion of the photophysics of the complexes. 71 Figure 2. 2 . X - ray crystal structure of [Fe(dmb) 3 ](PF 6 ) 2 , with solvent molecules and counteranions omitted for clarity. Crystals grown and solved by S. L. Adelman. Figure 2. 3 . X - ray structure of [Fe(terpy) 2 ](PF 6 ) 2 , with solvent molecules and counteranions omitted f or clarity. Crystals grown and solved by S. L. Adelman. 72 Table 2. 1. Bond distances and angles from X - ray crystallographic data for all four complexes. Complex Fe - N Distance (Å) Cis N - Fe - N Angle (º) Trans N - Fe - N Angle (º) Ref. [Fe(bpy) 3 ](PF 6 ) 2 1.967 81.86 - 94.31 174.61 [ 14 ] [Fe(dmb) 3 ](PF 6 ) 2 1.967 ± 0.006 80.92 - 97.52 175.10 ± 1.19 This work [Fe(dtbb) 3 ](PF 6 ) 2 1.957 ± 0.001 81.06 - 95.84 174.54 ± 1.66 [ 13 ] [Fe(terpy) 2 ](PF 6 ) 2 1.944 ± 0.049 80.82 - 99.97 167.75 ± 9.60 This work 3.3 Challenges of Variable - Temperature Ultrafast Spectroscopy It is well - established that ultrashort (sub - ns) laser pulses will temporally broaden when propagating through media. 24,25 This phenomenon, known as chirp, artificially increases the instrument response function. In cases in which the kinetics are <100 fs, this is severely detrimental to the data collection. In fact, the only previous report that was found in which variable - temperature ultrafast transient absorption spectroscopy was being performed on a transition metal complex in solution used 30 ps pulses. 22 A pulse duration on this order should experience minimal to n o effects due to dispersion. The exact amount of chirp introduced to an ultrafast pulse can be calculated (see Chapter 2 Section 3.3.1 ), as well as the extent to which the pulse will be broadened. The pump and probe pulses used i n this experiment were characterized by OKE spectroscopy in a 1 mm path length cuvette without the cryostat and found to be on the order of 150 fs. In this regime, the amount of dispersion introduced by the windows of the cryostat and 1 - cm path length cuvette is predicted to be negligible, a result observed in the OKE spectrum collected for the sample within the De war. We would also expect no meaningful effect of chirp on the kinetics measured here as the lifetimes of the complexes in this report are on the order of single nanoseconds, four orders of 73 magnitude larger than the predicted dispersion effect. To further verify the lack of effect the optical Dewar plays on the kinetics, ground state recovery dynamics of the four complexes were collected with the sample in the cryostat at room temperature. The lifetimes of [Fe(bpy) 3 ] 2+ and [Fe(terpy) 2 ] 2+ reported here are c onsistent with what has been observed previously. 6, 15 Creutz et al . reported a ground state recovery rate for [Fe(dmb) 3 ] 2+ in water, which has intrinsically different dynamics than in acetonitrile. 7, 12 To the best of our knowledge, a ground state recovery rate has not been reported for [Fe(dtbb) 3 ] 2+ . It should be noted that the lifetime of [Fe(terpy) 2 ] 2+ under these conditions is such that the ground state does not fully recover within the dynamic range possible here. Typically, data collection out to approximately 4 - 5 times the ground state recovery lifetime is required for the signal to completely return to zero (i.e. confidence in the lifetime from the fit). In this case, there will always be greater inherent error in the lifetime, and therefore all values calculated from the lifetime reported for [Fe(terpy) 2 ] 2+ than for the other complexes studied here. While the glass from the cryostat imposes a st atic form of error into the results, the change in temperature provides a dynamic one. Many different factors display a dependence on temperature that can present challenges to reproducible data collection. The first, and perhaps most obvious, difficulty c omes in the form of solvent purity, specifically, the presence of water. Water here acts to raise the freezing point of the solvent, thereby facilitating a higher temperature fluid - to - glass transition. This transition is notorious for altering observable r ates due to the disordered nature of the semi - solid solution. 26 The choice of HPLC grade acetonitrile here for use as the solvent helps to minimize this issue since this grade is intrinsically very pure. By 1 H NMR, the water cont ent in the acetonitrile used in these studies is <0.4% (see Chapter 2 Section 3.3.2 ). Related to this concept is the overall decrease in solubility of the solute as temperature decreases. 74 This is observed as a reduced I 0 does not alter the overall time constants measured for the sample. Finally, the effect of temperature on the index of refraction has been the most significant, and the most difficult to avoid or correct for. The temperature dependence of some common solvents 27,28 including acetonitri le 29,30 has been studied previously. Specifically, as temperature decreases, the refractive index increases; this means that relative to the path of the laser beam at room temperature, the beam will refract more at lower temperat ures. The result of this is two - fold. - cm cuvette will actually deviate with changing temperature. A greater effect will be seen for the pump rather than the probe as the pump enters the sampl e at a less collinear angle (5 - 10º relative to the probe). The best solution found for this problem is to optimize overlap on the side of the cuvette away from the detector (i.e. where the beams first enter the sample). In this configuration, the probe bea m should traverse a relatively straight path to the detector, and any beam refraction in the pump due to solvent should occur after the beams have overlapped, thus minimizing adverse effects. If a glass is not to be formed, a shorter pathlength cuvette cou ld also be used to aid in these efforts. The second way in which the change in index of refraction as a function of temperature is observed is the amount of pump scatter that mposed on the results in an artificially shortened observed time constant. Here, as with the case when water was present in the solvent, bimodal Arrhenius behavior is seen. The most straightforward approach to solve this problem would be the use of a monochromator as part of a two - color setup to attenuate the effec ts of the scatter. In these results, however, we were limited to the use of a white light 75 continuum probe and 10 nm bandpass filter, and therefore chose to probe at wavelengths spectrally far (> 50 nm) from the scatter so as to not distort the data. 3.3.1 Pulse Broadening Calculations Based on the optical material, the exact amount of dispersion introduced to a pulse as it propagates through that material. 31 These calculations are defined by variables such as group velocity dela y (GVD) and group delay dispersion (GDD), which is in turn determined by properties that are specific to the type of glass or material through which the pulse is traveling. For our purposes, the calculations were made for fused silica, the glass of the opt ical windows of the cryostat. There are four windows (two in the outer jacket, two in the inner jacket) plus the two glass faces of the sample cuvette, summing to approximately 12 mm of fused silica. Based on the material properties and this distance, the GVD can be found as a function of wavelength: ( 2. 1) 2 n 2 ) is the second derivative of the index 2 ) of the material is then the product of the GVD and the distance of material through which the pulse is propagating. Here, that distance is 12 mm. To in ), out can be calculated from the GDD at a specific wavelength: ( 2. 2) The results of this calculation can be found in Fig. 2. 4 comparing a pulse that travels through no media, and a pulse traveling through 12 mm of fused silica (i.e. the setup reported here). In general, as the amount of glass increases, the output pulse is lengthened more relative to the input pulse. This effect is especially dominant in pulses <40 fs. In the case of a 20 fs pulse, the output is 76 broadened to 119 fs, six times the original pulse duration. For the setup used in this work, however, the pulses were on the order of 150 fs, for which almost no broadeni ng is calculated or experimentally observed. These calculations serve to reinforce the idea that variable - temperature measurements are experimentally challenging on the ultrafast timescale for reasons such as pulse broadening. Figure 2. 4 . Calculated effects of group velocity delay (GVD) or dispersion on an ultrafast laser pulse. The red trace shows an input pulse that does not traverse through media and is therefore equivalent to its output pulse. In green is the calculated duration of a p ulse at 490 nm propagating through 12 mm of fused silica. The dashed line denotes 150 fs, which is the pulse duration used in the work reported here. 3.3.2 Water Content of Acetonitrile Fe(II) polypyridyl complexes are known to show a solvent dependence on ground state recovery rate. 7 Additionally, relative to acetonitrile (228 K), the solvent used in these studies, water 77 has a significantly higher freezing point at 273 K. The presence of water, then, in the solvent in large en ough quantities could serve to affect the observed rates, and therefore all subsequently calculated parameters. To prevent against this, HPLC grade acetonitrile was chosen, and the water content was measured by 1 H NMR ( Fig. 2. 5 a nd 2. 6 ). For both spectra, acetonitrile is the quintet at 1.96 ppm, and water is the singlet at 2.13 ppm. 13 C satellites are observable for the acetonitrile. In the blank spectrum ( Fig. 2. 5 ), residual acetone from cleaning the NMR tubes is seen at 2.11 ppm. For the blank, the amount of water by integration is 18% (i.e. the integrated value of water divided by the sum of integrated values). To determine the water content in the HPLC grade aceton itrile, the water peak integration was set to equal 0.24, which is seen in the blank. The amount of water in the solvent, then is <0.4%. This purity is sufficient for the variable - temperature experiments performed, and no adverse effects (e.g. bimodal Arrh enius behavior, unexpected room temperature lifetimes) are observed. Figure 2. 5 . 1 H NMR of CD 3 CN blank. Assignments can be found in the text. 78 Figure 2. 6 . 1 H NMR spectrum of HPLC - grade acetonitrile in CD 3 CN. Assignments can be found in the text. 3.4 3 ] 2+ Series The activation energy in the 5 T 2 1 A 1 conversion was measured first in the prototypical [Fe(bpy) 3 ] 2+ complex. To do this, the ground state recovery time constant, k nr, was found as a function of temperature (T), as given by the Arrhenius relationship ( 2. 3) in which A is the preexponential factor, E a is the activation energy, and k B Only the solution phase lifetimes were of interest, and thus the glass - to - fluid transition was avoided. For all of the complexes reported herein, care was taken to ensure that the same anion (PF 6 - ), solvent (acetonitrile), and e xcitation and probe wavelengths (490 and 530 nm, respectively) were used for each complex. This should minimize any outer - sphere effects and allow for direct 79 comparison of complex - only, or inner - sphere, dynamics. The freezing point of acetonitrile is 228 K , so 235 K was chosen as the lowest temperature point, and data were collected every 5 K. The data for [Fe(bpy) 3 ] 2+ in MeCN are shown in Fig. 2. 7 and summarized in Table 2. 2 . At room temperature, the lifetime of the complex is 1.05 ± 0.02 ns; when cooled to 235 K, the lifetime is 1.52 ± 0.03 ns; a 50% increase that is rather large considering that [Fe(bpy) 3 ] 2+ has long been believed to be near barrierless, but within the Marcus normal region. 8 The Arrhenius plot of the VT data ( Fig. 2. 8 ) yields an activation energy of 310 ± 15 cm - 1 and a frequency factor with a value of 230 ± 20 ps - 1 . For context, this 1.5k B T barrier causes a 4.5 - fold increase in k nr . The activation energy reported here is surprisingly similar to that reported by Hauser et al . considering these measurements are solution - phase, whereas the sample in their measurements was a solid. 10 All of thes e data place [Fe(bpy) 3 ] 2+ firmly in the normal region, but further from barrierless than previously believed. Figure 2. 7 . Variable - temperature lifetimes of [Fe(bpy) 3 ] 2+ upon excitation at 490 nm and probing at 530 nm. At room temperature (red), the lifetime of the complex is 1.05 ± 0.02 ns. This lengthens with decreasing temperature to 235 K (purple), at which point the lifetime is 1.52 ± 0.03 ns. 80 Table 2. 2. Summary of the lifetime of the complexes at room temperature and 235 K, and the Arrhenius val ues found from the variable - temperature experiments. Complex Lifetime at 292 K (ns) Lifetime at 235 K (ns) A (ps - 1 ) E a (cm - 1 ) [Fe(bpy) 3 ](PF 6 ) 2 1.05 ± 0.02 1.52 ± 0.03 230 ± 20 310 ± 15 [Fe(dmb) 3 ](PF 6 ) 2 1.32 ± 0.02 2.01 ± 0.04 240 ± 20 345 ± 10 [Fe(dtbb) 3 ](PF 6 ) 2 1.07 ± 0.01 1.56 ± 0.02 230 ± 15 315 ± 15 [Fe(terpy) 3 ](PF 6 ) 2 5.2 ± 0.1 12.6 ± 1.7 150 ± 55 755 ± 70 Figure 2. 8 . Arrhenius plot for [Fe(bpy) 3 ] 2+ showing average ln(k nr ) as a function of inverse temperature from variable - temperature lifetimes. The data fit very well (R 2 = 0.98) to a single mode, for which the barrierless rate is 230 ± 20 ps - 1 , and the activation energy is 310 ± 15 cm - 1 . - di - 3 ] 2+ family were stu died, the dimethyl - (dmb) and di - tert - butyl - (dtbb) derivatives. The methyl group is slightly more electron donating into the bipyridine backbone, with the t butyl being the much more sterically bulky 81 substituent. These electronic and steric effects may cha nge the activation energy for these complexes with respect to the parent compound, [Fe(bpy) 3 ] 2+ . In the case of [Fe(dmb) 3 ] 2+ , the room temperature ground state recovery lifetime is lengthened to 1.32 ± 0.02 ns in acetonitrile. Interestingly, the lifetime o f [Fe(dtbb) 3 ] 2+ in acetonitrile is much more analogous to [Fe(bpy) 3 ] 2+ , being 1.07 ± 0.01 ns at room temperature. It is not unexpected for the lifetime of [Fe(dtbb) 3 ] 2+ to be so similar to that of [Fe(bpy) 3 ] 2+ due to the fact that the t butyl group is not an especially good electron donor. The effect of the substituent is negligible on the lifetime with respect to both electronic and steric factors. In contrast, however, the methyl group is a very good electron donor, and as such, the lifetime of [Fe(dmb) 3 ] 2+ is longer by 300 ps. By electron donating ability alone, ligand field strength should decrease across the series [Fe(bpy) 3 ] 2+ > [Fe(dtbb) 3 ] 2+ > [Fe(dmb) 3 ] 2+ . Decreased driving force coinciding with a decreas e in k nr , as is seen for [Fe(dmb) 3 ] 2+ , confirms that the transition is occurring in the Marcus normal region. In the variable temperature data for the substituted - bpy complexes ( Fig. 2. 9 and 2. 10 ), the lifetime at 235 K for [Fe(dmb) 3 ] 2+ is 2.01 ± 0.04 ns, the same 1.5 - fold increase from room temperature. Analogous results are seen in [Fe(dtbb) 3 ] 2+ , for which ground state recovery is 1.56 ± 0.02 ns at 235 K. In each of these cases, the Arrhenius param eters were solved for, and activation energies for [Fe(dmb) 3 ] 2+ and [Fe(dtbb) 3 ] 2+ were found ( Fig. 2. 11 and 2. 12 ). More importantly, the preexponential factors for the complexes are identical for the wh ole family of Fe(II) bpy - based complexes. The frequency factor corresponds to the nonradiative rate in the absence of a barrier. The fact that this value is constant for the entire family, despite changes in E a for different complexes, is highly intriguing and will be explored further. 82 Figure 2. 9 . Ground state recovery lifetimes of [Fe(dmb) 3 ] 2+ as a function of temperature. Excitation was performed at 490 nm, and the probe was 530 nm. Figure 2. 10 . Ground state recovery lifetimes of [Fe(dtbb) 3 ] 2+ as a function of temperature. Excitation was performed at 490 nm, and the probe was 530 nm. 83 Figure 2. 11 . Arrhenius plot of the averaged [Fe(dmb) 3 ] 2+ variable - temperature data. The preexponential factor, A, was found to be 240 ± 20 ps - 1 , with the activation energy being 345 ± 10 cm - 1 . The data fit well (R 2 = 0.97) to a single mode. Figure 2. 12 . Arrhenius plot of the averaged [Fe(dtbb) 3 ] 2+ variable - temperature data. The preexponential factor, A, was found to be 230 ± 15 ps - 1 , with the activation energy being 315 ± 15 cm - 1 . The data fit well (R 2 = 0.99) to a single mode. 84 The goal of this work was to determine the reorganization energy associated with the ground state recovery process of these Fe(II) c omplexes. To this end, a relationship can be derived between the Arrhenius activation energy (E a ( 2. 4) This is possible because the semi - classical Marcus equ ation 32,33 was derived from the Arrhenius relationship, such that ( 2. 5) Here, there is the additional variable of H ab , the electronic coupling constant, or the extent to which and H ab for the 5 T 2 1 A 1 transition in [Fe(bpy) 3 ] 2+ . 8 The problem arises in attempting to unambiguously solve for these three u nknowns given only two pieces of data (i.e. k nr and T). To approximate one of these unknowns, the driving force of the other complexes will be calculated from the electrochemical data: ( 2. 6) Here, we are assuming an initial driving force ( ) and using the Fe(II/III) oxidation couple for [Fe(bpy) 3 ] 2+ as a reference. The difference between and is then taken f - point energy difference for the complex of interest. Although we are able to glean relative comparisons between the c omplexes, the use of eqn. ( 2. 6) 85 couple speaks to the energy required to remove an electron from the t 2g set of orbitals on the metal center. It does not, however, give any indication of the energy of the e g * orbitals relative to the t 2g , and therefore contains only half of the information required to estimate the zero - point energy difference between the 1 A 1 and 5 T 2 electronic states. Furthermore, electrochemical potentials are one - electr on processes, which is very much not the situation in the 1 A 1 5 T 2 transition, formally (t 2g ) 6 (e g *) 0 (t 2g ) 4 (e g *) 2 . That being said, the initial assumption of a value of - 7300 cm - 1 (as originally cited by Sutin 8 ) for [Fe(bpy) 3 ] 2+ is necessary to determine values for the other unknown parameters, H ab then inform the error bars for these calculations. Specifically, a range of approximately 2000 - 900 0 cm - 1 has been theorized, 8, 10, 17,18 so H ab arbitrary but is approximately one standard deviation over the range of v alues. The error we assume Gº but is not so large as to artificially broaden the error bars on all values solved for and thus falsely equating the different complexes. The first set of Marcus parameters determined are those of [Fe(bpy) 3 ] 2+ . From eqn. ( 2. 4) , E a = 310 ± 15 cm - 1 - 7300 ± 730 cm - 1 1000 cm - 1 . This reorganization energy value is nearly twice what Sutin origin ally estimated, which was approximately 4800 cm - 1 . 8 Due to the parabolic nature of the Marcus curve, two values for reorganization energy can be obtained. If, however, [Fe(bpy) 3 ] 2+ is in the normal region as Sutin - 32,33 Sutin cites a 4800 cm - 1 value for reorganization energy, this could only be true if the gro und state ~11000 cm - 1 , which is in excellent agreement with our experimentally determined reorganization 86 325 cm - 1 3 ] 2+ that we cite here. Using a further relationship between the Arrhenius and Marcus equations in eqn. ( 2. 7) , H ab is found to be 4.4 ± 0.3 cm - 1 . ( 2. 7) The electronic coupling constant found is consistent with what is to b e expected of the highly nonadiabatic - 2 orders of magnitude smaller than the commonly reported values in the literature. 8, 10, 17,18 The precision on the v alue is also tightly constrained due to the fact that it has negative quartic power dependence on the reorganization energy. For example, a change of H ab from 4 to 5 cm - 1 while holding A - 1 . To be clear, we do not believe that we know the value of H ab to the tenth of one wavenumber: experimentally determining the difference even between a 4 versus 5 cm - 1 electron coupling constant is unrealistic. The fact that the Arrhenius preexponential tracks to the Mar cus H ab ab 4 complexes, small perturbations on H ab will have huge consequences for the values of both A and mentally ab 4 only incredibly sensitive, but it has a very high degree of confidence. As a consequence of A, it may also be highly indicative of the nature of the exc ited states and the relaxation pathway of the complex at hand. In the case of [Fe(bpy) 3 ] 2+ , this ratio is 1/(30 ± 5). In order to determine the significance of all these Marcus parameters of [Fe(bpy) 3 ] 2+ , the same analysis is performed on the family of com plexes. A summary of these values can be found in Table 2. 3 . For [Fe(dmb) 3 ] 2+ , these values are clearly very similar to those of [Fe(bpy) 3 ] 2+ . In 87 moving to [Fe(dtbb) 3 ] 2+ , however, the parameters are slightly modified, but still within error of the other bpy - based complexes. Unsurprisingly then, the H ab 4 family; specifically, ratios of 1/(33 ± 4) and 1/(29 ± 4) are found for [Fe(dmb) 3 ] 2+ and [Fe(dtbb) 3 ] 2+ , respectively. Table 2. 3. Electrochemical potentials for the Fe(II/III) oxidation and the corresponding Marcus parameters of the four complexes. Complex ox (V) a - 1 ) - 1 ) H ab (cm - 1 ) H ab 4 [Fe(bpy) 3 ](PF 6 ) 2 0.68 - 7300 ± 730 11000 ± 1000 4.4 ± 0.2 1/(30 ± 5) [Fe(dmb) 3 ](PF 6 ) 2 0.52 - 6000 ± 600 9700 ± 900 4.2 ± 0.1 1/(33 ± 4) [Fe(dtbb) 3 ](PF 6 ) 2 0.53 - 6100 ± 610 9500 ± 900 4.3 ± 0.2 1/(29 ± 4) [Fe(terpy) 3 ](PF 6 ) 2 0.72 - 7600 ± 760 14100 ± 1200 6.2 ± 1.2 1/(14 ± 9) a Oxidation potentials vs. Fc/Fc + in 0.1 M TBAPF 6 in MeCN with a Ag reference electrode. Despite the differences in activation energies and driving forces between these three complexes, A is unchanged between them. The consequently nearly constant H ab 4 atio derived from A lead to the postulation that this ratio is in fact a measure of the relaxation pathway for the 5 T 2 1 A 1 transition. The reorganization energy of the transition can be related to the nuclear coordinate of interest, and the electronic coup ling constant describes the nature of the transition (e.g., nonradiative), so a ratio of these two parameters as a function of the barrierless rate could be construed to form a mathematical representation of the major vibrational mode(s) active for the ele ctronic transition. Though these Fe(II) complexes have various electronic and steric differences, the major mode of relaxation is believed to be along the Fe - N bond lengthening coordinate. This largely stems from ultrafast X - ray data showing the 10% increa se in bond length from 1.96 Å to 88 2.16 Å from the singlet to quintet state, respectively. 34 Recently, however, Ashley and Jakubikova have performed DFT and complete active space self - consistent field (CASSCF) calculations on [Fe(bpy) 3 ] 2+ and suggested that torsional motion could play a critical role in all intersystem crossing events, but partic ularly in the ligand field states which are longer - lived relative to the MLCT excited states. 35 They observe that the spin state of the complex is highly correlated to the symmetry of the transition state, which is attributed to the bond - lengthening that occurs concomitantly with twisting into a trigonal prismatic geometry. The Ray - Dutt twist (with C 2v geometry) is found to be significantly lower in energy than the classic Bailar ( D 3h symmetry), as well as a new intermediate geome away from the Fe(II) center and is D 3h symmetry. It is therefore presumed that 5 T 2 3 1 A 1 ground state recovery is facilitated by a Ray - Dutt twist due to this being the only intermediate en ergetically viable. The researchers conclude by saying that full multidimensional potential energy surfaces must be calculated in order to know the transition state with any certainty; this work will have the added benefit of helping to determine the struc tural changes (and therefore spin states) accessed by [Fe(bpy) 3 ] 2+ upon MLCT deactivation. Ashley and Jakubikova implied that the - positions were the most likely to influence the transition state by steric hindrance. Thus, these trigonal prismatic tors 3 ] 2+ series - positions and neither sterics nor electronics should greatly affect the active nuclear motion for ground state recovery. Likew ise, if H ab 4 unchanged in this family, then it is reasonable that the relaxation pathway is also consistent. 3.4.1 Effect of Diethyl Ether in Lattice on Lifetime of Complexes. As previously mentioned, solvent can play a huge role in the lifetimes of Fe(II) polypyridyl complexes. The authors were concerned with the presence of diethyl ether in the 1 H NMR spectrum 89 of [Fe(dmb) 3 ] 2+ . On its face, this is hardly unusual as recrystalli zations of these complexes are performed by diethyl ether diffusions into acetonitrile solutions. 13, 15 Diethyl ether has also been observed in the crystal structures of some of the compounds, indicating its presence in the lattice. 13 However, by 1 H NMR, diethyl ether existed in a 1:2 mol ratio to [Fe(dmb) 3 ] 2+ . As a solvent, its bulk properties are incredibly different from acetonitrile, which could be cause for concern. For exa mple, the dielectric constant of acetonitrile is 36.64, but is 4.27 in the case of diethyl ether. 36 Because the nature of the outer - sphere reorganization energy is unknown, the effect that the presence of ether will have on 5 T 2 1 A 1 transition is also uncertain. To ensure that the variable - temperature results for [Fe(dmb) 3 ] 2+ were unchanged by the diethyl ether, a sample of [Fe(bpy) 3 ](PF 6 ) 2 was doped with excess diethyl ether (125 mol equiv.). The lifetime at room temperature was f ound to be 1030 ± 20 ps, which is identical to the undoped sample. However, there was the possibility that the ether could somehow affect the energetics of one electronic state more than the other, thereby changing the activation energy (E a ). Variable - temp erature measurements were then made, and E a was found to be 310 ± 15 cm - 1 ( Fig. 2. 13 and 2. 14 ). Due to the similarity in nature of [Fe(bpy) 3 ] 2+ and [Fe(dmb) 3 ] 2+ , it can definitively be concluded that at this concentration, the diethyl ether does not significantly affect either the room temperature lifetime, or the Arrhenius parameters for these Fe(II) complexes. 90 Figure 2. 13 . Ground state recovery lifetimes of [Fe(bpy) 3 ] 2+ doped with 125 mol equiv. of diethyl ether, as a function of temperature. Excitation was performed at 490 nm, and the probe was 530 nm. Lifetimes at the various temperatures are within error of those reporte d for the sample without diethyl ether. 91 Figure 2. 14 . Arrhenius plot of the averaged variable - temperature data of [Fe(bpy) 3 ] 2+ doped with 125 mol equiv. of diethyl ether. The preexponential factor, A, was found to be 225 ± 20 ps - 1 , with the activation energy being 310 ± 15 cm - 1 . These values are in excellent agreement with the Arrhenius factors found for the undoped [Fe(bpy) 3 ] 2+ sample. The data fit well (R 2 = 0.99) to a single mode. 3.5 Arrhenius and Marcus Parameters of [Fe(terpy) 2 ] 2+ To test this hypothesis, the same analysis is performed for [Fe(terpy) 2 ] 2+ , which has been postulated to be in the normal region, and further from barrierless than [Fe(bpy) 3 ] 2+ due to its longer ground state recovery lifetime. Moreover, although [Fe(terpy) 2 ] 2+ sees an analogous bond lengthening from the 1 A 1 to the 5 T 2 state, it has been demonstrated by combined time - resolved X - ray techniques and theoretical work that the ground state relaxation of [Fe(terpy) 2 ] 2+ is not well - described by a single nuclear coordinate. 37 Additionally, recent calculations from Nance et al . identify the terpy rocking motion to be an important vibrational mode in this relaxati on pathway. 38 To remain consistent in our study between the complexes, the same pump (490 nm) and probe (530 nm) wavelengths were used, despite the red - shifted MLCT maximum for [Fe(terpy) 2 ] 2+ 92 Fig. 2. 1 ). For comparison, ground state recovery lifetimes as a function of temperature were collected with redder wavelengths and all results were consistent with those at the pump - probe energies used here, as is expected for ground sta te recovery. In looking at the variable temperature measurements, a much more noticeable change in rate of ground state recovery is observed in the TA data as the temperature changes ( Fig. 2. 15 ). As seen in Table 2. 2 , the lifetime of [Fe(terpy) 2 ] 2+ in MeCN at 235 K is 12.6 ± 1.7 ns, a nearly than 2.5 - fold lengthening from the 5.2 ± 0.1 ns lifetime at room temperature. This dramatic increase in room temperature lifetime and lengtheni ng at colder temperatures lends credence to the belief that [Fe(terpy) 2 ] 2+ is further normal of the barrierless region than [Fe(bpy) 3 ] 2+ . The Arrhenius plot ( Fig. 2. 16 ) confirms this, showing the E a for [Fe(terpy) 2 ] 2+ is 755 ± 70 cm - 1 , more than twice that of [Fe(bpy) 3 ] 2+ ( Fig. 2. 17 and 2. 18 ). Likewise, the preexponential factor is approximately 150 ± 55 ps - 1 . The disparity between the barrierless rate and k nr is greater than a factor of 30. Two points of interest arise here: 2 ] 2+ relative to any 3 ] 2+ family. These data tend to imply that terpy in fact has a stron ger ligand Chapter 2 Section 3.5.1 . - 7700 ± 770 cm - 1 , 15 it can then be determ ined that the reorganization energy is 14300 ± 1200 cm - 1 . This is significantly more energy H ab is increased to 6.2 ± 1.2 cm - 1 , indicating a greater extent of c oupling between the ground and excited electronic states, but still very clearly nonadiabatic as the magnitude remains less than 10 cm - 1 . As mentioned before, care was taken to measure as nearly as possible only the inner - sphere components. That may not b e entirely true, and efforts to parse out the outer - sphere parameters for 93 these complexes are expanded on in Chapter 3 of this work. 7 To a first approximation, however, we take all values here as being intrinsic to the Fe(II) complex at hand. That being said, the H ab 4 ratio for [Fe(terpy) 2 ] 2+ 3 ] 2+ series and is 1/(14 ± 9). Any change in this ratio we believe implies a change in the nature of the relaxation pathway from the 5 T 2 to the 1 A 1 state. The values found in this study then serve to reinforce the experimental 37 and theoretical 38 findings that imply that the major modes of the 5 T 2 1 A 1 3 ] 2+ - based complexes and [Fe(terpy) 2 ] 2+ lie along very separate coordinates. Future studies should include variable - temperature measurements of oth er Fe(II) polypyridyl families in order to begin to determine how generalizable these results are. For example, will [Fe(phen) 3 ] 2+ - type complexes relax along the Fe - N bond lengthening coordinate, or another coordinate altogether? To this end, collaboration with theory helps to give a physical origin to the otherwise inconclusive H ab 4 for these complexes. 94 Figure 2. 15 . Ground state recovery lifetimes of [Fe(terpy) 3 ] 2+ as a function of temperature. Excitation was performed at 490 nm, and the probe was 530 nm. Because of the delay stage used in this experiment, at no temperature does the molecule recover the ground state fully (i.e. the signal returns to zero). This effect is only worsened at cold temperatures, to such an extent that the signal appears to be linear. These issues give rise to the increase in uncertainty on the lifetimes and subsequently calculated values. 95 Figure 2. 16 . Arrhenius plot of the averaged [Fe(terpy) 2 ] 2+ variable - temperature data. The preexponential factor, A, was f ound to be 150 ± 55 ps - 1 , with the activation energy being 755 ± 70 cm - 1 . The data fit well (R 2 = 0.96) to a single mode. Figure 2. 17 . Overlay of the variable - temperature ultrafast transient absorption spectra for [Fe(bpy) 3 ] 2+ 2 ] 2+ ( -- ). The traces indicate the temperature of the sample, red being 292 K to purple being 235 K. The left axis shows the scale for the [Fe(bpy) 3 ] 2+ , whereas [Fe(terpy) 2 ] 2+ is plotted against the right axis. 96 Figure 2. 18 . Comparison of the Arrhenius plots for the four complexes. The data are displayed as diamonds, and the straight line is the fit of the data: [Fe(bpy) 3 ] 2+ in red, [Fe(dmb) 3 ] 2+ in orange, [Fe(dtbb) 3 ] 2+ in green, and [Fe(terpy) 2 ] 2+ in blue. 3.5.1 The Ligand Field Strength of [Fe(terpy) 2 ] 2+ The common wisdom among chemists who study polypyridyl complexes has long been that terpy has a lower ligand field strength than bpy. This is supported, in part, by the increased lifetime of [Fe(terpy) 2 ] 2+ relative to [Fe(bpy) 3 ] 2+ 1 A 1 and 5 T 2 potential energy surfaces become more degenerate, thereby increasing the activation barrier between them. This increase in k nr is most commonly studied in spin - crossover complexes, which can live for tens to hundreds - 1 . Further evidence for the reduced ligand field strength of terpy compared to bpy comes in the form of the Ru(II) analogues. [Ru(terpy) 2 ] 2+ has been shown to have a drastically reduced lifetime (~25 0 ps) , 39 3 ] 2+ . 40,41 Although the trend is opposite what is observed in the Fe(II) complexes, the phenomenon is described by the same origin. The supposed lower lig and field strength of terpy brings the ligand field states to be isoenergetic with the MLCT manifold in 97 [Ru(terpy) 2 ] 2+ , thereby providing an alternate route for ground state recovery. In direct contrast to this hypothesis, however, is the electrochemical and absorption data. A series of Co(III) analogues were prepared by J. T. Yarranton. 42 The benefit of Co(III) is that the MLCT excited states are much higher in energy, making LF transitions more readily observable. For example, the 1 A 1 3 T 1 in [Co(bpy) 3 ](PF 6 ) 2 is found at ca. 13800 cm - 1 . In the case of [Fe(terpy) 2 ] 2+ , it is found to be 15500 cm - 1 , thus demonstrating that, in the case of Co(III), terpy has a stronger ligand field than bpy. This is not unexpected given that terpy contains three basic N - donors to the two on bpy. The inherent limitations in the use of electrochemical data to determine ligand field strength has already been expanded on (see Chapter 2 Section 3.4 ). That being said, the oxidation potentials of [Fe(bpy) 3 ] 2+ and [Fe(terpy) 2 ] 2+ appear to give corroborating evidence to this trend, although it is poss ible and even likely that those potentials only reflect a 300 cm - 1 shift in the t 2g set of orbitals in [Fe(terpy) 2 ] 2+ relative to [Fe(bpy) 3 ] 2+ . 2 ] 2+ > [Fe(bpy) 3 ] 2+ and ground state recovery for [Fe(bp y) 3 ] 2+ occurs in the Marcus normal region, the only way the lifetime of [Fe(terpy) 2 ] 2+ can be longer than that of [Fe(bpy) 3 ] 2+ is if the 5 T 2 1 A 1 conversion is an inverted process. Unless, that is, ground state recovery in these two complexes are on two separate Marcus curves. This would be determined by a change in reorganization energy, which the data herein reflect. A marked difference in the H a b 4 / nuclear coordinate in [Fe(terpy) 2 ] 2+ than in [Fe(bpy) 3 ] 2+ (or any member of its family of complexes). It is probable, then, that the ligand field states in [Fe(terpy) 2 ] 2+ are further along one nucl ear coordinate than they are in [Fe(bpy) 3 ] 2+ , a fact which would appear in S, the Huang - Rhys factor, the electronic coupling between states, and could thus manifest as a greater activation rted by the crystal structure of 98 [Fe(terpy) 2 ] 2+ , wherein the average Fe - N ax bond distance is 1.884(5) Å but is elongated for the Fe - N eq distance to 1.978(5) Å. This nearly 5% increase in bond length shows the asymmetry of the complex, leading to weaker orb ital overlap in the equatorial positions. Interestingly, [Ru(terpy) 2 ] 2+ shows a similar 4% elongation from the axial to equatorial Fe - N bond distances, 1.985(11) to 2.067(5) Å, respectively. 43 Considering the much greater size an d radial distance of the orbitals of Ru(II) compared to Fe(II), the fact that [Ru(terpy) 2 ] 2+ experiences just as much asymmetry as [Fe(terpy) 2 ] 2+ suggests this is a result of the ligand itself. Decreased orbital overlap with two - thirds Force constant analysis was performed on harmonic potential energy surfaces of [Fe(bpy) 3 ] 2+ and [Fe(terpy) 2 ] 2+ in order to determine the effects, if any, on S. This value is the degree of separation between the minima of potential energy surfaces with respect to a single nuclear coordinate. While more routinely found through spectral analysi s of emission profiles, 44 Hauser has previously estimated S in [Fe(bpy) 3 ](PF 6 ) 2 doped into a [Zn(bpy) 3 ](PF 6 ) 2 matrix through the use of variable - temperature nanosecond transient absorption spectroscopy. 10 The force constants found here are an order of magnitude greater than those reported ( Table 2. 4 ). Using eqn. ( 2. 8) , S can be determined as a function of the force constant: ( 2. 8) - 300 cm - 1 - N bond distance betw een the ground and excited states). 10 As Table 2. 4 shows, S increases from the solid - state to solution - phase sample of [Fe(bpy) 3 ](PF 6 ) 2 , which may reflect the enhanced freedom allowed in solution vers us in a matrix. More importantly, S likewise increases from [Fe(bpy) 3 ] 2+ to [Fe(terpy) 2 ] 2+ . These are very preliminary results that lend credence to the hypothesis that terpy is both a stronger field ligand 99 than bpy, and forms more distorted complexes, thereby displacing the 5 T 2 potential energy surface farther along a nuclear coordinate from the 1 A 1 ground state relative to bpy - based complexes. Table 2. 4. Force constant analysis of [Fe(bpy) 3 ] 2+ and [Fe(ter py) 2 ] 2+ . Complex Å) f (10 6 dyn/cm) S exp (cm - 1 ) calc (cm - 1 ) [Zn 1 - x Fe x (bpy) 3 ](PF 6 ) 2 a 0.204 0.5 0.2 45 ± 5 - - [Fe(bpy) 3 ](PF 6 ) 2 0.197 b 0.482 1.12 280 ± 55 4800 11000 5500 18400 [Fe(terpy) 3 ](PF 6 ) 2 0.222 c 0.544 1.14 355 ± 70 4100 14100 6900 21900 a From ref. 10 , for comparison. b From the crystal structure from ref. 14 . The excited state was approximated as a 10% increase in Fe - N distance. c From ref. 37 . The bond distances were taken as an average of two Fe - N eq and one Fe - N ax . While these results do at first glance appear promising, further inspection shows that with these force constants, the reorganization energy from t he 5 T 2 to the 1 A 1 surface is not what has been experimentally determined (see Table 2. 4 and Fig. 2. 19 and 2. 20 ). For this analysis, the force constant was taken to be the same for the both electronic states, and the potential energy surfaces were assumed to be harmonic oscillators. Both of these assumptions were made simply for ease of calculation. Higher level calculations are needed to more precisely discuss the displacem ent between the LF manifold and the ground state in [Fe(terpy) 2 ] 2+ and [Fe(bpy) 3 ] 2+ . This may yield further insight into the nuclear coordinate(s) responsible for ground state recovery in these complexes. 100 Figure 2. 19 . Potential energy surfaces calculate d from harmonic oscillators for [Fe(bpy) 3 ](PF 6 ) 2 in MeCN. The blue traces represent the 1 A 1 ground state, whereas the red curves are the 5 T 2 excited states. The activation and reorganization energies are given (see text and Table 2. 4 for more details). 101 Figure 2. 20 . Potential energy surfaces calculated from harmonic oscillators for [Fe(terpy) 2 ](PF 6 ) 2 in MeCN. T he blue traces represent the 1 A 1 ground state, whereas the red curves are the 5 T 2 excited states. The activation and reorganization energies are given (see text and Table 2. 4 for more details). 4. Future Works and Conclusions In this study, we provide the first direct measurements of Arrhenius parameters of non - spin - crossover Fe(II) polypyridyl complexes. Variable - temperature ultrafast transient absorption spectroscopy was used to study the ground state recovery ra 3 ] 2+ - type complexes and [Fe(terpy) 2 ] 2+ . Each of the four complexes was found to lie in the Marcus normal region, confirming previous suspicions. From the Arrhenius values, a relationship to semi - classical Marcus theory was drawn in order to determine energetic parameters that have long been unknown. These findings revealed a nearly constant H ab 4 3 ] 2+ family of approximately 1/30, a value that changed drastically to 1/14 in the case of [Fe(terpy) 2 ] 2+ . Based on the unchanging nature of this ratio for the bpy - based series, we postulate this ratio to in fact be a mathematical 102 representation of the major nuclear coordinate accessed for the relaxation in these different types of complexes. In the case of [Fe(bpy) 3 ] 2 + , it is likely this mode is the Fe - N bond elongation, whereas the terpy ligand rocking mode is more likely to be the predominant relaxation pathway for [Fe(terpy) 2 ] 2+ . s forthright as possible as to the potential errors that may arise from the method we used. However, a starting value of the driving force was required such that relative ratios of the Marcus parameters could be determined. In these ratios there is a much greater degree of certainty than in the absolute ab ab . The 5 T 2 1 A 1 transition is doubly - spin forbidden, non - emissive, ligand field in nature, and a multi - incredibly elusive. It is possible, then, that an absolute zero - point energy difference for Fe(II) polypyridyl complexes will not be found experimentally. 4.1 5 T 2 Excited Stat e Energetics Determined by Photoredox Methods One method can be proposed at this time to experimentally narrow down the magnitude of Scheme 2. 3 . Analogous route s have been previously reported in the photoredox catalysis literature by Meyer 45,46 and others. 47 - 49 This involves the use of an Fe(II) complex of interest with a lifetime long enough to beat the diffusion limit, 46 such as [Fe(terpy) 2 ] 2+ , and a series of oxidants of increasing oxidizing strength. Considering the electron config uration of the 5 T 2 and 1 A 1 states, the former will be more easily oxidized than the singlet due its doubly occupied e g * non - bonding orbitals. Solutions of the iron dye with the various oxidants will be studied time - resolved transient absorption spectroscop y such that [Fe(terpy) 2 ] 2+ will be photoexcited then relax to the 5 T 2 state, allowing for the oxidizing agent 103 to generate [Fe III (terpy) 2 ] 3+ . The mild - to - strong oxidant will need to have an oxidation potential less than the Fe(II/III) couple, 0.72 V vs. Fc, leaving many options available. 50 Ideally, it would also be spectroscopically silent in the visible region such that only the dynamics of the chromophore are observed. Spectroelectrochemical data of the complex as both the Fe(II ) and the Fe(III) chromophore would aid in the spectral assignments associated with MLCT in the [Fe II (terpy) 2 ] 2+ as compared to the ligand - to - metal charge transfer (LMCT) states and any other spectral features corresponding to the [Fe III (terpy) 2 ] 2+ compoun d. Any bands specific to [Fe III (terpy) 2 ] 3+ when studying the 2+ species by time - resolved transient absorption spectroscopy will thus be assignable and will make known the fact that the oxidizing agent was capable of removing an electron from the e g * orbita ls in the 5 T 2 state of the Fe complex. Electrochemistry would give the oxidation potential of the Fe(II/III) couple and the reduction potential of the oxidizing agent. The Fe(II/III) couple, as discussed already, gives a measure of the energy of the t 2g or bitals in the 1 A 1 state. The reduction potential of the oxidant capable of generating Fe(III) energy of the e g * orbitals of the 5 T 2 . 104 Scheme 2. 3. Kinetic scheme for method p Abridged photophysical cycle for typical Fe(II) polypyridyl, [A]. (b) Expected photochemical reaction for Fe(II) complex excited in the presence of a strong oxidant, [B], thereby undergoing oxidation in the quintet state. In both cases, the [ 1 A] 2+ state represents the singlet ground state of the Fe(II) complex; k r is the sum of the relaxation processes from the 1 MLCT (here [* 1 A] 2+ ) to the lowest energy excited state, [* 5 A] 2+ or 5 T 2 ; and k GSR is the rec overy of the ground state. Diffusion (k d ) brings the product to within such a distance (here [* 5 A] 2+ --- [B]) that electron transfer (k ET ) can occur to form the [* 4 A] 3+ --- [B] - product which then relaxes with k to the respective ground states. This photo chemical process is likely what is occurring in studies of photoredox catalysis systems with Fe(II) compounds. 51 - alkylation of aldehydes, [Fe(bpy) 3 ]Br 2 was used as a photocatalyst with comparable yields to those obtained with [Ru(bpy) 3 ] 2+ . In the case of the ruthenium catalyst, electron transfer occurs from the MLCT excited state, which is very long - lived. With its metal - centered lowest - energy excited st ate, though, reduction from [Fe(bpy) 3 ]Br 2 must be occurring from the 5 T 2 . In addition to the novel nature of the use of Fe(II) to photocatalyze a reaction, this work serves to provide a smaller range of oxidation potential for 105 the brominated aldehydes used . Although the method outlined here is yet another estimation of only Fe(II/III) potentials that has been employed in this work. It will also serve to potent ially provide error bars smaller than the 10% that were used here, which will ultimately propagate into the error calculations and reduce uncertainty for all the Marcus parameters of these Fe(II) dyes. 4.2 Direct Quantification of Driving Force by Photoaco ustic Spectroscopy Another promising method for the determination of thermodynamic parameters of Fe(II) polypyridyl complexes is photoacoustic spectroscopy (PAS), though more recently referred to as LIOAS, or laser - induced optoacoustic spectroscopy. This m ethod is an incredibly sensitive probe for nonradiative kinetics and thermodynamics. 52,53 The general concept of LIOAS is simple: a sample is irradiated, some or all of that excess energy is dissipated via heat, the increase in t emperature of the sample results in an increase in local pressure that radiates as a wave if the irradiation is pulsed, at which point it is detected by an acoustic sensor, such as a microphone or piezoelectric device. While most notably used with mid - IR l asers on gaseous samples, 53 this technique has been successfully applied to solution - phase transition metal - based chromophores. Fe(II/III) porphyrins, 54,55 hexacyanoferrates, 5 6 and organoiron(II) carbonyl complexes 60 specifically have been studied by LIOAS and photoacoustic calorimetry (PAC), which monitors sound waves as a function of temperature. From gas law, volume is inversely proportional to the pressure of the system, therefore LIOAS and PAC are uniquely situated to measure any volume change of the complex in solution. Miller and McCusker have identified through DFT and Solid - G calculations that the relatively large volume expansion from the 1 A 1 ground state to the 5 T 2 excited state in low - spin Fe(II) polypyridyls to be inextricably tied to the solvation energy of the ground state recovery process. 7 Being able to confirm that postulation experimentally, and as a 106 function of solvent, would be a huge boon to this field. Previously, PAC has been performed on [Ru(bpy) 3 ] 2+ and used [Fe(bpy) 3 ] 2+ as a reference. 5 8 The Ru(II) sample was measured over a range of 5 - 25 ºC and was found to have two volume changes associated with it: the first being for MLCT 1 A 1 excitation, and the second being 1 A 1 relaxation. These two volumes were found to be equal and opposite, and calculated using eqns. ( 2. 9) and ( 2. 10) : ( 2. 9) ( 2. 10) ion volume and it consists primarily of two components, the inner - sphere or str solv ). 58 In the case of [Ru(bpy) 3 ] 2+ , solvent effects were assumed to str . The volume change was approximated by a sphere with ground state radius r 0 and excited state radius r * upon excitation, then expand 0.01 Å upon relaxation to the ground state. The enthalpy of reaction for [Ru(bpy) 3 ] 2+ - 1 for the absorption process, and - - 1 for relaxation, or an average of approximately 14500 cm - 1 for each transition . From this same work, the [Fe(bpy) 3 ]Cl 2 compound in water was found to expand by 15.5 cm 3 - 1 at 23 ºC. Using Å for the radius of the complex, 59 [Fe(bpy) 3 ] 2+ the radial exp ansion is ~0.04 Å. This is a factor of two larger than the Fe - N bond elongation observed from ultrafast X - ray spectroscopy, 34 solv is not negligible for this class of compounds, thus solvent - dependent PAC measurem ents are critical and expected to give more insight into the low - spin to high - spin interconversion in Fe(II) polypyridyls. LIOAS and 107 PAC have an intrinsic downside. While the entha lpic contributions are easily monitored by these have been abl e to quantify both the driving force and entropy associated with [Ru(bpy) 3 ] 2+ upon photoexcitation. 60 LIOAS measurements were performed of the chloride salt in water, and reaction enthalpy - structural volume change correlations were plotted, giving a line with the form: ( 2. 11) str str - 1 ; this would make - 1 . Considering the fact that the structural reorganization for [Ru(bpy) 3 ] 2+ , in principle, is very small based on the - 0.01 Å contraction upon photoexcitation, this 0.3% entropic contribution to the system makes sense in context. It is possible that the charge - separated nature of the MLCT excited state is giving rise to enhanced solute - solvent interactions, 3 ] 2+ . Although, ground state recove ry in [Fe(bpy) 3 ] 2+ is notably solvent - dependent, 7 so it would be interesting to see how the entropy for the iron systems compare relative to their Ru(II) counterparts. It is clear that PAC and LIOAS are potentially very powerful tools in the arsenals of low - spin Fe(II) chemists. determined relative ratios of Marcus parameters, which should be able to be used in conjunction with theoretical methods to de termine likely modes of relaxation - and the effects of substituents on these modes - in low - spin Fe(II) polypyridyls. 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Photo - Induced Charge Transfer in Prussian Blue Analo gues as Detected by Photoacoustic Spectroscopy. Spectrochim. Acta, Part A 2007 , 68 , 191 - 197; DOI: 10.1016/j.saa.2006.11.013 . 57. Butler, I. S.; Li, H.; Gao, J. P. Comparison of Photoacoustic, Atten uated Total Reflection, and Transmission Infrared Spectra of Crystalline Organoiron(II) Carbonyl Complexes. Appl. Spectrosc. 1991 , 45 , 223 - 226; DOI: 10.1366/0003702914337425 . 58. Goodman, J. L.; Herman, M. S. Reaction Volumes of Excited State Photoprocesses. Chem. Phys. Lett. 1989 , 163 , 417 - 420; DOI: 10.1016/0009 - 2614(89)85160 - 7 . 59. Hupp, J . T.; Weaver, M. J. Solvent, Ligand, and Ionic Charge Effects on Reaction Entropies for Simple Transition - Metal Redox Couples. Inorg. Chem. 1984 , 23 , 3639 - 3644; DOI: 10.1021/ic00190a042 . 60. Borsarelli, C. D.; Braslavsky, S. E. Volume Changes Correlate with Enthalpy Changes During the Photoinduced Formation of the 3 MLCT State of Ruthenium(II) Bipyridine Cyano Complexes in the Presence of Salts. A Case of the Entropy - Enthalpy Compensation E ffect. J. Phys. Chem. B 1998 , 102 , 6231 - 6238; DOI: 10.1021/jp981235o . 115 61. Chen, L. X.; Shaw, G. B.; Novozhilova, I.; Liu, T.; Jennings, G.; Attenkofer, K.; Meyer, G. J.; Coppens, P. MLCT State Structure and Dynamics of a Copper(I) Diimine Complex Characterized by Pump - Probe X - ray and Laser Spectroscopies and DFT Calculations. J. Am. Chem. Soc. 2003 , 125 , 7022 - 7034; DOI: 10.1021/ja02 94663 . 116 CHAPTER 3. THE INFLUENCE OF OU TER - SPHERE REORGANIZ ATION ENERGY ON A BARRIERLESS REA CTION IN THE EXCITED STATE DYNAMICS OF A N OCTAHEDRAL IRON(II) POLYPYRIDYL COMPLEX 1. Introduction In the ongoing quest to lengthen the lifetime of the charge - separated metal - to - ligan d charge transfer (MLCT) excited states in low - spin Fe(II) complexes, the most apparent and seemingly straightforward is through the manipulation of excited state ordering. A scenario can be imagined in which the ligand field (LF) strength of the Fe(II) co mplex is so increased that the metal - centered electronic excited states are significantly destabilized such that they lie energetically above the MLCT states. In this case, the excited state ordering of the Fe(II) - based compound would very closely represen t that of typical Ru(II) chromophores with long - lived MLCT lifetimes. In order to achieve such a goal, the ligands of the complex would have to be manipulated so as to drastically increase the ligand field strength. This would likely place the complex on t he Tanabe - Sugano diagram for d 6 electronic configurations in which the lowest - lying excited state is the 3 T 1 state. 1 Until very recently, there were no known Fe(II) complexes with this electronic state ordering; this is in large part due to the inherent difficulties of distinguishing the spin of the excited state, particularly in short - lived complexes. Simultaneous optical absorption and X - ray emission spectroscopies, however, have the advantageous of observing molecular structur e as excited state dynamics evolve, proving to be an incredibly useful tool. Gaffney et al. have recently used this technique to study [Fe(bpy)(CN) 4 ] 2 - in a series of solvents. 2,3 Cyano ligands have long shown a propensity toward s solvatochromism, 4 and this complex was no exception. In the aprotic solvents acetonitrile, dimethylsulfoxide, and tetrahydrofuran, the low energy MLCT absorption band was 117 very red - shifted and typically centered at ~700 nm. 2 For these solvents, it was observed that the lowest - energy excited state was actually MLCT in nature, and it decayed to the ground state on the order of 20 ps. This is still the only known example of an Fe(II) complex with this electronic state ordering. If the same complex is dissolved in a protic solvent like methanol or water, though, max ~550 and 490 nm, respectively. 3 Due to MLCT states being energetically destabilized, the lowest energy excited state reve rts back to being LF in nature, though it is the 3 T 1 excited state as opposed to the 5 T 2 . These studies represent an important benchmark in the field of low - spin Fe(II) photophysics, as they show the same complex being able to achieve either a MLCT or 3 T 1 lowest energy excited state, with the determining factor being the solvent. Although the case study provided above is a very unique example due to the highly solvatochromic nature of the - CN moieties, this method of outer - sphere reorganization energy impac ting excited state energetics is well worth pursuing, albeit in moderately more representative Fe(II) polypyridyl complexes. Another avenue pursued in the name of lengthened MLCT lifetimes was the synthesis of a more perfectly octahedral Fe(II) complex, n amely 2,6 - bis(2 - carboxypyridyl)pyridine iron(II), [Fe(dcpp) 2 ] 2+ ( Scheme 3.1 ). 5 With its high symmetry, the ligand field strength was greatly increased. Unfortunately, the lowest energy excited state was still a metal - centered ligand field state; ground state recovery from this excited state, however, was unique in its rate. The lifetime of [Fe(dcpp) 2 ] 2+ in acetonitrile was observed to be 280 ± 10 ps, which is 3 times faster than that of [Fe(bpy) 3 ] 2+ . It was postulated that either the ligand field strength was so much greater that the 3 T 1 lowest lying excited state was accessed, or that the reorganization energy of [Fe(dcpp) 2 ] 2+ was drastically increased relative to [Fe(bpy) 3 ] 2+ . With respect to the for mer, recent ultrafast X - ray studies 6 have determined that ground state recovery occurs from a quintet excited state along with 118 a Jahn - Teller distortion in this state. This leaves reorganization energy as the most probable influencer of the excited state dynamics in this compound. Scheme 3.1. Molecular structure of [Fe(dcpp) 2 ] 2+ ; the series of counteranions (X) for use in this work: tetrafluoroborate (BF 4 - ), hexafluorophosphate (PF 6 - ), and tetrak is[(3,5 - trifluoromethyl)ph enyl] borate (BAr F - ); and the solvents (Solv) of choice: ethyl acetate (EtOAc), acetone, acetonitrile (MeCN), and propylene carbonate (PC). 119 A large volume of work has previously been done on the solvation effects on ground state recovery in [Fe(bpy) 3 ] 2+ . 7 - 12 though the results were largely qualitative. Preliminary work has been performed in the way of ultrafast variable - temperature transient absorption (VT - TA) measurements on [Fe(bpy) 3 ]Cl 2 in a series of solvents in order to deter mine the effects of solvent on ground state recovery in this complex ( Appendix A ). Historically, outer - sphere reorganization energy in this class of compounds has been believed to be quite large, nearly 0.5 eV for both [Fe(bpy) 3 ] 2+ and [Fe(terpy) 2 ] 2+ by some accounts. 13 During the course of the VT work on [Fe(bpy) 3 ] 2+ , it became apparent that this estimation is over an order of magnitude too large. It then became highly desirable to expand this type of study to [Fe(dcpp) 2 ] 2+ , a complex whose reorganization energy is under question. The methodology outlined in Chapter 2 of this work was used to study the ground state recovery of this complex under a variety of conditio ns in order to parse out the outer - sphere contributions to the 5 T 2 1 A 1 transition. 14 We believe this is the first instance of quantitative outer - sphere reorganization energies being determined for various solvents and counteranio ns of any low - spin Fe(II) polypyridyl complexes. It is also the first time the Arrhenius parameters are being found for [Fe(dcpp) 2 ] 2+ . As was the case with Chapter 2 , Marcus nonradiative decay theory is applied and estimations a re made for these values as well. 2. Experimental 2.1 Materials and Synthesis 2.1.1 General All salts of [Fe(dcpp) 2 ] 2+ were prepared by J. T. Yarranton. The synthetic route to prepare [Fe(dcpp) 2 ](PF 6 ) 2 has been previously reported. 5 The solvents used were: propylene carbonate (Acros Organics, 99.5%), ethyl acetate (Macron Fine Chemicals, ACS gra de), dichloromethane 120 (Jade Scientific, spectrograde), acetonitrile (Sigma - Aldrich, HPLC grade), tetrahydrofuran (Fisher Scientific, ACS grade), and acetone (Jade Scientific, spectrograde). All samples were prepared in air. 2.1.2 Characterization Character ization by 1 H NMR and mass spectrometry of the different salts of [Fe(dcpp) 2 ] 2+ was performed by J. T. Yarranton. Timed 1 H NMR studies were carried out by M. C. Carey and were collected with a Bruker 500 MHz NMR spectrometer. Ground state absorption spectr a were collected on a Cary 50 spectrophotometer (Varian, now Agilent) at a fast collection rate with background subtraction. Single crystals of [Fe(dcpp) 2 ](BF 4 ) 2 were grown and mounted in paratone oil and transferred to the cold nitrogen gas stream of the diffractometer for data collection. Single crystal X - ray diffraction was collected on suitable crystals mounted on a Bruker APEX - II CCD diffractometer with CuK radiation at the Center for Crystallographic Research at Michigan State University. The crysta l structures were solved by J. T. Yarranton. 2,6 - Bis(2 - carboxypyridyl)pyridine iron(II) tetrakis[(3,5 - trifluoromethyl)phenyl]borate [Fe(dcpp) 2 ](BAr F ) 2 1 H NMR (500 MHz, [d 6 - J = 2.10, 5.77 Hz), 8.37 (t, 2 H, J = 7.78 Hz), 8.23 (d, 2 H, J = 7.78 Hz), 8.11 (d, 2 H, J = 5.35 Hz), 7.78 (m, 8 H), 7.67 (s, 4 H), 7.52 (t, 2 H, J = 6.74 Hz)]. 2,6 - Bis(2 - carboxypyridyl)pyridine iron(II) tetrakis[(3,5 - trifluoromethyl)phenyl]borate [Fe(dcpp) 2 ](BAr F ) 2 in dic hloromethane 1 H NMR (500 MHz, [d 6 - 7.76Hz), 8.48 (d, 2 H, J = 7.69 Hz), 8.32 (t, 2 H, J = 7.60 Hz), 8.18 (d, 2 H, J = 7.76 Hz), 8.01 (d, 2 H, J = 5.37 Hz), 7.75 (m, 8 H), 7.60 (d, 4 H, J = 2.08 Hz), 7.45 (m, 2 H)]. 121 2.2 Ultra fast Transient Absorption Spectroscopy 2.2.1 Variable - Temperature Measurements The ultrafast laser system used to measure ground state recovery lifetimes of the series of [Fe(dcpp) 2 ] 2+ salts has been previously described 7, 14 - 16 and is fully detailed in Chapter 2 . The variable - temperature setup has likewise been expanded on. 14 The samples prepared for these measurements had an absorbance of 0.3 - 0.5 AU at the excitation wavelength in a 1 - cm pathlength cryogen - safe quartz cuvette (FireFlySci) and were typically excited with ~5 wavelengths used in this study w ere 490 and 610 nm and are specified for the data collected. Only a 540 nm probe was used. Pulse characterization is performed with the cryostat in place by optical Kerr effect (OKE) measurements made in acetonitrile. The pulses are nominally 160 fs, givin g an instrument response function of approximately 300 fs. Any spectra displayed are an average of at least 10 scans, with no single scan being a statistical outlier. The Arrhenius plots and values given are for the combined total data of that type collect ed. Monoexponential and Arrhenius fits were performed using Igor Pro (v. 6.37) software, and unless otherwise noted, all error reported is propagated across multiple data sets. 2.2.2 MLCT Lifetime Measurements The MLCT lifetimes of Fe(II) complexes are we ll - known to be very short (<200 fs), 17 so a laser setup with a shorter IRF was desired to have the most accurate measure of this kinetic process. A shorter pulse system was used to collect MLCT lifetime data on [Fe(dcpp) 2 ] 2+ . In this setup, which has been previously described, 18 a Mantis oscillator (Coherent) is pumped by a 5 W optically pumped semiconductor laser, the output of which seeds a Legend Elite regenerative amplifier (Coherent) that is pumped by an Evolution pumping laser (Coherent) at a1 kHz repetition rate. The 122 output pulses are nominally 35 fs in duration and is split 80/20 to pump and probe OPerA Solo optical parametric amplifiers (Coherent), respectively. These are tunable across 240 - 20000 nm but were used in this instance in the visible region. Specifically, pump wavelengths of 490 and 610 nm and a probe wavelength of 540 nm were of interest. Both the pump and probe lines propagate through a folded Brewster prism pair (Thorlabs) to preempt ively compensate for dispersion. The probe is translated on a linear actuator stage (Soloist) relative to the probe in order to collect transients as a function of time delay. The pump line is optically chopped at approximately 480 Hz which is connected to a lock - in amplifier. A small portion of the probe line is picked off to act as a reference for fluctuations in the laser power over the course of data collection. The polarization of the beams is set magic angle to each other in order to collect only popu lation dynamics, and not polarization effects. Both the pump and probe are focused collinearly at <5º into the sample, at which point the pump is blocked and the probe is detected by a Si photodiode (Thorlabs) after traversing a monochromator with a ~1 nm bandwidth for wavelength selection. The samples prepared for these measurements were studied in 1 - mm pathlength quartz cuvettes (FireFlySci) with absorbances of 0.3 - 0.5 AU at the excitation wavelength. Due to the high peak power of the temporally short p ulses used in this experiment, the average power was kept lower than what was used for the VT measurements. Specifically, the pump power was 2 ex c = 490 nm was 60 fs and was <50 fs when ex c = 610 nm. The probe pulse duration remained constant at 96 fs throughout the measurements. These pulse duration measurements were made by OKE in methanol, and the IRF was determined by cross - correlation in acetonitrile. For more information on pulse and s ystem characterization, please see Appendix B . The data displayed are an average of more than 10 scans, each collected between 1 - 3 times. Mono - and bi - exponential fits were performed in Igor Pro 123 software. 3. Results and Discus sion The purpose of this work is to study the outer - sphere effects on the ground state recovery of [Fe(dcpp) 2 ] 2+ . To that end, the complex was prepared with three different counteranions: tetrafluoroborate (BF 4 - ), hexafluorophosphate (PF 6 - ), and tetrakis[ (3,5 - trifluoromethyl)phenyl] - borate (BAr F - ), as can be seen in Scheme 3.1 . The role of solvent was also investigated. In [Fe(dcpp) 2 ] 2+ , the carbonyl is highly susceptible to attack by proton sources, which results in the deter ioration of the ligand. Protic solvents, therefore, were precluded from use. Four solvents were chosen to span a wide range of bulk solvent properties (e.g., dielectric constant, viscosity); namely, ethyl acetate (EtOAc), acetone, acetonitrile (MeCN), and propylene carbonate (PC) were used. 3.1 Characterization 3.1.1 X - Ray Crystallography High quality single crystals of [Fe(dcpp) 2 ](BF 4 ) 2 were able to be grown and studied by single - crystal X - ray diffraction. The geometric measurements from this complex we re then compared to the same measurements of [Fe(dcpp) 2 ](PF 6 ) 2 . 5 The results of this comparison can be found in Table 3.1 . The crystals with the BF 4 - counteranion were observed to be birefringent, as indicated by the clear change in crystal color under polarized light upon a 90º reorientation. 124 Table 3.1. Single crystal X - ray data comparison between the PF 6 - and BF 4 - salts of [Fe(dcpp) 2 ] 2+ . [Fe(dcpp) 2 ](PF 6 ) 2 a [Fe(dcpp) 2 ](BF 4 ) 2 b Fe - N ax (Å) 1.9738 1.964 Fe - N eq (Å) 1.986(3) 1.982(2) C - O (Å) 1.212(1) 1.212(2) Cis N - Fe - N (º) 88.8 ± 0.1 88.8 ± 0.2 Trans N - Fe - N (º) 178.3 ± 0.7 177.8 ± 0.3 O - N (Å) 3.4800 - 3.5402 3.457 - 3.530 CO1 - Py torsion (º) 26.5 26.5 CO2 - Py torsion (º) 41.5 44.5 a Taken from ref. 5 . b Data collected by J. T. Yarranton. Interestingly, changes in the structure of the cation were observed with a simple metathesis of the counteranion. Both structures were of the same space group (Pbcn), and many of their geometric components are the same. All bond ligand - Fe bond angles are within error of each other, for instance. One of the hallmarks of a tridentate ligand is a shorter axial bond relative to the equatorial bond distances. This is present in both salts of [Fe(dcpp) 2 ] 2+ . However, in the case of the BF 4 - salt, the Fe - N ax distance is significantly shorte r even than the same Fe - N ax distance in the PF 6 - salt. This was confirmed by statistical analysis and error propagation of the single crystal data. Likewise, the distance between the O of the carbonyl and the N atoms of the pyridine rings was measured and a range is given for each complex. For each of those O - N distances, the BF 4 - salt displays bonds that are on average 0.02 Å shorter than the same bonds in the PF 6 - salt. Shorter bond distances in [Fe(dcpp) 2 ](BF 4 ) 2 would tend to imply a greater degree of stabilization in that salt over the PF 6 - . Notably, though, there is more torsion in the angle of the carbonyl relative to the plane of the pyridine. These data taken together would seem to suggest that the central p yridyl 125 moieties of the dcpp ligand are bound more tightly to the Fe(II) center, inducing greater distortion in the wrapping of the peripheral pyridyls around the metal. The net effect, however, is that the [Fe(dcpp) 2 ](BF 4 ) 2 is lower in energy than [Fe(dcpp ) 2 ](PF 6 ) 2 . This is a surprising result considering the BF 4 - and PF 6 - anions are typically regarded as being very similar. PF 6 - may be slightly more polarizable due to its larger size relative to BF 4 - . But in that respect, BF 4 - is a smaller, harder anion, a nd may in fact be able to fit closer to the metal center and provide a greater extent of stabilization. These results are very interesting, in large part due to the surprising nature of them. It should be remembered, though, that these structures are for the crystals as solids while also in their ground states. It may be tempting to extrapolate these results to the photophysical processes that will be described ( vide infra ) , but the solution - phase nature of the measurements will necessarily change the geo metry of the complex, to say nothing of the photoexcitation into excited states. That being said, work is ongoing to grow quality crystals of [Fe(dcpp) 2 ](BAr F ) 2 to have knowledge of the ground state geometry of all three complexes as well as the stabilizin g role of the counteranions for this study. 3.1.2 Ground State Absorption Spectra To further characterize the ground state properties of the [Fe(dcpp) 2 ] 2+ complexes, UV - Vis spectra were collected for each of the three salts in MeCN. As Jamula et al. origi nally described, 5 the visible spectrum shows a very broad progression of bands of increasing intensity ( Fig. 3.1 ). The absorption maximum for the BF 4 - , PF 6 - , and BAr F - salts are 607, 605, and 606 nm, respectively, and show very little change across the entire absorption profile. Albeit a minor spectral shift, this is our first indicator that the anion has an effect on the energy of the 1 MLCT excited state. Relative to t he PF 6 - salt, the BF 4 - analogue is stabilized by 54 cm - 1 , and the BAr F - salt is stabilized by 27 cm - 1 . To a first approximation, it would appear that the UV - Vis spectra and X - ray data are in 126 agreement when comparing the PF 6 - and BF 4 - analogues of [Fe(dcpp) 2 ] 2+ , suggesting that the latter is lower in energy. Figure 3. 1 . Ground state absorption spectra of [Fe(dcpp) 2 ] 2+ salts, normalized to the MLCT maximum: BF 4 - at 607 nm (purple), PF 6 - at 605 nm (red), and BAr F - at 606 nm (green). As discussed in the introduction, solvatochromism is not uncommon in these types of chromophores. 19 One might expect the high activity of the carbonyl to mimic the effects of the cyano ligand in the case of [Fe(bpy)(CN) 4 ] 2 - . 3 The obvious difference being that the cyano was bound directly to the Fe(II) center, amplifying its effects as compared to the carbonyl which is cross - conjugated into the pyridyl backbone of the dcpp ligand. Any interaction of the carbonyl with the sol vent would have an attenuated effect on the Fe(II) itself. Thus, it is unsurprising that solvatochromism is displayed in [Fe(dcpp) 2 ] 2+ , though only to a small degree. For the sake of comparison, only the BAr F - counteranion was used with all four of these s olvents; this was also a necessity due to the increased solubility of the BAr F - salt. Often, this property is correlated with the Gutmann acceptor number (AN), 20 - 22 of which a moderate range is available from EtOAc 127 (9.3), 23 acetone (12.5), MeCN (18.9), and PC (18.3). 24 For comparison purposes, the dielectric constant was also used as a parameter of interest: EtOAc ( 0 = 6.08), acetone ( 0 = 21.01), MeCN ( 0 = 36.64), and PC ( 0 = 66.14). 25 Despite this span of an order of magnitude, the difference between the absorption maximum in the different solvents is only 4 nm (109 cm - 1 ), between EtOAc max max = 609 nm), as can be seen in Fig. 3.2 . These results are somewhat unexpected as the most stabilized MLCT band corresponds to the solvent with the lowest dielectric constant, which is counter to what was seen with [Fe(dcpp)(CN) 4 ] 2 - . The correlation is no better when using AN as the parameter of interest, as one would expect the higher AN to correlate to higher MLCT energy, clearly the reverse of what is observed here. Figure 3. 2 . Ground state absorption spectra of [Fe(dcpp) 2 ](BAr F ) 2 in EtOA c (red), acetone (green), MeCN (blue), and PC (purple). The spectra are normalized to the MLCT maximum. 3.2 Measuring Outer - Sphere Reorganization Energy 3.2.1 [Fe(dcpp) 2 ](PF 6 ) 2 With the stru ctural and ground state absorbance data in hand, the ultrafast variable - 128 temperature methodology that has been previously designed 14 was used to study this unique complex. The PF 6 - salt was originally studied in MeCN by Jamula et al. and was found to have a ground state recovery lifetime of 280 ± 10 ps at room temperature. 5 With such a short lifetime, it was postulated that the reorganization energy of thi s complex must be extraordinarily high with respect to other more typical Fe(II) polypyridyl complexes, such as [Fe(bpy) 3 ] 2+ and [Fe(terpy) 2 ] 2+ . The VT measurements found that at 235 K, the lifetime has increased to 340 ± 10 ps ( Fig. 3.3 ). Based on the Arrhenius equation , eqn. (3.1) , the natural log of the rate of ground state recovery, k nr , can be plotted against the inverse temperature, T, thereby linearizing the data and allowing for the activation en ergy E a and preexponential factor A to be determined, according to eqn. (3.2) . (3.1) (3.2) In these equations, k B is the Boltzmann constant. From this Arrhenius plot ( Fig. 3.4 ), an activation energy of 115 ± 15 cm - 1 is found, which is nearly three times smaller than that of [Fe(bpy) 3 ] 2+ . The barrierless rate, A, is found to be 165 ± 15 ps - 1 . What is immediately apparent is the magnitude of E a for this complex, and the fact that E a < k B T. The 5 T 2 1 A 1 transition, then, must necessarily be in the Marcus barrierless region, an extraordinary finding for this transition in an Fe(II) polypyridyl complex. 26 - 28 This result is also confirmed by the DFT analysis performed on the ultrafast X - ray spectroscopies of [Fe(dcpp) 2 ] 2+ that found the only barrier possible to explain the data was that of ~30 meV, which is in very good agreement with the results presented here. 6 129 Figure 3. 3 . Representative variable - temperature lifetimes of [Fe(dcpp) 2 ](PF 6 ) 2 in MeCN. Excitation occurred at 490 nm, and a 540 nm probe was used. At room temperature (red) the lifetime of the complex is 290 ± 5 ps, and at 235 K (not shown) the average lifetime is 340 ± 10 ps. Figure 3. 4 . Arrhenius plot for average variable - temperature data of [Fe(dcpp) 2 ](PF 6 ) 2 in MeCN. From these data, the barrierless rate is 165 ± 15 ps - 1 , and the activation energy is 115 ± 15 cm - 1 . The corre lation was modest, with R 2 = 0.738. 130 To the best of our knowledge, this is the first time a barrierless photophysical process has been definitively identified in a transition metal complex. Barrierless electron transfer has been previously reported in comp ounds of this type, especially as intramolecular electron transfer in Ru(II) polypyridyls, 29,30 However, most other excited state reactions that proceed with E a ~ 0 cm - 1 occur in organic fluorophores, 31 ,32 with respect to some isomerization coordinate, 33 - 35 or concomitantly with proton transfer (known as excited state intramolecular proton transfer, or ESIPT). 36,37 5 T 2 conversion is likely to occur in a barrierless fashion simply due to the ultrafast timescale of the intersystem crossing, 38 which is observed to be ~130 fs. 39,40 The charge transfer deactivation process is expected to be adiabatic; = 2 5 T 2 1 A 1 transition, whi ch is highly nonadiabatic (i.e., H ab ~ 6 cm - 1 ), to be barrierless appears to be unprecedented. The barrierless nature of [Fe(dcpp) 2 ](PF 6 ) 2 can on its own explain the very short lifetime of the complex relative to more prototypical Fe(II) chromophores. In Chapter 2 , it was determined that the barriers of [Fe(bpy) 3 ] 2+ and [Fe(terpy) 2 ] 2+ are 310 ± 15 cm - 1 and 755 ± 70 cm - 1 , respectively. Knowing that [Fe(dcpp) 2 ] 2+ is on a separate Marcus curve from either of these complexes, it still follows that in order for this compound to be in the barrierless region, it must described 14 [Fe(dcpp) 2 ] 2+ , however, nonradiative decay theory must be used: (3.3) in which H ab is the electronic coupling element. 27,28 The VT - TA experiment measures k nr as a ab as unknowns. I t is possible to obtain a ratio of H ab 4 131 relating the Arrhenius and Marcus equations such that (3.4) Similarly, ratios of (3.5) These are only ratios, though, and no unique values for these three parameters may found without for any of these complexes, work is ongoing in this rea lm. We have, however, found a method of ground and excited states in t he process of interest. The energies of these electronic states are O between the t 2g and e g * set of orbitals. 1 In other six - coordinate compounds such as [Fe(b py) 3 ] 2+ or [Fe(terpy) 2 ] 2+ , the geometric distortions induced by the ligands make it so that it is inappropriate to discuss the orbitals (and therefore the electronic states) in terms of octahedral symmetry. It is very commonly done, but not the most accura te. In the case of [Fe(dcpp) 2 ] 2+ , however, the molecule is of higher symmetry and so the octahedral label may be more suitable. Electrochemistry has been used previously 14 O for ground state recovery in these Fe(II) polypyridyls. The premise being that the (II/III) oxidation potential for iron center should effectively give a measure of the energy of the t 2g orbitals. Assuming the e g * orbitals are unaffected, a stabilization w ould correspond to a greater ligand field strength, and therefore a greater displacement between the 5 T 2 and 1 A 1 . This assumption has inherent faults but is the best 2 ] 2+ , the oxidation potential is taken relative to that of [Fe(bpy) 3 ] 2+ , for which we have a high level of 132 confidence in its driving force. Specifically, eqn. (3.6) is used: (3.6) in which E ox 3 ] 2+ is taken as - 7300 cm - 1 . 14, 26 One of the intriguing aspects of [Fe( dcpp) 2 ] 2+ is the fact that its oxidation potential is so positively shifted compared to either [Fe(bpy) 3 ] 2+ or [Fe(terpy) 2 ] 2+ . Whereas the latter two complexes have Fe(II/III) potentials on the order of 0.66 and 0.71 V vs. Ag/AgNO 3 (respectively), the same potential for [Fe(dcpp) 2 ] 2+ is 1.29 V. A greater amount of energy, therefore, is required to remove an electron from the metal center for this complex than for the more traditional Fe(II) polypyridyls. Supposing that the energy of the e g * orbitals has remained constant across all three complexes, the driving force for [Fe(dcpp) 2 ] 2+ is - 12220 cm - 1 , nearly double that of the other two complexes. This is in keeping with the barrierless nature of [Fe(dcpp) 2 ] 2+ , which would require incr eased driving force to speed up the rate of reaction relative to transitions occurring in the Marcus normal region. ab , can be found ( Table 3.2 ). Error b error is propagated through the calculations (see Appendix C ). Using eqn. (3.5) 14800 ± 1600 cm - 1 . Likewise, H ab can be determined from eqn. (3.4) to be 5.6 ± 0.2 cm - 1 , reflecting = 2 spin transition from the 5 T 2 to the 1 A 1 state. This value of reorganization energy is already significa ntly higher than that of [Fe(bpy) 3 ] 2+ (11000 ± 1000 cm - 1 ) but 2 ] 2+ (14100 ± 1200 cm - 1 ). Similarly, the H ab 4 / which is postulated to represent the nuclear motion of the ground state recovery transition is 1/(15 ± 2), which is the same as that of [Fe(terpy) 2 ] 2+ . Considering the tridentate nature of the dcpp and 133 terpy ligands, it seems reasonable that the two complexes might relax via similar pathways. In the case of [Fe(terpy) 2 ] 2+ , ultrafast X - ray experiments 41 and theoretical considerations 42 have suggested that the complex relaxes along a ligand rocking motion coordinate. Unlike the terpy ligand which remains relatively planar when bound to Fe( II), the dcpp ligand with its extended distance between pyridyl rings from the carbonyl moieties has the capability of wrapping around the metal center. With this geometry, a rocking motion for dcpp as ground state recovery occurs seems less likely. Howeve r, the work by Britz et al. used extended X - ray absorption fine structure (EXAFS) spectroscopy to study the geometry of [Fe(dcpp) 2 ] 2+ as it relaxed through its excited state pathway upon photoexcitation. 6 EXAFS showed that while the Fe - N ax bond distance only increased from 1.96 ± 0.01 to 2.05 ± 0.02 Å between the 1 A 1 to 5 T 2 states, respectively, the equatorial bond distances changed much more drastically from 1.98 ± 0.01 to 2.21 ± 0.02 Å. T hese data seem to imply that a rocking mo tion could be possible, as could a scissoring - type motion. As was the case with the VT - TA results of [Fe(bpy) 3 ] 2+ and [Fe(terpy) 2 ] 2+ , these VT results of [Fe(dcpp) 2 ] 2+ (particularly the H ab 4 - ray spectroscopy results, thereby confirming the importance and relevance of this methodology. Table 3.2. Arrhenius and Marcus parameter values of [Fe(dcpp) 2 ] 2+ relative to [Fe(bpy) 3 ] 2+ and [Fe(terpy) 2 ] 2+ . Complex A (ps - 1 ) E a (cm - 1 ) - - 1 ) a - 1 ) H ab (cm - 1 ) H ab 4 / [Fe(dcpp) 2 ] 2+ 165 ± 15 115 ± 15 12220 ± 1220 14800 ± 1600 5.6 ± 0.2 1/(15 ± 2) [Fe(bpy) 3 ] 2+ 230 ± 20 310 ± 15 7300 ± 730 11000 ± 1000 4.4 ± 0.2 1/(30 ± 5) [Fe(terpy) 2 ] 2+ 150 ± 55 755 ± 70 7600 ± 760 14100 ± 1200 6.2 ± 1.2 1/(14 ± 9) a Values calculated from electrochemical data from ref. 5 and eqn. (3.6) of this work. 134 3.2.2 The Role of the Counteranion Although ultrafast X - ray studies have concluded that the lowest energy excited s tate of [Fe(dcpp) 2 ] 2+ is the 5 T 2 , those same studies showed a Jahn - Teller distortion, implying an amount of participation from a triplet ligand field state. 6 It is safe to say that the ligand field strength of dcpp is much greate r than that of either bpy or terpy, as evidenced by the barrierless ground state recovery transition. Thus, the original proposition of Jamula et al. that [Fe(dcpp) 2 ] 2+ appears to be near the 5 T 2 / 3 T 1 crossing point on the Tanabe - Sugano diagram is reasonable. 5 The goal of this work is to determine the role of outer - sphere effects on the barrierless transition. Reactions occurring in the Marcus barrierless region are by necess ity energetically very delicate: E a k B T, so in principle, very little outside influence would be required to tip the reaction from barrierless to either the normal or inverted region. Exactly how much energy would be required to push the ligand field str ength such that the 3 T 1 is the lowest energy excited state is as yet unknown, though work is ongoing in that respect, and will be discussed further ( vide infra ). The fine energetic balance between two ligand field states described here is very reminiscent of spin - crossover (SCO) complexes, which are predicated on that very concept. 43 The difference being that the two ligand field states for [Fe(dcpp) 2 ] 2+ are the lowest and second - lowest excited states, whereas with SCO complexes, it is the ordering of the ground and lowest energy excited state in question. While external forces such as pressure, temperature, and light are capable of driving the electronic configuration change necessary to switch the electronic states, it is also p B T. Historically, non - coordinating solvent and counterion have been used extensively. 44 - 47 We, therefore, will study these outer - sphere influences o n the ground state recovery of [Fe(dcpp) 2 ] 2+ to determine how parallel this reaction is to SCO complexes. 135 In solution - phase studies, the role of the counterion is to stabilize the charge of the ubility in the solvent of choice. It is apparent, then, that the counterion will play a role in the thermodynamics of the compound. Many systematic studies of the influence of counterion on an Fe(II) SCO complex observed magnetic properties of the solid - st ate material. These will be inherently different interactions (i.e., packing forces) than when the molecules are in solution (i.e., solvation energy). That being said, a clear trend has emerged from this literature. 45 - 47 To illus trate this point, tris{4 - [(6 - methanol) - 2 - pyridyl] - 3 - aza - 3 - butenyl}amine iron(II) emerges as a strong case study, in which the counterion was varied to study the effect of anion size. 46 These data, as well as analogous studies by Lemercier et al. suggest that smaller counterions are better able to stabilize the e g * orbitals, decreasing the ligand field strength, and forming the high - spin complex, whereas larger counterions allow for the complex to exist in its low - spin configuratio n. 47 The analysis of these results is predicated on the ability of the larger anions to disrupt the crystal lattice, which only presents as the sample is in the solid phase. In this work, the size of the counterion was increase d from BF 4 - to PF 6 - to BAr F - . These three complexes were studied in MeCN so as to isolate any effects from the anion. The VT measurements of the ground state recovery lifetimes of [Fe(dcpp) 2 ](BF 4 ) 2 and [Fe(dcpp) 2 ](BAr F ) 2 are shown in Fig. 3.5 and 3.6 , respectively. That of [Fe(dcpp) 2 ](PF 6 ) 2 can be found in Fig. 3.3 , and the corresponding overlay of the Arrhenius plots is in Fig. 3. 7 . The data is summarized in Table 3.3 . Considering the size and charge density differential between BF 4 - and BAr F - , it is surprising that so little difference was seen in any of the Arrhenius or Marcus parameters between these three salts. All values found are within error of each other. 136 Figure 3. 5 . Representative variable - temperature lifetimes of [Fe(dcpp) 2 ](BF 4 ) 2 in MeCN. Excitation occurred at 490 nm, and a 540 nm probe was used. At room temperature (red) the lifetime of the complex is 295 ± 5 ps, and at 235 K (purple) the average lifetime is 325 ± 10 ps. Figure 3. 6 . Representative variable - temperature lifetimes of [Fe(dcpp) 2 ](BAr F ) 2 in MeCN. Excitation occurred at 490 nm, and a 540 nm probe was used. At room temperature (red) the lifetime of the complex is 285 ± 5 ps, and at 235 K (not shown) the average lifetime is 315 ± 5 ps. 137 Figure 3. 7 . Overlaid Arrhenius plot for average variable - temperature data of [Fe(dcpp) 2 ](PF 6 ) 2 (red), [Fe(dcpp) 2 ](BF 4 ) 2 (green) , and [Fe(dcpp) 2 ](BAr F ) 2 (blue) in MeCN. The Arrhenius values from these plots can be found in Table 3.3 . The correlations were modest, with R 2 for the PF 6 - salt being 0.738, 0.580 for the BF 4 - salt, and 0.884 for the BAr F - compound. Table 3.3. Arrhenius and Marcus parameters of [Fe(dcpp) 2 ] 2+ with varying counteranions. Anion A (ps - 1 ) E a (cm - 1 ) - - 1 ) - 1 ) H ab (cm - 1 ) H ab 4 / BAr F - 170 ± 15 110 ± 20 12220 ± 1220 14800 ± 1600 5.6 ± 0.2 1/(16 ± 3) PF 6 - 165 ± 15 115 ± 15 12220 ± 1220 14800 ± 1600 5.6 ± 0.2 1/(15 ± 2) BF 4 - 175 ± 10 105 ± 10 12220 ± 1220 14700 ± 1600 5.5 ± 0.2 1/(17 ± 2) There are a few possible explanations for this apparent lack of dependence on the counteranion. Firstly, when a halide salt series was studied by Lemercier et al., only the F - salt was high - spin, whereas the all of the other three halide complexes were SCO, implying that the perturbation imposed from the counterion is very subtle. 47 It is possible that the changes observed 138 in the Arrhenius average values are real, but so small as to be obscured by the error on the measurements. The specific anions chosen could also be an issue, as there could not be enough size differential between the three. BF 4 - and PF 6 - are very similar in size relative to BF 4 - , so a smaller anion could be desirable. Chloride was considered, but the synthesis of this complex ferentially coordinate to the Fe(II) center over the dcpp ligand. Another option might be fluoride, but that would, on its face, appear to present the same challenges as chloride. Alternatively, it is highly probable that size is not the true parameter o f the anion that should be analyzed. While polarizability of the anion may seem like an attractive choice, it cannot tell the whole story. For example, BAr F - is undoubtedly more polarizable than BF 4 - . However, the sheer volume and bulk of BAr F - inhibits it s ability to get spatially close to the cation, thereby reducing its ability to stabilize the charged species. A far better parameter is coordinating ability. To be clear, none of the anions being discussed within this work are forming any type of bond wit h the cation in any way. In fact, all three are typically deemed weakly - or non - coordinating. But the describes how close any atom from the anion can get to the metal center of the Fe(II) complex. To get at this, density functional theory calculations have been performed previously, studying many factors of cation - anion pairs. 48 In this work, the coordinating ability of various anions wa s assessed by the partial charge of the most peripheral atoms. The logic, here, being that the stronger the Lewis base, the more stability afforded to the cation. However, the most basic atom may be at the center of the anion and therefore shielded by larg er ligands. The smaller the partial charge, the less coordinating ability of that counteranion. An interesting trend emerged when comparing the three ions of interest for this work. BAr F - showed the weakest coordinating ability (as expected) with a 139 partial charge on the fluorine of - 0.22, and also unsurprisingly, PF 6 - had a strong coordinating ability with a fluorine partial charge of - 0.44. What was unexpected was that in the case of BF 4 - , the partial charge on the fluorine was - 0.25, indicating that the n egative charge was equally distributed amongst the four fluorine atom s, and making its coordinating ability much more similar to that of BAr F - than to PF 6 - . Regardless of the calculated values, BAr F - and PF 6 - should have distinctly different sizes, polar izabilities, and coordinating abilities. And yet, the VT data show that there is no significant difference in ground state recovery between the two salts. The most obvious conclusion to draw is that the counterion does not effectively alter the ligand fiel d energy in the specific case of [Fe(dcpp) 2 ] 2+ , at least insofar as to cause the 3 T 1 to be the lowest energy excited state. This could be due to the lifetime of the complex not being long - lived enough for sufficient stabilization, or it could be that the dcpp ligand effectively shields the Fe(II) center from the counterion. If either of t hese is a contributing factor, solvation will not have the same limitations, and may provide more insight into the outer - sphere reorganization contributions of [Fe(dcpp) 2 ] 2+ . 3.2.3 Solvent Effects In a polar solvation mechanism, the solvent acts to reorie nt itself to the dipole moment of the solute (see Chapter 4 ). 15 It follows that a solvent with greater dielectric constant should be better able to lower the energy of a solute with a large dipole mome nt. Such a phenomenon gives rise to solvatochromism particularly in charge transfer species, 49 though in this work we are more interested in the solvatochromism of the 5 T 2 excited state. This state is metal - centered, so it would seem unlikely that solvent would play much of a role in its thermodynamics; however, recent work 7 has shown that the ground state recovery of [Fe(bpy) 3 ] 2+ is in fact highly dependent on solvent identity. The goal, then, will be t o determine if such a solvent exists that is capable of 140 destabilizing the 5 T 2 to such an extent that the 3 T 1 might actually be the lowest energy excited state. A quintet ligand field state should, in principle, be more susceptible to solvation effects due to the greater volume expansion with the doubly occupied e g * orbitals relative to the triplet state. With these goals in mind, the effect of solvent on ground state recovery for [Fe(dcpp) 2 ] 2+ was studied by VT - TA spectroscopy. The BAr F - salt was utilized so as to make for a clean comparison across the series. The results for MeCN can be seen in Figs. 3.6 and 3.7 (above), while those of EtOAc, acetone, and PC are in Figs. 3.8 - 3.11 . A summary of the solvent data can be found in Tables 3.4 and 3.5 . It is immediately apparent that, unlike the counteranions, the solvent does in fact affect the Arrhenius values. As was the case with [Fe(bpy) 3 ] 2+ , the ground state recovery lifetime at room temperature changes with solvent. The longest lifetime is observed in MeCN, whereas the shortest lifetimes are in PC and acetone, which are within error of each other. This is immediately noteworthy as MeCN and acetone are much closer in dielectric constant than acetone and PC, a first indication that the dielectric constant is not the parameter of interest in these systems. The AN of the solvent also does a poor job of predicting either the lifetime or the barrier of the rate of reaction. As it so happens, the activation energy does initially follow a trend in which it increases with increasing dielectric constant from EtOAc to MeCN. PC, however, does not follow that trend, with an activation energy much closer to 0 cm - 1 . A note on the average E a reported for [Fe(dcpp) 2 ](BAr F ) 2 in PC: two data sets were collected in which the activation energy was 60 ± 60 cm - 1 and 20 ± 35 cm - 1 . When all the data were collectively fit with the Arrhenius equation, the E a found was 50 ± 35 cm - 1 with an R 2 value of 0.115. We believe this value to essentially be 0 cm - 1 based on the individual plots and find it more likely that in combining the data, a correlation was found by the curve fitting software that does not truly exist. 141 Figure 3. 8 . Representative variable - temperature lifetimes of [Fe(dcpp) 2 ](BAr F ) 2 in EtOAc. Excitation occurred at 490 nm, and a 540 nm probe was used. At room temperature (red) the lifetime of the complex is 265 ± 5 ps, and at 235 K (cyan) the average lifetime is 275 ± 10 ps. Figure 3. 9 . Representative variable - temperature lifetimes of [Fe(dcpp) 2 ](BAr F ) 2 in acetone. Excitation occurred at 490 nm, and a 540 nm probe was used. At room temperature ( red) the lifetime of the complex is 240 ± 5 ps, and at 235 K (cyan) the average lifetime is 255 ± 10 ps. 142 Figure 3. 10 . Representative variable - temperature lifetimes of [Fe(dcpp) 2 ](BAr F ) 2 in PC. Excitation occurred at 490 nm, and a 540 nm probe was used. A t room temperature (red) the lifetime of the complex is 245 ± 5 ps, and at 235 K (not shown) the average lifetime is 255 ± 10 ps. 143 Figure 3. 11 . Overlaid Arrhenius plot for average variable - temperature data of [Fe(dcpp) 2 ](BAr F ) 2 in EtOAc (red), acetone (green), MeCN (blue), and PC (purple). The Arrhenius values from these plots can be found in Table 3. 4 . The correlations were modest to poor, with R 2 for the EtOAc data being 0.737, 0.821 for acetone, 0.884 for MeCN, and 0.077 for the PC data. Table 3.4. Summary of VT - TA data and Arrhenius parameters of [Fe(dcpp) 2 ](BAr F ) 2 in the four different solvents. Solvent Lifetime at 293 K (ps) Lifetime at 235 K (ps) A (ps - 1 ) E a (cm - 1 ) PC 245 ± 5 255 ± 10 195 ± 35 50 ± 35 MeCN 285 ± 5 315 ± 5 170 ± 15 110 ± 20 Acetone 240 ± 5 255 ± 10 185 ± 15 55 ± 15 EtOAc 265 ± 5 275 ± 10 225 ± 5 35 ± 5 144 Table 3.5. Comparison of Marcus parameters of [Fe(dcpp) 2 ](BAr F ) 2 in the four solvents. Solvent - - 1 ) - 1 ) H ab (cm - 1 ) H ab 4 / PC 12220 ± 1220 13800 ± 1700 5.1 ± 0.5 1/(22 ± 8) MeCN 12220 ± 1220 14800 ± 1600 5.6 ± 0.2 1/(16 ± 3) Acetone 12220 ± 1220 14000 ± 1500 5.2 ± 0.2 1/(19 ± 4) EtOAc 12220 ± 1220 13600 ± 1500 4.7 ± 0.1 1/(28 ± 2) Based on traditional solvatochromism models around charge transfer - type excited states, it would be expected that the solvents with the greater dielectric constants or ANs would better stabilize the excited states. This was generally observed in the UV - Vis spectra of [Fe(dcpp) 2 ](BAr F ) 2 in these solvents ( Fig. 3.2 ), in which max of the 1 MLCT in PC ( 0 = 66.14, AN max in EtOAc ( 0 = 6.08, AN = 9.3) was the highest energy (605 nm). 22 - 25 This clearly did not track to the ligand field excited state. One would expect that if ground state recovery is occurring on the normal side of the Marcus barrierless region, that by increasing one of these parameters of the solvent, the energy of the excited state should be stabilized, thereby resulting in an increased activation energy. The outli er is clearly PC with its barrier of nearly 0 cm - 1 despite having the largest dielectric constant. The correlation is no better when using AN. It is probable that neither of these solvent properties affects the ligand field states in the same way it affect s the 1 MLCT, and perhaps a different solvent parameter should be correlated to this trend. However, it may also be that a specific solute - solvent interaction is at work in PC that is not present with any of the other solvents. What can be said, however, is that the outer - sphere reorganization energy does appear to change with different solvents, more so than with counteranion. By using [Fe(dcpp) 2 ](BAr F ) 2 in 145 - sphere contributions as the salt is not changing ( Table 3.6 ). These values of outer - sphere reorganization energy is present in the BAr F - are smaller than the error bars on any one value of reorganization energy, but a few comments can be made on the trends in the data. First, as has been noted already, the difference induced by counterion is very smal l, especially relative to that of the solvents. Secondly, the supposed outer - sphere reorganization energy from the solvents is consistently much less than what has been previously reported in the literature (e.g. nearly 0.5 eV) for the 5 T 2 1 A 1 interconvers ion. 13 Precluding the idea that the BAr F - /MeCN conditions impose 5000 cm - 1 of outer - sphere reorganization energy, which seems unreasonable considering the non - coordinating nature of BAr F - and the small size of MeCN, it seems safe to say that the outer - sphere contributions are significantly less in this Fe(II) system than has long been estimated. Table 3.6. Difference in reorganization energy of [Fe(dcpp) 2 ] 2+ in different counteranions and solvents relative to BAr F - in MeCN. Coun teranion Solvent - 1 ) - 1 ) BF 4 - MeCN 14700 ± 1600 - 100 PF 6 - MeCN 14800 ± 1600 0 BAr F - MeCN 14800 ± 1600 - BAr F - PC 13800 ± 1700 - 1000 BAr F - Acetone 14000 ± 1500 - 800 BAr F - EtOAc 13600 ± 1500 - 1200 146 here is an order of magnitude greater than has been cited by Blackbourn and Hupp. 50 In their study of a mixed - valent Ru(II/III) dimer, the outer - sphere reorganization energy was found to be 125 - 150 cm - 1 in the first solvation she ll. It is difficult to compare their data to the systems studied herein due to the relative inner - sphere reorganizational - 1 due to contributions from spin - orbit coupling and ligand field asymmetry. The inner - to outer - sphere ratio for that system is on the order of 32:1, whereas the incredibly large inner - sphere reorganization energy in [Fe(dcpp) 2 ] 2+ gives a ratio closer to 140:1. Drawing a direct parallel to this complex is unwise but provides another p oint of comparison when analyzing these unique data for [Fe(dcpp) 2 ] 2+ . 3.2.4 Calculations of Marcus Parameters Thus far, all of the Marcus values reported have been calculated from the Arrhenius plots eqn. (3.6) and electroche mical data). Based on chemical intuition, however, this scenario is unlikely. As already mentioned, the purpose of counteranions and solvent is to be modified up on the addition of any of these variable. It has also been previously mentioned, in this class of complexes. Furthermore, if the driving force for groun d state recovery is changing, a < k B T, but there is no indication that a 1% change in the driving force should have outsized influence over the activation energy. In an attempt to more fairly, if not accurately, portray the relative changes of the Marcus parameters, these calculations were performed instead holding either ab constant, the result s 147 of which can be seen in Tables 3.7 and 3.8 , respectively. With this method, no single value was changed significantly; the only real difference amongst the results is the size of the error bars. A 2 ](BAr F ) 2 in acetone. The average value between the three methods changes from - 12220 to - 13100 cm - 1 , a 7% difference. The error bars ab con stant respectively. This serves to illustrate the very tight restraints on the value of H ab . Importantly, the ratio of H ab 4 wholly unaffected based on the method of calculation of the Marcus parameters because this ratio is determined only by A, an ex perimentally - derived Arrhenius value. The degree of confidence in this ratio is very high, then. Table 3.7. Marcus values calculated from a constant reorganization energy. Counteranion Solvent - - 1 ) - 1 ) H ab (cm - 1 ) H ab 4 / BF 4 - MeCN 12400 ± 1400 14900 ± 1490 5.4 ± 0.3 1/(17 ± 2) PF 6 - MeCN 14700 ± 1700 14900 ± 1490 5.6 ± 0.3 1/(15 ± 2) BAr F - MeCN 12300 ± 1700 14900 ± 1490 5.6 ± 0.4 1/(16 ± 3) BAr F - PC 13200 ± 5100 14900 ± 1490 5.2 ± 0.6 1/(22 ± 8) BAr F - Acetone 13100 ± 2600 14900 ± 1490 5.3 ± 0.3 1/(19 ± 4) BAr F - EtOAc 13500 ± 1600 14900 ± 1490 4.8 ± 0.2 1/(28 ± 2) 148 Table 3.8. Marcus values calculated from a constant electronic coupling matrix element. Counteranion Solvent - - 1 ) - 1 ) H ab (cm - 1 ) H ab 4 / BF 4 - MeCN 10900 ± 3200 12900 ± 6100 5.2 ± 0.5 1/(17 ± 2) PF 6 - MeCN 28400 ± 8700 11300 ± 5400 5.2 ± 0.5 1/(15 ± 2) BAr F - MeCN 9900 ± 3400 11800 ± 6000 5.2 ± 0.5 1/(16 ± 3) BAr F - PC 15200 ± 10000 17100 ± 10500 5.2 ± 0.5 1/(22 ± 8) BAr F - Acetone 13100 ± 5200 14300 ± 7100 5.2 ± 0.5 1/(19 ± 4) BAr F - EtOAc 19700 ± 5800 20700 ± 9300 5.2 ± 0.5 1/(28 ± 2) In all seems reasonable to expect that with a change in driving force, both the reorganization energy and electronic coupling constant will also be affected. Given the nature of thes e measurements, we are unable to parse out differences in one parameter over the other two. Additionally, given the scale of H ab , it seems highly unlikely for any experimental technique to be capable of determining this parameter to the tenth of a wavenumb er. As can be seen in Tables 3.7 and 3.8 , however, is that an increase in H ab for [Fe(dcpp) 2 ](BAr F ) 2 in EtOAc from 4.8 to 5.2 cm - 1 increases reorganization energy to 2.5 eV, a truly unrealistic value. 3.3 The Effect of Excitation Energy 3.3.1 Ground State Recovery Over the course of the study of [Fe(dcpp) 2 ] 2+ , the excitation wavelength has been a matter of interest. In work by Brow n, it was observed that the ground state recovery process occurs independently of the pump wavelength (as expected), but that the MLCT lifetime does not. 51 It was an open question, then, as to whether or not excitation wavelength would alter the activation 149 energy or frequency factor. Gaussian deconvolution was performed on the spectra of all three complexes in MeCN, and very little difference was observed between them. As a rule, Gaussian deconvolution of absorption spectra is sim ply a mathematical way of picturing underlying band structure to a UV - Vis spectrum and is in no way a certainty. Band shape and position is arbitrary based on the fitting software and best initial guess, but it is a method used to approximate electronic po tential energy surfaces. The deconvolved spectrum of [Fe(dcpp) 2 ](PF 6 ) 2 can be found in Fig. 3.12 . For the bands predominantly present in the visible region, five Gaussians were required. The band centered around ca. 360 nm has a poor fit owing to the fact that there is a hi gh intensity UV - The features in the visible region have been previously assigned as being MLCT in nature; visible bands in Fe(II) polypyridyls with extinction coefficients on the order of 10 4 M - 1 cm - 1 are commonly accepted as MLCT. 5, 51,52 Based on the spectrum in Fig. 3.12 , excitation at 490 nm should be preferentially exciting only the band centered at ~500 nm. By pumping at 610 nm, though, that same band may be accessed in addition to the two other lower energy states. The true nature of these MLCT states is unknown: the physical locatio n of the excited electron on the ligand may be crucial information when attempting to analyze the excitation wavelength - dependent MLCT lifetimes, for example. Pump wavelength dependence studies on the VT - TA spectroscopy of [Fe(dcpp) 2 ] 2+ attempts to probe t his question. 150 Figure 3. 12 . Gaussian deconvolution of the ground state absorption spectrum of [Fe(dcpp) 2 ](PF 6 ) 2 in MeCN. The experimental data are the blue diamonds, the calculated Gaussian bands are the black lines (offset for clarity), and the convolved fit is the red trace. The ground state recovery lifetime of [Fe(dcpp) 2 ] 2+ was studied by VT - TA as a function of pump wavelength with a variety of salts and solvents. A summary of these data can be found in Table 3.9 . In comparing the data, no changes are observed based on excitation wavelength. A an d E a in all cases are within error of each other, which propagates into the Marcus parameter calculations. What is noticeably different between the data sets, however, is the goodness of the Arrhenius fit, as represented by R 2 . In each case, this value was greater when the pump wavelength was 610 nm, even if the difference was relatively small, as was the case with the PF 6 - /MeCN conditions. 151 Table 3.9. Summary of parameters measured and calculated from VT - TA of [Fe(dcpp) 2 ] 2+ as a function of excitation w avelength. Counteranion Solvent ex c (nm) A (ps - 1 ) E a (cm - 1 ) H ab 4 / R 2 BAr F - MeCN 490 170 ± 15 110 ± 20 1/(16 ± 3) 0.884 BAr F - MeCN 610 160 ± 5 120 ± 10 1/(14 ± 1) 0.976 PF 6 - MeCN 490 165 ± 15 115 ± 15 1/(15 ± 2) 0.760 PF 6 - MeCN 610 185 ± 15 95 ± 15 1/(19 ± 3) 0.776 PF 6 - Acetone 490 190 ± 10 50 ± 10 1/(20 ± 2) 0.819 PF 6 - Acetone 610 195 ± 10 50 ± 5 1/(21 ± 2) 0.900 BF 4 - MeCN 490 175 ± 10 105 ± 10 1/(17 ± 2) 0.580 BF 4 - MeCN 610 165 ± 20 135 ± 20 1/(15 ± 4) 0.797 In more than one set of data there was the suggestion of bimodal Arrhenius behavior. In these cases, the barrier was essentially 0 cm - 1 at warmer temperatures (T > 245 K), and 50 - 100 cm - 1 at colder temperatures. Where MeCN is the solvent, this phenomenon w ould not be observable as the freezing point of MeCN is 228 K, limiting the number of lower temperature points able to be collected. As was discussed in Chapter 1 , the Arrhenius equation is well - suited to describe reactions in t he warm temperature limit. Under this condition, the classical, semi - classical, and quantum mechanical representations of reaction kinetics converge to the same description, which is represented by Arrhenius behavior. At colder temperatures, however, only the lowest vibrational modes will be accessible within an electronic state, and the reaction cannot proceed by surmounting the barrier. A reaction may occur, though, if the wavefunctions of the vibrational modes for both the reactant and product surfaces a re coupled. 28 In this case, quantum mechanical 152 tunneling may occur, in which the electronic conversion transpires via a horizontal process (i.e., energy is conserved). 53 Because thermal energy is not re quired to facilitate the reaction, these dynamics are temperature - independent. It is possible that any bimodal behavior seen in the Arrhenius plot may be caused by tunneling, as it is observed at colder temperatures. This has been seen in the 5 T 2 1 A 1 trans ition in an Fe(II) polypyridyl complex previously. 54 The application of VT - TA on the ground state recovery process of [Fe(dcpp) 2 ] 2+ at significantly colder temperatures will allow for identification or rejection of the tunneling hypothesis. Tunneling is temperature - independent, and thus the rate of ground state recovery should be unchanged. These data led to an interesting alternative proposition: if E a < k B T, does it necessarily follow that the Arrhenius plot will be linear? In acetone, for example, the coldest temperature attainable is 180 K, at which k B T = 125 cm - 1 . This value is larger than any measured E a for [Fe(dcpp) 2 ] 2+ . It may be entirely possible that for barrierless reactions, the Arrhenius plot should not be linear. 3.3.2 MLCT Lifetimes One other possibility insinuated by the excitation wavelength dependence results is that upon exciting into the different 1 MLCT el ectronic states, there is a different deactivation pathway into the LF manifold, such that the 3 T 1 state is more populated via one route than the other ( Scheme 3.2 ). Excitation at 490 nm should create a vibrationally hot 1 MLCT state that is highly coupled to lower - lying electronic states due to an increased density of states at higher energies. If the decay pathway is even slightly different from that followed by ex c = 610 nm, then it may more fully populate the 3 T 1 relative t o the 5 T 2 considering how coupled and degenerate these two states are postulated to be in this system. Ground state recovery from the 5 T 2 must occur via a triplet intermediate state due to the 5 T 2 1 A 1 = 2. If, however, that triplet state is 153 already partially formed, which may be especially true at warmer temperatures, then the barrier associated with ground state recovery will be lower, if not nearly 0 cm - 1 . At colder temperatures, the 3 T 1 may still be po pulated, though to a lesser degree as there will not be as much thermal energy. In this case, ground state recovery will occur in a more traditional way, i.e., from the 5 T 2 excited state, and will thus have a larger barrier. Scheme 3.2. Proposed potent ial energy surfaces versus some nuclear coordinate (not the Fe - N bond distance) for [Fe(dcpp) 2 ] 2+ illustrating the possible relaxation pathways upon excitation at 490 nm (blue arrow) or 610 nm (red arrow) when the 5 T 2 and 3 T 1 excited states are nearly dege nerate. See text for more details. Evidence of this proposed mechanism may be given by pump - dependence MLCT lifetime 154 measurements of [Fe(dcpp) 2 ](PF 6 ) 2 in MeCN. For these data, the shorter pulse laser system was used. To draw as close a comparison as possible to the VT - TA data, a 540 nm probe was used. At this wavelength, there is a ground state bleach that masks any excited state absorbance features tha t would be from the MLCT states. The kinetics are of the MLCT deactivation into the lower - lying 5 T 2 state, as evidenced by a decay from a positive feature (MLCT excited state absorption) into a negative signal (loss of the ground state) that is long - lived. Upon excitation at 490 nm, the MLCT is deactivated with a lifetime of 35 ± 5 fs ( Fig. 3.13 ). This is shorter than the IRF of this system and is corroborated by data previously collected which found a deactivation complete within the 75 fs IRF. 51 Unfortunately, the exact pump - probe combination used in that experiment is unknown. In moving to the 610 nm pump wavelength, the MLCT lifetime is increased by nearly a factor of four to 120 ± 20 fs ( Fig. 3.14 ). Figure 3. 13 . Single - wavelength kinetics of [Fe(dcpp) 2 ](PF 6 ) 2 in MeCN, pumped at 490 nm and probed at 540 nm. The kinetics measured (black diamonds) are those of the deactivation out of the MLCT manifold into the LF manifold and correspond to a MLCT lifetime (red trace) of 35 ± 5 fs. The solvent (red diamonds) data are shown for reference. 155 Figure 3. 14 . Single - wavelength kinetics of [Fe(dcpp) 2 ](PF 6 ) 2 in MeCN, pumped at 610 nm and probed at 540 nm. The kinetics measured (black diamonds) are those of the deactivation out of the MLCT manifold into the LF manifold and correspond to a MLCT lifetime (red trace) of 120 ± 20 fs. A portion of the data at 375 - 475 fs is omitted for clarity due to oscillations of unknown origin. The solvent (red diamonds) data are shown for referenc e. The decreased rate of deactivation out of the MLCT manifold upon lower energy excitation is unexpected, as pump wavelength - dependent MLCT lifetimes have not to the best of our knowledge been previously reported. It does appear to corroborate the n otion that at higher energies, there is a greater density of excited states leading to increased electronic coupling to facilitate relaxation into the LF manifold. Based on these results, a further characterization of MLCT lifetimes as a function of pump w avelength is highly desirable so as to gain further understanding of the charge transfer states. If the ultimate goal of work on Fe(II) polypyridyls is to extend the lifetime of the charge - transfer species, a complete characterization of mechanisms by whic h deactivation occurs is necessary. To further this understanding of the fundamental 156 photophysical processes in Fe(II) complexes, VT - TA may be performed while monitoring the MLCT lifetime. This will be an incredibly technically challenging experiment owing to the use of the cryostat with ultrashort (<50 fs) laser pulses. But this experiment may give insight into potential energy surface crossings between the MLCT and LF manifolds, information that may otherwise be restricted to theoretical work. This deacti vation is ultrafast, it is also highly non - adiabatic, and therefore cannot be represented by semi - classical Marcus theory. But if the vibrational modes associated with the relaxation process can be determined, synthetic modifications may be able to specifi cally target and hinder those modes, thereby decreasing the rate of deactivation. As to why a change in MLCT lifetime might affect the R 2 value on an Arrhenius plot of the ground state recovery, the postulation of a metastable 3 T 1 state degenerate with t he 5 T 2 surface has been put forth. To verify this hypothesis, variable temperature full spectral transient absorption data are desirable. If, as supposed, ground state recovery occurs from both the 5 T 2 and thermally populated 3 T 1 , then the TA spectrum should inh erently have a different appearance than at colder temperatures when only the 5 T 2 is populated. TA involves the excitation from the ground state, upon which the molecule undergoes its typical relaxation pathway to the lowest energy excited state. The probe then excites from that lowest energy excited state into spin - allowed excited states. When probe absorption occurs from a quintet state, only quintet - quintet transitions are allowed. If, however, both the 5 T 2 and 3 T 1 are acting as lowest energy excited sta te, then absorption into triplet states will also be allowed. The 3 MLCT band is present in the UV - Vis spectrum of these Fe(II) complexes (often visualized as a tail on the red edge of the 1 MLCT bands), though it is very low intensity, broad, and typically lies underneath the 1 MLCT transitions which have much higher extinction coefficients. In that way, VT - ground state absorption spectroscopy may also be 157 informative about the exact excited states being populated in [Fe(dcpp) 2 ] 2+ . 3.4 Additional Peculiarities : [Fe(dcpp) 2 ] 2+ in Dichloromethane Through the course of these studies, a wide selection of solvents has been considered and discarded for various reasons. As previously mentioned, protonated solvents react with the carbonyl of the dcpp ligand, and ultima tely destroy the complex. In the case of tetrahydrofuran (THF), this solvent was desired for its low dielectric constant ( 0 = 7.58) 25 and AN (8.0). 22 VT data were in fact collected on [Fe(dcpp) 2 ](BAr F ) 2 in THF, but after ca. 16 h, the solution had lost all color. A timed UV - Vis study ( Fig. 3.15 ) shows the disintegration of the complex over time in THF. Over the course of the first four hours, no visible change is observed to t he structure of the bands, apart from a systematic decrease in absorbance. Between hours four and five, however, all evidence of the MLCT band has disappeared, indicating the dissociation of the Fe(II) complex. Based on these results, the VT data collected in THF were considered null. Figure 3. 15 . Timed ground state absorption study of [Fe(dcpp) 2 ](BAr F ) 2 in THF. Another alternative with a low dielectric constant was considered: dichloromethane 158 (DCM), for which 0 = 8.93; 25 ho wever, this solvent is slightly more complicated by the fact that it has the highest AN, 20.4. 22 It was immediately apparent from the ground state absorption spectrum ( Fig. 3.16 ) that DCM was acting dif ferently upon [Fe(dcpp) 2 ] 2+ than any other solvent. The MLCT band centered at 350 nm was of much greater intensity when the complex was dissolved in DCM as opposed to any other solvent. Furthermore, the MLCT maximum is bluer max = 604 nm) than in any other solvent. No VT measureme nts were made of [Fe(dcpp) 2 ](BAr F ) 2 in DCM, but lifetimes were collected. As was true with [Fe(bpy) 3 ] 2+ , 7 the lifetime of [Fe(dcpp) 2 ] 2+ in DCM is greatly elongated from 280 ± 10 ps in MeCN to 470 ± 10 ps ( Fig. 3.17 ). That is more than a 50% increase in ground state recovery lifetime. The MLCT lifetime was also lengthened, ex c = 610 nm ( Fig. 3.18 ). This remains one of the longest MLCT life times for a simple Fe(II) polypyridyl complex. It also shows that the solvent is capable of affecting the rate of deactivation from the MLCT into the LF manifold. This has long been understood to be true in Ru(II) polypyridyl complexes, the MLCT in these t ypes of complexes is the lowest energy excited state and survives for nano - to microseconds. 55 Solvent interference in charge transfer excited states with these lifetimes is wholly expected. On the order of a few hundred femtosec onds, however, and as an intermediate to a lower lying excited state, as is the case with Fe(II) complexes, solvation dynamics surrounding the MLCT is not obvious. It is yet another effect that must be further characterized to better understand what influe nce we have over the lifetime of this charge transfer state. These specific results of [Fe(dcpp) 2 ](BAr F ) 2 in DCM max = 350 nm may actually indicate a higher concentrati on of free ligand. 1 H NMR studies were performed ( Fig. 3.19 ) in order to determine whether the solvent was having an adverse effect on the compound (e.g., destroying the ligand, dissociating the complex). In this experiment, [Fe( dcpp) 2 ](BAr F ) 2 was 159 dissolved in (CD 3 ) 2 CO, and then compared to the same solution with a drop of undeuterated DCM. Upon addition of the DCM, it was necessary to baseline correct the spectrum through the use of a fifth order polynomial. The reason for this needed correction is unclear. After this is performed, the integrations are unchanged with or without DCM. However, with DCM present, every aromatic signal is shifted upfield, indicating a greater degree of shielding. Furthermore, the signals are not shifted by one constant offset. For example, the triplet centered at 8.79 ppm in (CD 3 ) 2 CO shifts by - 0.06 ppm when DCM is added. However, the doublet at 8.11 ppm is shifted by - 0.10 ppm upon the addition of DCM. No sign of a paramagnetic species is observe d, but these spectra were only collected out to 14.0 ppm. In future studies, this window should be expanded to preclude the presence of any heteroleptic or paramagnetic sample present. Work is currently ongoing to determine the origin of these unusual NMR signals, with the ultimate goal of validating or rejecting the ultrafast measurements that were collected on this compound. Figure 3. 16 . Ground state absorption spectra of [Fe(dcpp) 2 ](BAr F ) 2 in MeCN (green) and DCM (blue). 160 Figure 3. 17 . Ground state recovery lifetime of [Fe(dcpp) 2 ](BAr F ) 2 in DCM (black diamonds) upon excitation at 490 nm and probing at 540 nm. The fit (red trace) showed a lifetime of 470 ± 10 ps. Figure 3. 18 . MLCT kinetics of [Fe(dcpp) 2 ](BAr F ) 2 in DCM measured at 540 nm upon excitation at 620 nm. The data (black diamonds) displayed vibrational coherence caused by the solvent interacting with a very temporally short pump pulse. The fit (red trace) gave a MLCT lifetime of 180 ± 55 fs. 161 Figure 3. 1 9 . 1 H NMR of [Fe(dcpp) 2 ](BAr F ) 2 in (CD 3 ) 2 CO (bottom, red) and doped with a small amount of undeuterated DCM (top, green). Assignments can be found in the text. 4. Future Works and Conclusions Through the use of ultrafast variable - temperature transient absorption spectroscopy, the ground state recovery process in [Fe(dcpp) 2 ] 2+ has been studied and found to be nearly barrierless with an activation energy less than k B T. From the VT - TA data, Arrhenius plots were prepared which allowed for the determination of Marcus parameters through relationships between these two theories. The outer - sphere reorganization energy was estimated by a method inspired by spin - crossover literature, in which the counteranion and solvent was systemat ically changed to alter the 162 [Fe(dcpp) 2 ](BAr F ) 2 in MeCN. It was found that changing the counteranion led to very small differences in reorganization energy (0 - 100 cm - 1 ), w hereas the solvent played a much more - 1200 cm - 1 . It was the BAr F - salt of the complex in propylene carbonate that displayed the most barrierless behavior. No set of conditions affected the ligand field strength so much that the 3 T 1 became the lowest - lying excited state. However, ultrafast X - ray 6 and pump wavelength dependence studies imply presence of the triplet state during the ground state recovery process. To complete the studies begun here, the best course of action would be for analogous work to be done using the simultaneous ultrafast X - ray absorption and emission spectroscopies described by Britz et al. 6 This method will give much more information on the s tructure of the complex as a function of counteranion, solvent, and excitation wavelength than can be obtained with visible transient absorption spectroscopy. Only then will real inferences regarding the outer - sphere reorganization energy be able to be mad e. The barrierless nature of this complex likely due to it being nearly perfectly octahedral. A secondary consequence of the higher symmetry is the unique absorption profile. These MLCT bands have been assigned, but the exact nature of them is unknown. It would be useful to have a more thorough understanding of these states in order to better design complexes with long - lived MLCT states. Spectroelectrochemistry is a method used to assign an absorption band as MLCT, but it is not capable of giving the physi cal origin of the charge transfer (e.g., metal - to - carbonyl, metal - to - central pyridyl ring). One technique that could begin to address this question is circular dichroism (CD) spectroscopy. This method uses circularly - polarized light to essentially collect a UV - Vis of a chiral molecule, such as [Fe(dcpp) 2 ] 2+ . 56,57 CD spectroscopy has been previously performed on [Fe(bpy) 3 ] 2+ , a D 3 molecule in its crystal form, and displayed bisignate features 163 centered around the MLCT bands. 58 2 ] 2+ can, to a first approximation, be deconvolved into two Gaussians. In the CD spectrum, a positive feature corresponded to the red Gaussian, and then flipped its sign such that a negative feat ure occurred in the position of the blue Gaussian. This has b een postulated to be caused by L along two separate axes, 58 though the exact assignment has been a source of debate for over 50 years. 56 Knowing the axes along which MLCT excitation is occurring can bring molecular - level insight into the analysis of the photophysical properties of [Fe(dcpp) 2 ] 2+ . Additionally, time - dependent density functional theory calculations on [Fe(dcpp) 2 ] 2+ may be a ble to provide a deeper understanding of the location of the wavefunctions at different excitation energies. Work is ongoing in that respect with our collaborators, the Jakubikova group at North Carolina State University. Finally, the outer - sphere reorga nization energy can be studied in a slightly modified way: via the solvation effects on iron(II) cyanides and cyano - substituted Fe(II) chromophores. This phenomenon 4 has already been looked at to a certain extent with the [Fe(bpy )(CN) 4 ] 2 - complex, 2,3, 19 but further work may help derive new understanding of solvent - solute and solvent - solvent interactions. In fact, Yang et al. used solvatochromism to estimate the reorganization e 4 ] 2 - complexes. 19 The polar N - end of the cyano ligand interacts strongly with solvent molecules, particularly very polar molecules, and those capable of forming hydrogen bonds. 4 When bound directly to the metal center, as is the case with [Fe(bpy)(CN) 4 ] 2 - , the influence of the solvent on the cyanide will be directly relayed to the iron center. Whereas when the - CN moiety is a substituent on the bpy ligand, as with tris(4 - dicyano - - bipyridine) - CN - bpy) 3 ] 2+ , CN - solvent interaction will be not affect the metal as strongly due to shielding from the bipyridine. An Arrhenius and Marcus analysis on compounds such as 164 - CN - bpy) 3 ] 2+ , [Fe(bpy) 2 (CN) 2 ], and [Fe(bpy)(CN) 4 ] 2 - will be able to get a measure of the outer - sphere reorganization energy with solvents that interact with various degrees of strength to the cyano group. Additionally, inner - sphere contributions may be able to be estimated from these me asurements as well, and the influence of the solvent directly through the CN group to the iron versus solvent effects on the CN mediated by the bipyridine linkage to the metal center. The ultrafast variable - temperature methodology is still very young but h olds limitless promise in its ability to educate us further on the fundamental properties of these iron chromophores. 165 REFERENCES 166 REFERENCES 1. Figgis, B. N.; Hitchman, M. A. Ligand Field Theory and Its Applications ; Wiley - VCH: New York, 2000. 2. Zhang, W.; Kjær, K. S.; Alonso - Mori, R.; Bergmann, U.; Chollet, M.; Fredin, L. A.; Hadt, R. Y.; Nielsen, M. 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Insights into the Spin - State Transitions in [Fe(tpy) 2 ] 2+ : Importance of the Terpyridi ne Rocking Motion. Inorg. Chem. 2015 , 54 , 11259 - 11268 ; DOI: 10.1021/acs.inorgchem.5b01747 . 170 43. Goodwin, H. A. Spin Transitions in Six - Coordinate Iron(II) Complexes. Coord. Chem. Rev . 1976 , 18 , 293 - 325 ; DOI: 10.1016/S0010 - 8545(00)80430 - 0 . 44 . Real, J. A.; Gaspar, A. B.; Muñoz, M. C. Thermal, Pressure, and Light Switchable Spin - Crossover Materials. Dalton Trans. 2005 , 2062 - 2079; 10.1039/B501491C . 45. Gütlich, P.; Hauser, A.; Spiering, H. Therm al and Optical Switching of Iron(II) Complexes. Angew. Chem. Int. Ed. 1994 , 33 , 2024 - 2054; DOI: 10.1002/anie.199420241 . 46. Klug, C. M.; McDaniel, A. M.; Fiedler, S. R.; Schulte, K. A.; Newell, B. S.; Shores, M. P. Anion Dependence in the Spin - Crossover Properties of a Fe(II) Podand Complex. Dalton Trans. 2012 , 41 , 12577 - 12585; 10.1039/C2DT31213A . 47. Lemercier, G.; Verelst, M.; Boussekssou, A.; Varre t, F.; Tuchagues, J. - P. Towards Control of the Intrinsic Characteristics of Spin - Crossover in Ferrous Materials. In Magnetism: A Supramolecular Function ; Kahn, O., Ed.; Springer: Dordrecht, 1996; Vol. 484; pp 335 - 356. 48. Krossing, I.; Raabe, I. Relative S tabilities of Weakly Coordinating Anions: A Computational Study. Chem. Eur. J. 2004 , 10 , 5017 - 1030; DOI: 10.1002/chem.200400087 . 49. Curtis, J. C.; Sullivan, B. P.; Meyer, T. J. Hydrogen - Bonding - Induce d Solvatochromism in the Charge - Transfer Transitions of Ruthenium(II) and Ruthenium(III) Ammine Complexes. Inorg. Chem. 1983 , 22 , 224 - 236, and references therein; DOI: 10.1021/ic00144a009 . 50. Blackbourn, R. L.; Hupp, J. T. Probing the Molecular Basis of Solvent Reorganization in Electron - Transfer Reactions. J. Phys. Chem. 1988 , 92 , 2817 - 2820; DOI: 10.1021/j100321a024 . 51. Brown, A. M. Excited - State Dynamics of Iron(II) - Based Charge - Transfer Chromophores. Ph.D. Thesis, Michigan State University, East Lansing, MI, 2011. 52. Creutz, C.; Chou, M.; Netzel, T. L.; Okumura, M.; Sutin, N. Lifetimes, Spectra, and Quenching of the Excited States of Polypyridine Complexes of Iron(II), Ruthenium(II) and Osmium(II). J. Am. Chem. Soc. 1980 , 102 , 1309 - 1319 ; DOI: 10.1021/ja00524a014 . 53. DeVault, D. Quantum - Mechanical Tunnelling in Biological Systems , 2 nd ed.; Cambridge University Press: New York, 1984, and references therein. 54. Conti, A. J.; Xie, C. - L.; Hendrickson, D. N. Tunneling in Spin - State Interconversion of Ferrous Spin - Crossover Complexes: Concentration Dependence of Apparent Activation Energy Determined in Solution by Laser - Flash Photolysis. J. Am. Chem. Soc. 1989 , 111 , 1171 - 1180; DOI: 10.1021/ja00186a002 . 55. Juris, A.; Balzani, V.; Barigelletti, F.; Campagna, S.; Belser, P.; von Zelewsky, A. Ru(II) Polypyridine Complexes: Photophysics, Photochemistry, Electr ochemistry, and Chemiluminescence. Coord. Chem. Rev. 1988 , 84 , 85 - 277, and references therein ; DOI: 10.1016/0010 - 8545(88)80032 - 8 . 171 56. Bosnich, B. Application of Exciton Theo ry to the Determination of the Absolute Configurations of Inorganic Complexes. Acc. Chem. Res. 1969 , 2 , 266 - 273; 10.1021/ar50021a002 . 57. Braterman, P. S.; Noble, B. C.; Peacock, R. D. - [Ru(bpy) 3 ] 2+/+/0/ - . J. Phys. Chem. 1986 , 90 , 4913 - 4915; 10.1021/j100412a006 . 58. Dragna, J.; Pescitelli, G.; Tran, L.; Lynch, V. M.; Anslyn, E. V.; Di Bari, L. In Situ Assembly of Octahedral Fe(II) Complexes for the Enantiomeric Excess Determination of Chiral Amines Using Circular Dichroism Spectroscopy. J. Am. Chem. Soc. 2012 , 134 , 4398 - 4407; 10.102 1/ja211768v . 172 CHAPTER 4. DUAL SOLV ATION MECHANISM IN R U(II) POLYPYRIDYL CO MPLEX DRIVEN BY EXCITATION ENERGY 1. Introduction In the realm of photovoltaic devices, Ru(II) - based polypyridyl complexes remain some of the most highly studied chromophores. 1 - 3 These compounds tick many of the most important boxes. They have long - lived charge - separated excited states that are primarily metal - to - ligand charge transfer (MLCT), formally , with lifetimes on the order of hundreds of nano seconds to microseconds. The MLCT excited state not only takes a metal - centered electron and promotes it onto the periphery of the compound, thereby making it useful for electron collection, but these types of excited states also absorb visible photons wel l which is critical for solar energy applications. If the goal is to use these complexes for light - to - energy conversion, it is critical to understand the various radiative and nonradiative ways through which energy is diverted and lost, as these processes will ultimately limit the efficiency of the chromophores. The prototypical Ru(II) polypyridyl is [Ru(bpy) 3 ] 2+ - bipyridine. This complex has been studied extensively, particularly as a point of comparison for some of its decorated analo gues. One such complex is [Ru(dpb) 3 ] 2+ - diphenyl - - bipyridine, Scheme 4.1 3 MLCT, by some estimates a factor of six greater than that of [Ru(bpy) 3 ] 2+ . 4,5 Damrauer and coworkers studied the photophysical properties of [Ru(dpb) 3 ] 2+ and found the specific nature of for - dimethy l - substituted [Ru(dmb) 3 ] 2+ complex is only twice that of [Ru(bpy) 3 ] 2+ . 6 Therefore it was postulated 173 that the delocalization afforded by the phenyl substituent was the main determinant of the increased the radiative rate (k r ) in [ Ru(dpb) 3 ] 2+ relative to its analogues. In fact, ab initio results found that while the ring was canted ~44º in the ground state, as a radical (mimicking the MLCT excitation) the phenyl rotated such that the entire system was coplanar. While these calculations were performed on 4 - phenylpyridine for simplicity, th e results were suggestive of a delocalized excited state. 6,7 Electrochemical data supported this conclusion by showing that the 3 MLCT/ 1 A 1 energy gap in [Ru(dpb) 3 ] 2+ was nearly identical to that of [Ru(dmb) 3 ] 2+ ; the measured diffe rence actually indicated the gap was 200 - 300 cm - 1 less in the phenyl version of the complex, which would imply a reduced k r . The alternative was that extended conjugation of the dpb ligand would decrease the nuclear coordinate between the ground and excite d states, thereby increasing reducing vibrational overlap and thus decreasing k nr . This hypothesis was tested by time - resolved resonance Raman spectroscopy of [Ru(dpb) 3 ] 2+ , and its mesitylated analogue, [Ru(dmesb) 3 ] 2+ ( Scheme 4.1 ). The mesityl substituent nominally extends delocalization just as is the case with the phenyl ring, however the ortho - methyl groups sterically hinder coplanarity from being achieved in the MLCT excited state. The results from the Raman spectroscopy ap peared to corroborate the hypothesis: upon excitation, the C=C ring stretch at 1615 cm - 1 in the ground state shifted to significantly lower energy (1548 cm - 1 ) in [Ru(dmesb) 3 ] 2+ than in [Ru(dpb) 3 ] 2+ (1599 cm - 1 ). These data were interpreted as the phenyl rin g with its ability to rotate to coplanarity with the bipyridine backbone was less distorted in the excited state than the mesityl. 6 174 Scheme 4.1. Perspective drawings of the two complexes that are featured most prominently in this work, inspired by Damrauer and coworkers 6 : (Left) [Ru(dpb) 3 ] 2+ and (Right) [Ru(dmesb) 3 ] 2+ . To further investigate the photophysical properties of [Ru(dpb) 3 ] 2+ , Damrauer and McCusker used ultrafast transient absorption (TA) spectroscopy. 8 Using spectroelectrochemistry, the excited state absorption feature centered around 532 nm was determined to be an indicator of the r educed intraligand excited state dynamics. Upon excitation at 400 nm into the 1 MLCT, two 1 2 = 2.0 ± 0.5 ps. The shorter kinetic component was also observed in [Ru(dmb) 3 ] 2+ on the order of 1 20 fs, and was attributed, in part, to 1 3 2 in [Ru(dmb) 3 ] 2+ was 5.0 ± 0.5 ps. From these results, it was concluded that at this pump - probe combination and in acetonitrile, vibrational cooling on the 3 MLCT surface was being observed with the faster rate in [Ru(dpb) 3 ] 2+ indicating that the ring rotation facilitated the vibrational relaxation process. 8 Not only did these 175 data serve as further confirmation of a delocalized excited sta te, they also indicated the timescale on which the phenyl rotation and consequent 3 MLCT excited state thermalization occurs. Polar solvation is the response of solvent molecules to the charge redistribution of a solute. 9,10 Intr amolecular charge transfer, as occurs in MLCT transitions, are commonly studied in the solute as these drive large solvent reorganization. There are primary two types of solvent effects, static and dynamic. Where static solvation raises or lower s the energ y of activation of a reaction, the dynamic response affect s the rate of reaction. This dynamic process is actually a combination of solvent reorientation modes and proceeds on a multitude of timescale s. The shortest (<500 fs) is modeled well by a Gaussian distribution and is often referred to as the 11 A single to tens of picoseconds process also occurs that is the relaxation of the bulk solvent; this may be known as dielectric fricti on if the solvent is dipolar (i.e., having a permanent dipole moment) or viscoelastic when nonpolar. The inertial component is typically more solute - solvent interactions, whereas the solvent relaxation involves solvent - solvent dynamics. 12,13 Thus, concentration of the solute can affect the time scale of the solvation response. 10 In a complex undergoing a MLCT transition, for example, the positive dipole of the solvent will reorient toward the ligand wit h the excited electron so as to stabilize the energy of this state. As the electron relaxes back to the metal center, the solvent molecules will have been forced to position their dipoles in the same direction; without a charged species to orient to, the e lectrostatic repulsion will force the solvent molecules to reorganize into lower energy, random directions. In low solute concentrations, then, the loss of the CT excited state affords an increased solvent reorientation rate as the solvent concentration is high. Likewise, the more polar the solvent, the faster the rate of solvent relaxation. 9 The shorter time component in solvation dynamics typically dominates the amplitude of 176 the response, but the slower kinetic process is criti cal, particularly in larger solute molecules. Collisions between the solute and solvent may occur in these types of chromophores. More commonly, dielectric friction may be present in polar solvents which is made up of the dipole - dipole interactions between solute and solvent molecules. Upon charge redistribution in the former, the solvent mechanically reorients, often via rotation, to the newly formed dipole moment in the solute. 10 Translation of the solvent may also occur but is less energetically efficient than rotation and librational motion. 11 [Ru(dpb) 3 ] 2+ provides a unique opportunity to study the effect of multiple driving forces for vibrational relaxation occurring simultaneously. Immediately upon excitation, the 1 MLCT excited state decays rapidly (<100 fs) 14,15 to a vibrationa lly hot 3 MLCT state. In the charge - separated excited state, a large instantaneous dipole moment exists which should induce a strong response from a polar solvent. Furthermore, the process being studied on the picosecond timescale is ascribed to vibrational cooling, in which excess energy from the excitation event is dissipated by the solute into the solvent bath. Polar solvation dynamics are likely to be the dominant mechanism coupled to MLCT excitation and vibrational cooling in [Ru(dpb) 3 ] 2+ . However, thes e dynamics are likely to be complicated by the large - amplitude motion of the phenyl. Rotation of a large aromatic on its own is a predominantly frictional force, and is therefore likely to induce bulk solvent translation, or even a nonpolar solvation respo nse. 11, 16 In this type of solvation mechanism, the viscosity of the solvent plays a much larger role, dictating the rate of solvent translation away from the solute. 17 No near transition metal analogue for the dichotomy of large instantaneous dipole versus bulky reorganization that is displayed in [Ru(dpb) 3 ] 2+ was able to be found in the literature. Large - amplitude motion dynamics have been studied previously in intramolecular electron transfer 177 - bianthryl and 4 - (9 - anthryl) - N,N - dimethylaniline. 10, 18 Some of the closest examples of what may be observed come in the form of organic complexes that display what is known as a twisted intramolecular charge transfer (TICT) - bianthryl exist in a certain nonpolar conformati on in the ground state, and upon excitation, produce a charge - separated species that forces a geometric rotation. In this compound, the rate of the electron transfer reaction was found to be much shorter than was predicted by the solvent longitudinal (i.e. , translational) relaxation time constant. 18 This time constant is a measure of the bulk solvent response in the absence of a solute molecule, and as such neglects any specific solute - solvent interactions that dictate particularl y the short - time kinetics of solvation. 1 - bianthryl were reported for a series of n - alkane nitrile solvents; specific solvation dynamics become increasingly more important in H - bonding species, such as n - alcoh ols. Studies were performed on a fluorescent probe molecule, 4 - N,N - dimethylaminobenzonitrile in a series of linear alcohols. 19,20 In shorter - chain alcohols like methanol and ethanol, the solvation dynamics were well - described by a single exponential function, whereas longer - chain solvents displayed multiexponential behavior. Again, the solvation relaxation time was found to be far shorter than the longitudinal relaxation time. Together, these data served to show that the solvent m olecules were more intimately to the excited state of the chromophore than is implied by the bulk solvent parameters. It is apparent then that the specific intermolecular interactions must be accounted for within a polar solvation model. The original wor k by Damrauer and McCusker provided insight into the photophysical behavior of [Ru(dpb) 3 ] 2+ , but ultimately left more questions to be answered. The exact nature of the solvation mechanism of this complex, as indicated above, may be guessed at but is yet un 1 were unable to be determined due to the ~250 178 instrument response function of the laser system being used. One method that will be used in attempt to address these questions is variable - excitation wavelength studi es; these may have the added benefit of shedding further light on the vibrational cooling and phenyl rotation dynamics of [Ru(dpb) 3 ] 2+ . The goal of this work is to expand on the previously acquired data of the excited state evolution of [Ru(dpb) 3 ] 2+ . The v ibrational cooling time constant is measured in a series of 1 - alcohols and 1 - nitriles of increasing chain lengths. A competition between the frictional forces of the alkyl chain and the dielectric response of the polar functional will be under investigatio n. Ultimately this will provide a more complete understanding of the mechanism of excited state evolution in [Ru(dpb) 3 ] 2+ . 2. Experimental 2.1 Materials and Synthesis 2.1.1 General All reagents and solvents were used as received, unless otherwise noted. Sodium tetrakis[(3,5 - trifluoromethyl)phenyl]borate (NaBAr F , >98%) was generously donated by Thomas Boussie of Rennovia. For synthesis and purification, ethanol (EtOH, Decon Labs, 100%), HCl (Macron Fine Chemicals, ACS grade), acetonitrile (MeCN, Sigma - Aldr ich, ACS grade), methanol (MeOH, Sigma - Aldrich, ACS grade), diethyl ether (Et 2 O, Sigma - Aldrich, ACS grade), SiO 2 gel (Sorbtech, 40 - - Aldrich, ACS grade) were used without further purification. Proton nuclear magnetic r esonance ( 1 H NMR) spectroscopy was performed on a Bruker 500 MHz NMR spectrometer. Electrospray - ionization mass - spectrometry (ESI - MS) data was collected on a Waters Xevo G2 - XS Quadrupole Time - of - Flight spectrometer in positive mode. 179 - diphenyl - - bipyridine) ruthenium(II) dichloride, [Ru(dpb) 3 ]Cl 2 . This synthetic route is based on what was reported by Damrauer et al . with modifications. 6, 21 - diphenyl - - bipyridine (dpb) ligand was synthesized by D. M. Arias - Rotondo according to a previously published procedure, 6 and Ru(DMSO) 4 Cl 2 was prepared by C. R. Tichnell based on a reported route. 22 Free dpb ligand (0.32 mmol, 0.102 g) and Ru(DMSO) 4 Cl 2 (0.1 mmol, 0.049 g) were added to 10 mL bubble - degassed EtOH. This suspension was heated to reflux on a Schlenk line. As the dpb dissolved, the solution turned a dark orange - brown. The solutio n was allowed to stir under N 2 with heating for 72 h. To drive precipitation of the chloride salt of the complex, 6 M HCl was added dropwise with stirring under positive N 2 pressure. 21 Immediate precipitation was observed to occu r as the suspension became a lighter, brighter orange color that was much more opaque than the solution. The product was filtered and washed with deionized water multiple times. 1 H NMR (500 MHz, [D 2 d, 6 H, J = 1.9, 6.1 Hz), 7.58 (m, 18 H)]. CHN analysis of RuC 66 H 48 N 6 Cl 2 4H 2 O: calculated C 67.80, H 4.83, N 7.19; found C 67.91, H 5.05, N 6.54. A portion of the [Ru(dpb) 3 ]Cl 2 synthesized above was metathesized to the hexafluorophosphate salt (PF 6 - ) with the intention of using this salt to grow single crystals for X - ray diffraction studies. This was previously performed by A. L. Smeigh. - diphenyl - - bipyridine) ruthenium(II) [(3,5 - trifluoromethyl)phenyl]borate, [Ru(dpb) 3 ](BAr F ) 2 . Metathesis to the BAr F salt was performed according to a previously published route. 6 Briefly, the [Ru(dpb) 3 ]Cl 2 product (0.091 mmol, 0.100 g) from above was dissolved in minimal MeOH (1.5 mL). NaBAr F (1.826 mmol, 1.618 g) was ad ded to DI H 2 O (~17 mL) to form a suspension. The BAr F - salt was added slowly to [Ru(dpb) 3 ]Cl 2 , and the suspension was allowed to stir for 1 h under N 2 . Unlike the chloride salt, [Ru(dpb) 3 ](BAr F ) 2 did not crash out of the water 180 system, and the solution rema ined an orange - brown color. The solvent was removed by rotary evaporation and the [Ru(dpb) 3 ](BAr F ) 2 product was dissolved in pure DCM for column chromatography. A silica gel column was prepared in DCM and used for separation of [Ru(dpb) 3 ](BAr F ) 2 from the i mpurities in the crude reaction mixture. The desired product ran first and was a yellow - orange color. The next band was colorless and was the excess NaBAr F . Unreacted Ru(DMSO) 4 Cl 2 , heteroleptic [Ru(dpb) 2 ], and free dpb ligand remain at the top of the colum n. 1 H NMR (500 MHz, [d 4 - 30 H), 7.63 (m, 18 H)]. ESI - MS (m/z): [C 66 H 48 N 6 Ru] 2+ calculated 513.15, found 513.16. CHN analysis: calculated C 56.72%, H 2.64%, N 3.05%; found C 57.25%, H 2.30%, N 2.9 4%. - dimesityl - - bipyridine) ruthenium(II) [(3,5 - trifluoromethyl)phenyl]borate, [Ru(dmesb) 3 ](BAr F ) 2 . The chloride salt, [Ru(dmesb) 3 ]Cl 2 was generated in situ via the previously published procedure. 6 The dmesb ligand was prepared by M. D. Woodhouse. Metathesis to the BAr F - salt was performed by the addition of 2.5 mol equiv. of NaBAr F (0.057 mmol, 0.050 g) in minimal MeCN (~0.5 mL) to [Ru(dmesb) 3 ]Cl 2 (0.023 mmol) in minimal M eCN under N 2 . The solution was a dark red - brown. Water was added and a light orange suspension formed, which was allowed to stir under N 2 for 3 h. The water was removed by rotary evaporation and the sample was pumped while in a vacuum desiccator for 4 d. Y ield 20 %. 1 H NMR (500 MHz, [d 3 - [8.39 (d, 6 H, J = 1.9 Hz), 7.97 (d, 6 H, J = 5.9 Hz), 7.68 (m, 22 H), 7.28 (m, 6 H), 7.02 (s, 16 H), 6.98 (s, 6 H), 2.30 (s, 18 H)]. ESI - MS (m/z): [C 84 H 84 N 6 Ru] 2+ calculated 639.29, found 639.29. 2.1.2 X - Ray Crystallography Single - crystal X - ray diffraction was collected on suitable crystals of [Ru(dpb) 3 ](PF 6 ) 2 . Crystals were grown by very slow diethyl ether diffusion into an acetonitrile solution of [Ru(dpb) 3 ](PF 6 ) 2 with two drops of toluene. The crystals were mounted in paratone oil and 181 transferred to the cold nitrogen gas stream of the diffractometer for data collection. The data were collected on suitable crystals mounted on a Bruker APEX - II CCD diffractometer with MoK radiation at the Center for Crystallog raphic Research at Michigan State University. The crystal structure was solved by S. Li and R. J. Staples. [Ru(dpb) 3 ](PF 6 ) 2 crystallographic data: C 66 H 48 F 12 N 6 P 2 Ru, M r = 1316.11, monoclinic, a = 35.263(4) Å, b = 17.6678(19) Å, c = 24.080(3) Å, T = 173 K, s pace group = C2/c, Z = 8, 53123 reflections measured, 12027 unique (Rint = 0.0980), which were used in all calculations. The final wR(F2) was 0.1461 (all data). Solvent molecules in the structure were heavily disordered and the program BYPASS implemented i n Olex2 showed the following void and electrons: 1263.5, 227.6. Possible solvents include Et 2 O, EtOH, and MeCN. 2.2 Density Functional Theory Calculations Density functional theory (DFT) calculations were performed on [Ru(dpb) 3 ](PF 6 ) 2 and [Ru(dmesb) 3 ](PF 6 ) 2 using the Gaussian 09 software package. 23 Geometry optimization was done on the ground and excited states of the se complex es ( Appendix D ) with a spin - unrestricted formalism at the B 3LYP/LANL2DZ level of theory; this basis set has been shown to perform well for Ru(II) complexes. 24,25 Frequency calculations showed that no imaginary frequencies were obtained, indicating that the calculation was at a global, an d not a local, minimum. T ime - dependent (TD) calculations were performed on the optimized ground state structures, for which a conductor - like polarizable continuum model (CPCM) with the properties of acetonitrile was used to account for the contributions of the bulk solvent. The first 250 electronic transitions were found for the optimized geometry, corresponding to both singlet and triplet transitions. The orbital pictures for the transitions were prepared in GaussView. 182 2.3 Steady State and Time - Resolved Spectroscopy 2.3.1 Steady - State Absorption and Emission Spectroscopy Steady state absorption spectra were collected with a Varian (now Agilent) Cary 50 UV - Vis spectrophotometer. Solvents used for ground state absorption spectra were used as received, with out further purification. These include: MeOH (Sigma - Aldrich, HPLC grade), EtOH (Decon Labs, 100%), 1 - butanol (1 - BuOH, Jade Scientific, ACS grade), 1 - hexanol (1 - HexOH, Spectrum Chemical, 98%), 1 - octanol (1 - OctOH, Jade Scientific, reagent grade), MeCN (Sigm a - Aldrich, HPLC grade), propionitrile (PrCN, Alfa Aesar, 99%), Butyronitrile (BuCN, Alfa Aesar, 99%), and hexanenitrile (HexCN, Sigma - Aldrich, 98%). Steady state emission spectra were collected with two separate instruments. A Fluorolog 2 (Horiba Jobin - Yv on) fluorimeter was used to measure the steady state emission and the excitation spectra. A photomultiplier tube detector is implemented in this set - up, and the temperature was not measured directly but assumed to be 293 K. For quantum yield determination, a Quantaurus - QY Absolute PL quantum yield spectrometer (Hamamatsu) with a cooled, back - thinned charge - coupled device (BT - CCD) detector was used. With this setup, an integrating sphere allows for absolute quantum yields to be found, whereas with the Fluoro log, a sample of [Ru(bpy) 3 ](PF 6 ) 2 (prepared by D. M. Arias - Rotondo) is used as a reference. 26,27 Samples used for emission were prepared in an air - free glove box, such that the absorbance at th e pump wavelength was 0.1 - 0.2 AU. Solvents used for steady state and time - resolved emission spectroscopies were: MeOH (Alfa Aesar, anhydrous, 99%), 1 - BuOH (Alf a Aesar, 99%, as received), 1 - OctOH, MeCN, and BuCN (as received). Unless otherwise specified, these solvents were also used in the absorption measurements and were freeze - pump - thaw degassed. 183 2.3.2 Nanosecond Transient Absorption and Emission Spectroscopy Nanosecond time - resolved measurements were carried out with the same pump source, a Vibrant 355 II Nd:YAG - pumped optical parametric oscillator (OPO, Opotek) which has tunable output from 300 - 2400 nm at a 10 kHz repetition rate. The IRF of this system is a pproximately 10 ns. For the emission spectroscopy, a portion of the pump was directed onto a photodiode (ThorLabs) to act as a reference and trigger. The pump is then focused into the sample, which is in a 1 - cm pathlength matched cell, and scatter is colle cted at a 90º angle to the pump. This scatter enters a MacPherson Model 272 f/2 monochromator, and is then detected by a R928 PMT. The signal is monitored and the data collected by a LeCroy Model 9360 300 MHz digitizing oscilloscope. Finally, the data are worked up by a home - built LabVIEW program. The samples for emission are prepared in the same way regardless of whether the experiment is steady state or time - resolved. In the case of the nanosecond transient absorption (TA) spectroscopy, the pump is immedi ately directed into a LP980 spectrometer (Edinburgh Systems). In this setup, the laser propagates through the sample, which is prepared such that the absorbance at the excitation wavelength is 0.3 - 0.7 A.U. This sample is again in a 1 - cm pathlength matched cell. White light generated within the LP980 spectrometer enters the sample at 90º to the pump, after which it is focused into the detector. This instrument was run in single - wavelength mode. The pump wavelengths in these two time - resolved experiments were 400, 480, and 550 nm; the pump power was also kept low enough that the kinetics measured were in the linear regime. The probe wavelength was kept at 530 nm unless otherwise specified. All of the nanosecond data were fit with LabVIEW to single - exponential kinetics. 184 2.3.3 Ultrafast Transient Absorption Spectroscopy In the ultrafast transient absorption data collected by Damrauer and McCusker, experimental considerations limited the pump wavelength to 400 nm. 8 To draw comparisons, e xcitation at 400 nm was desirable; however, vibrational dynamics have been demonstrated on occasion to be dependent on excitation energy, 28,29 so other pump wavelengths (i.e., 480 and 550 nm) were additionally used. The highest e nergy excitation was only possible with the l30 fs pulse system, whereas the lower energy excitation wavelengths were performed with both the 130 and the sub - 60 fs pulse laser setups. Another important consideration for these experiments was the instrument response function (IRF). In the original set of data collected, the early - time kinetic component was on the order of the IRF of the laser system used. Through the use of a shorter pulse setup with a shorter IRF, we will be able to more accurately and defi nitively pinpoint the timescale of that ultrafast lifetime. Ultrafast transient absorption (TA) spectroscopy measurements were carried out on two separate laser systems. The longer pulse setup has been previously described, 30 and can be found in Chapter 2 . The shorter pulse system has also been reported previously. 24 Briefly, a Mantis oscillator (Coherent) seeds a Legend Elite regenerative amplifier (Coherent) that is pumped b y Evolution diodes (Coherent). The output of the regen is a 1.2 W of 1 kHz repetition rate 800 nm laser with approximately 35 fs pulses that is split 80:20 to two identical OPerA Solo optical parametric amplifiers (OPAs, Coherent) that serve to tune within the visible region, affording pump and probe lines, respectively. Both the pump and probe traverse a folded Brewster prism pair in order to preemptively compensate for the dispersion introduced by optics along the laser paths. The pump pulse is delayed wi th respect to the probe pulse by a translating linear actuator (Soloist), affording ~1.3 ns delays. The pump beam passes through a chopper set to a frequency 185 of ~440 Hz which is coupled to a lock - in amplifier. A small portion of the probe beam is picked of f then attenuated and directed into a Si photodiode (ThorLabs) to act as a reference. The pump and probe are focused into the sample at an angle of less than 3º relative to each other. After entering the sample, the pump is blocked whereas the probe is foc used into a monochromator with 1 mm entrance and exit slits and then sent onto a Si photodiode (ThorLabs). For the data displayed here, the typical excitation energy was 2 - collected in the linear regime. The ground state absorb ance for each of the samples was approximately 0.3 - 0.7 in a 1 - mm sample cuvette (FireFlySci) at 400, 480 and 550 nm, the excitation wavelengths, and no spectral changes were observed after the variable - temperature experiments were complete. The probe wavel ength could be tuned to exactly 532 nm on the shorter pulse system through the use of the second OPA and the monochromator with ~2 nm spectral bandwidth in the detection setup. In the case of the longer pulse system, however, the pulse is composed of white light is generated by the 800 nm regen output through a translating CaF 2 window. Additionally, a 10 nm bandpass filter centered at 530 nm is used in the detection on this system. Care was taken to ensure that the measurements on both systems were comparab le regardless of detection scheme. Pulse characterization is performed within the cryostat by optical Kerr effect (OKE) measurements made in acetonitrile, yielding approximately 160 and sub - 60 fs pulses on the longer and shorter systems, respectively. Cros s - correlation performed in acetonitrile gives an IRF better than 300 fs on the long pulse system and shorter than 150 fs on the short pulse system. The spectra shown here are an average of more than 10 scans, with no single scan giving a fit that is a stat istical outlier. Biexponential fits to the data were performed with Igor Pro software (v. 6.37) . All error reported was propagated across multiple data sets. 186 3. Results 3.1 Synthesis 3.1.1 [Ru(dpb) 3 ](BAr F ) 2 In preparing the Ru(II) complexes for measurements of solvation dynamics, it was immediately apparent that a counteranion that allowed for the compound to dissolve in a wide array of solvents was required. The counterion of choice was tetrakis[(3,5 - trifluoromethyl)phenyl]borate, a very bulky, non - coordinating ion that allows [Ru(dpb) 3 ] 2+ to be dissolved in solvents like 1 - OctOH and HexCN, as well as the more traditional solvents of MeOH and MeCN. While there was a synthetic route already outlined for the preparation of [Ru(dpb) 3 ](BA r F ) 2 , 31 it was soon determ ined that purification of any BA r F - salt is complicated by its solubility properties. Thus, the Cl - salt was first isolated and purified, then the metathesis was performed. Precipitating [Ru(dpb) 3 ]Cl 2 through the us e of 6 M HCl requires a word of caution, however. 21 Good results were obtained in this instance, with the salt immediately crashing out as observed by the increased opacity and bright orange solid upon addition of the HCl. It sho uld be noted, though, that acid in the presence of a bipyridine can produce a protonated bipyridine, which would compete with the Ru - bpy coordination, thereby resulting in a heteroleptic complex. This was not observed in the formation of [Ru(dpb) 3 ]Cl 2 , but for other bpy - based ligands that may not coordinate to Ru(II) as readily (e.g., those with electron withdrawing substituents), this route may not be appropriate. 3.1.2 [Ru(dmesb) 3 ](BAr F ) 2 The mesitylated complex, [Ru(dmesb) 3 ] 2+ , was desired for these stud ies so as to begin to understand the nuclear coordinate accessed in the vibrational cooling process ( vide infra ). Surprisingly, the preparation of [Ru(dmesb) 3 ] 2+ was much more challenging than the [Ru(dpb) 3 ] 2+ 187 product. The free dmesb ligand as synthesized by M. D. Woodhouse was observed to go from a white to a pink powder in ~24 h. This is attributed to the iron - philic nature of the dmesb, which is apparently much greater in this ligand than in dpb. Although the dpb ligand could be recrystallized out of hot EtOH, this process was only done when the ligand was more than six months old to ensure good product formation. In the case of the dmesb reactions, though, dmesb was recrystallized out of hot EtOH as a matter of standard procedure. Despite the extra caution taken to ensure recrystallized starting materials (i.e., both the dmesb and Ru(DMSO) 4 Cl 2 ), oxidized {Ru III (dmesb) x } product has been observed in some reaction mixtures, in which both homo - (x = 3) and heteroleptic (x = 2) complexes were seen by 1 H NMR ( Fig. 4.1 ). While the steric bulk of the mesitylated ligand was originally believed to be r esponsible for this oxidation, previous reports have demonstrated that the presence of Cl - may have the effect of replacing bpy - type ligands, thereby greatly reducing the oxidation potential of the Ru(II/III) couple. 32 This allow s for ready oxidation to the Ru(III) heteroleptic complex. The studies of Pearson et al . report that during the growth of single crystals, [Ru II (bpy) 3 ]Cl 2 was observed to form [Ru III (bpy) 2 Cl 2 ]Cl. The oxidation potentials for these two complexes are 893 and - 84 mV vs. Fc/Fc + , respectively. 32 If this has been observed in [Ru(bpy) 3 ] 2+ , it seems reasonable to expect that the steric effects of the dmesb ligand only exacerbate this problem. In fact, while perhaps this complex dissociati on and oxidation is expected in solution, the oxidation was actually observed in solid, powdered [Ru(dmesb) 3 ](PF 6 ) 2 , which only had Cl - present for the initial complexation step of the reaction, as the metathesis to the PF 6 - salt was performed immediately after. This seems to illustrate how easily incorporated and how detrimental chloride ions can be to these complexes. 188 Figure 4. 1 . 1 H NMR spectrum of [Ru(dmesb) 3 ]Cl 2 reaction mixture in CD 3 CN. While many of the main features can be assigned to the desired homoleptic complex (see text for assignments), some features clearly belong to an oxidized and/or heteroleptic complex, as evidenced by the shifts ~10.1 ppm. Although the route outlined above did produce [Ru(dmesb) 3 ](BAr F ) 2 , a modified synthesis is proposed here to alleviate the problems that were observed, thereby improving the overall yield and purity. The original report by Damrauer et al . cites a 24 h reaction time for the complexation. 6 Increased reaction time will likely improve the amount of homoleptic complex formed, though reacting for too long may allow for displacement of a dmesb ligand with Cl - ions. The reaction mixture should remain air - free at all times, and ideally be performed in a glove box under inert a tmosphere. If possible, a Ru(II) starting material free of chloride would be ideal. Metathesis to 189 the BAr F - salt should be performed with deficient equivalents of NaBAr F so that excess counterion is not present. If the product is indeed a mixed salt, it ha s already been shown that the counteranion does not play a role in the vibrational cooling dynamics being studied here, and are unlikely to affect any of the photophysical processes of these Ru(II) polpyridyls. 4, 8, 27, 31 Additionally, based on the 1 H NMR and CHN analysis of the [Ru(dmesb) 3 ](BAr F ) 2 product, over 20 mol equiv. of water were present in the complex despite being pumped on in a desiccator for 4 d. Drying over P 2 O 5 may reduce the amount of water, but it is known that BAr F - is hygroscopic, despite not being soluble in H 2 O. 33 This would appear to recommend that this complex be stored either in a vacuum desiccator or in a glove box under inert atmosphere. It should be noted that [Ru(dpb) 3 ](BAr F ) 2 does not display hygroscopicity to nearly the same degree and has bee n observed to not decompose when stored in air for years at a time. Column chromatography was attempted to purify [Ru(dmesb) 3 ](BAr F ) 2 . It was later determined that using nearly any other counteranion would make purification much simpler. That being said, t he conditions used for [Ru(dpb) 3 ](BAr F ) 2 appeared to be viable by thin - layer chromatography (TLC): pure DCM on SiO 2 . 31 Unfortunately, these conditions only worked once to purify the product. It was determined by 1 H NMR that the m ajor impurity was free ligand, so a sequential solvent system was used on SiO 2 in which the ligand was driven off first by a 25% ethyl acetate (EtOAc) in hexanes solution, and then the complex was moved down the column by either pure EtOAc or pure DCM. Bot h second solvent systems were found to work, but EtOAc required more solvent and ended up smearing the product more, whereas DCM drove the product more cleanly off as one band. As with the pure DCM on SiO 2 , these conditions only purified the complex one ti me each. Subsequent performance of these exact conditions yielded large amounts of free ligand impurity. This was later attributed to the ease with which the dmesb ligand must dissociate 190 from the Ru(II) center. These column attempts and complex dissociatio n led to the rather low yield of the compound. It is therefore recommended that column chromatography not be used as a purification option for [Ru(dmesb) 3 ](BAr F ) 2 . One additional note on the characterization of the mesityl complex. In the mass spectrum of the compound ( Fig. 4.2 ), a repeating feature at m/z 890 is observed. The isotope pattern with the greatest intensity (centered at m/z 890) is assigned to [Ru(dmesb) 3 ] 2+ . The observed increase of m/z ratios are not typ ical for Ru(II) polypyridyls. The apparent centers of these isotope patterns are all separated by 14 mass units. It was determined that this corresponds to the oxidation of the methyl groups on the mesityl to aldehydes. Furthermore, some of the sample used for ESI - MS was reserved for 1 H NMR, and no evidence of the aldehyde peak was observed ( Fig. 4.3 ), which would be expected to appear around 10 ppm. This indicates that it was impurity on the MS column that was doing chemistry wit h the sample. Previously, Ru(II) has been observed to catalyze the reaction of methylarenes to the corresponding aromatic aldehyde. 34 That being said, it is critical to thoroughly characterize solution - phase [Ru(dmesb) 3 ] 2+ before and after any type of spectroscopy is performed on the sample. 191 Figure 4. 2 . Electrospray ionization mass spectrum of [Ru(dmesb) 3 ] 2+ in positive mode. (Top) Calculated spectrum for the [M] 2+ ion. (Bottom) Experimental spectrum for the [M] 2+ ion. The rep eating unit is attributed to the oxidation of the methyl substituents in the mesityl moiety to aldehydes. 192 Figure 4. 3 . 1 H NMR spectrum of the [Ru(dmesb) 3 ](BAr F ) 2 sample used to collect the mass spectrometry data in Fig. 4.2 . No evidence of an aryl - aldehyde is present, as indicated by the featureless area around 10 ppm. 3.2 X - Ray Crystallographic Data Single crystals of [Ru(dpb) 3 ](PF 6 ) 2 were able to be grown by very slow Et 2 O diffusion into MeCN solution. These crystals were obtained after approximately six months of growing, and were very fine, needle - like structures that ultimately did not diffract very well. Attempts were made to increase the thickness of the crystals through the addition - stack with the phenyl substituents and allow the crystals to grow outward. These were the crystals for which X - ray data were obtained. One system that appeared to show promise but was only explored briefly was through the slow di ffusion of Et 2 O into a solution of 1 - OctOH. Surprisingly, the PF 6 - 193 salt of this complex is soluble in 1 - OctOH, though only sparingly. The solubility must be improved to slow down the growth of crystals (thereby increasing their size and diffraction - ability ) so a few drops of EtOH were added. This process did grow large crystals, but they unfortunately grew too quickly (i.e., within hours), meaning they did not produce data any better than was already acquired. We are noting this should others wish to attemp t to improve the data reported here. We report, for the first time, the single crystal X - ray data for [Ru(dpb) 3 ](PF 6 ) 2 . These data can be found in Table 4.1 , along with the same structural data of [Ru(dmesb) 3 ](PF 6 ) 2 and [Ru(bpy ) 3 ](PF 6 ) 2 for comparison. The crystal structure itself is given in Fig. 4.4 . Relative to the prototypical [Ru(bpy) 3 ] 2+ complex, the structural data of [Ru(dpb) 3 ] 2+ are largely unchanged. The Ru - N bond distances and cis - angles are consistent between the two complexes, indicating that the phenyl substituent does not greatly affect the ground state geometry relative to the bpy analogue. The only difference of note is t he trans N - Ru - N angle, which is two degrees greater in [Ru(dpb) 3 ] 2+ , implying a very slightly more octahedral geometry. 194 Table 4.1. X - ray crystallographic data of [Ru(dpb) 3 ](PF 6 ) 2 compared to the dmesb and bpy analogues. [Ru(dpb) 3 ](PF 6 ) 2 [Ru(dmesb) 3 ](PF 6 ) 2 a [Ru(bpy) 3 ](PF 6 ) 2 b Ru - N (Å) 2.050 ± 0.009 2.075 ± 0.013 2.0554 ± 0.0001 bpy N - Ru - N (°) 78.6 ± 0.2 78.04 ± 0.35 78.65 cis N - Ru - N (°) 93.8 ± 0.3 94.23 ± 0.60 93.91 ± 3.59 trans N - Ru - N (°) 175.4 ± 0.2 170.54 ± 0.35 173 bpy - bpy torsion (°) 0 - 15 9 - 15 5.94 bpy - Ph torsion (°) 31.9 ± 1.8 68.54 ± 9.53 N/A bpy - Ph C - C (Å) 1.480 ± 0.017 1.4904 ± 0.0220 N/A a Data taken from r ef. 6 . b Data taken from r ef. 35 . Figure 4. 4 . The X - ray crystal structure of [Ru(dpb) 3 ](PF 6 ) 2 . The counteranions and solvent are omitted for clarity. 195 It is more informative to compare the structures of [Ru(dpb) 3 ] 2+ and [Ru(dmesb) 3 ] 2+ , in order to better understand the effect of the methyl groups in t he mesityl substituent. The most apparent difference between the complexes is the diplanar angle between the phenyl and bipyridine moieties: in the phenylated complex, it is an average of 32°, which is more than doubled to ~70° in [Ru(dmesb) 3 ] 2+ . This dipl anar angle in [Ru(dpb) 3 ](PF 6 ) 2 of 32º is an intermediate between the 9.60º angle of the free ligand 7 and the 44º calculated from 4 - phenylpyridine, which was used in place of the actual Ru(dpb) moiety for computational work. 6,7 This would suggest that the complex is more driven to coplanarity than the 4 - phenylpyridine (perhaps d ue to extended conjugation in dpb relative to 4 - phenylpyridine) but that driving force does not extend to the complex, likely caused by steric strain around the metal center. It should also be noted that the Ru - N bond distance is lengthened in the mesityl complex by approximately 0.025 Å. This bond distance can often be an indicator of the electron donating or withdrawing effect of the substituent. 7 As compared to [Ru(bpy) 3 ] 2+ , the bond distance is within error of that of [Ru(dpb) 3 ] 2+ , implying that any electronic [Ru(dmesb) 3 ] 2+ - electron withdrawing substituent. However, th e 70° angle between the mesityl and bpy backbone implies very little conjugation, which should effectively mitigate any electronic effects from the substituent. It therefore seems more likely that the increased Ru - N bond distance in [Ru(dmesb) 3 ] 2+ relative to that of [Ru(dpb) 3 ] 2+ is simply caused by the steric strain induced by the bulky mesityl groups (as evidenced by the increased bpy - phenyl C - C bond distance lengthening in Table 4.1 ), forcing the bipyridines into a geometry t hat decreases the M - L orbital overlap, weakening the Ru - N bonds. The effects of this can also be seen in the bpy torsion, or the degree of canting between the two pyridyl moieties in the bipyridine, which is much greater in [Ru(dmesb) 3 ] 2+ than either 196 [Ru(d pb) 3 ] 2+ or [Ru(bpy) 3 ] 2+ . Likewise, the bpy, cis , and trans angles in the dpb and bpy analogues are consistently much closer to an octahedral geometry than in the mesitylated complex. 3.3 Role of Solvent on the Ground State Absorption Properties of [Ru(dp b) 3 ] 2+ The studies originally published by Damrauer and McCusker utilized a 532 nm probe upon excitation at 400 nm. 8 In Fig. 4.5 . are shown the ground state absorption spectrum and the differential absorption spectrum of [Ru(dpb) 3 ](BAr F ) 2 in MeOH. These spectra are directly comparable to those reported previously, 8 indicating the identity of counteranion does not affect the photophysical properties being studie d, as expected. 4 The steady state absorption spectrum max =474 nm that is characteristic of an MLCT transition, here the 1 MLCT 1 A 1 absorption. The tail apparent at 3 MLCT band, al lowed by spin - orbit coupling due to the Ru(II) center. 36,37 The feature centered at ~350 nm has also been assigned as MLCT, likely due to the molar extinction coefficient which is on the order of 2.7×10 4 M - 1 cm - 1 . This value is approximately two times greater than that of [Ru(bpy) 3 ] 2+ , 4, 38 the increased oscillator strength owing to the extended conjugation in the dpb ligand. The exact nature of this band is an open question, a nd one that will be addressed further (vide infra). Finally, the feature farthest in the UV that is not entirely displayed in Fig. 4.5 is the dpb ligand - 197 Figure 4. 5 . (Left) Ground state absorption spectrum of [Ru(dpb) 3 ](BAr F ) 2 in MeOH. (Right) Differential absorption spectrum of [Ru(dpb) 3 ](BAr F ) 2 in MeOH of the thermalized 3 MLCT excited state. See text for assignments. As the pump wavelength assignments are made from the ground state absorption spectrum, so must the characteristics of the probe wavelengths be determined from the transient absorption spectrum ( Fig. 4.5 ). The excited state absorption in t he near - - transition of the reduced dpb ligand. This transition is echoed in the feature with the greatest oscillator streng - 474 nm is caused by the loss of the ground state upon absorption into the 1 MLCT excited state. The broad, featureless excited state absorption red of ~550 nm is attributed to ligand - to - metal charge transfer (LMCT) based on the spectroelectrochemistry. 8 The purpose of this work is to study the effect of protic and aprotic polar solvents on the vibrational cooling dynamics of [Ru(dpb) 3 ] 2+ that occur concomitantly with the phenyl ring rotation in the 3 MLCT excited state. From the spectroelectrochemical and transient absorption data , the optimal probe wavelength to monitor such kinetics would be at t he central wavelength of - 198 absorbance is beneficial in that ligand - based dynamics can be measured directly without the interference of the loss of the ground state. Probing in the MLCT bleach, as was done when the pr obe ) is 480 nm, was previously shown to decay within the IRF of the system with no additional dynamics. 8 Thus 532 nm is also taken as the probe wavelength for the ultrafast data reported herein. exc ) was the result of frequency doubling of the 800 nm regenerative amplifier output, and thus was exper imentally limiting. Upon Gaussian deconvolution of the ground state absorption spectrum ( Fig. 4.6 ), seven bands are found to describe the spectrum well. Gaussian deconvolution is highly arbitrary and should only be taken as a first approximation of the underlying transitions of any spectrum. From this analysis, it is apparent that excitation at 400 nm will populate multiple bands, particularly those centered at approximately 350 nm and at 430 nm. Gaussian deconvolution has been performed multiple times on this spectrum with various initial guesses; at every iteration, a minimum of two bands overlapped at 400 nm, bolstering this assertion. In an attempt to more thoroughly study the vibrational cooling kinetics of [Ru(dpb) 3 ] 2+ , ex citation at other wavelengths was desired. 480 and 550 nm were chosen as two additional pump wavelengths as these would (based on the Gaussian deconvolution) allow the molecule to be excited into only one band, thereby creating only one type of excited sta te initially. These wavelengths have the added benefit of forming two different excited states, in exc = 480 nm populates a 1 exc = 550 nm generates the 3 MLCT state. 199 Figure 4. 6 . Steady state absorption spectrum (black diamonds) of [Ru(dp b) 3 ](BAr F ) 2 in MeOH. Gaussian deconvolution of this region revealed seven separate bands (red traces) were required to reconstruct the spectrum (blue trace). The ground state absorption spectrum of [Ru(dpb) 3 ] 2+ was also collected and compared for all of the solvents used in the ultrafast transient absorption spectroscopy studies ( Fig. 4.7 ). The alcohol series is comprised of MeOH, EtOH, 1 - BuOH, 1 - HexOH, and 1 - OctOH. The general shape of the spectrum was consistent in all of the solvents, and only very minor solvatochromism was observed. In MeOH, the absorption maximum of the lowest energy MLCT transition is 474 nm, whereas it is red - shifted to 478 nm in 1 - OctOH. This is a difference of only 177 cm - 1 despite an eight - fold increase in alkyl chain length, indicating that only the polar - OH group is responsible for the spectral shifting. In the case of the nitrile series, MeCN, PrCN, BuCN, and HexCN are used. Again, these spectra show no major changes between these solvents, nor when compared to max (MeCN) = 474 nm and red - shifts in HexCN to 478 nm ( Table 4.2 ). The same magnitude spectral shift occurs 200 in this case over a lengthening of the alkyl chain by a factor of six. As appears true for the alcohols, these data would indicate that only the polar nitrile functional plays a role in the stabilization of the 1 MLCT excited state. Interestingly, the band centered ~350 nm also displayed solvatochromism, where between the maximum red - shifted approximately 250 cm - 1 in 1 - OctOH relative to MeOH. These affects were significantly attenuated in the nitriles, for which th e maximum in HexCN was only 80 cm - 1 redder than in MeCN. As can be seen in Fig. 4.7 and Table 4.2 , the relative intensities of the lowest and highest energy MLCT maximum of [Ru(dpb) 3 ] 2+ are variable d epending on the specific solvent, as evidenced by the spectral maxima ca. 350 nm not overlapping well. These data may provide some insight into the nature of that transition. Figure 4. 7 . Ground state absorption spectra of [Ru(dpb) 3 ](BAr F ) 2 in the solven ts used in the ultrafast transient absorption experiments. The spectra are normalized to the maximum of the lowest energy MLCT band. [Ru(dpb) 3 ] 2+ is modestly solvatochromic . 201 Table 4.2. Summary of the MLCT maxima of the ground state absorption spectra of [Ru(dpb) 3 ](BAr F ) 2 in the solvents used in the transient absorption spectroscopy measurements. Solvent E higher - energy 1 MLCT (nm) E lower - energy 1 MLCT (nm) E (cm - 1 ) E (cm - 1 ) a E (%) a MeOH 348 474 7639 - - EtOH 349 475 7601 - 38 - 0.5 1 - BuOH 351 477 7526 - 113 - 1.5 1 - HexOH 351 478 7570 - 69 - 1 1 - OctOH 351 478 7570 - 69 - 1 MeCN 350 474 7474 - - PrCN 350 475 7519 44 0.5 BuCN 350 477 7607 133 2 HexCN 351 478 7570 95 1 a The alcohols are referenced to MeOH, whereas the nitriles are referenced to MeCN A consistent trend can be observed throughout both the alcohols and the nitriles in which as the chain length increases, the lowest energy MLCT maximum red - shifts, indicatin g that the solvents with lower dielectric constants are better able to stabilize the 1 MLCT, which is a counterintuitive result. The MLCT excited states are species with large dipole moments and as such should be highly susceptible to polar solvation. 10, 39 Alternatively, one might be tempted to postulate that the 1 MLCT excited state is likely stabilized equivalently in each solvent of a given family (this seems reasonable given that the polar moiety is th e same for solvents within a series), and that the solvation effects on the ground state are driving the transition absorption energy. 202 However, the nonpolar 1 A 1 ground state is more likely to be increasingly stabilized by the solvents with longer chain len gths, resulting in a net blue - shift of the spectrum in solvents with lower dielectric constants. At this time, all that might be said about these spectra is that the ground state absorption spectra are only somewhat affected by the solvents being studied. 3.4 Vibrational Cooling Dynamics in [Ru(dpb) 3 ] 2+ 3.4.1 Ultrafast Kinetics Measured in Alcohol Solvents In the alcohol series, five solvents of increasing alkyl chain length were used. The polar - OH group is maintained while the degree of nonpolarity is sy stematically increased via the chain. The major motion in the solute dynamics being studied is the aryl rotation, thus it might be expected that frictional forces would dominate the kinetics. If true, the vibrational cooling time VC ) should incr ease as the alcohol chain length and by extension, the viscosity increased. On the other hand, vibrational cooling is occurring along the 3 MLCT potential energy surface, and this excited state has a very large dipole moment. This might alternatively el icit a VC to track a bulk solvent property such as dielectric constant or solvent polarity. Upon excitation at 480 and 550 nm, the vibrational cool dynamics are relatively consistent between the two pump wavelengths, as can be seen in Table 4.3 . A trend is observed in which as VC elongated. In MeOH, the time constant measured is ~ 1.8 ps, which then increases to ~18 .5 ps in 1 - OctOH. This can also be observed in the spectral comparison made in Fig. 4.8 . These spectra are both normalized such that growth to the thermalized 3 MLCT excited state. It is evident that [Ru(dpb) 3 ] 2+ in MeOH grows in a much faster rate than when the compound is in 1 - OctOH. The stepwise growth in 203 VC concomitant with the alkyl chain length tends to indicate that viscosity is playing a role in these vibrational cooling dynamics, such that it can be said a viscoelastic mo del represents these data well. Table 4.3. Vibrational cooling time constants for [Ru(dpb) 3 ](BAr F ) 2 in the alcohol solvents of as a function of excitation wavelength. Solvent (cP) a VC (ps) exc = 400 nm exc = 480 nm exc = 550 nm MeOH 0.544 3.3 ± 1.8 1.6 ± 0.9 1.9 ± 0.7 EtOH 1.07 4.6 ± 1.7 5.0 ± 2.6 6.0 ± 1.6 1 - BuOH 2.54 8.4 ± 4.9 5.9 ± 1.5 12.0 ± 3.9 1 - HexOH 4.58 8.5 ± 3.4 14.4 ± 1.5 15.0 ± 4.5 1 - OctOH 7.29 9.4 ± 5.0 17.1 ± 2.6 20.0 ± 3.6 a Taken from r ef. 40 . 204 Figure 4. 8 . Overlay of the vibrational cooling dynamics of [Ru(dpb) 3 ](BAr F ) 2 in MeOH (red diamonds) and 1 - OctOH (purple diamonds) upon excitation at 480 nm. The final 30 data points of each set are norma VC in MeOH (black trace) is 1.5 ± 0.3 ps, which is significantly lengthened in 1 - OctOH (red trace) to 17.1 ± 2.6 ps. VC change drastically upon excitati on at 400 nm. At this pump wavelength, the vibrational cooling lifetime of [Ru(dpb) 3 ] 2+ in MeOH and EtOH are consistent with the other excitation energies, that is 3.3 ± 1.8 and 4.6 ± 1.7 ps, respectively ( Table 4.3 ). Upon solv ation in longer chain alcohols, however, a saturation of the time constant is observed around ~9 ps. At no other excitation wavelength are the dynamics in 1 - BuOH and 1 - OctOH superimposable. It is apparent that the viscoelastic model that applied upon excit ation at lower pump wavelengths is not the major solvation mechanism at work in these data. There is no observable bulk solvent property of which we are aware that is consistent between these longer alkyl length alcohols. 205 3.4.2 Ultrafast Kinetics Measured in Nitrile Solvents With the vibrational cooling data for [Ru(dpb) 3 ] 2+ in the alcohol series in hand, the question of H - bonding became of concern. To rule out these strong solvent - solvent interactions, the polar aprotic nitriles were used. Unfort unately, the viscosity of the three shortest - chain solvents (i.e., MeCN, PrCN, and BuCN) is nearly unchanged, and are on the order of the viscosity of MeOH. It was necessary to include HexCN to the list, the viscosity for which is similar to that of EtOH. These will make for good direct comparisons to the alcohol series based solely on this bulk solvent property, as well as removing any effects inherent in H - bonding solvents. The vibrational cooling kinetics of [Ru(dpb) 3 ] 2+ were monitored in the nitrile se ries as a function of excitation energy. The summary of these results can be found in Table 4.4 and Fig. 4.9 . In these solvents, VC is observed to display little to no pump wavelength dependence. The time VC for vibrational cooling signal) make comparisons difficult, if VC are observed, it does appear as if the time constant is lengthened slightly in BuCN relative to MeCN and PrCN. Taken VC VC = 1.6 ps. These comparisons are perhaps sug gestive of an intermediate vibrational cooling lifetime in BuCN but should be viewed with skepticism without smaller error bars. Interestingly, the average values of VC taken for MeCN, PrCN, and BuCN versus HexCN agree well with the data collected in the alcohol solvents of corresponding viscosities. In MeOH, the vibrational cooling time constant is 2.3 ps, which is increased to 5.2 ps for EtOH. These are also the only t wo alcohol solvents that appear to be pump wavelength independent, as is observed for all of the nitriles. Based on these results, it is immediately appealing to attribute the solvation dynamics in [Ru(dpb) 3 ] 2+ in polar 206 aprotic solvents to a viscoelastic m odel, as the vibrational cooling lifetime appears to track viscosity. The appropriateness of that assignment will be discussed further below. Table 4.4. Vibrational cooling time constants for [Ru(dpb) 3 ](BAr F ) 2 in the nitrile solvents with varying viscosit Solvent (cP) a VC (ps) exc = 400 nm exc = 480 nm exc = 550 nm MeCN 0.369 1.2 ± 0.4 1.5 ± 0.3 2.3 ± 1.6 PrCN 0.294 0.9 ± 0.4 1.7 ± 0.5 1.8 ± 0.7 BuCN 0.553 4.2 ± 2.5 2.3 ± 1.4 3.4 ± 1.5 HexCN 0.912 5.8 ± 1.0 5.8 ± 1.6 7.4 ± 4.0 a Taken from r ef. 40 . Figure 4. 9 . Vibrational cooling kinetics of [Ru(dpb) 3 ](BAr F ) 2 in the nitrile solvents (diamonds) with their fits (traces) upon excitation at 480 nm: MeCN (red) = 1.5 ± 0.3 ps, PrCN (green) = 1.7 ± 0.5 ps, BuCN (blue) = 2.3 ± 1.4 ps, and HexCN (purple) = 5.8 ± 1.6 ps. 207 4. Discussion 4.1 Dual Solvation Mechanism The vibrational cooling dynamics of [Ru(dpb) 3 ] 2+ have an apparent dependence on both the nat ure of the polar solvent (protic vs. aprotic) and the excitation wavelength. The latter dictates the amount of excess vibrational energy put into the system, whereas the former determines the mechanism whereby that energy may be dissipated. In the nitriles at all excitation wavelengths, and in the alcohols at the lower pump wavelengths, one trend appears; in the alcohols at the highest pump energy, another. The former shows the vibrational cooling time constant to increase monotonically as the chain length VC increases from MeOH to EtOH to 1 - BuOH, and then remains constant from 1 - BuOH to 1 - OctOH. Maroncelli and coworkers have previously affirmed that solvation rates are dependent only the nature of the solvent, not the solvent. 10 Clearly in this instance, that assertion cannot be true. To understand the intricacies of the dual solvation mechanism at work in these data, the vibrational cooling time constant must be correlated to different solvent parameters. It is evident exc = 480 and 550 nm than the 400 nm data, and vice versa. In some instances, bulk constants are not known for the longer - chain solvents , specifically 1 - HexOH, 1 - OctOH, and HexCN. The solvent polarity, P( ), 9, 39, 41 and polarizability, R( n ), 41 are often found to be highly correlated t o the rate of solvent relaxation. These parameters can be solved simply via eqns. (4.1) and (4.2) : (4.1) (4.2) in which the polarity is a function of the static di electric constant ( 0 ), and polarizability is a function of the index of refraction ( n VC and polarity and polarizability 208 of all of the solvents are displayed in Figs. 4.10 and 4.11 , respectively. Modest correlations are observed for the vibrational cooling time constant versus polarity in Fig. 4.10 at the lower excitation wavelengths, as given by the coefficient of determinatio n, R 2 , being ~0.8 in both. The exc = 400 nm, where R 2 = 0.57. This indicates that a polar solvation mechanism is at work as the phenyl rotates while in the 3 MLCT excited state. VC on polari zability ( Fig. 4.11 ) is much weaker, with R 2 when the excitation wavelength is 400 and 480 nm both being approximately 0.38, and only moderately better with R 2 exc = 550 nm. This is likely a worse fit of the data due to the wavelength - dependence of n , where the values used to calculate R( n ) being taken at 589 nm in most instances. 40 Figure 4. 10 . Correlation of the vibrational cooling time constant to the solvent polarity as a function of exc = 400 nm (purple) fit with R 2 exc = 480 nm (blue) fit with R 2 exc = 550 nm (green) fit with R 2 = 0.80. 209 Figure 4. 11 . Correlation of the vibrational cooling time constant to the solvent polarizability as a exc = 400 nm (purple) fit with R 2 exc = 480 nm (blue) fit with R 2 exc = 550 nm (green) fit with R 2 = 0.52. No value of n , and therefore R( n ), could be found for 1 - HexOH, 1 - OctOH, or HexCN. A relationship can be made between the vibrational cooling time constant and the viscosity of the solvent ( Fig. 4.12 ). In this case, solvation of the phenyl rotation follows a power law, as has been described previously. 9, 16, 41 This function is derived from Maroncelli and coworkers, who describe the solvation reorientation to a change in charge distribution in the solute as approximately equal to the reorganization dynamics of the solvent to a power given by the solvent dipole density. 9 The power law used to fit the data in Figs. 4.12 and 4.13 is defined as: (4.3) for which y 0 is the y - offset, A is the amplitude, and x is taken to some power. This function may VC vs. the average solvation time, a constant given for a specific probe molecule (here, Coumarin 153). 13 In both ins tances, a good correlation is found, as indicated by 210 2 in Table 4.5 2 test is a method for determining the appropriateness of a nonlinear curve to describe some data. 42 To evaluat e the null hypothesis that the data follow the 2 (equal to the number of data points less the number of fit parameters) and s is the confidence interval accord ing to the chi - squared probability distribution. The closer to 1, the higher the probability of the data fitting the model well. Take, for example, the curve fitting parameters for VC exc 2 = 11.81, d = 3, s o the probability that the vibrational cooling data will fit the power - law function with respect to average solvation time is 0.992, or a 99.2% chance that this model describes these data well. Viscosity values could be found for all the solvents, so d = 6 here, whereas the average solvation time was only available for 6 of the solvents, making d = 3. Table 4.5 shows that the power law with respect to both viscosity and average solvation time describes the vibrational coolin g data more accurately than it does the exc = 480 VC exc = 400 nm. It is a lso notable that for the two lower excitation energies, the power that is found to describe the data is ~0.5 regardless of whether the fit is to the viscosity or the average solvation time; in the case of the higher excitation wavelength, the power is now closer to - 0.3 for these fits. This parameter, as described by Maroncelli and coworkers, 9 is meant to indicate the solvent dipole density. Considering the same solvents are used between the three different excitation wavelengths, it seems more reasonable to assume that the power has changed as a response to the fact that the nature of the solv ent reorientation is different between these two excitation regimes. 211 Figure 4. 12 . Correlation of vibrational cooling time constant of [Ru(dpb) 3 ](BAr F ) 2 with solvent exc = 400 nm are shown in exc exc = 550 nm are in green. Figure 4. 13 . Vibrational cooling time constant of [Ru(dpb) 3 ](BAr F ) 2 versus the average solvation time (taken from r ef s . 13 and 43 exc = 400 nm (purple), exc exc = 550 nm (green). 212 Table 4.5. 1 VC versus viscosity ( and average solvation time, , 13 using eqn. (4.3) . exc Fit Parameter 1 vs. 1 vs. VC vs. VC vs. 400 nm y 0 - 0.1 ± 81.1 0.3 ± 0.2 12.9 ± 5.1 17.6 ± 138 A 0.3 ± 81.2 - 0.1 ± 0.2 - 7.5 ± 5.4 - 14.7 ± 139 power 0.04 ± 8.81 - 0.5 ± 1.1 - 0.4 ± 0.3 - 0.1 ± 0.7 2 0.110 0.044 6.14 11.81 480 nm y 0 - 0.3 ± 2.0 - 0.8 ± 7.1 - 0.8 ± 3.0 1.0 ± 1.7 A 0.6 ± 2.0 1.0 ± 7.1 5.0 ± 3.3 1.0 ± 1.7 power 0.20 ± 0.64 0.1 ± 0.3 0.7 ± 0.3 0.4 ± 0.4 2 0.068 0.014 14.4 2.94 550 nm y 0 - 0.3 ± 2.0 0.9 ± 12.3 - 8.7 ± 7.9 1.5 ± 1.2 A 0.5 ± 2.0 - 0.7 ± 12.3 14.9 ± 8.3 0.8 ± 0.9 power 0.13 ± 0.50 - 0.04 ± 0.7 0.3 ± 0.1 0.6 ± 0.3 2 0.012 0.011 7.01 5.42 A general polar solvation model is given in Scheme 4.2 . Here, the molecules are randomly oriented around the dication [Ru(dpb) 3 ] 2+ complex in its ground state, largely with their negative dipoles pointed toward the chromophore . Immediately upon excitation, a major charge redistribution occurs in the complex, but this instantaneous dipole moment is formed before the solvent can reorient, creating a Franck - Condon state in which the solvent molecules are still positioned as they w ere pre - excitation. The inertial solvent response likely occurs concomitantly 213 with the 1 3 MLCT intersystem crossing. Vibrational cooling along this lowest energy excited state will also drive solvation relaxation such that the 3 MLCT is stabilized by th e solvent. This relaxation mechanism of the solvent is what we are attempting to determine from the vibrational cooling data for [Ru(dpb) 3 ] 2+ . Scheme 4.2. The d ielectric solvent mechanism present in [Ru(dpb) 3 ](BAr F ) 2 in alcoholic solvents at high excitation energy. As outlined in the introduction, solvent can affect excited state dynamics in two ways: static solvation affects the energetics of the states, and dynamic solvation influences the kinetics of the reaction. The energetic stabilization afforded by the solvents, as described in Table 4.2 , is less than 2% between MeOH and 1 - OctOH; this cannot possibly be responsible for an increase of a factor of four in the vibrational cooling time constant at the highest energy excitation wavelength, ex c = 550 nm. Static solvation is clearly not the primary factor in these data, leaving dynamic solvation models. Previously, the power - law de pendence of an excited state process has been correlated to both the viscosity and average solvation time for peridinin in a variety of solvents. 41 This chromophore undergoes a torsional 214 event that facilitates excited state evolu tion. The relationship to viscosity suggested that solvent friction hindered the torsion of the molecule, whereas a stronger association to the average solvation time indicated that the twisting of this charge - redistributed state also produced solvent reor ientation. A similar analysis can be performed on the vibrational cooling dynamics observed in [Ru(dpb) 3 ] 2+ . It is evident from Fig. 4.10 that a polar solvation model is appropriate to describe this excited state evolution, part ex c = 480 and 550 nm. More specifically, the strong VC at these excitation energies on viscosity demonstrates that the twisting of the phenyl ring during the vibrational cooling process is increasingly encumbered due to f riction from the longer alkyl chains of the solvent. It seems highly probable that the large - amplitude motion of the aryl rotation forces the solvent molecules to translate away from the chromophore. This viscoelastic diffusion process is almost nonpolar i n nature. 16 However, the dynamics observed ex c = 480 and 550 nm do not appear to follow a nonpolar mechanism as this type of response is directly proportional to the solvent viscosity. It is also relatively common for nonpolar solvation dynamics to become nonexponential in highly viscous solvents; 17 one would expect that in these data for 1 - OctOH, but biexponential kinetics are clearly descriptive of the data. The data given by Table 4.5 VC and the average solvati ex c = 480 and 550 nm. In addition to the viscosity - induced dynamics in these data, it is apparent that the solvent must also reorient to the large instantaneous dipole moment in the MLCT excited state of [Ru(dpb) 3 ] 2+ ( Scheme 4.2 ). This is not unexpected given that these dynamics are indicative of a polar solvation mechanism. ex c = 400 nm do follow the power - law dependence to viscosity as is seen upon excitation at 480 or 550 nm, a stronger cor relation is made instead to the average 215 solvation time, which implies that the solvent reorientation to the charge distribution of the MLCT is more prominent at this excitation wavelength than solvent translation. This is only observed in the alcohols, lik ely because the nitriles only span a limited viscosity range relative to the alcohol solvents. It can therefore be concluded that solvent reorientation (like by rotation) occurs as a response to the dipole moment of the MLCT excited state in [Ru(dpb) 3 ] 2+ a t every excitation wavelength, in every solvent. The lower energy excitation wavelengths incur a greater viscoelastic VC in the alcohol series upon excitation at 400 nm is curious, howe ver. To the best of our knowledge, this type of solvation response has not been previously reported. It would appear that for the longer - chain alcohols upon higher energy excitation exhibit a reorientation that is alkyl length - independent. A rotation about C - O bond to point the polar - OH head toward the charged chromophore seems to be the most likely response. This reorganization of the solvent becomes insensitive to the length of the alkane after a certain point specifically after four carbons, (CH 2 ) 3 CH 3 . There are a few possibilities as to why ex c = 400 nm only. The first is that the nature of the upper 1 MLCT excited state is substantially different from the lower excited states, inducing more specific solute - solvent interactions. The second is the possibility of an alternate relaxation pathway being accessed from 1 MLCT 1 to the lowest energy excited state, driving the solvent reorientation. Finally, the amount of excess energy supplied to the 1 MLCT state relative to th e 3 MLCT forces the solvent to reorganize in the most efficient method available, a process which is not necessary when exciting at 480 or 550 nm. The third seems the most probable, but a combination of all three could be possible and will be explored furth er. 4.1.1 Anomalous Trend in the Shorter Kinetic Component Finally, the shorter time component in the ultrafast TA data must be discussed. This 216 component was found by Damrauer and McCusker to be 200 ± 50 fs in [Ru(dpb) 3 ] 2+ and <120 fs in the methylated ver sion of the complex, [Ru(dmb) 3 ] 2+ : an assignment was never made. 8 This feature, despite being <10% of the kinetic contribution, has an outsized amplitude, as shown in Table 4.6 1 follows separate trends for the different pump wavelengths dependi ng on the solvent series. Table 4.6. vibrational cooling transient absorption data for [Ru(dpb) 3 ] 2+ in alcohol and nitrile solvents. Solvent Series exc (nm) A 1 (%) A 2 (%) 1 (%) 2 (%) Alcohols 400 59 41 5 95 480 54 46 8 92 550 47 53 4 96 Nitriles 400 66 34 5 95 480 49 51 8 92 550 64 36 5 95 Despite using a laser system with shorter pulses, and therefore a shorter IRF, the order of 1 did not change, and in some cases increased ( Table 4.7 ). On average, this time constant was larger for the alcohol solvents with respect to the nitriles; this is however a somewhat dangerous statement as the error bars on the average data do not necessarily convey statistically significant values. While it ma y initially be appealing to assign this lifetime to 1 3 MLCT 1 exc = 550 nm, for which excitation directly populates the 3 MLCT excited state such that there is no intersystem crossing process. It is likely that this kinetic component reflects a combination of processes: inertial solvent response 217 (60 - 90 fs in MeCN 44 - 46 ) and 1 3 MLCT intersystem crossing at the higher excitation energies (<100 fs 14,15 ) are the two most likely processes. While 100s of fs is typical of IVR, [Ru(dpb) 3 ] 2+ is homoleptic, which reduces the chance that this relaxation process would be observed. 24 These time constants, while not being able to be assigned through the methods used here, have been definitively determined for this compound, paving the way for future studies to gain further insight into the photophysical processes of [Ru(dpb) 3 ] 2+ . Table 4.7. Short - 1 ) of [Ru(dpb) 3 ](BAr F ) 2 as a function of solvent and excitation wavelength. Solvent 1 (ps) exc = 400 nm exc = 480 nm exc = 550 nm MeOH 0.42 ± 0.15 0.33 ± 0.14 0.14 ± 0.08 EtOH 0.23 ± 0.13 0.45 ± 0.17 0.26 ± 0.11 1 - BuOH 0.33 ± 0.10 0.41 ± 0.06 0.30 ± 0.13 1 - HexOH 0.23 ± 0.22 0.61 ± 0.23 0.35 ± 0.26 1 - OctOH 0.15 ± 0.09 0.50 ± 0.32 0.32 ± 0.29 MeCN 0.11 ± 0.02 0.20 ± 0.11 0.14 ± 0.07 PrCN 0.05 ± 0.03 0.14 ± 0.07 0.10 ± 0.06 BuCN 0.18 ± 0.05 0.15 ± 0.05 0.21 ± 0.15 HexCN 0.19 ± 0.11 0.18 ± 0.05 0.15 ± 0.02 Alcohols 0.27 ± 0.10 0.46 ± 0.10 0.27 ± 0.08 Nitriles 0.13 ± 0.07 0.17 ± 0.03 0.15 ± 0.05 All (Alcohols and Nitriles) 0.21 ± 0.11 0.33 ± 0.17 0.22 ± 0.09 4.2 [Ru(dmesb) 3 ] 2+ : Determining the Nuclear Coordinate of Vibrational Cooling One assumption prevalent throughout this discussion is that the vibrational cooling 218 dynamics occur along the phenyl - bipyridine dihedral angle nuclear coordinate. This mode was identified by Damrauer and McCusker as the most probable due to an increased rate of vibrational energy relaxation in [Ru(dpb) 3 ] 2+ relative to [Ru(dmb) 3 ] 2+ . 8 From these data it was postulated that the aryl rotation actually facilitated vibrational cooling in this complex, and thus the process was less efficient in the methylated analogue. Based on the discussion of solvation dynamics above, the large - amplitude motion inherent in phenyl torsion is a prime candidate for redistributing energy into the bath. However, this hypothesis has not been directly verified. In its coplanar form in the thermalized 3 MLCT, the ligand likely exists in resonance with a form taking on a double - bond between the bipyridine and the phenyl. In this case, femtosecond stimulated Raman spectroscopy would be ideally suited to observe the gro wth of the C=C bond formation. 47 If the frequency for this stretch is seen on the same timescale as the vibrational cooling dynamics here, it seems very likely that the primary vibrational mode associated with this process is the phenyl twisting. In the absence of this technique, the age - old inorganic chemistry trick is to prepare and study analogues. We have done just that with the mesityl version of the complex in question, [Ru(dmesb) 3 ] 2+ . The methyl groups substituted in the ortho - positions of the peripheral phenyls inhibit rotation and ultimately reduce the delocalized nature of the excited state for this complex with respect to [Ru(dpb) 3 ] 2+ . When thinking about the nature of the mesity l group as a substituent, it is not immediately apparent how it should behave. Based on the ground state crystal structure, the ring is canted ~61° relative to the bipyridine backbone, which will greatly decrease any resonance effects that might have occur red from the extended conjugation. This is especially true with respect to [Ru(dpb) 3 ](PF 6 ) 2 , for which the peripheral phenyl - bipyridine torsion is only approximately 32°. With the methyl groups, it might have been anticipated that the mesityl moiety could be slightly 219 more electron - donating than the simple phenyl group but being oriented closer to orthogonal to the bpy backbone, those effects are expected to be drastically reduced. In such a case, it might actually be more reasonable to approximate the mesit yl simply as a bulky, greasy substituent with attenuated conjugation in comparison with the phenylated complex. This is confirmed by the ground state absorption spectrum of [Ru(dmesb) 3 ] 2+ ( Fig. 4.14 ), which shows a lowest energy MLCT maximum much closer in energy to that of [Ru(bpy) 3 ] 2+ than [Ru(dpb) 3 ] 2+ , implying that whatever conjugation is present in the excited state is greatly reduced relative to the phenyl complex. Figure 4. 14 . Ground state absorption spectra of [Ru(bpy) 3 ] 2+ (black), [Ru(dpb) 3 ] 2+ (blue), and [Ru(dmesb) 3 ] 2+ (yellow) in MeCN, normalized to the maximum of the lowest energy 1 MLCT in the excited state: 286 and 450 nm in [Ru(bpy) 3 ] 2+ , 292 and 459 in [Ru(dmesb) 3 ] 2+ , and 310 and 475 nm in [Ru(dpb) 3 ] 2+ . The vibrational cooling dynamics were studied for [Ru(dmesb) 3 ](BAr F ) 2 in MeOH, 1 - 220 OctOH, and MeCN at the same excitation wavelengths used previously namely, 400, 480, and 550 nm. As is evident from these data, the kinetics in 1 - OctOH were highly non - biexponential and showed the same slow rise ( Fig. 4.15 , Table 4.8 ) that was obser ved in [Ru(dpb) 3 ] 2+ . This may indicate a nonpolar solvation mechanism in this case, which would be unsurprising in the nonpolar nature of both the mesityl and 1 - OctOH but would be startling in the fact that the nature of solvation has completely changed simply via ligand substitution in a transition metal complex. Figure 4. 15 . Vibrational cooling dynamics in [Ru(dmesb) 3 ](BAr F ) 2 in 1 - OctOH at 532 nm upon excitation at 480 nm. The data (black diamonds) appear to rise slowly with a multiexponential fit (red trace) that was greater than the delay of the stage. 221 Table 4.8. Summary of the short - time kinetics observed upon probing at 530 nm in [Ru(dmesb) 3 ] 2+ . Solvent ex c (nm) 1 (ps) 2 (ps) 3 (ps) 4 (ps) MeOH 400 0.04 ± 0.05 2.0 ± 1.4 480 0.26 ± 0.23 31 ± 17 550 a <0.11 N/A 1 - OctOH 400 b N/A N/A 480 <0.11 48 ± 21 335 ± 375 1520 ± 180 550 0.05 ± 0.03 12 ± 7 145 ± 40 MeCN 400 c 0.09 ± 0.03 6.0 ± 0.7 480 0.10 ± 0.04 5.1 ± 1.3 550 0.10 ± 0.04 6.3 ± 4.3 a The kinetics were within the IRF of the system. No longer - time component was observed. b Unfortunately data could not be collected at this excitation wavelength due to laser stability. The kinetics observed at the lower energies were unusual (see text for details). c From r ef. 31 . The kinetics appeared well - behaved in both MeOH and MeCN, though. In each of these solvents, biexponential kinetics were observed. The difference here is the shape of the signal, in which the initial a mplitude is large and decreases by only a small amount to the long - lived trace representing the thermalized 3 MLCT excited state ( Fig. 4.16 ). This signal was also observed by Damrauer previously. 31 Disre garding the data in 1 - 1 is relatively unchanged in [Ru(dmesb) 3 ] 2+ relative to [Ru(dpb) 3 ] 2+ . It is not unexpected for the inertial response of the solvent 222 and intersystem crossing of the complex to be unchanged with only the addition of methyl subst 2 , which is VC . At all excitation wavelengths in MeCN, this time constant is longer than was observed in [Ru(dpb) 3 ] 2+ . The same trend is observed in MeOH upon exci tation at 480 nm. The VC exc = 550 nm is explained by the steady state absorption spectrum of [Ru(dmesb) 3 ] 2+ ( Fig. 4.17 ). The excitation wavelengths were kept consistent with what was used to study [Ru(dpb) 3 ] 2+ ; the ground state absorption spectrum of [Ru(dmesb) 3 ] 2+ is somewhat blue - shifted relative to the phenyl complex. This will reduce the amount of excited state population produced, particularly at 550 nm. Furthermore, at this energy, the lowest vibrational modes of the 3 MLCT excited state are being formed, which means very little excess energy will exist to be dissipated to the solvent. It does appear that vibrational cooling dynamics were observed in MeCN, however, despite the spectrum in these two solvents being nearly superimposable in this region of the spectrum. The lowest - energy MLCT band is broadened toward the red in 1 - OctOH, and also displays a greater oscillator strength at shorter wavelengths. 223 Figure 4. 16 . Vibrational cooling dyn amics of [Ru(dmesb) 3 ](BAr F ) 2 in MeCN upon excitation at 480 nm with probing at 530 nm. Initially the amplitude of the signal is relatively high but decays with biexponential kinetics to a long - lived signal. Figure 4. 17 . Ground state absorption spectra o f [Ru(dmesb) 3 ] 2+ normalized to the maximum of the lowest - energy MLCT band. The data presented are of the complex in MeOH (blue), 1 - OctOH (red), and MeCN (green). 224 [Ru(dmesb) 3 ] 2+ affords a complex that is similar in shape and size to [Ru(dpb) 3 ] 2+ , but effectively reduces the degree of conjugation in the excited state. This should reduce the driving force toward ring rotation and slow the vibrational cooling kinetics. In fact, this does appear to be VC is elongated relative to that of [Ru(dpb) 3 ] 2+ . The vibrational cooling observed in 1 - OctOH is greatly hindered to the point of perhaps achieving a nonpolar solvation mechanism. These data serve to verify the fact that the vibrational cooling process being observed is occurring along the phenyl - bipyridine dihedral angle coordinate. The exception based on Table 4.8 VC in MeOH upon excitation at 40 0 nm. These data were the anomaly in [Ru(dpb) 3 ] 2+ as well, and lifetimes in 1 - OctOH for [Ru(dmesb) 3 ] 2+ are still desired in order to better inform the assignment of solvation. However, based on this single (reproducible) data point, we are postulating that the vibrational dynamics observed are less due to any torsion of the mesityl as this should occur on a longer timescale , but are actually the reorientation of the solvent, as was seen at this excitation wavelength in the alcohol data for [Ru(dpb) 3 ] 2+ . In this way, the two complexes maintain similar solvation dynamics. 4.3 Further Understanding of [Ru(dpb) 3 ] 2+ 4.3.1 Ground State Recovery With an understanding of how the solvation mechanism proceeds in [Ru(dpb) 3 ] 2+ , the obvious next step was to determine why a dual response is observed based apparently on excitation wavelength. While the amount of excess energy provided to the chromophore via the excitation pulse is likely a contributing factor, it was necessary to determine if any other inherent differences were present. The two that immediately presented themselves are a significantly different excited state is populated or an alternate relaxation pathway is followed upon exciting at 400 nm, driving 225 local solute - solvent interactions. TD - DFT was performed on both [Ru(dpb) 3 ] 2+ and [Ru(dmesb) 3 ] 2+ with help from S. Li. The ground state geometry was taken from the X - ray crystal structures, and the excited state geometry was optimized. No imaginary frequencies were found, meaning a global minimum was f ound for the geometry. Due to the soft potential in the geometry calculation from the aryl rotation, the excited state geometry for [Ru(dmesb) 3 ] 2+ is in the process of being determined. The ground state absorption spectrum was calculated from the TD - DFT tr ansitions for [Ru(dpb) 3 ] 2+ , as shown in Fig. 4.18 , and was found to reproduce the experimentally - observed absorption spectrum well . No offset was applied though has been observed previously in calculations of Ru(II) - based chromop hores. 25 The oscillator strength of the triplet transitions are defined as zero due to their spin - forbidden nature. Figure 4.18. Overlay of the experimentally - determined ground state absorption spectrum of [Ru(dpb) 3 ] 2+ in MeCN (black trace) with the singlet (blue triangles) and triplet (red circles) transitions from time - dependent DFT calculations. 226 Orbital pictures corresponding to the transitions at the three excitation energies used in the ultrafast studies were calc ulated and are shown in Fig. 4.19 . At 400 nm, one transition is found with a 49% probability. The ground state is predominantly in nature, which then populates an excited state that is symmetrically distributed on the bpy b ackbone of all three dpb ligands. The that is supposed to be achieved by excitation at 400 nm, it is expected that a metal - centered ground state is excited to po - centered state. The results from TD - DFT appear to be consistent with what is expected upon excitation at 400 nm. Two 480 nm - based transitions were calculated, and each required two orbital pictures to be well - described, resulting in a to tal of four orbital pictures at 480 nm each with approximately 20% probability. In these transitions, two of four ground states are , whereas the other two are another metal - centered state, the exact nature of which is unknown. As with the 400 nm exci tation transition, the excited state s in the 480 nm transitions are largely centered around the bpy backbone of the ligands. It is notable, however, that for the 480 nm calculated excited states, the orbital pictures are asymmetric about the bipyridines. T moieties, as opposed to the symmetric distribution observed in the 400 nm transitions. Despite this asymmetry, the general picture described by the TD - DFT calcu lations is consistent with the metal - centered orbital - to - ligand - Finally, the 550 nm transition is well - described by one orbital picture with a 42% probability. Unlike the other two e xcitation energies, this transition is a triplet absorption, meaning the oscillator strength is defined as 0. The ground and excited states are very analogous to those in the 400 nm transition, in that a metal - centered - based excited state in the bpy backbone of the dpb ligand. 227 Figure 4.19. Orbital pictures of [Ru(dpb) 3 ] 2+ transitions as calcula ted from TD - DFT. The 400 nm o 480 nm absorptions are singlet transitions found at 464.15 The bottom two 480 nm absorptions are singlet transitions found at 463.6 nm with f = 0.3088 228 With the successful application of TD - DFT calculations to understand the transitions in [Ru(dpb) 3 ] 2+ , the method was applied to [Ru(dmesb) 3 ] 2+ in order to gauge the relative importance of the phenyl - bipyridine dihedral angle. Out of these calculations, the ground state absorption spectrum was calculated ( Fig. 4.20 ) and reproduces the experimentally - obtained spectrum well. No offset was applied to the calculated sp ectrum. Figure 4.20. Overlay of the experimentally - determined ground state absorption spectrum of [Ru(dmesb) 3 ] 2+ in MeCN (black trace) with the singlet (blue triangles) and triplet (red circles) transitions from time - dependent DFT calculations. From the ground state absorption spectrum, the orbital pictures corresponding to the three excitation energies may be calculated as well ( Fig. 4.21 ). Unlike [Ru(dpb) 3 ] 2+ , the processes in [Ru(dmesb) 3 ] 2+ only require one transition to describe each excitation energy. At 400 nm, an initially - formed metal - centered ground state (perhaps of the type) is excited to form a - based excited state that resides solely on the bipyridine backbone of the dmesb ligands. This 229 description mimics the expected M(d) - [Ru(dmesb) 3 ] 2+ . The process occurring a t 400 nm is believed to excite into a singlet state due to the oscillator strength of transition, which matches well with the calculated oscillator strength from TD - DFT, with f = 0.0271. The orbital pictures that describe the transitions at 480 and 550 nm excitation are very similar, and may be taken together, despite the fact that excitation at 480 nm is a singlet - singlet transition, whereas a 550 nm pump will prepare the 3 MLCT excited state. In both cases, a metal - centered ground state that is very analogous to that in the 400 nm transition (likely ) is initially present and upon excitation forms a ligand - - based. What is of particular interest is th e increasing asymmetry of the excited state upon decreasing excitation energy. In the 400 nm excited state, the orbital picture is highly symmetric with even distribution about all three bipyridine moieties. Moving to the 480 nm excited state picture, the wavefunction only resides on two bipyridines. Finally, at 550 nm excitation, two bipyridines are again required to describe the excited state, but one is more heavily favored than - based orbitals . Furthermore, the excited states of the two lower energy excitation processes incorporate more metal character than excitation at 400 nm, which shows a void around the metal center. This would imply that the instantaneous dipole exc = 480 and 550 nm is greatl exc = 400 nm. While this phenomenon is expected in general for [Ru(dmesb) 3 ] 2+ relative to [Ru(dpb) 3 ] 2+ owing to the ability of the phenyl substituents to rotate and alter the degree of conjugation in the excited state, it is surprising to see any kind of dependence of that sort on the excitation energy. It is apparent from the orbital pictures for [Ru(dpb) 3 ] 2+ ( Fig. 4.19 ) that the excited state wavefunction accesses the metal center for three out of four of the transitions used to describe the 480 nm excitation event, whereas at 400 and 550 nm, the metal only participates in the ground state. 230 Figure 4.21. Orbital pictures of [Ru(dmesb) 3 ] 2+ transitions as calculated from TD - DFT. The 400 nm absorptio probability. The 48 0 nm absorption is a sing let transition found at 467.67 nm with f = 0 ) with 35 % probability. The 55 0 nm absorption is a triplet transition found at 522.64 nm with f = 0 26% probability . From the TD - DFT results it is possible to conclude that the absorption processes for [Ru(dpb) 3 ] 2+ and [Ru(dmesb) 3 ] 2+ are dominated by 1 1 A 1 absorption for both the 400 and 480 nm excitation energies. At 550 nm excitation, however, the absorption process is 3 1 A 1 in nature, as evidenced by the weaker oscillator strength. The major result of note is the degree of asymmetry in the excited states. In the case of [Ru(dpb) 3 ] 2+ , the wavefunctions of the excited exc = 400 and 550 nm are evenly distributed among all three dpb ligands, whereas excitation at 480 nm biases the wavefunction towards only two of the three ligands. In [Ru(dmesb) 3 ] 2+ , however, the degree of asymmetry increases as the excitation energy is reduced. 231 Surprisingly, the excited state wavefunction never delocalizes to the substituents in either [Ru(dpb) 3 ] 2+ or [Ru(dmesb) 3 ] 2+ , despite the ability of the phenyl to rotate to coplanarity in th e excited state of the dpb analogue. These results are unfortunately not conclusive, but do imply that nature of the excited state prepared at each of the excitation energies may be different enough to explain the differences observed in the ultrafast solv ation dynamics previously described. To better understand the relaxation pathway incurred with different excitation energies, emission spectra were collected for [Ru(dpb) 3 ](BAr F ) 2 in MeOH and 1 - OctOH ( Fig. 4. 22 ). Excitation was p erformed at 340 nm to directly excite into the higher energy MLCT excited state. No change was observed with different pump wavelengths except differing intensities (which will be discussed thoroughly in Chapter 4 Section 4.3.2 ). The emission maximum is 10 nm blue - shifted in MeOH relative to 1 - OctOH. No other differences are observed here, indicating that emission is occurring from the same excited state, here the 3 MLCT, regardless of which state is formed upon excitation. A spe ctral overlay of the steady state emission and absorption spectra of [Ru(dpb) 3 ] 2+ in 1 - OctOH is shown in Fig. 4. 23 . Similar features are observed in the spectra for MeOH (not shown). 232 Figure 4. 22 . Steady state emission spectra of [Ru(dpb) 3 ](BAr F ) 2 exc = 340 nm (red), 470 nm (orange), and 550 nm (yellow), and in 1 - exc = 340 nm (green), 470 nm (blue), and 550 nm (purple). The emission spectra showed no dependence on excitation wavelength; the maximum in MeOH is 630 nm and is 640 nm in 1 - OctOH. 233 Figure 4. 23 . Overlay of the steady state absorption (red trace) and emission (blue trace) of [Ru(dpb) 3 ](BAr F ) 2 in 1 - OctOH. The lowest energy MLCT transition and the emission maxima are normalized to each other. To further clarify any pump wavelength dependence in the emission data, excitation spectra were collected in MeOH ( Fig. 4.2 4 ) a nd 1 - OctOH (not shown). In this experiment, the intensity at the emission maximum is reported as a function of excitation wavelength. The excitation spectrum should overlay nearly perfectly with the ground state absorption spectrum, as is observed in Fig. 4.2 4 . Any deviation indicates either an impurity, or emission from the chromophore in a different form. The disparity occurring at higher excitation wavelengths may be caused by a [Ru(dpb) 3 ] 2+ conformer in which the phenyl - bipyri dine dihedral angle is nearly 90º but is more likely explained by the fact that the absorbance at higher energy is outside the acceptable sensitivity range of the UV - Vis spectrophotometer. In either case, at the excitation wavelengths of interest, no impur ity or second conformational species is present, thus the pathway to the emissive 3 MLCT excited state must be consistent between the different pump energies. 234 Figure 4. 24 . Overlay of the ground state absorption (red, left axis) and excitation emission (bl ue, right axis) spectra of [Ru(dpb) 3 ](BAr F ) 2 in MeOH. The spectra match moderately well for ~340 - 550 nm, indicating the phosphorescence process from the 3 MLCT is well - behaved (see text for more details). 4.3.2 1 3 MLCT Intersystem Crossing The original motivation in studying the photophysical pr operties of [Ru(dpb) 3 ] 2+ was its reported quantum yields in [Ru(dpb) 3 ] 2+ . Cook and coworkers initially prepared this complex and 5 Alternatively, Damrauer et al. report a quantum yield for the same compound as being 0.20 ± 0.02. 6 This value is intrinsically dependent on such factors as solvent, 4 - 6, 27 temperature, 4, 27, 48 excitation wavelength, 4, 49 - 51 and the instrument detector. 27 The data presented by Cook et al. are colle cted in deaerated 4:1 (v/v) EtOH /MeOH at 293 K, whereas Damrauer and coworkers used deaerated MeCN at 298 K. A summary of these data can be found in Table 4.9 . These values were collected as relative quantum yields, in which the emission intensity of the 235 compound of interest is compared to that of a known standard. Here, the quantum yield of [Ru(bpy) 3 ] 2+ std ) well - known and thus used as a reference to determine the quantum yield of the unk ), 6, 26 according to: (4.4) for which I is the integrated emission intensity, A is the absorbance of the sample at the excitation wavelength, and n is the index of refraction of the solvent; unk and std denote the unknown and standard, respectively. The choice of reference is critica l and is meant to be nearly identical to the compound of interest. This minimizes uncertainty in the integrated intensities by calibrating the spectral sensitivity in the wavelengths that display emission. In the case of [Ru(dpb) 3 ] 2+ , the phosphorescence o f [Ru(bpy) 3 ] 2+ turns out to be a decent reference for quantum yield determination. As analogues of each other, they are emitting from the same state, and have similar max of [Ru(bpy) 3 ] 2+ 620 nm 27 and 630 nm in [Ru(dpb) 3 ] 2+ . As shown in Table 4.9 , the quantum yields for [Ru(bpy) 3 ] 2+ and [Ru(dpb) 3 ] 2+ are given for the data from Cook and coworkers, and Damrauer and coworkers, as both of these so urces calculated relative quantum yields. 236 Table 4.9. Quantum yield data and experimental setups for [Ru(bpy) 3 ] 2+ and [Ru(dpb) 3 ] 2+ . Suzuki et al. 27 Cook et al. 5 Damrauer et al. 6 This work Temperature (K) 298 293 298 298 Solvent MeCN 4:1 (v/v) EtOH/MeOH MeCN MeCN ex c (nm) 350 not specified 450 480 [O 2 ] air - free air - free air - free air - free Detector BT - CCD PMT PMT BT - CCD 3 ] 2+ 0.095 ± 0.003 0.089 0.062 ± 0.006 48 0.103 ± 0.002 3 ] 2+ N/A 0.306 0.20 ± 0.02 0.255 ± 0.006 Corrected 3 ] 2+ a N/A 0.354 0.33 ± 0.03 0.255 ± 0.006 a Calculated for using eqn. (4.5) 3 ] 2+ found in this work. Since the time of these publications, however, new studies have made use of back - thinned CCD (BT - CCD) detectors within an integrating sphere setup for the purposes of measuring abs olute quantum yields. Both of the quantum yields reported above were found using a setup that utilized a photomultiplier tube (PMT) in the detection scheme. While PMTs are good detectors for higher energy fluorescence signals, the emission from Ru(II) comp lexes comes from the 3 MLCT excited state. This phosphorescence is consequently lower energy (i.e., NIR), for which PMTs lose all spectral sensitivity. With these wavelengths, correction factors are critical to the integration of the spectra but may result in inaccurate quantum yields being reported. This is especially observable in the comparison of quantum yields for [Ru(bpy) 3 ] 2+ in Table 4.9 . When using a PMT - CCD. In the determination 3 ] 2+ , 237 however, this can be corrected through the use of eqn. (4.5) , in which the standard and sample under one set of conditions can be used, along with a standard, to find the quantum yield for a sample under a second set of conditions: (4.5) Using this relation, the corrected quantum yields for [Ru(dpb) 3 ] 2+ given the conditions used in this experiment were calculated and can be seen in Table 4.9 . This work utilized a BT - CCD detector in a setup with an integrating sphere. As such, the quantum yield in Ru(bpy) 3 ] 2+ was found to be 0 .103, which is slightly higher but still in good agreement with that found by Suzuki et al . In the case of [Ru(dpb) 3 ] 2+ , the quantum yield measured by the previous groups is a factor of three larger than that of the unsubstituted bpy complex. Although Damr auer and coworkers report a significantly smaller quantum yield, this can easily be attributed to both solvent and temperature. The quantum yield of [Ru(bpy) 3 ] 2+ has previously been shown to have a high temperature dependence, 27, 48 which is likely to be true for the phenylated complex as well. This temperature dependence is caused by energetically nearby ligand field states that depopulate the 3 MLCT when the thermal barrier is low enough (i.e., warm temp eratures). Ground state recovery from these ligand field states occurs via a nonradiative pathway, thereby decreasing the quantum yield of phosphorescence from the 3 MLCT excited state. The solvent dependence, on the other hand, is caused by the influence o f polar solvents on the charge - separated MLCT excited state. One can imagine that solvents with increased dielectric constants might better stabilize this potential energy surface relative to the ground state, as might be true for MeCN. Alternatively, spec ific solute - solvent interactions such as H - bonding in alcohols could also affect the energetics of the MCLT state, thereby shifting the energetics of the potential energy surface. 48 And in fact, the quantum yield reported by Cook et al. for [Ru(dpb) 3 ] 2+ is 0.306 in an alcohol 238 solvents are better able to stabilize the MLCT excited state su ch that there is little thermal deactivation through the ligand field states, whereas the polar aprotic solvent allows for greater mixing of these states to occur at warmer temperatures, thereby reducing the quantum yield. The degree of energetic stabiliz ation afforded by solvation is difficult to experimentally verify by ground state absorption measurements, as the 3 MLCT band is obscured by the higher energy 1 1 A 1 transition. Lifetime measurements of [Ru(dpb) 3 ] 2+ in MeCN and MeOH, however, are a more compelling as these provide a measure of k r and k nr . The use of eqn. (4.6) to determine these kinetic parameters 6, 26, 48 requires quantum yield data: (4.6) These emission and transient absorption lifetimes are given in Table 4.10 . The former are relatively constant for [Ru(dpb) 3 ] 2+ in MeOH, but vary in 1 - OctOH, particularly upon excitation at 550 nm. As a consequence, k r is found to be nearly constant in MeOH and less so in 1 - OctOH. However, this may also be a result of the change in quantum yield with different pump wavelengths, which are also proven to be more variable in 1 - OctOH than in MeOH. Originally, we had sought to perform quantum yield studies as a function of excitation energy and solvent in order to determine whether different conditions led to new relaxation pathways to the thermalized 3 MLCT. That was not found to be the case, but the studies performed herein did yield interesting results that help give new understanding to the excited state potential energy surfaces of [Ru(dpb) 3 ] 2+ . 239 Table 4.10. em abs ) lifetimes, and the radiative (k r ) and nonradia tive (k nr ) rates of [Ru(dpb) 3 ](BAr F ) 2 in MeOH and 1 - OctOH as a function of excitation wavelength. Solvent exc (nm) em abs k r ×10 5 (s - 1 ) k nr ×10 5 (s - 1 ) MeOH 400 0.244 ± 0.004 1.372 ± 0.008 - 1.78 ± 0.03 5.51 ± 0.18 480 0.243 ± 0.003 1.352 ± 0.003 1.321 ± 0.001 1.82 ± 0.02 5.66 ± 0.13 550 0.232 ± 0.006 1.380 ± 0.002 1.333 ± 0.002 1.71 ± 0.04 5.66 ± 0.27 1 - OctOH 400 0.205 ± 0.007 1.292 ± 0.008 - 1.59 ± 0.06 6.15 ± 0.38 480 0.239 ± 0.005 1.306 ± 0.006 - 1.83 ± 0.04 5.83 ± 0.23 550 0.195 ± 0.019 1.543 ± 0.005 - 1.26 ± 0.01 5.22 ± 0.90 Excitation - wavelength dependent quantum yields were found for [Ru(dpb) 3 ](BAr F ) 2 in air - free conditions in both MeOH and 1 - OctOH ( Fig. 4.2 5 ), as these represent the extreme ends of the alcohol solvent series. It is immediately apparent that the excitation energy plays a role in the quantum yield of the phosphorescence, particularly when the compound is dissolved in 1 - OctOH. exc = 350 nm, the quantum yield begins a t ~0.32, which decreases steadily to a local minimum exc exc = 440 - 500 nm, then decreases again for lower excitation energies. The error is much larger at these lower energies due to partial overlap with the emission band. Though greatly attenuated, a similar trend can be seen in the quantum yield data for [Ru(dpb) 3 ] 2+ exc = 400 - 500 nm but increases for bluer pump wavelengths and begins to decrease 240 at redder wavelengths before noise is introduced. No spectral shifting of the emission maximum was observed as a function of the excitation wavelength, which would affect the integrated area of the curve. Thus, the quantum yield dep endence on the pump energy was found to be truly inherent in [Ru(dpb) 3 ] 2+ . This phenomenon had not been previously reported for [Ru(bpy) 3 ] 2+ , so the quantum yield for this compound was measured in MeCN as a function of excitation wavelength ( Fig. 4.25 ). Indeed, no pump energy dependence is observed, indicating that this behavior is reserved for the phenyl - substituted complex. Figure 4. 25 . Quantum yields measured for deaerated [Ru(dpb) 3 ](BAr F ) 2 in MeOH (red diamonds) and 1 - OctOH (blue diamonds) depicting the excitation wavelength dependence, particularly in 1 - OctOH. These are shown in comparison to the quantum yield of air - free [Ru(bpy) 3 ](PF 6 ) 2 in MeCN which displays no excitation wavelength dep endence. To better understand the significance of the quantum yield dependence on excitation wavelength, Table 4.11 displays the values calculated for [Ru(dpb) 3 ] 2+ in MeOH and 1 - OctOH, 241 exc used in the tra nsient absorption experiments. Analogous data for [Ru(bpy) 3 ] 2+ in MeCN are given for comparison. The quantum yield for [Ru(bpy) 3 ] 2+ is unchanged value. Thi s is the only consistency between the data for the four solvents. As was observed in Fig. 4.2 5 - independent, whereas excitation at 480 nm in 1 - OctOH produces the highest quantum yield of th e three wavelengths. The trend observed in 1 - OctOH is amazingly also observed in MeCN ( Fig. 4.26 ). In BuCN, however, the highest quantum 3 ] 2+ appears to simply exc exc = 480 nm, followed by a systematic decrease at lower excitation energies. These data would imply that, at least with respect to quantum yields, [Ru(dpb) 3 ] 2+ in MeCN behaves much more similarly to 1 - OctOH than to either MeOH or BuCN, a very surprising result. Table 4.11. Quantum yield of deaerated [Ru(dpb) 3 ](BAr F ) 2 as a function of solvent and excitation wavelength relative to air - free [Ru(bpy) 3 ](PF 6 ) 2 i n MeCN. Solvent exc 400 nm 480 nm 550 nm MeOH 0.244 ± 0.004 0.243 ± 0.003 0.232 ± 0.006 1 - OctOH 0.205 ± 0.007 0.239 ± 0.005 0.195 ± 0.019 MeCN 0.222 ± 0.010 0.255 ± 0.006 0.180 ± 0.009 BuCN 0.296 ± 0.017 0.267 ± 0.009 0.242 ± 0.030 [Ru(bpy) 3 ] 2+ in MeCN 0.108 ± 0.004 0.103 ± 0.002 N/A 242 Figure 4. 26 . Excitation wavelength - dependent quantum yields of deaerated [Ru(dpb) 3 ](BAr F ) 2 in MeCN (red diamonds) and BuCN (blue - diamonds) as compared to the quantum yield of deaerated [Ru(bpy) 3 ](PF 6 ) 2 in MeCN (black diamonds) that is independent of the excitation wavelength. The structure observed for in the excitation - dependent quantum yield s for [Ru(dpb) 3 ] 2+ is reminiscent of the ground state absorption profile of the complex. Fig. 4.27 shows an overlay of the two spectra collected in 1 - OctOH. The local maxima and minima appear to mimic each other: the quantum yiel exc = 350 nm, which is the central wavelength of the higher energy 1 exc = 400 nm, which is a local minimum of the steady state absorption spectrum. The rise in quantum yield followed by subsequent plateau follows the rise of the lowest energy 1 MLCT peak. And finally, the 3 1 A 1 transition coincides with the lowest quantum yields for [Ru(dpb) 3 ] 2+ . 243 Figure 4. 27 . Overlay of the ground state absorption spectrum (blue trace, left axis) of [Ru(dpb) 3 ](BAr F ) 2 in 1 - OctOH with the excitation wavelength - dependent deaerated quantum yield (red diamonds, right axis). There is a modest agreement between the trends of both. It is highly unusual for chromophores to display excitation wavelength depend ence. Kasha - quantum yield is independent of excitation. 50 The assumption here is that regardless of the specific state that is formed upon pumping, the relaxation cascade always follows the same route to the same emissive excited state. Very few organic fluorophores have exhibited this type of behavior. One class of compounds that has recently been studied for excitation wavelength depen dent quantum yields is the napthanediimide dyes. Yushchenko et al. prepared a series of compounds of this type with various substituents on the core of the molecule. 50 They found that heavier substituents like Br - induced ultrafa st (<200 fs) intersystem crossing from the initially populated S 2 excited state into the emissive S 1 state. This was due to the heavy atom effect caused by the bromide, in which the spin - orbit coupling is increased for the Br substituted dye, which results in 244 spin mixing in the upper electronic states, allowing for faster intersystem crossing. In compounds with lighter substituents, that conversion rate was on the order of ~2 ps. The quantum yields were found to be excitation wavelength dependent in the cas e of the Br - core - substituted napthanediimide dyes, which was not the case when light substituents were used. Ultimately this was believed to be a consequence of the altered photophysical pathways upon heavy atom substitution. The heavy atom effect is not specific to organic chromophores; in fact it is often cited as the cause for increased spin - orbit coupling in second - and third - row transition metal complexes. 37 It is therefore unsurprising that excitation wavelength - dependent quantum yields have been observed previously in Ru(II) chromophores. 49, 51 Yoshikawa and coworkers prepared a heteroleptic [Ru II (bpy) 2 (biquinoline)] 2+ complex which was observed to show decreased emissio n intensity (proportional to quantum yield if the excitation conditions are held constant 26 ) with increasing excitation wavelength in the visible region. 49 When pumping in the UV part of the spectrum, d ual emission was observed. The overall excitation wavelength dependence in this complex was attributed to emission from MLCT states associated with the two different types of ligands. Malouf and Ford studied a series of [Ru(NH 3 )(py - X)] 2+ compounds in which the X substituent on a pyridyl ligand was varied to understand photosolvation reactions, which is the photoinitiated ligand dissociation and subsequent coordination by a solvent molecule. 51 The complexes for which the 3 LF was the lowest energy excited state were found to have quantum yields for photosolvation that were wholly independent of the excitation energy. For compounds with a lowest energy excited state that was MLCT in nature, the p hotolability of the ligand was drastically decreased and the photosolvation quantum yield was highly dependent on pump wavelength. This was found to be especially true at very high energy excitation, presumably 245 e nergies at which ligand - - n occurred which would increase the likelihood of photodissociation of the complex. Particularly of interest for the studies presented here, when the ligand was 4 - phenylpyridine (analogous to the dpb ligand), the quantum yield was observed to increase by a n order of magnitude from excitation at 546 to 405 nm when the compound is dissolved in dimethyl sulfoxide. These quantum yields were also dependent on solvent, as when [Ru(NH 3 ) 5 (4 - phenylpyridine)] 2+ - dimethylformamide, the quantum yie ld exc = 405 - 520 nm. Care should be taken when observing these values as the quantum yield of photosolvation in no way is equivalent to the quantum yield of emission. However, emission is occurring in these complexes, particula rly in the 4 - phenylpyridine derivative, from the MLCT excited state. When emission occurs with a high yield, then the photosolvation cannot be occurring as they require two separate lowest energy excited states. Thus, photodissociation of the pyridyl can o nly occur upon higher energy excitation in dimethyl sulfoxide, for which it is presumed the 3 LF states have been significantly stabilized relative to the MLCT manifold. These results echo what is observed in [Ru(dpb) 3 ] 2 + and may aid in the analysis of the emission quantum yields reported here. This dependence of the quantum yield on pump wavelength is believed to give an indication of the seams and conical intersections between the MLCT excited states. A seam is where two potential energy surfaces meet, mak ing it the site of population transfer from one state to the other; a conical intersection is a single point at which a transition can occur due to the meeting of the two states. 52 The potential energy surfaces for Ru(II) polypyr idyl complexes are traditionally viewed along one nuclear coordinate, but can occur along as many dimensions as there are nuclear motions to describe the complex. And while the surfaces are almost certainly nested along the standard Ru - N bond distance coor dinate ( Scheme 4.3 ), other modes such as the 246 phenyl - bipyridine torsion angle or the C=C stretching in the rings could serve to bring the potential energy surfaces into contact with each other. Based on the ultrafast intersyste m crossing observed in [Ru(bpy) 3 ] 2+ , 1, 15 it is expected for the electronic coupling between states in the MLCT manifold to be on the order of an adiabatic system. And considering the fact that this exci tation wavelength dependence for the quantum yield has previously been observed in systems with extended conjugation, 51 it is probable then that phenyl rotation and subsequent delocalization are playing a critical role in the way in which the potential energy surfaces cross, thereby affecting the fundamental photophysical processes. 247 Scheme 4.3. Simplified potential energy surface diagram for [Ru(dpb) 3 ] 2+ from ground state absorption (green dashes) and steady state emission (red dash) spectroscopy. Although not known for certain in this specific complex, it is expected that the Ru - N bond distance will decrease in the 3 MLCT due to electrostatic interactions with the oxidized Ru(III) center, as has been shown to occur in [Ru(bpy) 3 ] 2+ . 53 The following is a discussion of the possible internal conversion and intersystem crossing pathways possible in [Ru(dpb) 3 ] 2+ ; it is largely based on the quantum yiel d data for the complex in 1 - OctOH or MeCN, as these showed very similar excitation wavelength dependence. This type of analysis is generalizable for all of the solvents for which there is steady state absorption and 248 emission, transient absorption, and quan tum yield data. From the latter, it would appear as though population transfer from the upper MLCT excited state through the manifold or even directly into t he 3 MLCT such that phosphorescence occurs with a high yield, but decreases with decreasing excitation energy. With ultrafast conversion of the upper 1 3 MLCT, hot vibrational states would be created in the lowest energy excited state, providing an incre ased driving force for vibrational energy redistribution via vibrational cooling. This likely explains the predominantly dielectric solvation mechanism apparent in the alcohol series only upon excitation at 400 nm. Using Schem e 4.3 reasonable as the upper 1 MLCT electronic state is only being partially populated, with the bulk of the excitation energy putting the complex into the lower 1 MLCT 2 state. At the 4 00 nm pump wavelength, most of the excess energy is being converted to thermal energy via vibrational cooling, as per the transient absorption spectroscopy data. This will necessarily increase k nr , 1 MLCT 2 state into lower - lying excited states near this energy. At lower excitation energies the quantum yield begins to increase again, plateauing at wavelengths for which the 1 A 1 to lowest energy 1 MLCT state oscillator strength is the greatest. Another seam or conical intersection is likely to occur here, increasing the efficiency of intersystem crossing into the phosphorescent 3 MLCT excited state. Finally, at the lowest ex citation energies, the 3 MLCT state is being accessed directly. The only barrier to emission here is the nonradiative loss of excitation energy into the solvent. This analysis is based on the experimental data reported here but shows the need for rigorous c alculation of the potential energy surfaces of [Ru(dpb) 3 ] 2+ . 249 5. Future Works and Conclusions The impetus for this work was to more thoroughly understand the photophysical process of [Ru(dpb) 3 ] 2+ . As an analogue of the prototypical [Ru(bpy) 3 ] 2+ , excitatio n in the visible region initially populates the MLCT manifold, whereupon intersystem crossing into the 3 MLCT excited state may precede vibrational cooling to the thermalized lowest energy excited state. This energetic redistribution process has been found to be facilitated by phenyl rotation in the dpb ligand, leading to coplanarity and therefore extended delocalization in the 3 MLCT excited state. The timescale of vibrational cooling and ring rotation has been found to be both solvent and excitation wavelen gth dependent. At higher excitation energy (i.e., 400 nm), the polar head of the solvent reorients to the large instantaneous dipole moment of the excited [Ru(dpb) 3 ] 2+ complex. This is a much more efficient solvation mechanism, allowing vibrational cooling to occur on the same timescale in 1 - BuOH, 1 - HexOH, and 1 - OctOH, despite having varying alkyl chain lengths. Excitation at lower energies such as 480 and 550 nm induces a more viscoelastic solvent response, in which frictional forces dictate the timescale of ring rotation. Viscosity of the solvents, then, plays a critical role, with the vibrational cooling time constant increasing with a power dependence on viscosity. It was found that the viscoelastic mechanism also occurred in [Ru(dpb) 3 ] 2+ in nitrile solv ents at all of the moiety or could be caused by the lower viscosity of each of these solvents relative to the alcohol series. The latter is more likely to be true if both the dielectric and visc oelastic solvation models are acting simultaneously but one is being driven over the other by excess energy delivered to the system by the pump pulse. The three excitation wavelengths chosen for this study each populated different excited ex c = 55 0 nm corresponds to the 3 ex c = 480 nm is the 1 ex c = 400 nm excites into at least two separate 1 MLCT excited states. It was desirable to ensure that the unusual 250 solvation dynamics upon excitation at 400 nm were simply due to the driving fo rce delivered by the excess energy from the pump, as opposed to a separate relaxation pathway being accessed or a new type of excited state being formed. To address these questions, time - dependent density functional calculations were performed in a compari son of the excited states formed upon excitation at different wavelengths. The results were not conclusive, but did indicate the probability of distinctly different excited states at each of the three excitation energies. This is not unexpected when pumping into three significantly different excited states. Additionally, nanosecond emission and transient absorption spectroscopy as well as quantum yield determinations were performed on [Ru(dpb) 3 ] 2+ in various solvents at the different pump wavelengths. Both the solvent and excitation wavelength played a role in the quantum yield of phosphorescence from the 3 MLCT state. This was believed to be indicative of points of intersection between the potential energy surfaces of the excited states, where populati on transfer might occur. These seams and/or conical intersections are likely found along non - traditional nuclear coordinates, potentially the phenyl - bipyridine dihedral angle. Analysis of the quantum yield data provided the explanation of the increased dri ving force producing the dielectric solvation model ex c = 400 nm in the alcohols series of solvents. In an attempt to better define the nuclear coordinate associated with vibrational cooling, and possibly the population dynamics associated with the excitation wavelength - dependent quantum yields observed in [Ru(dpb) 3 ] 2+ , an analogous complex was prepared in which the phenyl rotation was sterically hindered. The mesitylated [Ru(dmesb) 3 ] 2+ complex was studied as a function of both solvent and p ump wavelength. The vibrational cooling time constants observed in this complex are consistently longer than in [Ru(dpb) 3 ] 2+ at each pump wavelength in MeOH, 1 - OctOH, and MeCN, implying that the phenyl rotation is not only much more sterically restricted 251 d ue to the ortho - methyl groups on the phenyl substituent, but it is also a major vibrational mode in the energy redistribution process. 1 , the shorter time component observed concomitan tly with the vibrational cooling response, showing the limitations of transient absorption spectroscopy. To parse out the photophysical process(es) occurring on this timescale , it is likely that other forms of ultrafast spectroscopies are required, such as time - resolved infrared spectroscopy 54,55 or time - resolved resonance Raman spectroscopy. 56 - 59 Additionally, two - dimensional spectroscopy (either in the visible or infrared regions) could be incredibly u seful as this tool provides an understanding of the electronic communication between excited states. 46, 60 To fully understand the surprisingly complex photophysics of [Ru(dpb) 3 ] 2+ , more structural and vibrational data are required, as well as critical computational work on the potential energy surfaces of this compound. Extended delocalization in the excited state has already shown to both increase the extinction coefficient and ex tend the spectral range of absorption for this Ru(II) chromophore, both of which are highly desirable properties in molecular dyes for photovoltaic applications. 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In work that appears to have begun by Reynal et al., the goal was to systematically increase the linkage be tween a cobalt - based d ye and the titanium dioxide ( TiO 2 ) it was bound to in order to force an electron to travel a linear path to the semiconductor, thereby reducing recombination. 1 The half - lives of these chromophores were found to increase as the di stance between the cobalt center and the TiO 2 interface increased: by adding 2 Å in linkages between the two entities, the half - life of recombination was slowed by an order of magnitude. Analogous work has been done on organic photovoltaics 2 and Zn porphyrins, 3 all showing that through delocalization, an excited state can be extended spatially from the point of origin; if the electron and hole are separated by a great enough distance, then the lifetime o f that charge - separated state will be drastically lengthened. The Schmehl group has explored the concept of this very research extensively. 4,5 They have prepared complexes of Fe(II), 6 Ru(II), 4 - 7 Os(II), 7 and Zn(II) 8 in which the ligand structure is modified by the addition of aromatics and fused rings so as to understand the effect on the - substituted terpyridine ligands were prepared in which an extended c hain of phenylene and vinylene linkers were added. 6 The photophysical properties of Rutvt were compared to those of Rutvpvt; here, t is a terpyridine, p is a phenylene, and v is a vinylene group. The emission lifetime of Rutvt wa s found to be less than 260 10 ns in aerated solution, which is comparable to the parent complex, [Ru(terpy) 2 ] 2+ considering the temporal resolution of their spectrometer. Upon addition of a phenylene - vinylene linker to form Rutvpvpt, the emission lifetime inc reased to 320 ns. This lifetime is four orders of magnitude longer than that of [Ru(terpy) 2 ] 2+ . They then prepared a Ru 2 Fe trimer, which follows their naming convention to be RutvtFetvtRu (with capping terpyridine ligands on both ruthenium atoms). This com plex was found to behave very analogously to a typical Fe(II) compound, with a very short - lived excited state absorption feature, here indicative of the metal - to - ligand charge transfer (MLCT) state. Again, by extending the distance between the Ru and Fe ce nters such that RutvpvtFetvpvtRu was prepared, the MLCT lifetime of this complex was found to be 275 ± 10 ns. These results would seem to indicate that if excited electron is removed a far enough distance from the Fe(II) center, then the complex will exhi bit a very long - lived MLCT, particularly for an iron - based system. The rationale behind this is the delocalization of the excited state wavefunction, spreading further away from the metal center, which is the physical origin of the lower - lying ligand field excited states. With enough distance between the metal and the electron, it can be imagined that the electron would lose all memory of the metal center to which it would otherwise normally return. It is quite probable that there would be limitations on th e length of conjugated ligand the electron would travel before recombining with the metal center (i.e., a Goldilocks problem). Care should be taken, though, when discussing this strategy for Fe(II) chromophores when nearly all the work thus far has been p erformed on second - or third - row transition metal - containing complexes. With the heavier atoms in place, the ligand field strength will be high enough that the lowest - energy excited states are most likely MLCT in nature. This is a point of some contention considering that the tridentate terpyridine Ru(II) complex is believed to actually relax to the ground 261 state from a triplet ligand field state, thus its very short lifetime. 9 With the complexes studied here, it is observed that t he ligand modification to extend delocalization decreases the energy of the MCLT excited state. In order for the charge - separated state to exist for hundreds of nanoseconds, the decrease in MLCT energy must be sufficient to reaffirm its status as lowest - ly ing excited state, bypassing any ligand field states. When moving to Fe(II) systems, though, the relative energetics of the MLCT and ligand field manifolds will not be quite so degenerate. The lengthening of the charge - separated lifetime in Ru(II) complexe s works because that is a system that already has MLCT states as the lowest - energy excited state, or at least energetically nearby. This is not true for iron chromophores. Any MLCT lifetime lengthening we observe here will have to be explained in terms of the nuclear coordinate, not the energetic coordinate. But in the quest to decrease the deactivation rate out of the MLCT for Fe(II) complexes, many strategies must be attempted, and here we take our inspiration from Ru(II) photophysics. 2. Experimental 2.1 Materials and Synthesis 2.1.1 General - diphenyl - - bipyridine) iron(II) hexafluorophosphate, [Fe(dpb) 3 ](PF 6 ) 2 - diquinolinyl - 2,6 - pyridine) iron(II) hexafluorophosphate, [Fe(dqp) 2 ](PF 6 ) 2 ; - quinolinyl - 2 - phenanthroline) iron(II) hexafluorophosphate, [Fe(qphen) 2 ](PF 6 ) 2 ; - (di - 2,5 - dimethylisoxazolyl) - - bipyridine] iron(II) hexafluorophosphate, [Fe(dmib) 3 ](PF 6 ) 2 - cyanoacrylic acid - - bipyridine) iron(II) hexafluorop hosphate, [Fe(caab) 3 ](PF 6 ) 2 ; bis(phenyl - trans - vinyl - phenyl - trans - vinyl - phenyl - - terpyridine) iron(II) hex a fluorophosphate, [Fe(tpvpvp) 2 ](PF 6 ) 2 . [Fe(dqp 2 ](PF 6 ) 2 and 262 [Fe(qphen) 2 ](PF 6 ) 2 were synthesized and characterized by L. Wickramasinghe of the Thummel group from the University of Houston. [Fe( d mib) 3 ](PF 6 ) 2 and [Fe(caab) 3 ](PF 6 ) 2 were synthesized and characterized by C. R. Tichnell. [Fe(tpvpvp) 2 ](PF 6 ) 2 was provided by R. Schmehl of Tu lane University. [Fe(dpb) 3 ](PF 6 ) 2 was synthesized by a route commonly employed to prepare iron(II) polypyridyl complexes. 10 Ferrous ammonium sulfate hexahydrate (Jade Scientific, ACS grade), ammonium hexafluorophosphate (Sigma - A ldrich, > 95%), and methanol (Fisher Scientific, ACS grade) were all used as received. The dpb ligand was prepared by C. R. Tichnell. 11 On a Schlenk line, the dpb ligand (0.081 mmol, 25.0 mg) was added to hot methanol (15 mL) and bubble - degassed for 15 min. This solution was heated until no white solid of the ligand was visible, indicating complete solvation. A solution of (NH 4 )Fe(SO 4 ) 2 6H 2 O (0.028 mmol, 11.0 mg) was prepared in minimal water (3 mL) under N 2 and was bubble - degassed for 15 min. The dpb solution was allowed to come to room temperature, at which time the iron solution was cannula - transferred into the ligand by positive N 2 pressure. Immediately, the solution turned a deep purple color. The comple x was allowed to stir under N 2 for 3.5 h, while the reaction was monitored by 1 H NMR spectroscopy. When the reaction was complete, a solution of NH 4 PF 6 (0.280 mmol, 45.6 mg) in water (10 mL) was added, causing the sample to appear to be a lighter pink colo r, and a precipitate to form and coat the surface of the flask. Addition water (~300 mL) was added to further induce precipitation of the product. The product was dried on a medium frit attached to a vacuum filter flask and washed with excess water. It was allowed to dry on the frit for ~ 21 h. Yield: 96% (33 mg). 1 H NMR spectra were collected on a Bruker 500 MHz NMR spectrometer. Electrospray - ionization mass - spectrometry (ESI - MS) was performed on a Waters Xevo G2 - XS Quadrupole 263 Time - of - Flight spectrometer in positive mode. HPLC grade acetonitrile and methanol were purchased from Sigma - Aldrich and used as received for spectroscopic measurements. Ground state absorption spectra were collected with a Varian (now Agilent) Cary 50 UV - Vis spectrophotometer. [Fe (dpb) 3 ](PF 6 ) 2 was recrystallized by evaporation of acetonitrile solution doped with ethanol. The single crystal was mounted in paratone oil and transferred to the cold nitrogen gas stream of the diffractometer for data collection. Single crystal X - ray diff raction was collected on suitable crystals mounted on a Bruker APEX - II CCD diffractometer with CuK radiation at the Center for Crystallographic Research at Michigan State University. The crystal structure was solved by S. Li and R. J. Staples. 2.1.2 Char acterization of Free Ligands and Complexes - diphenyl - - bipyridine (dpb) 1 H NMR (500 MHz, [d 3 - H), 7.79 (m, 2 H), 7.57 (dd, 1 H, J = 1.84, 5.08 Hz), 7.52 (m, 2 H), 7.47 (m, 1 H). - diphenyl - - bipyridine) iron(II) hexafluorophosphate [Fe(dpb) 3 ](PF 6 ) 2 1 H NMR (500 MHz, [d 6 - - MS (m/z): [C 66 H 46 N 6 Fe] 2+ calcd. 490.1646; found 490.1701, [C 44 H 30 N 4 Fe] 2+ calcd. 336.0988; found 336.1005, [C 44 H 31 N 4 FeF] + calcd. 691.1961; found 691.1951, [C 44 H 31 N 4 FeCl] + calcd. 707.1666; found 707.1656. CHN analysis for FeC 66 H 48 N 6 P 2 F 12 2H 2 O calcd: C 60.65, H 4.01, N 6.43, found: C 61.25, H 4.52, N 5.77. 2.1.3 Crystal Structure Determination [Fe(dpb) 3 ](PF 6 ) 2 crystal data: C 66 H 48 F 12 FeN 6 P 2 , M r = 1270.89, monoclinic, a = 34.8978(9) Å, b = 17.7797(3) Å, c = 23.7698(7) Å, T= 173 K, space group C2/c, Z = 8, 46917 reflections measured, 12616 unique (Rint = 0.1954), which were used in all calculations . The final wR(F2) was 0.1986 (all data). CCDC 1810752. Solvent molecules in the structure were heavily disordered 264 and the program BYPASS implemented in Olex2 showed the following void and electrons: 1230.4, 72.4. Possible solvents include Et 2 O, EtOH, and MeCN. 2.2 Ultrafast Transient Absorption Spectroscopy Ultrafast transient absorption (TA) spectroscopy was used to carry out ground state recovery and MLCT lifetime measurements as previously described in Chapters 2 and 3 of this work. Variable - temperature studies of these lifetimes were collected using the variable - temperature setup also described in Chapter 2 . Various pump - probe combinations were used and are specified for each measurement. The instrument response function (IRF) was measured as the cross - and self - phase modulation of the pulses in a cuvette of MeOH and was found to be dependent on the specific pump and probe wavelengths, but overall it was approximately 150 fs. Pulse durations were measured by optical Kerr effect in MeOH and were consistently ~130 fs. 3. Results and Discussion 3.1 [Fe(dpb) 3 ](PF 6 ) 2 3 .1.1 Synthesis - positions, the phenyl rings of dpb proved to be quite problematic for the complexation and stability of [Fe(dpb) 3 ] 2+ . Initially, it was presumed that the synthetic route used to acquire [Ru(dpb) 3 ] 2+ (as describe d in Chapter 4 ) would be able to be implemented with an iron(II) starting material to achieve the iron analogue. This was attempted with FeCl 2 2H 2 O and the addition of tetrakis[(3,5 - trifluoromethyl)phenyl]borate salt (BAr F - ) as the counteranion. It was immediately apparent that the BAr F - salt was complicating the purification of the [Fe(dpb) 3 ] 2+ product. This route was attempted again but no BAr F - counterion was added, thereby presumably generating [Fe(dpb) 3 ]Cl 2 . The 1 H NMR of th e crude reaction mixture showed 265 free ligand was still present. Solubility studies on this product showed that the product was soluble in solvents such as 1 - octanol and dichloromethane, which are two solvents that are not typically very good at solvating a doubly charged product, particularly not chloride salts of iron(II) complexes. This was the first indication that the product formed was perhaps not the tris - ligated species. The next sign came from the recrystallization attempts. In this instance, recryst allization by vapor diffusion was attempted, in which diethyl ether was allowed to diffuse into a solution of [Fe(dpb) 3 ]Cl 2 in acetonitrile. Over the course of ~24 h, the solution of iron complex was observed to change from the pink color to colorless ( Fig. 5. 1 ). From the loss of the MLCT absorption, it is apparent that the ligand has dissociated from the iron(II). Furthermore, a comparison of the absorption spectrum of the free dpb ligand and the colorless recrystallization product shows that the ligand itself also decomposes, which is very unexpected. Based on what was observed with [Ru(dmesb) 3 ]Cl 2 ( Chapter 4 ) and previously reported with [Ru(bpy) 3 ]Cl 2 , 1 2 it was expected that the Cl - was preferentially binding to the iron center over the dpb ligand. Metathesis to the BF 4 - salt produced no better results, indicating that the counteranion may have in fact coordinated to the metal center. Attempts to purify the complex by column chromatography were made; similar conditions to those used for [Ru(dpb) 3 ](BAr F ) 2 showed promise by thin - layer chromatography. This involved the use of a silica gel stationary phase with pure dichloromethane as the mobile phase. Under these conditions, the free ligand should remain at the top of the column while the complex runs with the mobile phase. However, the product appeared to dissociate on the column as indicated by the presence of free ligand by 1 H NMR spectroscopy. 266 Figure 5. 1 . Steady state absorption spectrum of [Fe(dpb) 3 ](PF 6 ) 2 in acetonitrile (black) prior to recrystallization. After ~24 h, the solution was observed to go colorless (red). This indicated ligand dissociation from the metal center, but also suggests decomposition of the ligand itself, as the spectrum does not match that of the free dpb ligand (blue). The route that was ultimately used attempted to deal with the issues outlined above. To decrease the risk of oxidation of the metal center, the free dpb ligand was recrystallized out of hot ethanol before the complexation. Each of the reactants were kept under nitrogen throughout the reaction, and every solvent was carefully sparged. To reduce the amount of free ligand in the final product, an excess o f the iron(II) starting material was used. The dpb was fully dissolved in the reaction solvent first to improve the likelihood of coordination. No chloride was used at any point, and the counterion PF 6 - was chosen as it is slightly larger than BF 4 - . A bett er choice might even be tetraphenylborate BPh 4 - in the future since it both larger in size than either BF 4 - or PF 6 - and there is no chance of coordination to the metal center due to its lack of fluorides. The product was kept out of solution as much as pos sible, and the solvents of choice were intentionally non - coordinating. 267 The complex was recrystallized, and it was the single crystals that grew out of CD 3 CN/EtOH that were used for further characterization. Despite being able to get a crystal structure of the product with no indication of free ligand, when the crystals were redissolved in (CD 3 ) 2 CO for 1 H NMR, the spectrum indicated ~40% free ligand impurity, as well as <5% heteroleptic complex impurity ( Fig. 5. 2 ). This may imply t hat product is inherently unstable in solution. Additionally, the CHN analysis indicated the presence of EtOH, despite the product being pumped on while in a desiccator for multiple days. The mass spectrum, it should be noted, does show the presence of a b is - ligated species that has abstracted a fluorine presumably from the PF 6 - at m/z 691.1961. It also shows the same species but instead with a Cl atom at m/z 707.1656, despite the fact that care was taken to never introduce Cl - . The bis - nature of the comple x may imply that the tris - product was not formed, or it may simply be caused by fragmentation in the instrument. In any event, the product seems relatively unstable in solution, so any solution - phase characterization presented here are subject to a relativ ely high degree of uncertainty. 268 Figure 5. 2 . 1 H NMR spectrum of [Fe(dpb) 3 ](PF 6 ) 2 in (CD 3 ) 2 CO. This product was first recrystallized and used for single crystal X - ray diffraction studies, and then redissolved for this spectrum. The main product, as well as the free ligand and bis - ligated complex are present. In the literature, reports of the synthesis of [Fe(dpb) 3 ] 2+ have been published. 13 - 1 6 In a number of these studies, it is found that free ligand is a common byproduct , indicating that dissociation is often occurring in this complex. 13 ,1 4 An analogous c omplex, [Fe(4,7 - diphenyl - phenan throline) x (phenanthroline) 3 - x ]I 2 2H 2 O (x = 1, 2), likewise showed a proclivity towards dissociation, particularl y with the iodide salt. 1 7 When they metathesized to the perchlorate salt, though, this appeared to be less of a problem. It is possible, due to the highly polarizable nature of 269 iodide, that this halide anion was able to coordinat e or disrupt the coordination of the diphenyl - phenanthroline ligand. But this would seem to require that the ligand itself is easily displaced from the metal center. That the dpb ligand should have trouble binding to Fe(II) but no such problems are observe 3 ] 2+ - based complexes are known to have very high formation constants, 1 8 indicating that the phenyl substituent on the ligand is the cause of the problems. To a first order approximation, this is highly unexpected because the ring should be only slightly withdrawing, and much more electron - withdrawing groups have been substitu ted on a homoleptic iron(II) complex previously: the carboxylic acid, in fact, should be more electron - withdrawing than phenyl, and also displays resonance. 1 9 In this work, Ferrere reports no complex dissociation. The next most o bvious cause is the size of the phenyl ring, that it may be so sterically encumbering that it cannot be supported in a tris - ligated complex. Work done by Bergman et al. studied the tris(eilatin) iron(II) complex and found that for this ligand (that is even bulkier than dpb), free ligand was always observed when the complex was in solution. 20 It is not obvious that a phenyl ring would be so bulky as to reduce binding ability of the bipyridine to the iron(II), especially when in sol ution and able to rotate freely. However, as was shown in the case of [Ru(dpb) 3 ] 2+ from Chapter 4 , the dihedral angle between the phenyls and the bipyridine backbone is approximately 30º, which is more coplanar than orthogonal, indicating that the ring bulk is not as out of the way as it could be. Furthermore, the size of the metal cation here may play a large role. The ionic radius of Ru(II) is ~0.94 Å, highly analogous to the radius of the high - spin Fe(II) radius of 0.95 Å. 2 1 However, in the case of low - spin Fe(II), as is being studied here, the radius is much closer to 0.75 Å; 2 1 a smaller ionic radius of the metal may in fact bring the ligands even closer to each other, as w ell as increase the distortion in the ligands. The torsion between the two moieties also implies that there is a degree of electronic communication. We therefore propose 270 that it is the dual effects of slight electron - withdrawing ability and sterics that de creases the binding strength of dpb to the Fe(II) center, particularly in a tris - ligated homoleptic complex. With a reduced coordinating ability, the molecule will be especially susceptible to coordination from nearby anions (e.g., Cl - , F - ), solvent (e.g., MeCN), and will ultimately result in a heteroleptic complex and free ligand in solution. 3.1.2 Crystal Structure Data To the best of our knowledge, the crystal structure of [Fe(dpb) 3 ](PF 6 ) 2 has not be reported. X - ray crystallographic data were collected o n single crystals of [Fe(dpb) 3 ](PF 6 ) 2 that was grown out of evaporation of an MeCN solution with a drop of EtOH. We believe that higher quality crystals can be grown by ether diffusion into a solution of 1 - OctOH and EtOH. The complex is sparingly soluble i n 1 - OctOH, so the addition of EtOH increases solubility in order to slow the growth of the crystals. The structure can be found in Fig. 5. 3 , and the relevant angles and distances are in Table 5. 1 along with those of [Ru(dpb) 3 ](PF 6 ) 2 for comparison. The Fe - N bond distances are indicative of a low - spin Fe(II) complex but are shorter than those of [Fe(bpy) 3 ](PF 6 ) 2 , w hich were found to be 1.967 Å. 2 2 These data would tend to support the phenyl group being slightly electron - donating into the bipyridine ring. Interestingly, in terms of Fe - N distance and cis N - Fe - N angles, [Fe(dpb) 3 ](PF 6 ) 2 most n early resembles [Fe(dtbb) 3 ](PF 6 ) 2 . 2 3 When comparing the trans N - Fe - N angles, however, [Fe(dpb) 3 ](PF 6 ) 2 is closer to 180º than any other Fe(II) complex studied in this work. 2 4 With the relatively shorter Fe - N distances in [Fe(dpb) 3 ] 2+ , it is reasonable that the bulkier phenyl substituents also force the bipyridines further from ea ch other. 271 Figure 5. 3 . Single crystal X - ray structure of [Fe(dpb) 3 ](PF 6 ) 2 . The protons, counterions, and solvent are omitted for clarity. Table 5. 1. Single crystal X - ray data of [Fe(dpb) 3 ](PF 6 ) 2 and [Ru(dpb) 3 ](PF 6 ) 2 . [Fe(dpb) 3 ](PF 6 ) 2 [Ru(dpb) 3 ](PF 6 ) 2 M - N (Å) 1.958 ± 0.012 2.050 ± 0.010 cis N - M - N (º) 80.9 97.2 78.1 99.2 trans N - M - N (º) 176.4 ± 1.1 175.4 ± 0.9 bpy torsion (º) 1 17 0 15 Ph - bpy torsion (º) 33.2 ± 4.1 31.9 ± 3.5 272 In its ground state, the torsion between the phenyl groups and the bipyridine backbone is 33º, which is the same as that in the Ru(II) analogue, 32º. The M - N distance is 0.1 Å longer in [Ru(dpb) 3 ](PF 6 ) 2 relative to [Fe(dpb) 3 ](PF 6 ) 2 . A minor, but important, difference between the two complexes is the bpy dih edral torsion, measuring the angle between the planes of the individual pyridyl moieties. This angle was measured in all three bpy groups of both complexes and was found across the board to be larger in the Fe(II) complex. The most readily apparent explana tion for this is the smaller ionic radius of Fe(II) compared to Ru(II), and the inability of that Fe(II) size to support the sterically bulky dpb ligand, thus forcing the torsion of the ligand backbones. 3.1.3 Extinction Coefficient The molar extinction coefficient was measured for [Fe(dpb) 3 ](PF 6 ) 2 in MeCN. The data can be seen in Figs. 5. 4 and 5. 5 . The extinction coefficient is 15980 M - 1 cm - 1 at the maximum of max = 18263 cm - 1 - - bipyridine iron(II) complex and is similar to [Ru(dpb) 3 ] 2+ in that it has another MLCT band of nearly equal intensity in t he bluer part of the visible spectrum. This band displays a molar absorptivity of 15860 M - 1 cm - 1 max = 26285 cm - 1 (380 nm). Relative to [Fe(bpy) 3 ] 2+ ( Fig. 5. 5 ), the extinction coefficient of [Fe(dpb) 3 ] 2+ has nearly doubled (88 00 M - 1 cm - 1 ) and is red - max = 19196 cm - 1 , 521 nm), with the parentheticals indicating the values of [Fe(bpy) 3 ] 2+ . The lowest - energy MLCT band is also much sharper than that of [Fe(bpy) 3 ] 2+ . This is exactly as expected based on the analogous Ru(II) complexes. 2 5 Interestingly, more fine structure is observed in [Fe(bpy) 3 ] 2+ , particularly in the higher energy part of the spectrum. These features are likely due to ligand field transitions lying underneath the MLCT band centered at ~360 nm, whereas in [Fe(dpb) 3 ] 2+ , the Gaussian at 380 nm appears to be of such a high intensity that it swamps out any lower - strength transitions. 273 Figure 5. 4 . Ground state absorption spectrum of [Fe(dpb) 3 ](PF 6 ) 2 in MeCN, with molar extinction coefficients. Figure 5. 5 . Comparison of the steady - state absorption spectra of [Fe(dpb) 3 ] 2+ (red) and [Fe(bpy) 3 ] 2+ (blue). 274 To further analyze the spectral features of [Fe(dpb) 3 ] 2+ , Fig. 5. 6 shows the overlay of the absorption spectra of the Fe(II), Ru(II), and Zn(II) complexes, as well as the free ligand. In the case of the fre - 40330 cm - 1 (248 nm). This band is r ed - shifted upon complexation to Zn(II), which is expected due to the stabilization afforded by coordination. In this complex, the maximum is found at approximately 39530 cm - 1 (253 nm), a net stabilization of 810 cm - 1 Zn(II) is d 10 , and therefore no MLCT transition will occur, as evidenced by the spectroscopically silent visible region of the spectrum. When dpb is coordinated to Ru(II), though, MLCT bands appear centered at 28650 and 21100 cm - 1 (349 a nd 474 nm, respectively). The - further red - shifts, in this case to 38930 cm - 1 (257 nm), which corresponds to a stabilization of 1410 cm - 1 relative to the free ligand. An additional feature is observed to grow in on the red shoulder of the ligand - - max = 32470 cm - 1 (308 nm). Spectroelectrochemistry on this complex has previously been performed, however, this band was much further into the UV than was measured. 2 5 The oscillator strength of this transiti on is on par with t - this band is also very blue - shifted, both pieces of information making an MLCT assignment very unlikely. From the intensity, a ligand - based transition would make sense. However, the appearance of the band with the presence of a non - d 10 metal center is curious. The transition may be an MLCT featur - most likely explanation, as a ligand - field state would most probably be swamped out by the ligand - b ased feature or appear only as a shoulder. In the spectrum for [Fe(dpb) 3 ] 2+ - most red - shifted of all the complexes, centered at 38170 cm - 1 (262 nm), a stabilization of 2170 cm - 1 relative to the free ligand. Again, as with the spectrum of [Ru(dpb) 3 ] 2+ - absorption in [Fe(dpb) 3 ] 2+ has a large oscillator strength, though in this case, it is not quite as 275 intense as was observed for [Ru(dpb) 3 ] 2+ . It also appears to have more fine structure, possibly indicating the existence of ligand field transitions overlaying with other bands. At t his time, it is difficult to make an exact assignment of these features. When comparing the MLCT bands in [Ru(dpb) 3 ] 2+ and [Fe(dpb) 3 ] 2+ , it is apparent that the transitions in the latter are lower in energy. This is likely due to the greater extension of t he d orbitals in Ru(II) relative to Fe(II), allowing for greater M - L overlap and therefore higher energy transitions. Increased spin - orbit coupling in Ru(II) (owing to it being a second - row transition metal) perpetuates mixing of the triplet and singlet ex cited states, thereby increasing the oscillator strength of the nominally spin - forbidden 3 1 A 1 transition (red shoulder of lowest energy MLCT band) in [Ru(dpb) 3 ] 2+ , a phenomenon that is not observed in the [Fe(dpb) 3 ] 2+ analogue. Figure 5. 6 . Overla y of the ground state absorption spectra of [Fe(dpb) 3 ] 2+ (purple), [Ru(dpb) 3 ] 2+ (red), [Zn(dpb) 3 ] 2+ (blue), and the free dpb ligand (black). The spectra are normalized to the maximum of the dpb - - 276 3.1.4 Ultrafast Spectroscopy Results The ultrafast kinetics of [Fe(dpb) 3 ](PF 6 ) 2 were measured in MeOH. By exciting at 490 nm and probing at 540 nm, the ground state recovery lifetime was found to be 760 ± 10 ps ( Fig. 5. 7 ). When in MeCN, the life time is 800 ± 15 ps. This complex shows a ~20% decrease in lifetime as compared to [Fe(bpy) 3 ] 2+ in the same solvents. In the Ru(II) analogues of these compounds, the addition of the phenyl substituents increases the lifetime by over 50%. However, that is g round state recovery from a 3 MLCT state, as opposed to the 5 T 2 ligand field state in the Fe(II) complexes. It was therefore desirable to measure the MLCT lifetime in [Fe(dpb) 3 ] 2+ . While this process could be measured from the deactivation into the lower - ly ing ligand field states using the pump - probe combination used for ground state recovery, these kinetics are so fast that they are likely to be complicated by the solvent - related dynamics on the same timescale . It is much better, then, to find a probe wavel ength capable of measuring the MLCT lifetime directly. In Fe(II) complexes, this is signified by a low energy, low intensity excited state absorption. These may be found on the red side of the lowest energy MLCT bands where the ground state does not absorb . In this case, the pump produces the 5 T 2 , and then the probe absorbs into the 5 MLCT, the lifetime of which is then measured. More definitive identification of the MLCT process may be found by spectroelectrochemical methods; 2 6 ho wever, no electrochemistry was done in - house on this complex due to its proclivity to dissociate. In this complex, excited state absorption was observed upon excitation at 490 nm and probing at 690 nm ( Fig. 5. 8 ). The data were fo und to fit well to a single exponential with a time constant of 160 ± 20 fs. This is a 20% increase in MLCT lifetime relative to [Fe(bpy) 3 ] 2+ . 27 ,2 8 A summary of the kinetics measured in this complex and all complexes discussed in this chapter can be found in Table 5. 2 . 277 Figure 5. 7 . Ground state recovery dynamics of [Fe(dpb) 3 ](PF 6 ) 2 in MeOH (black diamonds) measured by p robing at 540 nm after exciting at 490 nm. The fit (red trace) gives a lifetime of 760 ± 10 ps. Figure 5. 8 . Presumed MLCT decay of [Fe(dpb) 3 ](PF 6 ) 2 in MeOH upon excitation at 490 nm and probing at 690 nm. The data (black diamonds) show a positive feature that in Fe(II) complexes is indicative of MLCT absorption. The lifetime (red trace) was found to be 160 ± 20 fs. 278 Table 5. 2. Kinetic parameters of the Fe(II) complexes studied to determine the effect of extended delocalization on the rate of MLCT deactivation. Complex Ground State Recovery (ns) MLCT Lifetime (fs) [Fe(dpb) 3 ](PF 6 ) 2 0.76 ± 0.01 160 ± 20 [Fe(dqp ) 2 ](PF 6 ) 2 4.29 ± 0.03 145 ± 10 [Fe(qphen) 2 ](PF 6 ) 2 3.16 ± 0.03 170 ± 40 [Fe(dmib) 3 ](PF 6 ) 2 0.94 ± 0.01 900 ± 400 [Fe(caab) 3 ](PF 6 ) 2 0.79 ± 0.01 150 Prior to the ultrafast measurements made here, it was hoped that a similar set of solvent - and excitation wavelength - dependent kinetics would be able to be collected on [Fe(dpb) 3 ] 2+ in analogy to those of [Ru(dpb) 3 ] 2+ expanded on in Chapter 4 . In the case of the Ru(II) complex, the vibrational cooling (VC) associated with solvation dynamics occurs on the 3 MLCT surface, which is the lowest energy excited state. If such kinetics were to be measured in Fe(II), it is obvious that they would not ap pear in the MLCT due to its lifetime. Vibrational cooling is typically thought of as a 1 - 10 ps process; 29 - 3 1 by the time this could occur, the MLCT state would already be depopulated. On the other hand, if VC is occurring along t he lowest energy excited state in [Fe(dpb) 3 ] 2+ , that would be on the 5 T 2 surface. These dynamics have previously observed in [Fe(bpy) 3 ] 2+ , 3 2 and other Fe(II) complexes. 3 1 However, it is difficult to cle anly monitor these kinetics as VC is a subtle modulation overlaid on the electronic state population dynamics. When those dynamics happen to present as a ground state bleach, it is all the more difficult to observe 279 p of a much larger signal. These studies are still worth pursuing, however, though it may be fruitful to initially attempt to view the VC dynamics as the band sharpening and blue - shifting in the full spectral data spectral tags for the vibrational coolin g process. Singular value decomposition and global analysis ( Appendix E ) may be of use in this endeavor. To further characterize [Fe(dpb) 3 ] 2+ , VT measurements were performed with the complex in MeOH. The same pump - probe combin ation of 490 - 540 nm (respectively) was used. The data can be seen in Fig. 5. 9 , and the Arrhenius plot is given in Fig. 5. 10 . From these data an activation energy of 260 ± 10 cm - 1 3 ] 2+ complexes found in Chapter 2 . The frequency factor, however, is the same as those measured for 3 ] 2+ family, at 205 ± 10 ps - 1 . The Marcus valu es were determined for this complex using the same method outlined in Chapters 2 and 3 . Electrochemical data was not collected in - house but work by Leidner et al. did determine oxidation potentials fo r both [Fe(bpy) 3 ](PF 6 ) 2 and [Fe(dpb) 3 ](PF 6 ) 2 under identical conditions, making the relative difference between the two usable 1 4 In this data, the Fe(II/III) couples were 1.02 V for [Fe(bpy) 3 ] 2+ and 0.96 V for [Fe(dpb) 3 ] 2+ 3 ] 2+ would be - 6650 ± 670 cm - 1 - 1 and H ab = 4.6 ± 0.2 cm - 1 . Both the reorganization energy and H ab are the sam wholly unexpected considering the electron - donating ability of the methyl and t butyl groups discussed in Chapter 2 ab were dras tically altered relative to the parent complex. In fact, what is most interesting about these results, is the fact that 3 ] 2+ trends in the direction expected of an electron - donating group, which is in agreement with the crystallographic dat a. This may imply more complicated effects caused by the 280 phenyl group than previously believed. That being said, the H ab 4 ± 2). This is rather unexpected as the ratio is calculated solely from A, the preexponential factor , ratio for [Fe(dpb) 3 ] 2+ 3 ] 2+ and [Fe(terpy) 2 ] 2+ or [Fe(dcpp) 2 ] 2+ . Interestingly, the ratio for the dpb compl ex is actually within error of all of the compounds measured in Chapters 2 and 3 . Figure 5. 9 . Ground state recovery lifetime of [Fe(dpb) 3 ](PF 6 ) 2 in MeOH as a function of temperature. Excitation occurred at 490 nm with probing at 540 nm. 281 Figure 5. 10 . Arrhenius plot of the variable - temperature lifetimes of [Fe(dpb) 3 ](PF 6 ) 2 in MeOH, as shown in Fig. 5. 9 . From these data an activation energy of 260 ± 10 cm - 1 i s found, as well as a barrierless rate of 205 ± 10 ps - 1 . The data fit well to a single mode, with R 2 = 0.996. The increased rate of ground state recovery relative to [Fe(bpy) 3 ] 2+ is clearly due to the reduction in activation energy. The magnitude of this barrier, however, may either be caused by greater ligand field strength in [Fe(dpb) 3 ] 2+ or by this transition occurring via an alternate nuclear coordinate. It is possible that th e former is playing a role: increased ligand field strength caused by the phenyl substituent withdrawing electron density out of the bipyridine backbone, decreasing the strength of the Fe - N bonds. This is expected based on the slight electron withdrawing n ature of phenyls, but there is no real indication of this, at least in the ground state from the crystal structure for which the Fe - N distances are 0.01 Å shorter in [Fe(dpb) 3 ] 2+ than in [Fe(bpy) 3 ] 2+ . 22 , 3 3 This is not a true representation of the ligand field strength, only an approximation. As for the second hypothesis, an alternate nuclear coordinate seems much more likely given the unusual effects the phenyl substituents have already displayed (partic ularly in the synthesis of the complex). The substituent itself may not even be playing a role in ground state recovery, it is 282 possible that its mere presence increases the steric bulk of the ligand such that the vibrational 3 ] 2+ for the 5 T 2 1 A 1 transition become blocked or energetically disfavored. The MLCT lifetime lengthening in [Fe(dpb) 3 ] 2+ is of much greater interest, due to the goal of this work. Increasing the extent of delocalization in the MLCT excited state, as was obser ved in [Ru(dpb) 3 ] 2+ , increased the oscillator strength in the MLCT bands of the ground state absorption profile of [Fe(dpb) 3 ] 2+ . For this to be true, the 1 MLCT states must be shifted along one nuclear coordinate relative to the 1 A 1 ground state such that F ranck - Condon overlap is much greater than in the unsubstituted bipyridine complex. This means more nested potentials in the case of [Fe(dpb) 3 ] 2+ . A longer - lived MLCT lifetime, then, requires that the electronic communication between the MLCT and ligand fie ld manifolds be weaker, and/or the barrier between these states be larger. With a more delocalized wavefunction in the excited state, the coupling to the lower - lying electronic states should be weakened, thereby reducing the rate of deactivation from the M LCT manifold. As discussed in the introduction, the work described here is intended to study the effect of increased delocalization in the MLCT as a possible path to increase the lifetime of that state. While this is only a first step toward that route, th e results are promising. Clearly, though, further characterization of the excited states in this (and other) Fe(II) complex(es) is necessary, and that work is currently ongoing. 3.2 Extending Delocalization By Synthetic Modification of the Ligand 3.2.1 I ncreased Conjugation Around the Metal Center When considering extending the delocalization in a ligand system, there are two alternatives possible: increasing the conjugated moieties encircling the metal center or expanding the delocalized state away from the metal center. Obviously both can be utilized simultaneously, 283 but our hypothesis is that the latter mechanism will push the wavefunction away from the metal survives away from the metal (i.e., the MLCT lifetime). This mechanism is likely to make a greater impact in decreasing the rate of MLCT deactivation. The role of delocalization in the excited state must be thoroughly examined, though. Is increased deloca lization in any arbitrary direction sufficient to improve the MLCT lifetime? That is the question being addressed through the use of the two quinoline - substituted complexes shown in Scheme 5. 1 . These compounds were prepared by L. Wickramasinghe of the Thummel group and use quinoline moieties to extend conjugation around the iron center. Scheme 5. 1. - diquino linyl - 2,6 - pyridine) iron(II), [Fe(dqp) 2 ](PF 6 ) 2 - quinolinyl - 2 - phenanthroline) iron(II), [Fe(qphen) 2 ](PF 6 ) 2 . These compounds display very unusual ground state absorption spectra ( Fig. 5. 11 ). Both are very broad, wi th MLCT features expanding over 400 - 700 nm. When both are taken in MeCN, [Fe(dqp) 2 ] 2+ displays a MLCT maximum at 17392 cm - 1 (575 nm), while [Fe(qphen) 2 ] 2+ is slightly 284 more blue - max = 17761 cm - 1 (563 nm). However, the lowest energy MLCT band in [Fe(qphen) 2 ] 2+ actually has a shoulder that extends farther into the red than [Fe(dqp) 2 ] 2+ . Both complexes display interesting structure in their steady state absorption spectra, perhaps owing to the highl y asymmetric nature of the ligands. Additionally, it can be expected that the complex is vastly distorted from octahedral symmetry due to the rigid quinoline ligand. Figure 5. 11 . Overlay ground state absorption spectra of [Fe(dqp) 2 ](PF 6 ) 2 (black) and [Fe(qphen) 2 ](PF 6 ) 2 (red). The dqp ligand might be likened to an extended terpyridine in that it contains three separate N - donating moieties, with the quinoline increasing the distance between the central pyridine and the peripheral ends of t he ligand. With that in mind, the ground state recovery dynamics of [Fe(dqp) 2 ](PF 6 ) 2 ( Fig. 5. 12 , Table 5. 2 ) are unsurprising, with a lifetime of 4.29 ± 0.03 ns in MeCN that is very close to that of [Fe(terpy) 2 ] 2+ , which is 5.2 ± 0.1 ns. The shortening of the lifetime of [Fe(dqp) 2 ] 2+ relative to [Fe(terpy) 2 ] 2+ in fact mimics the relationship between [Fe(terpy) 2 ] 2+ and 285 [Fe(dcpp) 2 ] 2+ , though to a much lesser extent. Analogously to dcpp, dqp has an exten ded ligand distance that likely improves the overlap of the N - donor atoms with the d orbitals on the Fe(II) center. While [Fe(dqp) 2 ] 2+ is probably not as perfectly octahedral as [Fe(dcpp) 2 ] 2+ , it is certainly more symmetric than [Fe(terpy) 2 ] 2+ , thus making it slightly more barrierless than the terpy complex. This is what decreases the ground state recovery rate in [Fe(dqp) 2 ] 2+ . What is unexpected, though, is the drastic increase in MLCT lifetime, as evidenced by Fig. 5. 13 . This li fetime was previously measured by A. M. Brown in [Fe(terpy) 2 ] 2+ in MeCN and found to be 60 ± 15 fs ( exc probe = 410 nm). 3 4 In [Fe(dqp) 2 ] 2+ in MeCN, though, the MLCT lifetime is 145 ± 10 fs, an increase of more than a factor of two. Figure 5. 12 . Ground state recovery of [Fe(dqp) 2 ](PF 6 ) 2 in MeCN, upon excitation at 570 nm and probing at 480 nm. The data (black diamonds) fit well to a lifet ime of 4.29 ± 0.03 ns (red trace). 286 Figure 5. 13 . The MLCT deactivation of [Fe(dqp) 2 ](PF 6 ) 2 in MeCN (black diamonds) fit to single exponential kinetics (red trace) with a 145 ± 10 fs lifetime. The solvent data (blue diamonds) are shown for comparison. Th e ligand structure of [Fe(qphen) 2 ] 2+ is not quite as simple to compare to any one prototypical Fe(II) polypyridyl complex. Obviously [Fe(phen) 3 ] 2+ is a well - known and commonly studied compound, but its bond to the quinoline makes the structure not exactly terpy - like, but not a true phen - based system. The ground state recovery lifetime ( Fig. 5. 14 , Table 5. 2 ) shows kinetics that are essentially right between [Fe(phen) 3 ] 2+ and [Fe(terpy) 2 ] 2+ , being 3.16 ± 0.03 ns in MeCN when pumped at 570 nm and probed at 480 nm. This may imply that the ligand field strength in [Fe(qphen) 2 ] 2+ is weaker than that of [Fe(phen) 3 ] 2+ (not unexpected for tridentate vs. bidentate ligand), but more likely indicates an alter nate relaxation pathway for the process. No variable - temperature studies were performed on either [Fe(dqp) 2 ] 2+ or [Fe(qphen) 2 ] 2 + but considering that the quinoline will contain vibrational modes that are not present in a simple phen or terpy ligand 287 system, it seems reasonable to expect that those modes will play a role in the photophysical processes of the iron(II) complexes at hand. Figure 5. 14 . Ground state recovery lifetime of [Fe(qphen) 2 ](PF 6 ) 2 in MeCN (black diamonds). Excitation occurred at 570 nm and probing at 480 nm. The data fit well to a single exponential (red trace) with a lifetime of 3.16 ± 0.03 ns. The MLCT deactivation was likewise measured in [Fe(qphen) 2 ](PF 6 ) 2 in MeCN and showed a lifetime of 170 ± 40 fs ( F ig. 5. 15 , Table 5. 2 ). While the average is slightly longer than that of [Fe(dqp) 2 ] 2+ , the two are within error of each other. Unfortunately, no excited state absorption was observed for either of these complexes, meaning the ML CT lifetime had to be measured as the deactivation into the ground state bleach. In addition to the problem of solvent dynamics obscuring this decay feature that was mentioned previously, the error associated with these kinetics will also be larger due to MLCT occurs before the ground state recovery process begins, further complicating the fitting of these data. Regardless, both of the 288 quinoline - substituted complexes displayed MLCT lifetimes that were longer than those previously m easured in standard Fe(II) compounds, such as [Fe(bpy) 3 ] 2+ and [Fe(terpy) 2 ] 2+ . 27,28 , 3 4 These data in combination with the those measured in [Fe(dpb) 3 ] 2+ support the proposal that increased delocalization across the ligand is able to lengthen the lifetime of the MLCT state in Fe(II) polypyridyl chromophores. Figure 5. 15 . MLCT deactivatio n of [Fe(qphen) 2 ](PF 6 ) 2 in MeCN (black diamonds) fit to a lifetime of 170 ± 40 fs (red trace). The data were collected at 660 nm upon 570 nm excitation. The solvent trace (blue diamonds) is given for reference. 3.2.2 Extending Delocalization Away from th e Fe(II) Center The next series of complexes that will be studied to understand the role delocalization plays in the MLCT lifetime is shown in Scheme 5. 2 . These two compounds (prepared by C. R. Tichnell) are more analogous to [Fe(dpb) 3 ] 2+ than either [Fe(dqp) 2 ] 2+ or [Fe(qphen) 2 ] 2+ were. In part, this is caused by the bidentate nature of these complexes versus the tridentate quinoline - based systems. 289 - disubstituted bipyridine analogues, making for a better comparison between the two. In the first complex, [Fe(dmib) 3 ] 2+ , a 2,5 - dimethylisoxazole is the substituent in question. The aromatic nature of the group will extend delocalization away from the metal center, though it may be slightly mediated by the methyl groups, which may serve to sterically hinder full coplanarity of the isoxazole relative to the bpy backbone. The whole of the isoxazole group, though, is taken to be electron - withdrawing, which is a great comparison to the second complex, [Fe(caab) 3 ] 2+ - s ubstituent is a cyanoacrylic acid moiety. The cyano - and carboxylic acid groups both serve to pull electron density away from the metal center, and the whole appendage is conjugated via the vinyl moiety into the carboxylic acid group. Both the dmib and caa b ligands have electron - withdrawing functional groups; they also have steric bulk in their own unique ways. The main difference, and therefore the point of comparison, between these two is the way in which the conjugation is extended. In [Fe(dmib) 3 ] 2+ , the MLCT excited state would be delocalized across an aromatic ring (as was true with [Fe(dpb) 3 ] 2+ ), whereas the conjugation in [Fe(caab) 3 ] 2+ extends in a linear fashion. The comparison of these two complexes will help determine if the mode of delocalization matters for MLCT lifetime elongation. 290 Scheme 5. 2. Two complexes that extend delocalization away from the metal center via two different mechanisms. (Left) The - (di - 2,5 - dimethylisoxazolyl) - - bipyridine] iron(II) complex, [Fe(dmib) 3 ] 2+ - cyanoacrylic acid - - bipyridine) iron(II) complex, [Fe(caab) 3 ] 2+ , which extends delocalization across a linear chain. As with [Fe(dqp ) 2 ] 2+ and [Fe(qphen) 2 ] 2+ , it is worthwhile to compare the absorption spectra - disubstituted Fe(II) bipyridine - based complexes ( Fig. 5. 16 ). The spectra for these two compounds are very similar, not only to each other but also relative to [Fe(dpb) 3 ] 2+ and [Fe(bpy) 3 ] 2+ from Fig. 5. 5 . The lowest energy MLCT band in [Fe(dmib) 3 ] 2+ is at 542 nm, whereas the maximum occurs at 543 in [Fe(caab) 3 ] 2+ . Comparing this to [F e(dpb) 3 ] 2+ max = 548 nm) and [Fe(bpy) 3 ] 2+ max = 521 nm). As expected, delocalization in the 1 MLCT lowers the energy of that state, thus causing the red - shift observed for all three of the disubstituted complexes relative to the parent compound. Interes tingly, it would appear that the degree of delocalization is the greatest in [Fe(dpb) 3 ] 2+ as its MLCT absorption maximum is the farthest to the red. This may be a consequence of the larger size of the phenyl ring relative to the other two conjugated substi tuents, 291 increasing its instantaneous dipole moment and thus the delocalization in its excited state wavefunction. Based on this reasoning, one could argue that the extent of delocalization in both [Fe(dmib) 3 ] 2+ and [Fe(caab) 3 ] 2+ is very similar, making the m great candidates in this study. Figure 5. 16 . Comparison of the ground state absorption spectra of [Fe(dmib) 3 ](PF 6 ) 2 (black) and [Fe(caab) 3 ](PF 6 ) 2 (red). One other point of interest in the comparison of steady state spectra of the four 3 ] 2+ complexes: the shape of the spectra. All members of this family have the same band shape for the lowest energy 1 MLCT absorption: the asymmetric double Gaussian with the redder feature having a slightly greater oscillator strength. In the thre e disubstituted complexes, there is another band toward the blue edge of the spectrum. The central wavelength of this feature shifts max = 368 nm in [Fe(dmib) 3 ] 2+ max = 380 nm in [Fe(dpb) 3 ] 2+ max = 39 1 nm in [Fe(caab) 3 ] 2+ ), but more importantly, it is altogether absent from the spectrum of [Fe(bpy) 3 ] 2+ . This band has long been assigned as being MLCT in nature; if true, it seems most likely that the wavefunction of this excited state must be weighted mo re on the 292 substituents, whereas the lower energy bands must be a largely bpy - based wavefunction. It is unreasonable to believe that a MLCT excited state would ever lie fully on one the substituent with 0% probability of the wavefunction existing on the bip yridine, or vice versa. The two communicate electronically with one another, it is simply a question of whether the excitation energy biases the excited electron to more fully occupy one moiety over the other. This is a very interesting fundamental physica l organic chemistry question, and one that is being studied currently by S. L. 3 ] 2+ analogues and showing exciting results. 3 5 The ground state recovery dynamics of [Fe(dmib) 3 ] 2+ are shown in Fig. 5. 17 and Table 5. 2 . They were measured in MeCN at 510 nm upon excitation at 570 nm. The lifetime of this complex is 0.94 ± 0.01 ns, which is very similar to that of [Fe(bpy) 3 ] 2+ . Moreover, the MLCT lifetime was measured ( Fig. 5. 18 , Table 5. 2 ) at 650 nm where excited state absorption was observed to occur. These data were best fit with a double exponential, though the error bars on the fit are qu ite large as the time delay was not long enough to observe the full relaxation of the molecule. The first time constant is 45 ± 10 fs, which is too short to be believed with the IRF of this system (here, 150 fs). However, the longer kinetic component was f ound to be 900 ± 400 fs, which is nearly a factor of seven longer than the lifetime of [Fe(bpy) 3 ] 2+ . This is fascinating considering that the isoxazole would not extend delocalization any farther than a phenyl group, and yet the MLCT lifetime of [Fe(dmib) 3 ] 2+ is possibly a factor of five longer than that of [Fe(dpb) 3 ] 2+ . This may in fact be caused by the methyl groups on the isoxazole. These functional groups would sterically hinder the ring from rotating into coplanarity with the bipyridine; coplanarity he re would actually be expected to allow for delocalization back onto the bpy, thereby decreasing the charge - separated distance and possibly decreasing the MLCT lifetime. If borne out, this method of blocking the electron from returning to the metal center m ay need to be employed in more conjugated systems. 293 Figure 5. 17 . Ground state recovery dynamics (black diamonds) of [Fe(dmib) 3 ](PF 6 ) 2 in MeCN. The complex was excited at 570 nm and probed at 510 nm. The data were fit with a single exponential (red trace) with a lifetime of 0.94 ± 0.01 ns. 294 Figure 5. 18 . MLCT kinetics (black diamonds, lower) measured for [Fe(dmib) 3 ](PF 6 ) 2 in MeCN upon excitation at 570 nm and probing at 650 nm. The data required a double exponential (red trace) for an adequate fi t, with two lifetimes of 45 ± 10 fs and 900 ± 400 fs. Because the data did not fit the second exponential very well, the residuals are plotted (black diamonds, upper) along with the solvent trace (red diamonds) for reference. The photophysical kinetics o f [Fe(caab) 3 ] 2+ were then studied for comparison to [Fe(dmib) 3 ] 2+ . The ground state recovery dynamics are shown in Fig. 5. 19 , along with the MLCT lifetime in Table 5. 2 . First, the ground state recover y of the complex is observed to have a time constant of 0.79 ± 0.01 ns associated with it when in MeCN and probed at 550 nm upon excitation at 605 nm. This lifetime is very comparable to that of [Fe(dpb) 3 ] 2+ , perhaps indicating greater ligand field strength than [Fe(bpy) 3 ] 2+ , as induced by the electron - withdrawing nature of the cyanoacrylic acid substituents. However, when the MLCT deactivation was attempted to be measured, it was found to be much shorter than the IRF of the system, essentially makin g it unmeasurable. 295 Figure 5. 19 . Ground state recovery measurement of [Fe(caab) 3 ](PF 6 ) 2 in MeCN (black diamonds). These data were collected at 550 nm with 605 nm excitation. The lifetime (red trace) was found to be 0.79 ± 0.01 ns. The huge disparity in MLCT lifetimes between [Fe(dmib) 3 ] 2+ and [Fe(caab) 2 ] 2+ yields some interesting conclusions for this research. It should first be acknowledged that an isoxazole and cyanoacrylic acid are in no way perfect analogues of each other. However, both are electron system of the substituent will likely not be coplanar with the bipyridine. The latter point is based on the bulkiness of the two groups. The most impo rtant structural difference between these two functionals is that the isoxazole is aromatic, while the cyanoacrylic acid is a conjugated chain. Based on these results, it would appear as though aromaticity is a requirement for a longer - lived charge - separat ed excited state. At first glance, one might argue that the reason for the lengthened MLCT lifetime in [Fe(dmib) 3 ] 2+ is that the methyl groups are better able to hinder delocalization back into the bipyridine backbone once the electron is on the isoxazole. However, in the case of [Fe(dpb) 3 ] 2+ , there are no steric barriers to deter ring rotation into coplanarity with the bpy. In that complex, the MLCT lifetime is outside of the IRF of the laser system, a fact which invalidates the 296 sterics argument. One way i n which this hypothesis could be tested is through the MLCT lifetime - diisoxazole - - bipyridine) iron(II) complex in which there are no methyl groups present. If the theory put forward here is correct, this complex will display MLCT - based kinetics more similar to those of [Fe(dpb) 3 ] 2+ . Alternatively, an [Fe(dmesb) 3 ] 2+ - type - dimesityl - - bipyridine ligand) might also be telling and would be expected to have a longer - lived MLCT state than the un substituted [Fe(dpb) 3 ] 2+ . 4. Future Works and Conclusions 4.1 Results from Extended Delocalization Studies The dpb, dmib, and caab ligands were useful in the determination of the role of - d isubstituted bipyridine complexes, they separated the excited electron from the oxidized metal center to varying degrees of distance and via different mechanisms (i.e., aromaticity , chain). In comparison, the dqp and qphen ligands extended the conjugation not away from the metal center, but around it. When comparing these two different types of complexes, it appears as though delocalization in general improves the MLCT lifetime. This conclusion has one caveat: con jugation via a chain - type substituent such a vinyl group appears to have no effect on the MLCT lifetime or may in fact shorten it relative to the parent compound, [Fe(bpy) 3 ] 2+ . These studies have not only generated a complex with a nearly 1 ps MLCT lifetim e in [Fe(dmib) 3 ] 2+ , but they have also provided invaluable insight into the mechanisms by which delocalization may lengthen a charge - separated state. To further understand the excited state wavefunctions, time - dependent density functional theory may be of use. This method provides snapshots of the orbital contributions to different transitions from the ground state. While theoretical, this may yield insights into extent of 297 delocalization in the excited states, or the amount of participation of the substitu ents. In terms of future experimental work, a full variable - temperature study of these complexes should be performed so that the barriers associated with ground state recovery may be known. These data will also be crucial in determining (to a first - order a pproximation) if the 5 T 2 1 A 1 transition occurs 3 ] 2+ series of compounds. In that vein, VT - TA should be attempted on the MLCT kinetics of these Fe(II) polypyridyls. This will be a technicall y challenging experiment to set up owing in large part to the fact that very short pulses would be desired to get the most accurate measure of the MLCT lifetimes. These pulses will be readily broadened by the glass introduced by the cryostat, but that chir p can be compensated for with the folded Brewster prism pair used in the laser system outlined in Chapters 3 and 4 . Not only for these compounds, but for all future Fe(II) complexes prepared, a full M LCT kinetic work - up should be done in order to gain the most information from these photophysical processes as possible. For the chromophores discussed in this chapter, electrochemical da ta was collected only on [Fe(dqp ) 3 ] 2+ and was measured by L. Wickram asinghe of the Thummel group. These data should be recollected along with the electrochemical properties of the other complexes. The oxidation and reduction potentials garnered from this experiment will provide more insight into the energetics of these mol ecules and may help inform the synthetic modifications of future ligands. To the best of our knowledge, spectroelectrochemical measurements have not been performed on any of the complexes here, and these data should likewise be collected so as to ascertain if there are spectrally selective signatures for the MLCT states. This will allow for ultrafast measurements to be unencumbered by extraneous, complicating photophysical processes and thus yield the most accurate MLCT lifetimes. 298 4.2 Proposed Future Comple xes There is a series of Fe(II) polypyridyls that was hinted at in the introduction of this chapter that have an incredibly high potential for a long - lived MLCT lifetime as caused by extended delocalization in the excited state. These are homoleptic comple xes with a terpy - based ligand with - position. The linkers include phenyl rings and vinylene moieties, as shown in Scheme 5. 3 . In the mid - 2000s, a graduate student from this researc h group, A. L. Smeigh, studied a variety of complexes of this type that were prepared by the Schmehl group. Notably, the ligands that contained the highest number of linkers (i.e., the longest conjugated chains) had very long - lived excited state absorption features. It was never confirmed that this positive signal was caused by the MLCT. Upon excitation into the MLCT, electron delocalization into the conjugated chain is likely; the farther the electron travels down the chain, the more spread out the wavefun ction and less probable the return of the electron to the metal center. These ligands, then, are very attractive options to study the hypothesis set forward at the beginning of this chapter. That is further bolstered by the promising results obtained by Sm eigh on these Fe(II) complexes. 299 Scheme 5. 3. Terpy (t) - based ligands with extended conjugation with phenyl (p) and vinyl (v) linkers. From left to right: tp, tpvp, and tpvpvp. These ligands and the naming scheme are based on those originally prepared by the R. Schmehl group. What we propose here is a systematic study of the tp - type ligands as bound to Fe(II). The exact ligands proposed can be found in Scheme 5. 3 . This set of compounds would increase the chain len gth by one vinylene and one phenylene linkage at a time, allowing for a more thorough study of the distance dependence of MLCT lifetime. To determine whether it is in fact the conjugation that allows for an extended MLCT lifetime, or a secondary feature of these ligands, the compounds [Fe(tpvp) 2 ] 2+ and [Fe(tpmp) 2 ] 2+ should be studied, in which m stands for a methylene linker ( Scheme 5. 4 ). This would require a simple reduction of the vinylene moiety, but 300 that would essentially c ut out communication between the two phenyl rings. If conjugation is the method by which the MLCT lifetime is lengthened, then [Fe(tpmp) 2 ] 2+ should behave more analogously to [Fe(tp) 2 ] 2+ than [Fe(tpvp) 2 ] 2+ . For any and all of the complexes proposed here, f ull electrochemical and spectroelectrochemical analyses should be performed to know with certainty that the MLCT is the excited state being probed. Scheme 5. 4. Proposed hydrogenation reaction of the tpvp ligand into tpmp. The homoleptic iron(II) complexes of these ligands are expected to have very different MLCT lifetimes if conjugation in the excited state is the main determinant of the kinetics. There are a f ew potential issues with the ligands outlined in Schemes 5. 3 and 5. 4 . As was shown extensively in Chapter 4 of this work, phenyl rings rotate in solution; 30 , 3 6 alkenes, additionally, are known to undergo cis - trans isomerizations upon photoexcitation. 37 ,3 8 These processes will not o nly require energy (thereby reducing the driving force of the electron to 301 perform photochemistry), but they may also change the nature of the ligand such that the MLCT lifetime is shortened. One way this may occur is by the phenyl rotation that produces a substituent excited electron back to the metal center. A few proposed substituents to extend the MLCT lifetime but that may not have the inherent issues of t he { tp... } ligands are shown in Scheme 5. 5 . The first is a pyrene extender, which has the benefits of delocalization across four fused aromatic rings as well as a large size that will require much greater reorganization energy to cant into a coplanar position to the bpy backbone. The second is very similar to tpvp, but replaces the vinylene linker with an acetylene group, thereby eliminating the cis - trans isomerization reorganization energy. The triple bond also serves to maint terpyridine is coplanar, increasing delocalization. With these two linkers, though, there is still the possibility of energy being used to reorient the substituent to be coplanar with the bipyr idine. And because these are designed to be rigid, they will use a much greater amount of energy during the rotation. To avoid this altogether, inspiration is taken from the dmib ligand and appends methyl groups in the ortho - positions on the phenyl direct ly bound to terpy, thus sterically hindering coplanarity and reducing the inner - sphere reorganization energy. 302 Scheme 5. 5. - position (top): pyrene (bottom left), phenyl - acetylene - phenyl (bottom middle), and 2,6 - dimethylphenyl - acetylene - phenyl (bottom right). One latent question that may come up when looking a t these complexes is the concern that the extenders may drastically alter the ligand field strength of the complexes, thereby preemptively changing the energetics of the excited states and potentially increase electronic coupling that leads to a faster MLC that has come up repeatedly in this work, and efforts are ongoing to experimentally and/or theoretically derive that value in Fe(II) complexes. For the time being, though, ap proximations and guesswork must be made. An interesting observation was made when comparing the ground 303 state absorption spectra of [Fe(terpy) 2 ] 2+ and [Fe(tpvpvp) 2 ] 2+ ( Fig. 5. 20 ). In both complexes, two very small bumps appear to sit on top of larger features. In [Fe(terpy) 2 ] 2+ , these are present at 36759 and 35706 cm - 1 (272 and 280 nm, respectively). For the extended complex, these peaks are centered at 36506 and 35213 cm - 1 (274 and 284 nm, respectively). As has been discussed pre viously, these may be underlying ligand field states that borrow in tensity from the ligand - based - the Fe(II) center will not have changed considerably betwee n [Fe(terpy) 2 ] 2+ and [Fe(tpvpvp) 2 ] 2 + and knowing that the phenyl ring is only slightly affecting the electron density on the N atoms in the terpyridine, it seems reasonable to believe that if these features are in fact ligand field transitions, then they m ust be the same ligand field transitions in both complexes. In the case of the higher energy transition, a red - shift of 253 cm - 1 occurs when the extender is added. For the lower energy bands, the red - shift corresponds to a 493 cm - 1 energetic stabilization. The exact transition occurring in these two bands is unknown but can be narrowed down based on the fact that the lower energy absorption changes at twice the rate of the higher energy feature. This limits the high and low energy transitions to either the 3 T 1 1 A 1 and 5 T 2 1 A 1 , respectively, or to the 1 T 2 1 A 1 and 5 1 A 1 . The high energy of the transitions make the latter choice much more likely. Of course, neither of these terpy - based complexes is actually octahedral in symmetry, so the T and E term states ca nnot be supported and will split into A and B states. This exercise is simply to show that the application of group theory here may help in determining the Racah B and C parameters, which are largely unknown in Fe(II) polypyridyls. 3 9 Moreover, the energy of the transitions is affected by less than 3k B T, and the same general low - energy MLCT features are observed, implying that the ligand field strength was not so drastically affected by the addition of conjugated linkers. 304 Figure 5. 20 . Overlay of the steady - state absorption spectra of [Fe(terpy) 2 ] 2+ (black) and [Fe(tpvpvp) 2 ] 2+ (red). 4.3 The Future of the Quest for Long - Lived MLCT Lifetime in Fe(II) Complexes Charge - separated species are capable of being utilized in many important photovoltaic applications. These states are highly desirable in the fields of photoredox catalysis and solar energy conversion, to name two. The metal - to - ligand charge transfer excite d states that dominate the photophysics in Ru(II) complexes are present in Fe(II) analogues but are quickly deactivated into lower - lying ligand field states. Not only are they energetically below the MLCT (therefore providing less driving force for the rea ction of interest), but these states are also metal - centered, meaning the charge separation that was present in the MLCT is now gone. For photovoltaic applications, these ligand field excited states are essentially useless. From the outset of this work, th ree methods have been outlined that could extend the MLCT lifetime in Fe(II) complexes. As a graduate student, I have worked on research that addresses all three strategies. Below are the ways in which I have impacted this field, and the directions I see a s the future of these endeavors. 305 4.3.1 Altering the Nuclear Coordinate The development and implementation of the ultrafast variable - temperature transient absorption spectroscopy experiment is without doubt the most important work I have done in my time he re. This setup has enabled us to measure barriers and estimate reorganization energies of large number of iron(II) complexes, for which these values were only ever estimated. This is a major contribution to the fundamental understanding of these chromophor es. More importantly, the experiment is able to be used for any ultrafast process. It has been previously suggested that Cu(I) systems could be studied, in which they undergo massive reorganizations in the excited state. 40 Being able to broadly apply this work to the inorganic chemistry community at large is incredibly valuable and may help shape future complexes and/or experiments. One potentially very exciting result that came from this work is the H ab 4 curren tly believe to be indicative of the major relaxation pathway accessed by the molecule to undergo the transition being studied. Further work must be done to verify or reject this hypothesis, but at the very least, relative ratios of these Marcus parameters can instruct computational chemists in the determination of the nuclear modes relevant to the photophysical processes. This pertains to the ultimate question of which vibrational modes are facilitating the ultrafast MLCT deactivation. With this information in hand, one can imagine designing a ligand system to purposefully hinder or remove altogether the relaxation pathway. Analogous work has already been done in this group on [Cr(acac) 3 ], in which sterically bulky t butyl groups were installed on the ligand backbone and served to slow down the intersystem crossing in this complex. 41 ,4 2 Additionally, studies on [Fe(terpy) 2 ] 2+ (prior to the ultrafast X - ray 4 3 or theoretical 4 4 work that were published more recently) sought to slow down the MLCT deactivation process by appending large substituents on the periphery of the ligand. 10 Ultrafast transient absorption results showed that these synthetic 306 modifications were not hindering the terpy - rocking mode, and therefore did not hinder this process. Moreover, in some cases, the MLCT lifetime was made even shorter relative to the parent complex. 3 4 While th ese data did not display the desired result, they clearly depict the power of substituents to affect the kinetics of the excited state processes. Current work is being done in which a ligand scaffolding was designed to impede the vibrational modes in the 5 T 2 1 A 1 relaxation in an Fe(II) chromophore and shows promise in the goal of lengthening the MLCT lifetime. 4 5 The key to this work will be the use of vibrational techniques, such as vibrational coherence and ultrafast infrared tra nsient absorption spectroscopy, to more directly determine the modes involved in ground state recovery in these Fe(II) complexes. Simultaneous work with theoretical chemists may help in the identification of the importance of certain modes. It may also aid in the understanding of the coupling between excited electronic states, which will play a role in the photophysics of the chromophores. Ashley and Jakubikova have recently published results on what they have found to be important nuclear modes in the rela xation of [Fe(bpy) 3 ] 2+ . 4 6 With these data, synthetic chemists will be better armed to intelligently design ligands that slow down the deactivation of the MLCT state or stop it entirely. 4.3.2 Inverting the MLCT and LF Manifolds P erhaps the most obvious strategy towards increasing the MLCT lifetime is through the increase of ligand field strength of the complex, such that the ligand field manifold now lies energetically above the MLCT manifold. This excited state ordering is analog ous to what is observed for most Ru(II) compounds. The way in which this might be achieved is open to debate. Work in our group has largely focused on the increased octahedral symmetry of the complex, thereby improving metal - ligand orbital overlap. A highe r symmetry molecule is better able to 307 support E and T states that are higher in energy than their split counterparts. [Fe(dcpp) 2 ] 2+ has been prepared and studied to that end, including in Chapter 4 of this work. 47 ,4 8 Complexes with a similar ligand scaffolding but with modified extenders are in the process of being synthesized so as to better understand whether this phenomenon is more broadly applicable. Early results indicate that this method is not viable, though ( Appendix A ). The dcpp ligand was modified such that the carbonyl was replaced with a vinyl group, resulting in [Fe(dvpp) 2 ] 2+ . Though the two complexes are nearly identical, the ground state recovery of [Fe(dvpp) 2 ] 2+ is greatly e longated to ~1 ns, more in line with [Fe(bpy) 3 ] 2+ . True, this says nothing about the MLCT lifetime, which should be measured for this complex. But the variable - temperature data imply that [Fe(dvpp) 2 ] 2+ is more similar to [Fe(bpy) 3 ] 2+ than it is to [Fe(dcpp ) 2 ] 2+ , implying that the higher symmetry around the metal center is not the only requirement to increasing the ligand field strength. Another method that is currently being hotly pursued by other research groups in this field is through the use of N - heterocyclic carbenes and other ligands with C - donor atoms. 49 - 5 2 The - donor carbon as the atom on the ligand bonding to iron will greatly increase the ligand field strength, much more than any simple substituent on a pyridine - based ligand as calculations show. 5 3 This work is showing tremendous resu lts, with MLCT lifetimes on the order of 100s of picoseconds. 5 1 One complex with a 16 ps lifetime has even been used in a DSSC device 49 , 5 2 and shown improved efficiency relative to the Ferrere cell, the first improvement on this device reported since Ferrere and Gregg first published their findings. 5 4 The single greatest downside to this work is that synthetic modi fications to the ligand to fine - tune the energetic or kinetic properties of the complex are nearly impossible. Still, as a general strategy, switching away from pyridine groups may serve to open up an entirely new and promising realm of Fe(II) chromophores . 308 4.3.3 Increasing Charge - Separated Distance via Delocalization The strategy of MLCT lifetime lengthening by extended delocalization in the excited state only developed very recently in our group. Limited work has been done in this realm, but the rational e has been examined and we believe it to be promising. The synthesis of [Fe(dpb) 3 ] 2+ to begin to understand the effects of increased delocalization on the MLCT lifetime was a positive first step. The extended conjugation of the ligand allowed for a more de localized wavefunction in the excited state, removing the electron physically farther from the metal center than in the traditional [Fe(bpy) 3 ] 2+ . The proposition is that the greater the distance of the charge - separated state, the less memory of the ground state the electron will have, thereby decreasing the rate of MLCT deactivation. This was observed in [Fe(dpb) 3 ] 2+ , as well as in two complexes with ligands that had increased conjugation around the metal center relative to either bpy or terpy. Both of thes e Fe(II) compounds exhibited a longer - lived MLCT state. Even more promising was the isoxazole - substituted complex, wh ich displayed an extremely (~900 fs) long - lived MLCT. From these data, it was also observed that the use of an aromatic system to increase conjugation performs better than a chain linker (such as a vinylene) when attempting to decrease the rate of deactivation. This - dicyanoacrylic acid - substituted iron(II) complex. A series of complexes have be en proposed to increase the delocalization even farther from the iron center, using a chain of phenyl and vinylene linkers. Data collected by a past group member shows a multi - hundreds of picosecond lifetime for a positive feature in compounds of that type . 5 5 The key to MLCT identification will be spectroelectrochemistry, and possibly Zn(II) analogues to eliminate any LMCT or ILCT (interligand charge transfer) features. Of the three avenues being pursued, this route currently appe ars to have the most promise. That being said, it should be evident that no single strategy will be the silver bullet to 309 increasing the MLCT lifetime. Each and every piece of information that is known about these chromophores must be put to use to build high efficiency iron dyes for photovoltaic applications. is proposed in Scheme 5. 6 . This complex uses information garnered from many experiments on these Fe(II) compounds. First, an N - heterocyclic carbene ligand scaffolding is used to drive the ligand field strength up. The ligand is tridentate to increase conjugation around the metal center. To further increase that delocalization, a phenyl - acetylene - phenyl linker is attached at the p ara - position of the central pyridine ring. Taking inspiration from the work on hindering vibrational modes, methyl groups are substituted in the ortho - positions of the phenyl directly bound to the pyridine moiety. The goal is to direct the excited electron to delocalize down the chain of linkers, so a cyano group is placed in the para - position of the furthest phenyl group, acting to draw electron pull the electron density evenly across both ligands, which would be counterproductive to the goal. Thus, a heteroleptic system must be devised in which the alternate ligand is incredibly electron donating. While this complex is clearly a synthetic nightmare, and may not ev en ultimately perform very well, it draws inspiration from all the work being performed on Fe(II) systems, and even work not on Fe(II) systems. Only in this way can we move the bar forward toward making Fe(II) have long - lived charge - separated excited state s. 310 Scheme 5. 6. Proposed Fe(II) complex that incorporates all of the strategies used in this work to lengthen the MLCT lifetime. R substituents here refer to electron - donating groups, such as methyl, methoxy, amine, or dimethylamine moieties. 4.4 Fe(I I) and Ru(II) Complexes as Analogues One of the major themes of this research project in general is the idea that methodologies can be developed on the photophysically more simple Ru(II) complexes, and then used to study 311 the true molecules of interest, the Fe(II) analogues. In [Ru(dpb) 3 ] 2+ and [Fe(dpb) 3 ] 2+ , we have a perfect case study of how this technique works. The energetics of the excited states in [Ru(dpb) 3 ] 2+ were relatively straightforward to determine and assign with the use of electrochemistry and emission spectroscopy. 25 , 5 6 The role of delocalization in the excited state was expanded on through the use of stimulated Raman scattering and ultrafast transient absorption spectroscopy. 25, 30 , 3 6 Once the more fundamental characteristics of the chromophore were understood, more nuanced studies of the influence of solvent and excitation wavelength could be used to give insight into solvation dynamics and conical intersections ( Chapter 4 ). 3 6 In moving to iron, though, there were more differences between the two complexes than was originally presumed. It is likely that the smaller ionic radius of the low - spin iron(II) center in conjunction with th e bulky, slightly electron - withdrawing phenyl substituents on the ligand caused complex dissociation to be a favorable mechanism when in solution or in the presence of anions or solvents capable of coordinating. This led to purity issues that were not obse rved for the Ru(II) complex. Additionally, no excited state absorption was observed in the ultrafast transient absorption spectroscopy that was performed on [Fe(dpb) 3 ] 2+ . In [Ru(dpb) 3 ] 2+ , this broad positive feature red of ~510 nm is assigned to ligand - bas - 3 MLCT surface, convolved with a ligand - to - metal charge transfer (LMCT) feature further to the red. The 532 nm probe wavelength was chosen for its ability to measure ligand - based dynamics in the long - 3 MLCT excited state. In the [F e(dpb) 3 ] 2+ analogue, though, it was expected that switch from a second - to a first - row transition metal would drastically decrease the ligand field strength, thus reducing the ligand field manifold energy to such that those states were energetically below the MLCT manifold. As with the other Fe(II) polypyridyls, this decreased the MLCT lifetime drastically, in this case to 160 ± 20 fs. Upon population of the lowest - energy excited state, the 5 T 2 , no vibrational cooling was observed at the pump - probe combinat ion 312 used. Exciting with a greater amount of energy will increase the driving force for excess energy to be dispersed via vibrational mechanisms. This may allow for vibrational cooling to be observed in the ground state bleach of [Fe(dpb) 3 ] 2+ . The side - by - side comparison of Fe(II) and Ru(II) analogues does not appear to be appropriate, not just from this study but from other results. The inherent differences in the two types of complexes allow for different techniques to be used to study one relative to the other. For example, Ru(II) chromophores are often analyzed by various emission spectroscopies. This would be an incredibly useful experiment to help determine the energetics of excited states in Fe(II) compounds, but due to the excited state structure, th ey do not emit. Even something as simple as electrochemistry performed on a Ru(II) dye can give information on the excited states, clearly not the case with Fe(II) complexes. Instead of comparing the photophysics of polypyridyl complexes of two metals with nothing more in common than a valence electron count, it would be more useful to begin considering alternative experiments to study the Fe(II) complexes, at least until they truly do begin to photophysically resemble their Ru(II) congeners. In many cases, theoretical work will be the first and best choice to understand the excited state dynamics. But experimental techniques that have not yet been explored on Fe(II) compounds should be considered. These methods might include 2D spectroscopy, to understand t he coupling of the excited states; ultrafast vibrational spectroscopies, to more directly probe vibrational modes and solute - solvent interactions; simultaneous ultrafast X - ray absorption and emission spectroscopies have already proven incredibly powerful o n a small number of Fe(II) complexes; and thermodynamic measurements to The latter point may be the most crucial piece of information needed for non - spin - crossover Fe(II) compounds. Without it, only ap proximations can be made, possibly leaving open more 313 questions than answers. In the work done throughout this dissertation, it became more and more apparent that fundamental questions with respect to Fe(II) photophysics were still largely unknown. To that end, an old inorganic chemistry trick has been to use large series of complexes to compare to each other and determine the effects of the changes made. That tactic is being used currently to address questions of ligand field strength, electron - donating and - withdrawing ability of substituents, and other various aspects of Fe(II) chromophores that have largely been taken for granted until now. With these data, a more complete understanding of the thermodynamic and kinetic factors that affect these iron - based complexes can be harnessed and used to design molecules with long - lived MLCT states, such that a more earth - abundant material can be used in photovoltaic applications. While this will improve the viability of photoredox catalysis and other applications, i t is much more important on a global level that solar energy conversion become more cost - effective but also more environmentally efficient. 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[Fe(bpy) 3 ]Cl 2 Initially, the question of outer - sphere reorganization energy in Fe(II) complexes was going to be studied in [Fe(bpy) 3 ] 2+ - bipyridine) as it is the prototypical Fe(II) compound. It was soon determined that the magnitude of change in reorganization energy as imposed by the solvent and 3 ] 2+ family of complexes. This in part led to the use of the [Fe(dcpp) 2 ] 2+ (dcpp = 2,6 - bis(2 - carboxypyridyl)pyridine) and its barrierless kinetics to study outer - sphere components. Th e work presented in this section is the initial results of the study of solvent and counteranion and their effects on the ground state recovery process in [Fe(bpy) 3 ] 2+ . The results of the solvent series of the Cl - salt will be analyzed on their own, and th en compared to the results of [Fe(bpy) 3 ](PF 6 ) 2 in acetonitrile. 1.1 Four Different Solvents 1.1.1 Acetonitrile Variable - temperature transient absorption (VT - TA) spectroscopy was performed to study the ground state recovery dynamics of [Fe(bpy) 3 ]Cl 2 in acet onitrile (MeCN) as outlined in Chapter 2 . The results of these experiments are shown in Figs. A . 1 and A .2 . When excited at 490 nm and probed at 530 nm, the room temperature lifetime is 1.03 ± 0.01 ns, as has been previously observed for other [Fe(bpy) 3 ] 2+ salts in MeCN. 1, 2 For everything reported herein, room temperature is approximately 293 K. The lowest tempera ture accessible in solution phase is 235 K. Over this temperature range, an activation energy of 320 ± 25 cm - 1 is obtained. The barrierless rate from the Arrhenius fit is found to be 220 ± 25 ps - 1 . Both of these values are within error of those found for 323 t he PF 6 - salt of this complex, also in MeCN. Figure A .1 . Representative ground state recovery data as a function of temperature of [Fe(bpy) 3 ]Cl 2 in MeCN. Excitation occurred at 490 nm and probing at 530 nm. Figure A .2 . Arrhenius plot of VT - TA data of [Fe(bpy) 3 ]Cl 2 in MeCN. The fit (black trace) of these data (red diamonds) gave an activation energy of 320 ± 25 cm - 1 and a preexponential factor of 220 ± 25 ps - 1 . The data fit well to a single - mode with R 2 = 0.947. 324 As was o utlined in Chapter 2 , the electrochemical data of the Fe(II/III) oxidation potential can be used in eqn. (A .1) to estimate the driving force for this reaction, according to: ( A . 1) In this equation, E ox is the (II/III) oxidation potential for the iron complex specified. To use this equation, an initial assumption of must be made, and here it is - 7300 ± 730 cm - 1 , as discussed in Chapter 2 . 3 Because we have not performed electrochemical experiments in - house on [Fe(bpy) 3 ] 2+ as a function of counteranion or solvent, we must assume the same driving force for the studies herein. Considering the relatively large error bars, we believe that the actual change in Marcus parame ters were calculated for [Fe(bpy) 3 ]Cl 2 in MeCN from the Arrhenius values. The reorganization energy was found to be 11100 ± 1000 cm - 1 , and the electronic coupling constant is 4.6 ± 0.2 cm - 1 . From these, the H ab 4 es are completely within error of the same parameters of [Fe(bpy) 3 ](PF 6 ) 2 in MeCN. 1.1.2 Methanol VT - TA was performed on [Fe(bpy) 3 ]Cl 2 in methanol (MeOH) to study the ground state recovery dynamics as a function of temperature. Those data are shown in Fig. A . 3 . From these results, an Arrhenius plot can be made ( Fig. A . 4 ). Based on the curve fitting, E a = 290 ± 20 cm - 1 , which is within error of the MeCN data. The frequency factor is likewise unchanged from the data in MeCN, at A = 250 ± 25 ps - 1 . Using eqn. (A .1) - 7300 ± 730 cm - 1 10800 ± 1000 cm - 1 . H ab , again, is within error of the MeCN data, 4.3 ± 0.1 cm - 1 , such that H ab 4 = 1/(32 ± 4). 325 Figure A .3 . Representative ground state recovery data as a function of temperature of [Fe(bpy) 3 ]Cl 2 in MeOH. Excitation occurred at 490 nm and probing at 530 nm. Figure A .4 . Arrhenius plot of VT - TA data of [Fe(bpy) 3 ]Cl 2 in MeCN. The fit (black trace) of these data (red diamonds) gave an activation energy of 250 ± 25 cm - 1 and a preexponential factor of 250 ± 25 ps - 1 . The data fit well to a single - mode with R 2 = 0.968. 326 1.1.3 Acetone The ground state recovery dynamics of [Fe(bpy) 3 ]Cl 2 were studied in acetone, probed at 530 nm upon excitation at 490 nm. It should be noted that these data were only collected once and need to be recollected for reproducibility. The VT - TA dat a are shown in Fig. A . 5 . At room temperature, the lifetime is 1.13 ± 0.05 ns. The lowest temperature that could be accessed while keeping the sample in solution was 185 K. At this temperature, the lifetime of the complex is 2.47 ± 0.06 ns. From the VT data, an Arrhenius plot can be made ( Fig. A . 6 ), from which E a = 295 ± 10 cm - 1 and A = 255 ± 20 ps - 1 . With these values, the reorganization energy is found to be 10900 ± 1000 cm - 1 and H a b is 4.2 ± 0.2 cm - 1 . The ratio of H ab 4 Figure A .5 . Ground state recovery data as a function of temperature of [Fe(bpy) 3 ]Cl 2 in acetone. Excitation occurred at 490 nm and probing at 530 nm. 327 Figure A .6 . Arrhenius plot of VT - TA data of [Fe(bpy) 3 ]Cl 2 in acetone, collected once. The fit (black trace) of these data (red diamonds) gave an E a of 295 ± 10 cm - 1 and A = 255 ± 20 ps - 1 . The data fit well to a single - mode with R 2 = 0.989. 1.1.4 Water As with the o ther three solvents, the ground state dynamics of [Fe(bpy) 3 ]Cl 2 are determined as a function of solvent ( Fig. A . 7 ). One of the major issues with water, however, is the very high freezing point. This limits the temperature range ac cessible in the fluid solution to 275 K to room temperature. As has been previously observed, 1 the lifetime of [Fe(bpy) 3 ]Cl 2 in H 2 O at room temperature is 0.68 ± 0.01 ns. This is a more than 30% reduction in the lifetime relative to any of the other solvents studied here. Additionally, from the VT - TA data and Arrhenius fitting ( Fig. A . 8 ), the barrier associated with this process is 175 ± 30 cm - 1 , which is significantly different from the other sol vents. The barrierless rate, likewise, is also outside of error with A = 295 ± 40 ps - 1 . 328 Figure A .7 . Representative ground state recovery data as a function of temperature of [Fe(bpy) 3 ]Cl 2 in acetone. Excitation occurred at 490 nm and probing at 520 nm. The kinetics were not significantly different when probed at 530 nm. 329 Figure A .8 . Arrhenius plot of VT - TA data of [Fe(bpy) 3 ]Cl 2 in acetone. These data were only collected once. The fit (black trace) of these data (red diamonds) gave an activation energy of 175 ± 30 cm - 1 and a preexponential factor of 295 ± 40 ps - 1 . The data fit modestly to a single - mode with R 2 = 0.804. The Arrhenius values obtained from Fig. A .8 can be used with eqn. (A .1) to find the Marcus parameters associated with the 5 T 2 1 A 1 transition in [Fe(bpy) 3 ]Cl 2 in H 2 O. With an initial - 7300 ± 730 cm - 1 - 1 . Surprisingly, the reorganization energy in H 2 O is not significantly different from those found in MeCN, MeOH, or acetone. H ab , however, is only within error of the value calculated in acetone; the electronic coupling constant in water is found to be 3.8 ± 0.3 cm - 1 , such that H ab 4 1.2 Analysi s of Results A summary of the data discussed above can be found in Tables A . 1 and A .2 . From these results, it is clear that no significant difference in observed in the data collected in MeCN, MeOH, o r acetone. Even with the slightly longer lifetime in acetone at room temperature, all of the Arrhenius and Marcus parameters for those three solvents are calculated to be within error of each 330 other. Furthermore, they are all within error of the same parame ters found for [Fe(bpy) 3 ](PF 6 ) 2 in MeCN. This verifies that for these dynamics, in these complexes, the counteranion does not affect the kinetics or energetics. Table A . 1. Summary of lifetimes and Arrhenius parameters of the ground state recovery dynamics in [Fe(bpy) 3 ]Cl 2 in various solvents. Solvent Lifetime at RT (ns) E a (cm - 1 ) A (ps - 1 ) MeCN 1.03 ± 0.01 320 ± 25 220 ± 25 MeOH 1.00 ± 0.03 290 ± 20 250 ± 25 Acetone a 1.13 ± 0.05 295 ± 10 255 ± 20 Water 0.68 ± 0.01 175 ± 30 295 ± 40 a Data only collected once. Table A . 2. Marcus parameters for ground state recovery of [Fe(bpy) 3 ]Cl 2 in various solvents. Solvent - - 1 ) - 1 ) H ab (cm - 1 ) H ab 4 MeCN 7300 ± 730 11100 ± 1000 4.6 ± 0.2 1/(25 ± 5) MeOH 7300 ± 730 10800 ± 1000 4.3 ± 0.1 1/(32 ± 4) Acetone a 7300 ± 730 10900 ± 1000 4.2 ± 0.2 1/(36 ± 5) Water 7300 ± 730 9900 ± 1000 3.8 ± 0.3 1/(49 ± 14) a Data only collected once. The biggest (and only) difference is observed when water is used as the solvent. In this case, the activation energy is nearly half of what is found in the other three solvents. Interestingly, 331 though, the barrierless rate in water is within error of those in MeOH and acetone. This could, however, be an artifact of the larger error bars on the data collected in water. These error bars are likely so large simply because only five temperature points are being considered. It does make sense that the data in H 2 O would be substantially different in some way to the other solvents measured. The work done by Miller and McCusker expands on the idea that as a solvent, H 2 O fundamentally changes the dynamics of ground state recovery in [Fe( bpy) 3 ] 2+ compared to other solvents like alcohols, nitriles, and diols. 1 The only true indicators of what may be occurring come from the activation energy and H ab 4 VT - TA o n [Fe(bpy) 3 ] 2+ in H 2 O through the use of cryostat heaters may help improve error bars on the measurements, thereby ensuring which parameters are within error of each other. 2. [Fe(dcpp) 2 ] 2+ These results are a continuation of those presented in Chapter 3 of this work. The data showed in that chapter are for the three counteranions (i.e., BF 4 - , PF 6 - , BAr F - ) of [Fe(dcpp) 2 ] 2+ in acetonitrile, whereas here those three salts are still of interest, but in acetone. This was to address the question of whether or not counteranion interaction and therefore the outer - sphere reorganization energy was influenced by the specific solvent. Although previous work on [Fe(bpy) 3 ] 2+ has shown that the counteranion plays no real role in the ground state recovery dynamics, 1 it is also known that the nature of the solvent can influence the relationship between a cation and anion. 4, 5 These results will be analyzed on their own but also in comparison to the analogous data collected in acetonitrile. 332 2.1 Different Counteranions in Acetone 2.1.1 BF 4 - The ground state recovery lifetime of [Fe(dcpp) 2 ](BF 4 ) 2 was measured as a function of temperature when in acetone; representative data are shown in Fig. A . 9 . The excitation wavelength was 490 nm, and the dynamics were probed at 540 nm. When the Arrhenius plot ( Fig. A . 10 ) was made, an activation energy of 50 ± 10 cm - 1 was found. Additionally, the preexponential rate was 190 ± 10 ps - 1 . Because electrochemical data was not collected for [Fe(dcpp) 2 ] 2+ in different supporting electrolytes, the oxidation potential for the Fe(II/III) couple is only observed in the PF 6 - salt. Based on past work on different complexes, 6 we do not believe that the counteranion will drastically change this potential. That b 2 ] 2+ is calculated from the same Fe(II/III) oxidation potential regardless of counteranion or solvent. From eqn. (A .1) estimated to be - 12220 ± 1220 cm - 1 - 1 and H ab = 5. 2 ± 0.3 cm - 1 . Finally, the H ab 4 and solvents will be reserved until Appendix A Section 2.2 . 333 Figure A .9 . Representative VT - TA data of the ground state recovery of [Fe(dcpp) 2 ](BF 4 ) 2 in ex c pr obe = 540 nm. Figure A .10 . Arrhenius plot of all the VT - TA data collected of [Fe(dcpp) 2 ](BF 4 ) 2 in acetone. From this plot, E a = 50 ± 1 0 cm - 1 and A = 190 ± 10 ps - 1 . The data were found to fit modestly to a single mode with R 2 = 0.747. 334 2.1.2 PF 6 - The VT - TA data for the 5 T 2 1 A 1 transition in [Fe(dcpp) 2 ](PF 6 ) 2 in acetone are shown in Fig. A . 11 . They were measured at 540 nm upon excitation at 490 nm. The dynamics were also collected when pumped at 610 nm, and all values were within error between the two excitation energies; the only difference being the average R 2 value of the Arrhenius plot, with R 2 = 0.90 0 for ex c = 610 nm and R 2 ex c = 490 nm. The Arrhenius plot ( Fig. A . 12 ) yielded E a = 50 ± 10 cm - 1 and A = 190 ± 10 ps - 1 . As with the BF 4 - - 12220 ± 1220 cm - 1 13900 ± 1500 cm - 1 with H ab = 5.2 ± 0.3 cm - 1 . The ratio, H ab 4 Figure A .11 . Representative VT - TA data of [Fe(dcpp) 2 ](PF 6 ) 2 in acetone at 540 nm when excited at 490 nm. 335 Figure A .12 . Arrhenius plot of all the data collec ted by VT - TA of [Fe(dcpp) 2 ](PF 6 ) 2 in acetone. From this fit, the activation energy was found to be 50 ± 10 cm - 1 and the frequency factor is 190 ± 10 ps - 1 . The data fit modestly to a single mode with R 2 = 0.816. 2.2 Analysis of Results The data for the BF 4 - and PF 6 - salts of [Fe(dcpp) 2 ] 2+ in acetone are shown above whereas the BAr F - salt data can be found in Chapter 3 . Table A . 3 gives a comparison of the Arrhenius values of the three salts, and Table A . 4 does the same with the Marcus parameters. From these data, it is apparent that even without the perhaps overly generous 10% error bars, all of the Arr henius and Marcus values are identical in acetone. In fact, in most cases the parameters measured for [Fe(dcpp) 2 ] 2+ in acetone were within error of those measured in acetonitrile. The only exception to this, obviously, is the activation energy, which is tw ice as large in acetonitrile than in acetone. Based on these results, it does not appear as though the solvent significantly affects how the counteranion interacts with and therefore stabilizes the Fe(II) cation. Because the mechanism of solvation is yet u nknown for this complex (and in Fe(II) polypyridyls in general), it is unlikely that these results are applicable to all solvents. That being said, as was true with 336 acetonitrile, the counteranion does not appear to significantly affect the energetics or ki netics of ground state recovery in [Fe(dcpp) 2 ] 2+ . Table A . 3. Summary of lifetimes and Arrhenius values of [Fe(dcpp) 2 ] 2+ in acetone. Anion Lifetime at RT (ps) Lifetime at 245 K (ps) E a (cm - 1 ) A (ps - 1 ) BAr F - 240 ± 5 255 ± 5 55 ± 15 185 ± 15 PF 6 - 240 ± 5 255 ± 5 50 ± 10 190 ± 10 BF 4 - 245 ± 5 250 ± 5 50 ± 10 190 ± 10 Table A . 4. Marcus parameters for [Fe(dcpp) 2 ] 2+ in acetone. Anion - - 1 ) - 1 ) H ab (cm - 1 ) H ab 4 BAr F - 12220 ± 1220 14000 ± 1500 5.2 ± 0.3 1/(19 ± 4) PF 6 - 12220 ± 1220 13900 ± 1500 5.2 ± 0.3 1/(20 ± 2) BF 4 - 12220 ± 1220 13900 ± 1500 5.2 ± 0.3 1/(20 ± 2) 3. [Fe(dvpp) 2 ](PF 6 ) 2 In this complex, dvpp is the vinyl analogue of dcpp as seen in Scheme A . 1 , such that dvpp = 2,6 - bis(2 - divinylpyridyl)pyridine. By replacing the carbonyl moiety in dcpp with a = CH 2 group, it was expected that only specific carbonyl - solvent effects would be mitigated, and that the overall dynamics of [Fe(dvpp) 2 ] 2+ would be overal l very similar to those of [Fe(dcpp) 2 ] 2+ . This premise was furthered by the fact that the X - ray crystal structures of the two analogues overlay nearly 337 perfectly on top of each other. 7 However, the room temperature ground state rec overy lifetime of [Fe(dvpp) 2 ] 2+ immediately told a different story ( Fig. A . 13 ). This process was found to occur with a 1.06 ± 0.03 ns lifetime at room temperature, which is within error of the lifetime of [Fe(bpy) 3 ] 2+ . Electrochemical data helped, in part, to explain this disparity: while the Fe(II/III) oxidation couple in [Fe(dcpp) 2 ] 2+ occurred at 1.29 V vs. Fc/Fc + , 8 in [Fe(dvpp) 2 ] 2+ , that same one - electron process occurred at 0.64 V vs. Fc/Fc + . 9 Relative to the 0.665 V vs. Fc/Fc + oxidation potential of [Fe(bpy) 3 ] 2+ , it is apparent that the electronics of [Fe(dvpp) 2 ] 2+ have been drastically altered relative to [Fe(dcpp) 2 ] 2+ . As has previously been discussed, electrochem istry is only a measure of the t 2g orbitals in these Fe(II) complexes and does not truly describe the electronic states. 2 We will continue to use it as a first - approximation of the ligand field strength difference, and therefore the driving force difference between iron chromophores. Based on eqn. (A .1) [Fe(dvpp) 2 ](PF 6 ) 2 is found to be - 710 0 ± 710 (with 10% error bars by convention 2 ). This is within error of [Fe(bpy) 3 ] 2+ . From all of these data, it was highly desirable to perform variable - temperature studies in order to determine further kinetic and energetic paramete rs of [Fe(dvpp) 2 ] 2+ so as to be compared to the carboxy - analogue, [Fe(dcpp) 2 ] 2+ . 338 Scheme A . 1. General structure for both [Fe(dcpp) 2 ] 2+ and [Fe(dvpp) 2 ] 2+ . Figure A .13 . Room temperature ground state recovery dynamics of [Fe(dvpp) 2 ](PF 6 ) 2 in MeCN. The data (black diamonds) fit well to a single exponential (red trace), as determined by the residuals (black trace, above) centered around 0. These data have been collected mul tiple times and the error propagated to determine a lifetime of 1.06 ± 0.03 ns. 339 3.1 Acetonitrile The VT - TA data of the ground state recovery in [Fe(dvpp) 2 ](PF 6 ) 2 in acetonitrile are shown in Fig. A . 14 . For these data, excitation o ccurred at 480 nm and probes of 530 and 510 nm were used. Without further experiments being performed, it cannot be said that the results of these two probes yielded significantly different Arrhenius and Marcus values. The lifetime at 240 K was found to be 1.44 ± 0.05 ns, which is an approximately 35% increase from the room temperature kinetics. This corresponds to a barrier of 310 ± 40 cm - 1 ( Fig. A . 15 ), which is the same as that of [Fe(bpy) 3 ] 2+ . Similarly, the barrierless rate was found to be 265 ± 40 ps - 1 . The error bars on these measurements were very large, possibly because the sample was too concentrated for the pump and probe wavelengths used here. Figure A .14 . Representative VT - TA data of [Fe(dvpp) 2 ](P F 6 ) 2 in MeCN upon excitation at 480 nm and probing at 530 nm. 340 Figure A .15 . Arrhenius plot for [Fe(dvpp) 2 ](PF 6 ) 2 in MeCN. Fitting these data yielded E a = 310 ± 40 cm - 1 and A = 265 ± 40 ps - 1 . The data fit modestly to a single mode with R 2 = 0.885. From the electrochemical data and the Arrhenius plot, the Marcus values for [Fe(dvpp) 2 ](PF 6 ) 2 - 7100 ± 710 cm - 1 , the reorganization energy is determined to be 10700 ± 1000 cm - 1 . The electronic coupling con stant was then determined to be 4.1 ± 0.5 cm - 1 , from which H ab 4 bars, particularly on H ab and H ab 4/ of those of [Fe(bpy) 3 ](PF 6 ) 2 , as were shown i n Chapter 2 . It is apparent that major electronic changes have been imparted on this Fe(II) complex by the change of the carbonyl to a vinyl group. By this seemingly simple substitution, a bis - reatly resemble those of a tris - bidentate. Clearly these data will need to be recollected under various conditions (e.g., solvent, pump and probe wavelengths). It would also be beneficial to have further characterization of [Fe(dvpp) 2 ] 2+ by simultaneous ul trafast X - ray absorption and emission spectroscopies as were performed for the carboxy - version. 10 341 4. [Fe(dtbb) 3 ]Br 2 These data were originally collected in order to better understand the dynamics at work in the studies by Miller a nd McCusker. 1 [Fe(dtbb) 3 ] 2+ - di - t butyl - - bipyridine) had been shown via theoretical work to display a larger difference in solvation energy than [Fe(bpy) 3 ] 2+ . This corresponds to the energetic de - 5 T 2 and 1 A 1 potential energy of these states, and thus with larger differences (i.e. 3 ] 2+ , it was believed that the best experimental verification of these results would be obtained by the variable - temperature study of ground state recovery of this complex in two solvents of the same family with variable chain l ength (i.e., MeOH and 1 - BuOH). Those results are presented here. 4.1 Two Different Solvents 4.1.1 Methanol The ground state recovery dynamics of [Fe(dtbb) 3 ]Br 2 were measured in MeOH upon excitation at 550 nm and probing at 490 nm. Representative data are s hown in Fig. A . 16 . The room temperature lifetime of this complex in MeOH is 1.08 ± 0.05 ns. The lowest temperature achieved in MeOH was 180 K to maintain fluid solution, at which temperature the lifetime was 2.87 ± 0.14 ns. From t he Arrhenius plot ( Fig. A . 17 ), an activation energy of 325 ± 20 cm - 1 is determined and a barrierless rate of 225 ± 30 ps - 1 3 ] 2+ family. Applying these parameters to Marcus theory and using the driving force found in Chapter 2 - 6100 ± 600 cm - 1 ), the reorganization energy is found to be 9600 ± 900 cm - 1 with H ab = 4.3 ± 0.3 cm - 1 , which are unchanged from the data collected in MeCN in Chapter 2 . The H ab 4 ratio was determined to be 1/(28 ± 7), which is completely in keeping with the ratio found for all 3 ] 2+ compounds. It is unsurprising that the ground stat e recovery process in 342 [Fe(dtbb) 3 ] 2+ should occur with the same kinetics and energetics when in MeCN and MeOH. The more telling results will be in the comparison to the data collected in 1 - BuOH. Figure A .16 . Representative variable - temperature data of [ Fe(dtbb) 3 ]Br 2 in MeOH. Excitation occurred at 550 nm, with probing at 490 nm. 343 Figure A .17 . Arrhenius plot of all the data of [Fe(dtbb) 3 ]Br 2 in MeOH. This fit gives an activation energy of 325 ± 20 cm - 1 and a barrierless rate of 225 ± 30 ps - 1 . These data fit well to a single Arrhenius mode with R 2 = 0.971. 4.1.2 1 - Butanol When studied at room temperature, the ground state recovery lifetime of [Fe(dtbb) 3 ]Br 2 in 1 - BuOH is lengthened relative to the dynami cs in MeOH, at 1.28 ± 0.04 ns. From the variable - temperature transient absorption studies ( Fig. A . 18 ), the coldest temperature lifetime is 2.15 ± 0.08 ns at 220 K. The Arrhenius plot of all the combined data are shown in Fig. A . 19 . An initial fit of these data yielded a barrier of 250 ± 10 cm - 1 . However, it can be seen that the Arrhenius line does not fit the data well as determined by the residuals, despite the fact that the R 2 = 0.938. If the lowest three temperatures are excluded ( Fig. A . 20 ), though, the fit is greatly improved, with R 2 = 0.961. this fit yields an E a of 330 ± 15 cm - 1 and A = 255 ± 20 ps - 1 . 344 Figure A .18 . Representative data of the v ariable - temperature ground state recovery dynamics of [Fe(dtbb) 3 ]Br 2 in 1 - BuOH upon excitation at 550 nm and probing at 500 nm. The dynamics did not change significantly when probed at 490 nm, as is expected of ground state recovery. 345 Figure A .19 . Arr henius plot of the ground state recovery lifetimes of [Fe(dtbb) 3 ]Br 2 in 1 - BuOH. The data (red diamonds) are not represented well by the fit (black trace, lower) as determined by the residuals (black trace, upper). This is likely due to the water content of 1 - BuOH (see text for details). 346 Figure A .20 . Arrhenius fit of the temperature - dependent lifetimes of [Fe(dtbb) 3 ]Br 2 in 1 - BuOH. The data (red diamonds) are fit (black trace, lower) best when excluding the lowest three temperatures, as indicated by the residuals (black trace, upper). This fit yields an E a = 330 ± 15 cm - 1 and A = 255 ± 20 ps - 1 . The most likely explanation for the need to exclude the lowest three temperatures is the greater water content of 1 - BuOH relative to MeOH. Water has a muc h higher freezing point (272 K) than 1 - BuOH (183 K), serving to raise the freezing point and perhaps inducing the fluid - to - glass transition at a higher temperature than would normally occur. This transition is known to cause the kinetics measured to behave in a non - Arrhenius fashion. 11 Considering the bi - modal Arrhenius behavior, only the warmer temperatures (T > 220 K) were considered in the fitting. From the E a - 6100 ± 600 cm - 1 , it was found that the reorganization energy is 9700 ± 900 cm - 1 . The electronic coupling constant is 4.1 ± 0.2 cm - 1 , and the H ab 4 - BuOH used here was ACS reagent grade, indicating that it likely 347 has a higher water content than either spectrop hotometric or HPLC grade would. In that case, these data should simply be recollected in fresher solvent with higher purity. If the Arrhenius plot is linear, then water was most likely the culprit. If however, the Arrhenius plot remains bimodal, pump scatt er could be an issue, or there truly are two separate barriers associated with ground state recovery kinetics of [Fe(dtbb) 3 ] 2+ that are only observable when the compound is in 1 - BuOH. This would clearly be a phenomenon of considerable interest, if it is re al. 4.2 Analysis of Results A summary of the data of [Fe(dtbb) 3 ] 2+ complex in various solvents, can be found in Tables A . 5 and A .6 . Despite the difference in room temperature lifetimes in [Fe(dtbb) 3 ] 2+ in MeOH versus 1 - BuOH, the Arrhenius and Marcus parameters show no substantial change with the different solvents. From these results, it cannot be said that the increase in chain length in the solvent affects the solvation energy of the 5 T 2 and 1 A 1 electronic states any differently than with a short - chain alcohol, or even with the short - chain nitrile. The data should not be extrapolated to other systems, though. It is probable that the specific alcohol - solute interaction is not changing with the chain length (as is expected). What would be more telling, likely, is a comparison of the effect of chain length with different polar heads; for example, a comparison of the results in 1 - BuOH to 1 - BuCN. In general, it should be apparent that VT - TA is a strong tool that should be used regularly to give greater insight into the photophysical processes of various chromophores. 348 Table A . 5. Summary of lifetimes and Arrhenius values of [Fe(dtbb) 3 ] 2+ in three different solvents. Anion/Solvent Lifetime at RT (ns) Lifetime at 240 K (ns) E a (cm - 1 ) A (ps - 1 ) PF 6 - in MeCN 1.07 ± 0.01 1.48 ± 0.02 315 ± 15 230 ± 15 Br - in MeOH 1.08 ± 0.05 1.54 ± 0.07 325 ± 20 225 ± 30 Br - in 1 - BuOH 1.28 ± 0.04 1.86 ± 0.09 330 ± 15 255 ± 20 Table A . 6. Marcus parameters of [Fe(dtbb) 3 ] 2+ in various solvents. Anion/Solvent - - 1 ) - 1 ) H ab (cm - 1 ) H ab 4/ PF 6 - in MeCN 6100 ± 600 9500 ± 900 4.3 ± 0.2 1/(29 ± 4) Br - in MeOH 6100 ± 600 9600 ± 900 4.3 ± 0.3 1/(28 ± 7) Br - in 1 - BuOH 6100 ± 600 9700 ± 900 4.1 ± 0.2 1/(34 ± 5) 349 REFERENCES 350 REFERENCES 1. Miller, J. N.; McCusker, J. K. Outer - Sphere Effects on the Excited State Dynamics of Ligand Field States in Fe(II) Polypyridyl Complexes. Manuscript in preparation. 2. Carey, M. C.; Adelman, S. L.; McCusker, J. K. Insights Into the Excited State Dynamics o f Fe(II) Polypyridyl Complexes from Variable - Temperature Ultrafast Spectroscopy . Submitted . 3. Sutin, N. Nuclear, Electronic, and Frequency Factors in Electron - Transfer Reactions. Acc. Chem. Res. 1982 , 15 , 275 - 282; DOI: 10.1021/ar00081a002 . 4 . Marcus, R. A.; Sutin, N. Electron Transfers in Chemistry and Biology. Biochim. Biophys. Acta 1985 , 811 , 265 - 322; DOI: 10 .1016/0304 - 4173(85)90014 - X . 5. Barbara, P. F.; Meyer, T. J.; Ratner, M. A. Contemporary Issues in Electron Transfer Research. J. Phys. Chem. 1996 , 100 , 13148 - 13168; DOI: 10.1021/jp9605663 . 6 . Shinkle, A. A. Non - Aqueous Single - Metal Redox Flow Batteries. Ph.D. Thesis, University of Michigan, Ann Arbor, MI, 2013. 7 . Yarranton, J. T. ; Staples, R. J. U npublished results. 8 . Jamula, L. L. Design and Synthesis of Iron(II) Terpyridyl Complexes for Application in Dye - 9 . Jamula, L. L. Exploring Design Strategies to Tune the Electronic S tructure and Ultrafast Dynamics of Iron(II) Polypyridyl Chromophores. Ph.D. Thesis, Michigan State University, 2013. 10 Németh, Z.; Pápai, M.; Roszályi, E.; Cho, H.; K im, T. K.; Yarranton, J. T.; Mukherjee, S.; Schoenlein, R. W.; Jakubikova, E.; Huse, N.; McCusker, J. K.; Southworth, S. H.; Young, L.; Vankó, G.; Bressler, Ch. [Fe(dcpp) 2 ] 2+ Ligand - Field Excited State Geometry and Spin Characterized with Combined Ultrafas t X - ray Spectroscopies. Submitted . 1 1 . Lumpkin, R. S.; Meyer, T. J. Effect of the Glass - to - Fluid Transition on Excited - State Decay: Application of the Energy Gap Law. J. Phys. Chem. 1986 , 90 , 5307 - 5312; DOI: 10.1021/j100412a080 . 351 APPENDIX B . ULTRAFAST PULSE DURATION DETERMINATION 1. Ultrafast Pulses The advent of ultrafast laser systems brought about an entirely new set of challenges to spectroscopists, evoked by the ultrashort nature of the laser pulses. Many applications for l aser spectroscopy require that pulses be as short as possible, a restriction that brings about many unwanted side - effects in the generation and characterization of these pulses. From the Heisenberg Uncertainty Principle the time - bandwidth product can be de rived: (B .1) are inversely related, their product yielding a value no less than 0.441 for pulses with a Gaussian shape. 1 A pulse is said to be transform - limited if the temporal duration is as short as possible given the amount of available spectral bandwidth. The more spectral bandwidth provided, the shorter the pulses may be in the time domain. The generation of ultrashort pulses, therefore, requires large amounts of bandwidth in the frequency domain, which explains the appeal of broadband lasers. 2 One laser system in our laboratory is shown in Scheme B .1 . It is described in more detail in Chapter 4 of this work, and elsewhere. 3 - 5 The optical parametric amplifier (OPA) uses the output from the regenerative amplifier (regen) to generate a singl e wavelength beam with some approximately Gaussian distribution of frequencies. There are three main methods by which data may be collected: 1) one - color, 2) two - color, and 3) full spectra. These differ in their origin of the pump and probe beams and may b e further differentiated in the detection scheme used to collect data. In (1), a one - color experiment refers to the use of the output from only a single OPA. This generates the pump beam, which is then separated by the use of beam splitter to allow for bot h a 352 pump and probe line of the same color. The two - color experiment (2), then, refers to the use of two OPAs to generate the pump and probe individually ( Scheme B .1 ). This increases the number of pump - probe wavelength combinati ons that are available to the spectroscopist. Finally, (3) full spectral data collection uses one OPA to generate the pump, while the probe uses the regen output directly and propagates through some white light generating medium such that spectra can be co llected over the entire visible region. Scheme B .1. Schematic of the ultrafast laser setup that produces nominally 35 fs pulses out of the OPAs. A two - color experiment is shown in this layout, in which both OPAs are used to produce single wavelength pum p and probe beams. For a more complete description, please see Chapter 4 . 353 These experimental setups may be further altered in the choice of detection setup. If single - wavelength kinetics are desired, it is typical to use some type of wavelength separator, like a bandpass filter or monochromator (MC) with a single - channel photodi ode. This setup is shown in Scheme B .2 , but can be used in combination with any of the experiments mentioned. In this scheme, both the pump and probe are focused by a lens and turned by steering mirrors (black lines) such that the probe is focused directly into the sample and the focal point of the pump is slightly behind the sample (on the side of the detector). A beam block is used to keep the pump from entering the detector. A Glan - Taylor polarizing beam splitter (analyzing p olarizer, AP) may be used after the sample in order to correct for polarization effects, or for use in pulse characterization. Scheme B .2. Enhanced view of the two - color setup near the sample and detection unit, from Scheme B .1 . This layout and detection scheme may be used for other experiments, not just a two - color setup. 354 Alternatively, full spectral data collec tion may be desired. This can be used in conjunction with any of the three setups outlined above. In this case, no wavelength selector is used, and instead the probe beam after the sample is focused onto the face of a liquid light guide (as seen in Scheme B .1 ) or a fiber optic cable. This directs the beam into a spectrometer equipped with a grating to disperse the transmitted light that is then recorded by a multichannel photodiode array or charge - coupled device detector. This a llows for all the probe wavelengths to be detected individually, as opposed to being treated as identical, which occurs with the single - channel photodiode. Ultimately, full spectral detection increases the spectral resolution of the data. The pulses that e merge from the regen and the OPAs are nominally 35 fs in duration. Due to dispersion, however, these ultrashort pulses that have large spectral bandwidth are high in susceptibility to smearing temporally when they propagate through media. See Chapter 2 or Appendix F for further explanation. The laser system as shown in Scheme B .1 requires that the pump and probe propagate through at a minimum an ND filter (neutral dens ity), a waveplate, a polarizer, a lens, and the sample in its cuvette. To preemptively compensate for the positive chirp introduced by these materials, a Brewster prism pair is used on the respective pump and probe lines to present negative or anomalous ch irp. 6 This pair is implemented in a folded fashion, such that two prisms may do the work of four. When the pulse propagates through the first prism, spectral smearing occurs; passage through the second prism essentially acts to co llimate beam such that no further spectral expansion happens. The beam is then reflected by a mirror back into the second prism, slightly above the position where it originally propagated through. In this step, the additional spectral bandwidth introduced allows the beam to be temporally compressed. The reverse passage through the prism also spectrally compresses the pulse. Finally, the beam traverses back through the first prism to recombine the pulse temporally, producing an ultrashort pulse. As 355 this puls e propagates through the optics on the laser table, it will be spread temporally; the precompensation of chirp afforded by the Brewster prism pair means that by the time the pulses reach the detector, they should be approximately 35 fs in duration again, p rovided the prism compensation is ideal. Many applications require pulses that are as temporally short as possible. In conjunction with the highly susceptible nature of these pulses to dispersion, it is critical to thoroughly characterize ultrafast pulses. Unfortunately, there is no real consensus in the literature as to the best method for this. The methods outlined below are simply the techniques that we have chosen to use in our lab. Others exist, such as two - photon absorption, 7 ,8 frequency - resolved optical gating, 9 or spectral phase interferometry for direct electric - field reconstruction, 10 but will not be expanded on here. Ultimately, the methods utilized herein provide two cr itical pieces of pulse exc probe for the pulse durations of the pump and probe respectively) and the instrument response function, or IRF. The latter refers to the dead time in a spectral measurement at early time that is due to the system itself. Any kinetics that are occurring during this time will be obscured by the response of the system. The IRF is then measured so that only true kinetics specific to the sample may be reported. Pulse d urations may be found through the use of the optical Kerr effect or autocorrelation, whereas a cross - correlation measurement is used to determine the IRF of the system. In each of these collection methods, it is important to use the solvent that the sample of interest will eventually be dissolved in. Some solvents have drastically different responses to ultrafast laser pulses than others. 5 Furthermore, a sample cuvette should be used when characterizing the pulses that is similar if not identical to the spectroscopist to differentiate between laser - related phenomena and true features originating from 356 the sample molecule. Our laboratory also houses a second laser system, which is limited to (3). This discussion generally applies to that system, but due to its longer pulses and intended use (i. e., measuring nanosecond ground state recovery lifetimes in Fe(II) chromophores), chirp compensation and pulse characterization are not as critical. There is no prism pair on this laser system, and pulse characterization by the methods outlined below is pe rformed only when short - time kinetics are collected. 2. Characterization Techniques 2.1 Cross - Correlation Cross - correlation allows for the measurement of the time associated with the ultrashort pump and probe pulses interacting with each other and with t he surrounding medium. 11 This interaction is known as cross - phase modulation and is used to describe two different pulses. These pulses may have been generated by two different means (e.g., two different OPAs, output from the rege n and an OPA), and thus they must be mathematically treated as two separate entities. Cross - phase modulation occurs because of the very high peak powers present in ultrafast pulses. While the energy of the pulse (E pulse he peak power accounts for the ultrashort time duration of the pulse. when the average power (P ave ) of the laser beam is 3 mW, for example, the energy per pulse may be found by (B .2) in which f is the repetition rate of the laser, 1 kHz for the systems used herein. In this example, the pulse ) , P peak may be calculated using eqn. (B .3) : (B .3) 357 Under these conditions, P peak = 60 MW . Not only could such a power be extremely damaging, but it clearly will induce many power - related phenomena within the sample. This incredibly high peak power may be utilized to measure the IRF of the system through the use of cross - phase modulation in a cross - correlation spectrum. The pump and probe are polarized at magic angle with respect to one another. When they meet temporally and spatially in the solvent, a huge amount of energy is transferred between the two pulses and into the solvent itself, ind ucing a large transient signal, despite the solvent not absorbing visible light. This can be seen in F ig. B .1 one - half the difference between when the signal starts to appear at negative time and when the signal returns to baseline at positive time. In a nanosecond system, the pulse powers are much weaker and thus a Gaussian is observed for this process, which is why the IRF for these systems is frequen tly reported in terms of a FWHM. With higher peak powers, the measured signal is often some derivative of a Gaussian, such as is seen in Fig. B .1 . 358 Figure B . 1 . Single - wavelength kinetics of acetonitrile upon excitation at 550 nm and probing at 530 nm. The resultant cross - correlation can be used to identify the IRF of the system, or one - half the time from when signal begins to appear until it returns to baseline. From the inset, the IRF for this experiment is 135 fs. 2.2 Optical Kerr Effect The optical Kerr effect is a lensing process in which the high intensity of the pump beam induces a thermal change within the solvent. This effect may be used to characterize pulses through the use of the AP. The pump and probe enter the solvent at magic angle relative to each other, and the AP is set behind the solvent 90º to the polarization of the probe. This orientation means that when the pump and probe are not present at the same time within the sample, no light is transmitted - order nonlinear distortion in the sample, causing a change in the polarization of the sample. As the probe propagates t hrough this sample, it too is repolarized; the birefringence induced by the pump is then transmitted by the probe and allowed to pass through the AP to the detector. The 90º repolarization can only occur with both the pump and probe in the same at the same time. OKE, then, provides a 359 convolved Gaussian made up of the two pulses meeting in the sample ( Fig. B .2 ), as expressed by (B .4) conv pump ) and probe ). Figure B . 2 . OKE spectrum of methanol (black diamonds) upon excitation at 550 nm and probing at 530 nm. The data can be fit with a Gaus sian curve (red trace) to yield pulse durations of the pump or probe pulses. The Igor Pro curve fitting software can be used to determine the fit parameters for the Gaussian, according to eqn. (B .5) . (B .5) - width at half maximum (FWHM), another common measure of ultrafast pulses. Instead, width in Igor corresponds to twice the deviation (c), which can then be relat ed to the FWHM by 360 (B .6a) (B .6b) conv , and the two can be used interchangeably. When implementing a one - color experiment, it is assumed that the pump and probe pulse durations are the same. This may or may not be a fair assumption, but it is used to simplify the math. Combining eqns. (B .5) and (B .6b) allows for the pump pulse duration to be found, according to: (B .7) If a two - color experiment is the final desired setup, a one - color experiment must be performed first in order to separately identify the pulse duration of the pump. Moving directly to a two - color setup without performing an OKE to solv exc probe to be found. Once the OKE exc probe may be determined by eqn. (B .8) , in which the factor of 1.665 is derived from the fact that the two pulses interacting in the sample are distinct from one another. (B .8) As was mentioned previously, different solvents produce different signals. Methanol and acetonitrile are typically used for OKE measurements, but acetonitrile often exhibits a lo ng exponential decay on the positive side of the Gaussian, as shown in Fig. B .3 . 12 Where the Gaussian function is induced by electronic reorientation caused by the change in instantaneous dipole moment, t he exponential tail is the nuclear motion of the solvent reorganizing to accommodate that new electronic redistribution. Additionally, wings may be visible near the baseline of the Gaussian function; these may be seen on either the positive or negative sid e but are typically large on the positive end. The cause of these wings is third - order dispersion, often introduced by the Brewster prism pair. They may also be induced by the huge energy transfer of the pump pulse into the solvent, making the average pump power an important variable. 361 Figure B . 3 . OKE spectrum of acetonitrile (black diamonds) upon excitation at 550 nm and probing at 530 nm. Although the main signal is fit well with a Gaussian (red trace), there is an exponential decay at positive times. 2.3 Autocorrelation It should be noted that a more commonly employed method for the determination of pulse durations is through the use of an autocorrelator. 13 This may be done in different ways, but the general theory is that a copy of a single pulse is made when it passes through a beam splitter. The two pulses are then directed to meet within a material, such that some nonlinear process occurs. One beam oscillates in time relative to the other so that a time - resolved pat tern may be generated for the two pulses interacting with each other. An autocorrelator exists in our lab in which one beam is temporally shifted through the use of a mirror mounted on a speaker. The two pulses - barium borate). when the pulses meet spatially and temporally inside BBO, frequency doubling occurs, allowing for the generation of 400 nm light. This light is collected as a function of the distance the mirror 362 on the speake r is moved, providing a time - resolved autocorrelation spectrum. 3. Results as a Function of Experimental Setups The cross - correlation and OKE spectra are highly dependent on the experimental conditions. This is not limited to the type of experiment being used (e.g., one - versus two - color), but is very specific to the exact pump and probe wavelengths, the pulse duration, peak powers of the respective pulses, the solvent being used, and other factors. Below is an accounting of some of these variables and th eir observed effects. 3.1 Pump/Probe Power Ratios Because of the high prevalence of energy transfer in the cross - phase modulation and OKE phenomena, the powers of the pump and probe beams are of great importance. Moreover, the ratio of the powers between t hese two pulses is also of interest. A 10:1 power ratio of the pump/probe is often cited in the literature. This ensures that the pump is generating the excited state whereas the probe is monitoring the kinetics; if the probe power is too high, nonlinear e ffects may be observed. On the other hand, the pump power is meant to be greater than that of the probe, but if it is too high, similar nonlinear effects will be generated. This is why it is critical to ensure that the kinetics being monitored occur within the linear region. (To perform this check, look at the maximum of the signal when the pump and probe overlap. Then place a 0.3 ND filter in front of the pump, which should block 50% of the photons. If the signal now is equal to or less than 50% of what it was without the ND filter, then the system is in the linear regime. If the signal is greater than 50%, nonlinearity is occurring, and the pump power should be reduced until the linear regime is obtained.) The effects of the pump and probe powers and the power ratio were measured in 1 - octanol 363 (1 - OctOH) and are displayed in Table B .1 . To draw the most fair comparison, care was taken to ensure that regardless of probe power, I 0 at the sample was consistent. This was done by rotating the AP to be parallel with the probe polarization and attenuating the signal using the ND filter. The AP was turned back to 90º for the measurement. The pump pulse duration had been measured independ ently in a one - probe is under investigation here. Table B .1 . Summary of signal - to - probe ) from OKE data in 1 - exc probe = 530 nm, as a function of the pump/pr obe power ratio. Average Power (mW) Pump/Probe Power Ratio Signal/Noise Ratio probe (fs) Pump Probe 4.0 0.4 10:1 1875 141 3.0 1.6 2:1 225 138 3.0 0.3 10:1 125 138 3.0 0.2 15:1 25 109 2.0 0.4 5:1 25 76 2.0 0.2 10:1 5 132 From these data, it can be seen that a reduction in either pump or probe power necessarily correlates with a reduction in S/N. Decreasing the pump power by 1 mW reduces the S/N ratio by an order of magnitude. Reducing probe power also decreases S/N, but to a lesser extent. At the probe is nearly constant at ~135 fs. Upon changing the ratio to 15:1 probe is observed, yielding 109 and 76 fs pulses, respectively. It is unusual that both an increase and decrease in the power ratio results in a decrease in pulse duration. Alternatively, when the power ratio is 2:1, the same ~135 fs probe pulse is observed. This is an effect of this combination being in the nonlinear regime. While these results may be generally 364 observed, the exa ct powers and power ratio must be determined for the sample and wavelengths being used, with reiterative checking of the linearity of the signal. 3.2 One - vs. Two - Color Experiments One - and two - color experimental setups utilize laser beams that are generat ed from different sources, and therefore will inherently produce slightly different data when the pulses are being characterized. As discussed previously, a one - color OKE assumes that the two pulses meeting in the sample are nearly identical. This assumpti on is carried through to the cross - correlation performed. When a pulse is introduced from a different source, such as a second OPA or the regen, that pulse is more likely than not to be fundamentally different from the first pulse. Even if the wavelengths were the same between the pump and probe of a two - color experiment - wavelengths for the pump and probe beams), the spectral bandwidths of the pulses are likely to be different, which then propagates to the pulse duration. A comparison of cross - correlation spectra are shown in Fig. B .4 . In this case, the amplitude of the observed signal greatly reduced for the two - color data relative to thos e collected in the one - color setup. That being said, the measured IRF was approximately constant between these two experiments at ~145 fs, indicating that the pump and probe pulses are likely similar. 365 Figure B . 4 . Cross - correlation spectra of ethanol in a one - (blue) and two - color (red) experiment. In each the pump was 490 nm, and the probe for the two - color experiment was 530 nm. Both yielded an IRF of 145 fs. 3.3 Solvent The nature of the solvent may play a role in the observed spectra used for pulse characterization. This is why it is critical to perform cross - correlations and OKE measurements in the solvent that will be used for the real experiment. These effects may appear benign or small in magnitude. Take, f or example, the OKE spectra for a two - color experiment collected in methanol (MeOH) and ethanol (EtOH), shown in Fig. B .5 . These spectra appear very similar and indeed yield pump and probe durations that are within 5 fs of each ot her. These differences, however, are more noticeable upon the collection of cross - correlation data ( Fig. B .6 ). Relative to methanol, the IRF in ethanol has been increased by 20 fs, from 125 to 145 fs. When short - time kinetics are desired, this can be a major loss of observable temporal signal. 366 Figure B . 5 . exc p robe = 530 nm in both methanol (black diamonds) and ethanol (red diamonds). When fit with a Gaussian, the pulse durat ions in methanol (black trace) and ethanol (red trace) may be found. Figure B . 6 . Cross - correlations found in methanol (black) and ethanol (red) in a two - color setup utilizing a 490 nm pump and 530 nm probe. The IRF was found in each solvent, being 125 f s in methanol, and 145 fs in ethanol. 367 These cross - correlation spectra are changed more dramatically in moving to longer - chain alcohols ( Fig. B .7 ), or when moving out of the alcohol family of solvents altogether. The shape of the signal changes noticeably from MeOH to 1 - OctOH. It should also be pointed out that there are more third - order dispersion effects present in some of the spectra in comparison to others, as evidenced by the wings at both the negative and positive time ends o f the signal. These wings will elongate the measured IRF for the system. From these data, it is clear that simply collecting a solvent spectrum in one solvent of a family is not sufficient when comparing data in many solvents. Some effects may be observabl e in a data set of one solvent that cannot be explained by a solvent trace collected in another. Figure B . 7 . Cross - correlation spectra in a series of 1 - alcohols: methanol (blue), ethanol (green), 1 - butanol (orange), and 1 - octanol (purple). The pump and probe wavelengths used for this two - color experiment were 490 and 530 nm, respectively. 368 3.4 Detection Scheme 3.4.1 Monochromator and Single - Channel Photodiode The first commonly employed detection setup is with a monochromator, or some other probe wa velength separator, and a single - channel photodiode. The input beam has a large spectral bandwidth owing to its ultrafast nature. It is therefore possible to probe at any wavelength within the probe bandwidth, as was done by tuning the MC for Fig. B .8 . Here, a one - color experiment was being performed in which the pump and probe were nominally 600 nm. With this red wavelength, a very large bandwidth is achieved, and thus the effective probe wavelength was scanned from one end to the other, allowing for the time - p robe = 579 - 617 nm to be measured. I 0 through the sample was kept constant through the use of the ND filter, a necessary precaution as the intensity of the signal at the red - and blue - most edges of the spectr um was very low. An interesting inversion of the Gaussian derivative signal was observed. 369 Figure B . 8 . One - color cross - exc p robe = 600 nm with the analyzing polarizer in place. The effective probe wavelength measured was scanned over the bandwidth of the probe (579 - 617 nm) through the use of a monochromator. Care was taken to ensure I 0 was the same for every probe wavelength. In the data collected above, the AP was in place after th e sample. To test its effect, the AP was removed and the same experiment was performed ( Fig. B .9 ). In this case, the same sign swapping was observed, but the spectra collected show the inverted signal to begin with. Take p robe = 579 nm, for instance: in Fig. B .8 (with the AP in place), the first peak is a minimum, followed by a positive signal; in Fig. B .9 (without the AP), the first peak is positive and then decays into a negative signal. It is evident from these data that the AP is playing some role in the observed processes. 370 Figure B . 9 . One - color cross - correlation spectra collected in acetonitrile fo exc p robe = 600 nm without the analyzing polarizer in place. The effective probe wavelength measured was scanned over the bandwidth of the probe (579 - 617 nm) through the use of a monochromator. Care was taken to ensure I 0 was the same for every pro be wavelength. OKEs were collected using this same technique of scanning the MC across the probe probe and are compiled with a summary of the measured IRFs taken from Figs. B .8 and B .9 probe decrease. This likely indicates that with bluer probes there is a greater degree of energy transfer, inducing third - order dispersions that affect the pulse duration and cons equent IRF. A trend is not so evident in the IRFs measured without the AP. It can be said, however, that these values are consistently greater than those measured with the AP, evidence of the fact that pre - compensation with the prism pair was performed wit h the AP in place. The system must have been optimized in this setup, so removing the AP would actually result in longer observed pulses. 371 Table B .2. Summary of the cross - correlation results with and without the analyzing polarizer (AP) from Figs. B .8 and B .9 probe ). probe (nm) IRF (fs) probe (fs) With AP Without AP 579 185 245 80 582 195 225 92 585 170 240 70 588 165 220 79 590 180 200 73 592 215 190 89 594 180 185 72 596 190 215 94 598 160 250 86 600 170 190 74 602 180 170 74 604 175 225 71 606 150 255 76 608 145 265 67 611 150 170 79 614 155 230 64 617 155 >375 57 Monochromators traditionally have both entrance and exit slits that serve to reduce the amount of ambient light entering the housing, as well as to limit the spectral bandwidth of the diffracted light exiting the housing and hitting the photodiode. In order to understand the effects of these slits, as well as the MC itself, on the measured IRFs and pulse durations, cross - correlation spectra were collected in acetonitrile with and without the AP in place ( Figs. B .10 and B .11 , respectively). There are huge temporal shifts in the remo val of any one set of slits. The shape of 372 the spectra are also substantively different depending on which set of slits is in place or removed. Again, the AP appears to play a definitive role in the IRFs measured based on the inversion of the cross - correlat ion signal between Fig. B .10 (without the AP ) and Fig. B .11 (with the AP in place). Figure B . 10 . Cross - correlation spectra in acetonitrile adjusting the use of entrance and exit slits with the monochr omator: both slits in (blue), only exit slits in (red), only entrance slits in (green), no slits (purple), and the removal of the monochromator entirely (orange). Excitation occurred at 600 nm with probing at 480 nm. No analyzing polarizer was used to coll ect these data. 373 Figure B . 11 . Cross - correlation spectra in acetonitrile adjusting the use of entrance and exit slits with the monochromator: both slits in (blue), only exit slits in (red), only entrance slits in (green), no slits (purple), and the remov al of the monochromator entirely (orange). Excitation occurred at 600 nm with probing at 480 nm. The analyzing polarizer was used to collect these data. OKE spectra were then collected in acetonitrile while adjusting the placement of the slits in the MC, and also by removing the MC entirely. Temporal shifts are again observed. A significant attenuation in the magnitude of the signal is observed both when the exit slits are removed (but the entrance slits remain in place), and when the MC is removed. Intere stingly, a double - Gaussian feature is observed when both sets of slits are in place. In this case, it appears as if two distinct pulses are propagating through the MC to reach the detector. The cross - correlation spectra appear to confirm this, as the shape of those have many features, a characteristic of multiple pulse phenomena. This double peak is not observed in any of the other spectra, implying that the use of both sets of slits in some way perpetuated the unusual behavior. 374 Figure B . 12 . OKE spectra in acetonitrile adjusting the use of entrance and exit slits with the monochromator: both slits in (blue), only exit slits in (red), only entrance slits in (green), no slits (purple), and the removal of the monochromator entirely (orange). Excitation occu rred at 600 nm with probing at 480 nm. No analyzing polarizer was used to collect these data. A comparison of the results given by Figs. B .10 - 12 are shown in Table B .3 . Despite being measured at different pump/probe combinations with different amounts of excitation bandwidth probe ), the results are very similar between the two data sets. For these data, when the MC was in place, it was tuned to the central waveleng th of the probe pulse. Primarily, the longest measured IRF is found when the AP is in place, and both sets of slits are in the MC. In this case, the chirp compensation was performed without the AP, meaning that its unt of chirp that effectively elongates the measured pulse duration. The IRF is consistently shorter by an average of nearly 50% without the AP in place. It is further shortened either by the removal of both sets of slits, or by removing the MC entirely. F rom the spectra above, however, it is known that without the slits or the MC, the magnitude of the signal is drastically reduced. The observed pulse durations as measured by OKE is relatively 375 constant regardless of the detection scheme. Removing the entran ce slits should have the effect of increasing I 0 and thus allowing for a greater signal to be observed. The exit slits, however, reduce the effective bandwidth that is measured. There are indications that this will result in a longer observed pulse duratio n, in which case full spectral detection of the pump and probe is desirable. Table B .3. Summary of one - color studies for acetonitrile, including the cross - correlations with and without the analyzing polarizer, OKE - determined pulse durations. exc probe (nm) Slits IRF probe (fs) % Change b With AP (fs) % Change a Without AP (fs) % Change a 600 Front and Exit 260 - 115 - 56 68 - None 210 - 19 1600 - 39 65 - 4 No MC 185 - 29 100 - 62 73 +7 590 Front and Exit 260 - 105 - 60 36 - None 215 - 17 125 - 52 37 +3 No MC 200 - 23 60 - 43 35 - 3 a Percent change for cross - correlations calculated relative to the value found with the AP both slits in place. b Percent change for OKE pulse durations calculated relative to the value found with both slits in place. 3.4.2 Full Spectral Detection Full sp ectral detection allows for each of the probe wavelengths to be measured 376 individually. This experiment is incredibly useful when a white light probe is used but can also give meaningful information for one - and two - color experiments in which the probe puls e has less spectral bandwidth. Cross - correlation spectra were collected in acetonitrile in a one - color setup exc probe = 600 nm) both with and without the AP in place, as shown in F igs. B .13 and B .14 . For these data, no MC was used. An inversion of the sign of the signal occurs as the probe wavelength shifts from bluer to redder wavelengths. The point of inversion appears to be around 0 - 670 nm, which is much greater another indication of energy transfer between the two pulses, otherwise these frequencies would be inaccessible given the spectral bandwidth of the pump and probe. Figure B . 13 . Full spectral cross - correlation data collected in acetonitrile. The pump and probe wavelengths were 600 nm in this one - color setup. No analyzing polarizer or monochromator was used to collect these data. 377 Figure B . 14 . Full spectral cross - correlation data collected in acetonitrile. The pump and probe wavelengths were 600 nm in this one - color setup. No monochromator was used to collect these data, but the analyzing polarizer was in place after the sample. The AP does not appear to play much of a role in these spectra, and the relative signs of the observed signals are the same with or without it in place, which was not true when the MC was used. It is likely, then that the unusual effects observed previously ( Figs. B .8 and B .9 ) were due to the combined use of the MC and AP. An OKE may also be collected by full spectral detection, as is shown in Fig. B .15 . The same one - colo exc probe = 600 nm in acetonitrile was used without the MC in any select probe wavelength ( Fig. B .16 ), only one Gaussian would be visible ( Fig. B .17 ). Additionally, neither of these peaks is centered around 600 nm, which is the central wavelength of both the pump and probe beams. Based on Fig. B .16 , for which the the two features are centered around 560 and 615 nm. This is likely another manifestation of energy transfer between the pulses in the solvent medium. 378 Figure B . 15 . Full spectral OKE data collected in acetonitrile. The pump and probe wavelengths were 600 nm in this one - color setup. No monochromator was used to collect these data. Figure B . 16 . A full spectral snapshot taken from Fig. B .15 trace of the pump and probe within the acetonitrile solvent during the OKE event. The setup was a one - color experiment, with the pump and probe being 600 nm. 379 Figure B . 17 . Taken from Fig. B .15 , these are the kinetic traces of the pump and probe within the acetonitrile sample during the OKE event for the probe wavelengths of 560 (blue) and 620 (red) nm. The setup was a one - color experiment, with the pump and probe being 600 nm. Fig. B .17 shows the spectrum from Fig. B .15 probe = 560 and 620 nm, approximately the center of the two Gaussians observed in the full spectrum. The observed pulse duration for the bluer pe ak is slightly longer by ~10 fs than that seen for the redder Gaussian. These data show how critical the choice of central wavelength is when performing single - wavelength experiments, particularly when the detection scheme utilizes a single - channel photodi ode that is not capable of differentiating between different wavelengths of the probe spectra. The results displayed in Fig. B .15 are unusual and may be caused by the very large spectral bandwidth observed for 600 nm beams. It is also possible that this spectrum indicates that the pump and/or probe pulses are not chirped well. 5,9 To further understand these effects, full spectral OKEs were performed in 1 - exc probe = 550 nm, as shown in Fig. B .18 . In this case, the observed spectrum is perfectly round, indicating that the pump line is well chirp - corrected. 5 Upon the introduction of a 530 nm probe, 380 however, the OKE became more oblong and distorted ( Fig. B .19 ). In neither case, however, was there a double - Gaussian present as was observed for the 600 nm one - color experiment from above. Performing the one - and two - color experiments with full spectral detection allows the spectroscopist to obser ve that while the pump beam is compensated well for chirp through the prism compressor, the probe line is not nearly as well corrected for dispersion. At some probe wavelengths, particularly on the blue - and red - most edges, a very short OKE may be measured , which would not be representative of the true pump - probe interaction in the sample. Figure B . 18 . Full spectrum of a one - color OKE experiment in 1 - OctOH, for which the pump and probe wavelengths are 550 nm. 381 Figure B . 19 . Full spectrum of a two - color OKE experiment in 1 - OctOH, for which the pump wavelength is 550 nm, and the probe is 530 nm. Under the same set of conditions, a two - color cross - correlation was measured in 1 - OctOH with full spectral detection ( Fig. B .20 ). The s ame sign - switching is observed here as was found in the cross - correlation in acetonitrile for the 600 nm one - color experiment. The IRF also appears to become shorter as the probe wavelength energy is decreased. The kinetic traces for the two main features, probe = 495 and 535 nm, are shown in Fig. B .21 , as taken from the full spectral data. The sign inversion of the signal is the most dominant feature. It should also be noted that the relative magnitudes of the n egative signals are vastly different between these two probe wavelengths. A small amount of temporal shifting is observed to occur (as is expected considering the wavelength - dependence of dispersion), but the overall IRF measured between these two probe wa velengths is largely unchanged. 382 Figure B . 20 . Full spectrum of a two - color cross - correlation in 1 - exc = 550 nm and p robe = 530. Figure B . 21 . Single - wavelength kinetics abstracted from the full spectrum in Fig. B .20 . When probing at two different wavelengths, 495 nm (blue) and 535 nm (red), in the same spectrum, a similar IRF is observed despite having opposite signals. 383 The cross - correlation data taken from Fig. B .20 may also be plotted against the wavelength axis, as is done in Fig. B .22 . While not as meaningful as the single - wavelength cross - correlation plot in Fig. B .21 , these spectra serve to illustrate the extent of energy transfer within the sample through which the high - intensity pump and probe beams propagate. The pump and probe wavelengths used in this one - color experiment were 550 an d 530 nm. It is not unusual in full spectral data to observe a high - intensity signal in the region of the pump pulse. Often, it appears as a distinct Gaussian sitting on top of other signals with smaller magnitudes. In this spectrum, however, no such featu re is observed. This is highly unusual given the fact that 1 - OctOH does not absorb in the visible region, in which the pump and probe lie. Many fluctuations are observed centered right around time - zero, as one would expect for a cross - correlation spectrum. However, max = 490 nm), which is likely an effect of chirp in addition to energy transfer. Figure B .22 . Full spectral data from Fig. B .20 represented in a two - dimensional fashion. Here, a two - color cross - correlation is collected in 1 - exc p robe = 530. 384 4. Future Studies and Comments Prior to ca. 2014, it was a long - held belief in this research group that only optics or processes that occur before or during the moment that the pump and probe pulses meet in the sample will have any effect on the respective pump and probe pulse durations . This has been repeatedly proven to be incorrect, and if taken for granted, may drastically alter data analysis. The effect of specific optics and changes were tested during the collection of two - color data, in which a 490 nm pump was used with a white li ght generated probe. A monochromator was placed after the sample and tuned to allow 530 nm light to pass into the photodiode. For the baseline setup, after the sample, the probe beam would traverse through an ND filter wheel, the monochromator, and a lens that was being used to focus onto the face of the photodiode. OKEs were taken in EtOH, as shown in Fig. B .23 , upon the change in optic placement after the sample. Further results are summarized in Table B .4 . They depict a clear trend of decrease in pulse duration as optics are removed. Additionally, the angling of optics so that they are more perpendicular to the beam also reduces the pulse duration as the pulse propagates through less optic material. 385 Figure B . 23 . OKE traces that were collected in ethanol in a two - color setup, in which a pump of 490 nm and a probe of 530 nm were used. The pump pulse duration was known from the one - color experiment, allowing for the probe pulse duration to be found. Th pulse = 138 fs, pulse pulse = 86 fs. Table B .4 . Summary of pulse durations by OKE as optics are removed and reangled after the sample for the data show n in Fig. B .23 . Change After the Sample pr obe (fs) Baseline 138 Removed ND filter, reangled CaF 2 113 Removed lens focusing into photodiode 97 Reangled waveplate after CaF 2 91 Reangled lens focusing into CaF 2 86 386 Despite some of these changes being made after the sample position, including the removal of the ND filter and lens, the probe pulse duration is clearly affected. The lens after the monochromator alone appears to have accounted for 16 fs. This is not a per fect correlation as the OKE performed on the pump in the one - color experiment kept the optics and positions that were used for the baseline measurement in the two - color experiment, meaning that for a true understanding of the effect of these optics on the pump and probe, the one - color OKE should be repeated. Furthermore, chirp is wavelength dependent, as discussed in Appendix F . The result of this is an unequal effect of the optic medium on pump and probe beams of different wavelengths. A white light probe will see the greatest amount of dispersion due to its broad bandwidth. To fully understand dispersion as it is affecting the experiment being performed, these tests should be undergone in the setup desired. Partic ularly, the choice of pump and probe wavelengths on the pulse duration is an undetermined quantity. The data reported herein largely displayed a one - color setup, or a two - color setup with specifically a ~480 nm pump and a 530 nm probe. The pulse duration s hould be tested as a function of pump - probe cross - sections, and the wavelengths observed should be expanded to include redder pumps and both redder and bluer probes. It would be interesting, as well, to determine if a 530 nm pump with a 480 nm probe behave s similarly as when these are reversed, as was reported here. There is an indication that the energy transferred from the pump into the sample is bandwidth - dependent, and redder wavelengths are capable of achieving greater bandwidths on this laser system. This may result in shorter measured two - color OKEs and IRFs. Ultimately, to produce the shortest ultrafast pulses possible, the pulses must be allowed to propagate to the sample and again to the detector along a pathway that uses as few optics as possible. The Brewster prism pair can correct for an amount of chirp produced by these optics, but 387 (especially for the probe line) this system is as yet imperfect. It is therefore useful to remove unnecessary optics or select those that are specified for use with u ltrafast pulses. These optics tend to be made of thinner materials, allowing for a reduction of dispersion relative to thicker optics. However, this may be a game of give - and - take, in that the removal of a lens after the monochromator will undoubtedly redu ce the measured pulse duration, but it may have the unfortunate side - effect of also reducing the quality of the data. Polarization optics, especially, should be moved with care, and the polarization of the beams at the sample position should be checked bef ore and after doing this in order to ensure that no unwanted polarization effects are observed. 388 REFERENCES 389 REFERENCES 1 . Berera, R.; van Grondelle, R.; Kennis, J. T. M. Ultrafast Transient Absorption Spectroscopy: Principles and Application to Photosynthetic Systems. Photosynth. Res. 2009 , 101 , 105 - 118; DOI: 10.1007 /s11120 - 009 - 9454 - y . 2. Megerle, U.; Pugliesi, I.; Schriever, C.; Sailer, C. F.; Riedle, E. Sub - 50 fs Broadband Absorption Spectroscopy with Tunable Excitation: Putting the Analysis of Ultrafast Molecular Dynamics on Solid Ground. Appl. Phys. B 2009 , 96 , 2 15 - 231; DOI: 10.1007/s00340 - 009 - 3610 - 0 . 3. Brown, A. M.; McCusker, C. E.; Carey, M. C.; Blanco - Rodriguez, A. M.; Towrie, M.; Clark, tribution Dynamics in Ru thenium (II) Polypyridyl - Based Charge - Transfer Excited States: A Combined Ultrafast Electronic and Infrared Absorption Study. J. Phys. Chem. A ; DOI: 10.1021/acs.jpca.8b06197 . 4. Miller, J. N. Ultrafast Dynamics of Iron(II) - Based Complexes in Solution and Semiconductor - Chromophore Assemblies. Ph.D. Thesis, Michigan State University, East Lansing, MI, 2018. 5. Foszcz, E. D. Understanding the Interplay Be tween Geometry and Ultrafast Dynamics in Ligand Field Excited States of Inorganic Chromophores. Ph.D. Thesis, Michigan State University, East Lansing, MI, 2015. 6. Fork, R. L.; Martinez, O. E.; Gordon, J. P. Negative Dispersion Using Pairs of Prisms. Optic s Lett. 1984 , 9 , 150 - 152; DOI: 10.1364/OL.9.000150 . 7. Damrauer, N. H.; McCusker, J. K. Ultrafast Dynamics in the Metal - to - Ligand Charge Transfer Excited - - diphenyl - - bipyrid ine) 3 ] 2+ . J. Phys. Chem. A 1999 , 103 , 8440 - 8446; DOI: 10.1021/jp9927754 . 8. Rasmusson, M.; Tarnovsky, A. N.; Åkesson, E.; Sundström, V. On the Use of Two - Photon Absorption for Determination of Femtosecond Pump - Probe Cross - Correlation Functions. Chem. Phys. Lett. 2001 , 335 , 201 - 208; DOI: 10.1016/S0009 - 2614(01)00057 - 4 . . Optics Commun. 2000 , 186 , 329 - 333, and references therein; DOI: 10.1016/S0030 - 4018(00)01077 - 4 . 10. Iaconis, C.; Walmsley, I. A. Spectral Phase Interferometry for Direct Electric - Field Reconstr uction of Ultrashort Optical Pulses. Optics Lett. 1998 , 23 , 792 - 794; DOI: 10.1364/OL.23.000792 . 11. Nicholson, J. W.; Jasapara, J.; Rudolph, W.; Omenetto, F. G.; Taylor, A. J. Full - Field Characterizatio n of Femtosecond Pulses by Spectrum and Cross - Correlation Measurements. Optics Lett. 1999 , 24 , 1774 - 1776; DOI: https://doi.org/10.1364/OL.24.001774 . 390 12 . Nikiforov, V. G.; Shmelev, A. G.; Safiullin, G. M.; Lobkov, V. S. Coherent Control of Vibrational and Rotational Molecular Motions Using Double - Pulse Optical Kerr Effect. Chem. Phys. Lett. 2013 , 592 , 196 - 199; DOI: 10.1016/j.cplett.2013.12.023 . 13. Steinmeyer, G. A Review of Ultrafast Optics and Optoelectronics. J. Opt. A: Pure Appl. Opt. 2003 , 5 , R1 - R15; DOI: 10.1088/1464 - 4258/5/1/201 . 391 APPENDIX C . MARCUS ANALYSIS 1. Initial Assumption of Driving Force In Chapter 2 of this work, the variable - temperature methodology was developed and described in detail. An integral component of that research is the analysi s of the ground state recovery lifetimes of the various Fe(II) polypyridyl complexes as a function of temperature. For reasons outlined in Chapter 1 , Arrhenius theory , eqn. ( C . 1 ) , is well - suited to described the high ( C . 1) temp erature (i.e., 235 - 293 K) data. Here, k nr is the nonradiative rate of ground state recovery, A is the frequency factor (rate in the absence of a barrier), E a is the activation energy (energy required to overcome the barrier from reactants to products), k B tem perature. Arrhenius theory can be modified to achieve semi - classical Marcus theory , eqn. (C . 2 ) : 1 ( C . 2) Here, H ab force for the reaction. The pictorial representation of these and the Arrhenius constants can be seen in Scheme C . 1 . H ab is essentiall y a measure of the degree of communication between the two electronic states. Two states of the same spin would be expected to be highly coupled (H ab adiabatic), whereas two states of different spins are likely uncoupled (H ab 1, 2 Diabaticity, though, is an idealized state in which H ab = 0 cm - 1 and does not exist. What is used instead is the term non - adiabatic, which describes a system under the same H ab but is not constraine d to 0 cm - 1 392 between the two electronic states of interest. It is slightly different from the zero - point energy difference, which is specifically between the lowest vibrational states in each potential energy in the system. Finally, the reorganization energy is the energy required to transform the reactants into products without completing the electron transfer or surface crossing. Ultimately, while this parameter is described as being an energetic value, it also encapsulates all vibrational and nuclear motion of the complex prior to reaction, and thus gives an idea as to the nuclear coordinate. It should be noted that the potential energy surfaces in question are multi - dimensional and incorporate an array of nuclear coordinates made up of vibrational modes. However, implicit in each of the Marcus parameters (and Marcus theory in general) is that coordinate is accessed and therefore H ab - mode picture. 393 Scheme C . 1. Generalized schematic for an exothermic reaction as defined with both Arrhenius and Marcus theory. Two potentia l energy surfaces (PESs) representative of the reactants with a singlet spin state ( 1 R) and quintet products ( 5 - headed arrow) shows the energetic difference between these two surfaces (E R and E P ), and reorganizat ion energy ( is the given by a vertical green double - headed arrow but in fact represents motion from the reactants equilibrium position (x R ) along the side of the reactant PES to the equilibrium position of the product curve (x P ). The activation energy ( E a , blue double - headed arrow) is the energy required for the reactants to overcome the barrier to cross into the product curve. The magnitude of H ab as given by the purple double - headed arrow determines the type of crossing: the gray lines that cross imply no electronic coupling and represent a diabatic reaction, whereas in an adiabatic scenario, the coupling is large enough such that an upper surface is accessed to act as an intermediate ( 3 I). 394 While this formulation is apt to describe the data collected h erein, application of Marcus theory is made more complicated by the need to determine three unknown variables (H ab nr and T). The most that can be done with the information we have available to us, either through experimentally - determined or literature values, is to define the relative ratio of the three Marcus parameters to each other. This will be the most accurate rep resentation of the data collected. However, we are also able to make educated approximations as to an appropriate range of values. For example, it is possible to calculate a range of values of H ab - 50000 cm - 1 , with the upper limit being taken arbitrarily: this would yield an unreasonable range of both the coupling constant and the driving force. There is no literature precedence for Fe(II) polypyridyl complexes having a reorganization energy even approaching 2 eV (17700 cm - 1 ). To be fair, This would require both variable - temperature magnetic and transient absorption data to be collected. Sutin approximates this energy in [Fe(bpy) 3 ] 2+ - bipyridine) specific ally to be on the order of 0.5 eV. 3 However, this value reflects the ground state recovery of the complex being in the inverted region, so when corrected for the Marcus normal behavior of [Fe(bpy) 3 ] 2+ , a value closer to 1.3 eV is found. For spin - crossover complexes, this value is expected to be much lower, closer to 0.5 eV, due to the fact that the low - and high - spin states are structurally much more similar than in non - spin - crossover chromophores, thus reducing their reorganizatio n energy. 4 much more restrictive, and thus the reorganization energy is increased; still the relative order of magnitude is less tha n ~1.5 eV. 5 Alternatively, SCO complexes are not always the best analogues for the Fe(II) polypyridyls being invested here, and in general are expected to have lower reorganization energies than chromophores such as [Fe(bpy) 3 ] 2+ . To a first approximation, the 395 coordination environment around the Fe(II) center is generally more distorted in SCOs; this weakened metal - ligand orbital overlap is one cause for the SCO behavior. 6, 7 The dr iving force for the 5 T 2 1 A 1 interconversion in these complexes is also drastically smaller relative to that of Fe(II) polypyridyls (~200 vs. ~7000 cm - 1 , respectively). With ground state recovery occurring in the Marcus normal region, the reorganization ene rgy of SCO complexes must therefore also be greatly reduced relative to other Fe(II) compounds. Thus, while initially appealing, a comparison to Fe(II) SCO compounds may in fact be misleading. Unfortunately, the only other remotely comparable studies in wh ich Marcus parameters are found are performed on Fe(II) porphyrins, 8 Fe(II) centers in proteins such as heme, 9 and Co(III/II) polypyridyls, 10 each a worse analogue than the last. We will therefore base our analysis on SCO complexes where appropriate but will largely work within ranges that seem scientifically reasonable. All that being said, the easiest path is to assume an initial value of one of the Marcus constants and calculat e the other two. While this may potentially be more misleading than just reporting simple ratios of unknown quantities, this method still provides information for a more constrained set of conditions. Previously, H ab for Fe(II) has been determined by Buhks and coworkers to be 170 cm - 1 . 11 This value was later cited by Hauser in fitting low - temperature data of the lifetime of [Fe(bpy) 3 ] 2+ as doped into a [Zn(bpy) 3 ](PF 6 ) 2 matrix. 12 From these data, Hauser determined that the free energy difference between the 5 T 2 and 1 A 1 states was on the order of 3000 cm - 1 when H ab ~ 150 cm - 1 . This is less than half of the driving force predicted by Sutin, who - 7300 cm - 1 in [Fe(bpy ) 3 ] 2+ . 3 Even more interestingly, Sutin predicted this driving force from an estimate of H ab that covered two orders of magnitude, specifically 20 - 200 cm - 1 , which clearly encompasses the values calculated and used by Jortner and Ha user, respectively. It should be pointed out, though, that the assumptions Jortner based his calculations on 396 were inherently faulty. For example, the Fe(II) free ion was used as the basis, which has almost zero covalent character a far cry from the high ly covalent {Fe(N) 6 } 2+ complexes studied by Hauser, Sutin, and others. The degree of covalency is propagated through the calculation by a spin - - orbit coupling value, as evidenced by eqn. ( C . 3) . ( C . 3) E n here denotes the free energy between the excited states. Typically, this would involve only the two states that make up the interconversion. However, the 5 T 2 1 A 1 doubly spin - forbidden interconversion that must therefore occur via a triplet intermediate, here the 3 T ligand - field excited state , eqn. (C .4) . The assumption explicit in these calculations is the near degeneracy of the 1 A 1 and 5 T 2 electronic states, as would exist in a spin - crossover complex. ( C . 4a) ( C . 4b) Furthermore, the Racah B and C parameters used by Jortner were found for a compound with octahedral symmetry, which [Fe(bpy) 3 ] 2+ does not have. This was an assumption made for simplicity, and many frequently make this assumption (including us), but it will result in inaccurate energies being found for states with degeneracies that could not possibly be supported by the actual geometry of the complex at hand. It should therefore be obvious that ab estimate is likely than would be true for [Fe(bpy) 3 ] 2+ ; H ab 2 , and thus is likely to be drastically smaller than 170 cm - 1 Hauser, as given by eqn. (C .5) : 12 ( C . 5a) 397 ( C . 5b) of the active vibrational mode, (FC) denotes the Franck - Condon factor, and p is the reduced energy gap that is deemed appropriate for spin - crossover conditions. The vibrational frequency of the active mode here is ~250 cm - 1 . Again, we know H ab must be an o verestimated value; Hauser also explicitly states that p in this work is being used based on a SCO that H ab must be 150 cm - 1 , as is appropriate for a hig hly non - adiabatic transition such as is undergone in the 5 T 2 1 A 1 process, though the exact value cannot be narrowed down much more than that. Contrary to what has been done by Jortner and Hauser, we are choosing to begin with an rather than H ab . We believe the driving force is a slightly more known quantity. To a certain extent, we can experimentally limit the range of values to being between k B T and 19200 cm - 1 . [Fe(bpy) 3 ] 2+ is not a spin - crossover complex and must therefore have a driving force greater than 200 cm - 1 . The upper estimate comes from the fact that this energy is the maximum of the 1 1 A 1 transition from ground - state absorption spectroscopy. This remains a rat her large range of values available. Fortunately, there is a bit more consensus among the - 9000 cm - 1 , generally g - 7300 cm - 1 . 3 There is a danger, though, that in reporting an exact driving force as opposed to Marcus parameter ratios we will be misleading in our confidence of any of the values calculated here. We attempt to mitigate any seem ing dishonesty by applying rather large error bars such that the degree of uncertainty is represented. If the error bars were much larger, though, they would cause all the values to be statistically equal, thus the uncertainty was restricted to 10%. 398 Finall y, the data that is analyzed and discussed in this appendix will be specific to [Fe(bpy) 3 ] 2+ 3 ] 2+ series of complexes, and in many ways, of all Fe(II) polypyridyls. Except where specified, the conclusi ons drawn here can be more broadly applied to all {Fe(N) 6 } 2+ complexes. Even when spin - crossover and high - spin Fe(II) compounds are studied, the methods used herein are appropriate. 13 The major complication to this assessment is t to researchers for all the reasons outlined in Chapter 2 . The ratios of parameters herein are accurate, ically. 1.1 Averages and Error Reported Within the Chapters In this first section, a detailed description of the method of working up and analyzing variable - temperature ultrafast transient absorption measurements of the ground state recovery lifetimes that were used in Chapter 2 will be given, along with the error analysis. Other methods will then be explicated and compared. Data were collected for [Fe(bpy) 3 ] 2+ at each temperature at least twice ( Fig. C . 1 ). The Arrhenius parameters were checked in three different ways to determine self - consistency and the appropriate size of error. In the first method ( Fig. C . 2 ), each complete data set was worked up to determine the Arrhenius parameters for those data. All Arrhenius values for a given complex were averaged. Secondly, all the data were plotted as k nr versus inverse temperature and A and E a were calculated from the fit of the accumulated data ( Fig. C . 3 ). Finally, the average of all the data were plotted in an Arrhenius plot, and parameters were determined from the fit ( Fig. C . 4 ). In the case of [Fe(bpy) 3 ] 2+ , the averages of E a were within 10 cm - 1 of each other. The same procedure was performed on A, and similar results were seen. Th ese methods verify the robustness of the data collected. 399 Figure C .1 . Two sets of variable - temperature transient absorption data collected on the ground state recovery process of [Fe(bpy) 3 ](PF 6 ) 2 in MeCN. Excitation occurred at 490 nm with probing at 530 nm. One set is represented with a solid line, and the other with a dashed line. Even without normalization, both sets overlay well indicating good reproducibility. Figure C .2 . Arrhenius plots for the data (red diamonds) shown in Fig. C .1 with the fits being the black trace. (Left) Data set 1 with R 2 = 0.961, E a = 309 ± 19 cm - 1 , and A = 233 ± 24 ps - 1 . (Right) Data set 2 with R 2 = 0.993, E a = 309 ± 8 cm - 1 , and A = 229 ± 10 ps - 1 . Both data sets are in good agreement with each other. 400 Figure C .3 . Arrhenius plot fitting the combined total data from Fig. C .1 with the data in red diamonds and the fit being the black trace. This fit gives R 2 = 0.975, E a = 309 ± 10 cm - 1 , and A = 230 ± 13 ps - 1 . Figure C .4 . Arrhenius plot fitting the data from Fig. C .1 when averaged at each temperature point, with the data in red diamonds and fit being the black trace. This fit gives R 2 = 0.980, E a = 308 ± 14 cm - 1 , and A = 232 ± 18 ps - 1 . 401 In order to solve for Marcus parameters, relationships to the Arrhenius equation must be - 7300 ± 730 cm - 1 assumed from Sutin 3 and the v alue of A found from the Arrhenius plots, eqn. ( C . 6) parabolic nature of the Marcus activation energy: ( C . 6) For example, for [Fe(bpy) 3 ] 2+ - 7300 ± 730 cm - 1 and E a = 310 ± 15 cm - 1 4850 or 10980 cm - 1 . [Fe(bpy) 3 ] 2+ is believed to be barrierless, and in this region, - - 1 nd E a Table C . 1 - 1 . Table C . 1. a Gº (cm - 1 ) E a (cm - 1 ) - 1 ) a - 6570 325 10200 a - 6570 295 12000 a - 8030 325 10000 a - 8030 295 11700 Average - 7300 ± 730 310 ± 15 11000 ± 1000 While this method is not the analytical method of propagating error, it has the added benefit of returning realistic error bars. Eqn. ( C . 7) 14 may be used with the values from T able C . 1 in 402 conjunction For ( C . 7a) For ( C . 7b) For ( C . 7c) with eqn. ( C . 8) which is derived from eqn. ( C . 6) to determine the statistical uncertainty of the reorganization energy. ( C . 8a) ( C . 8b) ( C . 8c) Lowercase delta refers to the error associated with that value. Any constants in eqn. ( C . 6) are ± 4600 cm - 1 which is rat her large and does not reflect the uncertainty associated with the masking any trends that might be observed when comparing across different complexes by causing al l calculated values to be within error of each other. Therefore, the method outlined in Table C . 1 is predominantly used when propagating error through the Marcus values within this work. eqn. ( C . 9) can be used to solve for H ab analytically. ( C . 9) This is also how H ab 4 ab that were found using this method, A is used to calculate the H ab 4 ab 403 values as determin ed above to find the appropriate H ab average and its uncertainty. For example: the preexponential factor for [Fe(bpy) 3 ] 2+ is 230 ± 20 ps - 1 . In solving for H ab 4 using eqn. ( C . 9) is 0.0286 - 0.0412. Using this ratio and the reorganization energy gives H ab = 4.4 ± 0.2 cm - 1 . From Table C . 1 - 12000 cm - 1 . A table is made for H ab = 0 - 10 cm - 1 in steps of 0.1 cm - 1 - 12000 cm - 1 . The only values of H ab that give a ratio within the window found from the experimentally determined value of A for [Fe(bpy) 3 ] 2+ are 4.1 - 4.7 cm - 1 , or H ab = 4.4 ± 0.3 cm - 1 . This range is in excellent agreement with the values found analytically. The error associated with the H ab 4 - 1 is determined. These are both inverse functions of the true values that are found. In [Fe(bpy) 3 ](PF 6 ) 2 in MeCN, for example, A = (4.36 ± 0.40)×10 9 s - 1 . We have chosen to show this in inverse pico seconds to describe the time constant of the barrierless process, which is more convenient and informative. Simply inverting the time constant and its error would yield A = 229 ± 2525 ps - 1 . Instead, the inverse of (4.36 + 0.40)×10 9 and (4.36 - 0.40)×10 9 ar e taken, giving 210 and 252 ps - 1 , respectively. The average, therefore, is 231 ps - 1 , and the difference between the average and the sum/difference is 21 ps - 1 , thus A = 230 ± 20 ps - 1 . In all likelihood, this is an overestimate of the error bars. The process is repeated with H ab 4 in a more easily digested fashion (i.e., 1/(30 ± 5) vs. 0.035 ± 0.006). 1.2 Relative Ratios of Marcus Parameters The three Marcus parameters can be found either as discrete numbers as outlined abov e provided there is an initial estimate of one of those constants, or as ratios relative to each other. These are simply rough ratios and will vary with the complex being studied. From the exponential 404 in the Marcus equation, the driving force and reorganiz 0 ) 2 / [Fe(bpy) 3 ] 2+ (which is in the Marcus normal region), this ratio is 4900 ± 1200. It was found that 3 ] 2+ series of complexes and is within error at 4200 ± 1000 in [Fe(terpy) 2 ](PF 6 ) 2 - terpyridine) in MeCN, but is doubled to 10200 ± 2600 for [Fe(dcpp) 2 ](PF 6 ) 2 (dcpp = 2,6 - bis(2 - carboxypyridyl)pyridine) in MeCN. While the numbers themselves are meaningless, the trend seems to indicate that from [Fe(terpy) 2 ] 2+ to [Fe(bpy) 3 ] 2+ to [Fe(dcpp) 2 ] 2+ , the incre region toward the barrierless region. This analysis is consistent with what is observed directly f rom the activation energy and in the comparison between k nr and A. One would expect that upon 0 ) 2 / The second ratio comparing the electronic coupling constant and driving force is a more of the activation energy, whereas H ab is a function of the preexpon ential factor. If the exponential ab ratio. On the surface, this may be a decent approximation of the inverse proportionality between these parameters for these Fe(II) complexes. increases (i.e., the separation between the electronic states increases), H ab would decrease. To be fair, the rate of change is likely not 1:1 as implied by this ratio. In low - spin Fe(II) polypyridyls, specifically, an increase in the electronic coupling i ncreases the degree of coupling to the 3 T 1 intermediate state ( Scheme C . 1 ). From the Tanabe - Sugano diagram, it is observed that as ligand field strength increases, the energy of the 5 T 2 state increases with essentially a slope of 2 whereas in the 3 T 1 state, the slope is closer to 1. 15 It is apparent th en that the inverse 405 ab is only a rough approximation and will change in magnitude with various ligand field strengths. ab were calculated, with [Fe(bpy) 3 ] 2+ = - 1660 ± 210, [Fe(terpy) 2 ] 2+ = - 1270 ± 320, and 3 ] 2+ complexes being within error of both of these compounds. The only compound that showed any difference was [Fe(dcpp) 2 ] 2+ ab = - 2190 ± 290, which is very slightly outside of error of the others. It is unsurprising tha 3 ] 2+ family yielded the same results as they have been shown to be nearly identical by most metrics. Interestingly, the ratio for [Fe(terpy) 2 ] 2+ was the same as the bpy - based series, just as was true with 2 / on the electrochemical data and a series of Co(III) analogues, 16 the ligand field strength of terpy appears to be greater than that of bpy, but only slightly greater. Based on the longer lifetime and increased reorganization ener gy in [Fe(terpy) 2 ] 2+ , however, we have postulated that ground state recovery in this complex is occurring along a nuclear coordinate for which the Huang - Rhys factor (i.e., nuclear displacement) is greater between the 5 T 2 and 1 A 1 states than is observed in any of the [Fe(bpy) 3 ] 2+ - type analogues. 12 ab are parameters een [Fe(bpy) 3 ] 2+ and [Fe(terpy) 2 ] 2+ is not substantial, it is ab ratio would be nearly constant between the two compounds as well. The 2 / d by a drastic increase in reorganization energy. These two modifications would offset each other to yield a nearly constant 2 / 2 ] 2+ relative to that of [Fe(bpy) 3 ] 2+ . In the case of [Fe(dcpp) 2 ] 2+ ab da ta that the energetic difference between the 5 T 2 and 1 A 1 is increased more than the electronic coupling. This likely indicates that this compound exists at a different point on the Tanabe - Sugano diagram than any of the other complexes discussed 406 thus far. 1 .3 The H ab 4 1.3.1 Calculation Methods The final ratio of Marcus parameter is the H ab 4 / Chapter 2 . There are two ways in which this can be calculated: (1) Directly from the preexponential factor, A, or (2) as a ratio taken from the independently - determined H ab that the former is greatly preferred as it can be taken from the experimental Arrhenius parameters, whereas the latter requires the use of an initial estimate of one of the Marcus constants. When calculating the ratio from A, eqn. ( C . 9) is rearranged to solve for H ab 4 using the method outlined in Appendi x C Section 1.1 using Table C . 1 . The ratio is found to be 1/(30 ± 5) for [Fe(bpy) 3 ](PF 6 ) 2 in MeCN. Alternatively, H ab 4 ab 3 ] 2+ , - 1 and H ab = 4.4 ± 0.2 cm - 1 , as is shown in Table C . 2 . Using these values and their errors, the H ab 4 with that found using the Arrhenius frequency factor. When calculated using this method, the ratio is consistently underestimated relative to w hen taken from A; the error bars are also smaller when finding H ab 4 reorganization energy used to determine H ab 4 interesting point eqn. ( C . 6) but is then being used to calculate a ratio in the preexponential term. It is unclear what the significance of this is. On the other hand, the red uced uncertainty when calculation the ratio from H ab 407 described above. The uncertainty is propagated, but the ratio is found explicitly from its individual functio ns, not through a slightly more circuitous route in which error inherently increases. Ultimately, this analysis serves to reinforce the ratio reported in Chapter 2 and our confidence in the data workup and error propagation methods. Table C . 2. H ab 4 ab Complex a A (ps - 1 ) - 1 ) H ab (cm - 1 ) H ab 4 from A H ab 4 H ab [Fe(bpy) 3 ] 2+ 230 ± 20 11000 ± 1000 4.4 ± 0.2 1/(30 ± 5) 1/(28 ± 3) [Fe(dmb) 3 ] 2+ 240 ± 20 9700 ± 900 4.2 ± 0.2 1/(33 ± 4) 1/(32 ± 2) [Fe(dtbb) 3 ] 2+ 230 ± 15 9500 ± 900 4.3 ± 0.2 1/(29 ± 4) 1/(28 ± 2) [Fe(terpy) 2 ] 2+ 150 ± 55 14100 ± 1200 6.2 ± 1.2 1/(14 ± 9) 1/(7 ± 3) a Data collected for PF 6 - - dimethyl - - bipyridine. dtbb - di - tert - butyl - - bipyridine. 1.3.2 The Physical Meaning of the H ab 4 / The Arrhenius frequency factor, A, is a measure of the rate of the reaction should it be exponential is a measure of the electronic movement. The two major unknown entities in the Marcus preexponential are H ab ng between electronic states and the energy of transformation from reactants into products, respectively. The former is strictly energetic, whereas the latter incorporates both an energetic and a nuclear displacement quantity. Taken as a ratio derived from A, H ab 4 the excited and ground states as inner - sphere reorganization occurs. In these Fe(II) polypyridyls, this would be the electronic coupling between the 5 T 2 and 3 T 1 states, as well as betwee n the 3 T 1 408 and 1 A 1 states. The fact that this value was so similar between all three bpy - based complexes and distinctly unique for [Fe(terpy) 2 ] 2+ led to the postulation that this parameter could in fact be a numerical representation of the vibrational mode( s) associated with the photophysical process, or in this case the nuclear coordinate linked to ground state recovery. Upon comparing this ratio to a wider array of complexes including [Fe(bpy) 3 ] 2+ in various solvents (see Ap pendix A ), terpy - based complexes with bulky substituents, 17 [Fe(phen) 3 ] 2+ and its spin - crossover analogue [Fe(mono - 2 - OMe - phen) 3 ] 2+ , 13 an Fe(II) chromophore in a sterically - hindered Lehn cage motif 18 it was determined that the above analysis is still open for debate. For example, H ab 4 3 ]Cl 2 in MeOH = 1/(32 ± 4), but in H 2 O it is 1/(49 ± 14). 19 These two ratios are just within error of each other, but the average values differ drastically despite being for the exact same complex. If this ratio represented the major mode of ground state recovery, the only way this should be significantly different in different solvents is if there is a massive reorganization energy for one (both are ~10500 cm - 1 ) or if the solvent were somehow coordinating to the complex itself (which has never been suggested and X - ray evidence does not suppo rt 20, 21 ). It is absolutely probable that this ratio does not suggest any inherent property of the compounds themselves and is simply a mathematical by - product, as it were. However, in performing dimensio nal analysis, the units for the H ab 4 - 3 , inverse volume. As Miller and McCusker note, solvation dynamics of the ground state recovery of [Fe(bpy) 3 ] 2+ appears to be related to the volume of expansion from the 1 A 1 to the 5 T 2 state. 22 Furthermore, H 2 O is often noted to be a special case for solvation of these polypyridyl chromophores, a factor that may lead to H 2 O being better able to intercalate into the more elongated 5 T 2 excited state than any other solvent molecule might. 21 - 23 Interestingly though is the fact that the Fe - N bond distance in [Fe(dmb) 3 ] 2+ has be en observed by ultrafast X - ray spectroscopy 409 to lengthen less when the complex is dissolved in water than when it is dissolved in MeCN - N = 0.181 ± 0.003 Å in H 2 O and 0.199 ± 0.003 Å in MeCN). 21 If H ab 4 fa ct a measure of the volume change the complex undergoes during the ground state recovery process, then this ratio would be its smallest (inverse of the largest number) for the complex that has the smallest degree of volume change, i.e., [Fe(bpy) 3 ] 2+ in H 2 O . This is purely speculation, as is the proposal that the ratio may represent the active nuclear coordinate of ground state recovery. There are other complexes that would seem to support this volume expansion hypothesis, such as [Fe(paniterpy) 2 ] 2+ (paniter - bis - (4 - methoxy - 2,6 - di - iso - propylphenyl) - - terpyridine), a highly sterically encumbered terpy derivative, for which H ab 4 24 Further work must be performed in order to determine the true nature of this ratio , and whether any physical origin can be ascribed to it. 2. The Influence of Holding Different Variables Constant As was discussed in Chapter 2 , the Marcus parameters calculated from the variable - temperature ultrafast transient = - 7300 ± 730 cm - 1 for [Fe(bpy) 3 ] 2+ . 3 The driving forces of the other complexes are found from the electrochemical oxidation potential of the Fe(II/III) couple for t he specific compounds as referenced to that of [Fe(bpy) 3 ] 2+ . This is clearly an imperfect system with many potential pitfalls. However, without using other methods either not currently available to us or that would require a database of complexes and techniques, this appeared to be the best system for acquiring a crucial element for all future Marcus analysis. The question arose, however, as to how much the individual Marcus parameters might change in magnitude or uncertainty if a different constant was assumed, such as H ab de as to the direction of the t 2g set of orbitals 410 that play a role in the ligand field strength of the Fe(II) complexes. With no measure to base initial values of H ab meant to be taken as true estimates of either parameter but are instead to give a sense of how much Table C . 3 can be found the original Marcus parameters as given in Chapter 2 . Table C . 3. Marcus parameters calculated for four Fe(II) polypyridyl complexes using an assumed Complex a - - 1 ) - 1 ) H ab (cm - 1 ) [Fe(bpy) 3 ] 2+ 7300 ± 730 11000 ± 1000 4.4 ± 0.2 [Fe(dmb) 3 ] 2+ 6000 ± 600 9700 ± 900 4.2 ± 0.2 [Fe(dtbb) 3 ] 2+ 6100 ± 610 9500 ± 900 4.3 ± 0.2 [Fe(terpy) 2 ] 2+ 7600 ± 760 14100 ± 1200 6.2 ± 1.2 a Data collected for PF 6 - salts of complexes in MeCN. so as to better discern the relationship between variables. These data are given in Table C . 4 , for which the free energy is defined as - 6 800 ± 680 cm - 1 . With this as a starting point, all 3 ] 2+ series are the same, as are the H ab values for those based on elec - 6800 ± 680 cm - 1 was chosen as it is the mean free energy of the bpy - based family. Despite it not being the average driving force for any of the complexes, there is a high degree of similarity between the values in Tables C .3 and C .4 . Even ab for even [Fe(terpy) 2 ] 2+ . These parameters are outside 3 ] 2+ complexes but remain consistent with those calculated for 411 [Fe(terpy) 2 ] 2+ in Table C . 3 ab for all four complexes as outlined in Chapter 2 . Table C . 4. Marcus parameters calculated for four Fe(II) polypyridyl complexes using an assumed Complex a - - 1 ) - 1 ) H ab (cm - 1 ) [Fe(bpy) 3 ] 2+ 6800 ± 680 10400 ± 1000 4.4 ± 0.3 [Fe(dmb) 3 ] 2+ 6800 ± 680 10600 ± 1000 4.3 ± 0.2 [Fe(dtbb) 3 ] 2+ 6800 ± 680 10400 ± 1000 4.4 ± 0.2 [Fe(terpy) 2 ] 2+ 6800 ± 680 13100 ± 1100 6.1 ± 1.4 a Data collected for PF 6 - salts of complexes in MeCN. The reorganization energy is taken to be constant at 10000 ± 1000 cm - 1 across all four 3 ] 2+ family but is highly unlikely to be consistent with [Fe(terpy) 2 ] 2+ . [Fe(terpy) 2 ] 2+ is known to relax by multiple nuclear coordinates, which is not the case for [Fe( bpy) 3 ] 2+ . 25 The specific value was chosen due to it being the mean value of the bpy - based series. If the expectation is that all {Fe(N) 6 } 2+ complexes will have similar Marcus parameters, then the values found for [Fe(terpy) 2 ] 2+ should be within those of 3 ] 2+ assuming a constant reorganization energy. Taking the first three complexes in Table C . 5 , all parameters are very similar and within error of each other. This is to be expected with complexes that have the same ligand skeleton. H ab is essentially unchanged from Table C . 4 to Table C . 5 in this series of compounds, again showing the restricted range possible for H ab due to its magnitude. The greatest difference is seen in [Fe( terpy) 2 ] 2+ , which has a driving force outside 2 ] 2+ is 4500 ± 500 cm - 1 , whereas that same parameter is more on the order of 6500 ± 600 cm - 1 3 ] 2+ compounds. Furthermore, 412 while the H ab values for all four complexes are within error of each other, the average value for [Fe(terpy) 2 ] 2+ is increased from 4.3 to 5.7 cm - 1 . This is a relatively large change of 28% (despite being small in overall magnitude, ~1 cm - 1 ) and is indicative of the greater electronic coupling between the 5 T 2 and 1 A 1 states in [Fe(terpy) 2 ] 2+ , as is observed in both Tables C . 4 and C .5 . Table C . 5. Marcus parameters calculated for four F e(II) polypyridyl complexes using an assumed Complex a - - 1 ) - 1 ) H ab (cm - 1 ) [Fe(bpy) 3 ] 2+ 6500 ± 600 10000 ± 1000 4.3 ± 0.3 [Fe(dmb) 3 ] 2+ 6300 ± 600 10000 ± 1000 4.2 ± 0.2 [Fe(dtbb) 3 ] 2+ 6500 ± 600 10000 ± 1000 4.3 ± 0.2 [Fe(terpy) 2 ] 2+ 4500 ± 500 10000 ± 1000 5.7 ± 1.3 a Data collected for PF 6 - salts of complexes in MeCN. ab is held at 4.3 ± 0.3 cm - 1 , again being chosen due to it being the average H ab 3 ] 2+ s eries of complexes. With the values found in Table C . 6 , it is immediately apparent that restricting the electronic coupling parameter greatly increases the relative uncertainty of each of the other Marcus constants. In Tables C . 3 - C . 5 , the error associated with the parameters not being held constant was ~10% (with the exception of H ab for [Fe(terpy) 2 ] 2+ ). When H ab is limited to 4.3 ± 0.3 cm - 1 , however, the size of the uncertainty increases to 20 - 40% for the [Fe(bpy) 3 ] 2+ - based complexes, and even further to 45 - 85% in [Fe(terpy) 2 ] 2+ Tables C . 3 - C . 5 for 2 ] 2+ are signifi cant. Here, the driving force has been reduced from - 7600 cm - 1 in Table C .3 to 1100 cm - 1 . Reorganization energy also demonstrated a sizeable decrease from 14100 cm - 1 to 4900 cm - 1 . The data in this table serve to illustrate the p oint 413 that H ab is a highly - constrained parameter due to its magnitude. Substantial changes to the 3 ] 2+ are identical to those calculated above, whereas the parameter s of [Fe(terpy) 2 ] 2+ are drastically attenuated. Table C . 6 also appears to reinforce the approximate magnitude of H ab for [Fe(terpy) 2 ] 2+ being closer to 6 cm - 1 than 4 cm - 1 ; when H ab = 4.3 ± 0.3 cm - 1 complex are on the order of a spin - [Fe(terpy) 2 ] 2+ clearly is not spin - crossover. Table C . 6. Marcus parameters calculated for four Fe(II) polypyridyl complexes using an assumed value of H a b . Complex a - - 1 ) - 1 ) H ab (cm - 1 ) [Fe(bpy) 3 ] 2+ 6800 ± 1500 10400 ± 4000 4.3 ± 0.3 [Fe(dmb) 3 ] 2+ 7500 ± 1400 11400 ± 4000 4.3 ± 0.3 [Fe(dtbb) 3 ] 2+ 6700 ± 1400 10300 ± 3700 4.3 ± 0.3 [Fe(terpy) 2 ] 2+ 1100 ± 500 4900 ± 4200 4.3 ± 0.3 a Data collected for PF 6 - salts of complexes in MeCN. 3. Conclusions This appendix was not intended to be a tutorial on the determination of Marcus parameters from Arrhenius data, nor is it meant to define error propagation methods. The data shown herein a re the Marcus values calculated for the four Fe(II) complexes outlined in Chapter 2 , and this appendix shows how they were obtained as well as a full accounting of how the magnitude of the uncertainty was determined. This is a n ew field of work being done, not just on these types of chromophores, but on complexes without well - defined excited state energetics in general. Trial and error is the path forward, and we are simply attempting to be transparent in the methods 414 employed. T rue analytical error propagation was shown to grossly overestimate the uncertainty of the Marcus parameters calculated. Instead, a method was introduced that accounted for the error associated with the constants but was not so incredibly large as to put al l values calculated within error of each other. Then, the ratios of Marcus constants were examined, with H ab 4 determined to be the most readily digestible. The exact nature of this ratio is yet unknown, but work is ongoing to further define it. Fin of other parameters was tested by holding each of the other Marcus values constant. [Fe(terpy) 2 ] 2+ 3 ] 2+ complexes. It was also determined that even small (~1 cm - 1 ) perturbations on H ab well as grossly overestimated error bars for those parameters. Ultimately, this analysis helped bolster confidence in the values reported, but serve to rem ind us that this research is yet in its infancy. 415 REFERENCES 416 REFERENCES 1. Marcus, R. A.; Sutin, N. Electron Transfers in Chemistry and Biology. Biochim. Biophys. Acta 1985 , 811 , 265 - 322; DOI: 10.1016/0304 - 4173(85)90014 - X . 2. Barbara, P. F.; Meyer, T. J.; Ratner, M. A. Contemporary Issues in Electron Transfer Research. J. Phys. Chem. 1996 , 100 , 13148 - 13168; DOI: 10.1021/jp9605663 . 3. Sutin, N. Nuclear, Electronic, a nd Frequency Factors in Electron - Transfer Reactions. Acc. Chem. 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CARTESIAN COORDINATES USED IN TIME - DEPENDENT DENSITY FUNCTIONAL THEORY CALCULATIONS 1. [Ru(dpb) 3 ](PF 6 ) 2 Ground State Atom X Y Z Ru 10.485 0.963 5.563 N 11.377 1.475 7.338 N 9.314 - 0.039 6.918 N 11.588 2.24 4.309 N 9.333 2.731 5.588 N 9.61 0.083 3.915 N 11.725 - 0.659 5.241 C 12.492 2.21 7.499 C 13.13 2.382 8.682 C 12.612 1.808 9.844 C 11.408 1.098 9.712 C 10.827 0.933 8.475 C 13.364 1.946 11.141 C 13.641 3.24 11.645 C 14.469 3.352 12.756 C 15.039 2.261 13.363 C 14.711 1.002 12.896 C 13.843 0.826 11.814 419 C 8.198 - 0.761 6.634 C 7.403 - 1.325 7.616 C 7.691 - 1.167 8.955 C 8.836 - 0.404 9.253 C 9.612 0.127 8.236 C 6.783 - 1.718 10.004 C 5.603 - 1.039 10.317 C 4.688 - 1.647 11.16 C 4.874 - 2.899 11.712 C 6.084 - 3.524 11.422 C 7.039 - 2.956 10.585 C 12.673 1.852 3.61 C 13.22 2.662 2.623 C 12.627 3.881 2.309 C 11.556 4.273 3.105 C 11.062 3.415 4.081 C 13.066 4.681 1.129 C 14.374 5.168 1.029 C 14.737 5.901 - 0.132 C 13.833 6.133 - 1.155 C 12.563 5.606 - 1.052 C 12.13 4.887 0.053 C 8.246 2.908 6.333 420 C 7.619 4.146 6.453 C 8.186 5.248 5.846 C 9.33 5.03 5.03 C 9.856 3.756 4.936 C 7.689 6 .632 6.069 C 8.455 7.536 6.829 C 7.968 8.849 7.003 C 6.787 9.272 6.412 C 6.039 8.354 5.714 C 6.432 7.042 5.537 C 8.448 0.473 3.344 C 7.825 - 0.291 2.351 C 8.412 - 1.469 1.886 C 9.622 - 1.834 2.453 C 10.203 - 1.055 3.454 C 7.696 - 2.283 0.875 C 7.234 - 3.56 1.196 C 6.433 - 4.225 0.266 C 6.107 - 3.661 - 0.954 C 6.651 - 2.454 - 1.283 C 7.444 - 1.738 - 0.392 C 12.884 - 0.923 5.909 C 13.735 - 1.905 5.541 421 C 13.446 - 2.725 4.443 C 12.281 - 2.437 3.744 C 11.437 - 1.425 4.158 C 14.32 - 3.855 4.047 C 14.007 - 5.131 4.459 C 14.828 - 6.212 4.067 C 15.902 - 6.019 3.224 C 16.22 - 4.74 2.881 C 15.451 - 3.634 3.237 H 12.857 2.636 6.733 H 13.931 2.892 8.721 H 10.992 0.728 10.481 H 14.642 4.216 13.111 H 15.087 0.239 13.318 H 7.955 - 0.884 5.722 H 6.64 - 1.833 7.365 H 9.077 - 0.254 10.159 H 3.889 - 1.176 11.369 H 6.265 - 4.372 11.811 H 13.069 1.008 3.797 H 14.004 2.382 2.16 H 11.169 5.133 2.981 H 15.621 6.239 - 0.209 422 H 11.954 5.741 - 1.769 H 7.884 2.163 6.802 H 6.809 4.231 6.946 H 9.72 5.754 4.554 H 8.461 9.457 7.541 H 5.216 8.633 5.336 H 8.043 1.284 3.626 H 6.995 - 0.003 1.99 H 10.059 - 2.623 2.156 H 6.104 - 5.092 0.477 H 6.484 - 2.092 - 2.146 H 13.103 - 0.396 6.668 H 14.537 - 2.04 6.031 H 12.061 - 2.944 2.971 H 14.639 - 7.083 4.394 H 17.01 - 4.596 2.374 H 4.13108 - 3.36219 12.32716 H 7.95968 - 3.46526 10.39031 H 5.40979 - 0.06726 9.91291 H 6.46557 10.28901 6.49731 H 9.38472 7.23464 7.26455 H 5.80731 6.34938 5.01265 H 14.115 6.71095 - 2.01019 423 H 11.13433 4.49852 0.10435 H 15.08452 4.99215 1.80947 H 15.72114 2.38212 14.17843 H 13.55095 - 0.15669 11.50754 H 13.22346 4.10975 11.18229 H 7.48688 - 4.01714 2.12979 H 5.44 157 - 4.16123 - 1.62621 H 7.85395 - 0.7891 - 0.66846 H 16.46736 - 6.84749 2.85134 H 13.14723 - 5.30288 5.07231 H 15.71078 - 2.65011 2.9063 2 . [Ru(dpb) 3 ](PF 6 ) 2 Excited State Atom X Y Z Ru 0.002601642542 - 0.000059459906 - 0.000686979186 N - 0.142622971292 - 1.806554489876 - 1.046069711160 N - 1.499540409950 - 0.988432978459 1.067631973168 N 1.632221937520 0.772399494614 - 1.061847605894 N 1.618798976616 - 0.800238094655 1.060480571828 N - 0.111302900637 1.808333070349 1.045053087658 N - 1.482632404369 1.014202029938 - 1.068403016112 C 0.610677891318 - 2.163950245931 - 2.122033309597 C 0.469802866431 - 3.395756034871 - 2.763638227316 424 C - 0.481070620859 - 4.335796688956 - 2.296918423503 C - 1.251450614375 - 3.955814014481 - 1.175375850155 C - 1.074483891959 - 2.702793998092 - 0.570204735622 C - 0.662509581792 - 5.656614476552 - 2.954643655943 C 0.421547323783 - 6.293299379757 - 3.608444949421 C 0.251491907599 - 7.542236598187 - 4.230397559139 C - 1.006680252178 - 8.17 7587181060 - 4.214750799809 C - 2.093137979713 - 7.552595718304 - 3.569782622257 C - 1.922380506244 - 6.305297520443 - 2.944827640978 C - 2.160627325276 - 0.491716065534 2.148634613948 C - 3.168039625328 - 1.200438619397 2.805356457607 C - 3.540116662188 - 2.490168838812 2.353678357196 C - 2.847359416988 - 2.993715063548 1.230064467834 C - 1.843464018080 - 2.239340593517 0.604757324414 C - 4.605407904642 - 3.277174698613 3.028990688328 C - 4.851399644879 - 3.116895526552 4.415313385786 C - 5.855588864140 - 3.861665832422 5.057412946608 C - 6.636367662890 - 4.778950432468 4.325390943035 C - 6.402739947044 - 4.944874104975 2.945182639508 C - 5.396371369659 - 4.202552545470 2.303618484311 C 1.555453596607 1.596019337148 - 2.142606264230 C 2.686827901484 2.103697271694 - 2.783529665205 C 3.980324095172 1.766305842902 - 2.315673040579 425 C 4.046380185431 0.907019906309 - 1.196294992517 C 2.878022002953 0.426341405233 - 0.586663348041 C 5.208746960053 2.291244130380 - 2. 968167366895 C 5.216171565002 2.598777179686 - 4.351390287144 C 6.376141383831 3.095300185677 - 4.970560334929 C 7.550778894194 3.297971632791 - 4.218208872324 C 7.554687608728 2.998102519410 - 2.84 0847563346 C 6.395718929676 2.498480805147 - 2.222238707991 C 1.527977816336 - 1.622159701691 2.141452684374 C 2.650505490101 - 2.148835225028 2.782616908605 C 3.949547148720 - 1.833515412474 2.314722924068 C 4.030298389518 - 0.975895733200 1.195046996864 C 2.870305884862 - 0.475530506967 0.585249196036 C 5.168874796204 - 2.378795589356 2.967505847758 C 6.351550730619 - 2.608120226646 2.221263021637 C 7.501916205367 - 3.126983718523 2.840118066105 C 7.493508267453 - 3.424370736790 4.218007832610 C 6.323044959829 - 3.199795120982 4.970649421912 C 5.171613441719 - 2.684030289751 4.351243731516 C 0.648551654482 2.152464745666 2.120727109743 C 0.528941496657 3.386221055338 2.762879757623 C - 0.406104009277 4.342425390217 2.297037811173 C - 1.183208932284 3.976142399283 1.175550208753 426 C - 1.027858691372 2.720520677856 0.569837809437 C - 0.564761343682 5.665753102356 2.955537663794 C - 1.813496157121 6.335670440096 2.947153364226 C - 1.962565307988 7.585284740764 3.573033987570 C - 0.865153215352 8.191357853724 4.217527048657 C 0.382062671112 7.534728102774 4.231828867069 C 0.530413281881 6.283487640544 3.608949795061 C - 2 .152459030552 0.529132849252 - 2.149285464872 C - 3.148084077620 1.255000520302 - 2.805251627602 C - 3.498098414878 2.550686523364 - 2.353019483945 C - 2.796333213602 3.042107493757 - 1.229596352384 C - 1.805077069443 2.270624147769 - 0.604983727591 C - 4.550001997840 3.355825735614 - 3.028059590446 C - 5.324715166337 4.294939758073 - 2.302758275007 C - 6.318375288470 5.054245080167 - 2.944238338655 C - 6.555342588761 4.891826751575 - 4.324293196666 C - 5.790770212449 3.960928401075 - 5.056227494409 C - 4.799312816906 3.199235690713 - 4.414208506109 H 1.327626393232 - 1.435587862595 - 2.477223428588 H 1.084877927189 - 3.601220796798 - 3.632140478218 H - 1.973783499678 - 4.648938016529 - 0.763126240837 H 1.096697243021 - 8.019753040541 - 4.718720112307 H - 3.069075110447 - 8.030328964561 - 3.560136690139 427 H - 1.869845793265 0.494940737033 2.483895083163 H - 3.667035270036 - 0.733079156758 3.646432236971 H - 3.078640565295 - 3.983899369854 0.858548078352 H - 6.023490389382 - 3.732250910469 6.123185893784 H - 7.005521736520 - 5.643099502316 2.370802002488 H 0.562581403463 1.849803021278 - 2.489495159183 H 2.549469727999 2.773872805577 - 3.624297712146 H 5.011588687477 0.599169705227 - 0.814702412804 H 6.365693414861 3.316852236376 - 6.034345507297 H 8.452746576356 3.159530154183 - 2.250755348081 H 0.530920413567 - 1.858883538133 2.488384924232 H 2.501802434610 - 2.816347928614 3.623577549591 H 5.000651293090 - 0.684567799263 0.813516447303 H 8.396650670100 - 3.305216613829 2.249812100290 H 6.309324347329 - 3.419297747729 6.034822613468 H 1.353243327431 1.411899953950 2.475240257623 H 1.147900270971 3.580932925803 3.631101317058 H - 1.893729899652 4.681647676899 0.763789543301 H - 2.930271462958 8.079495348189 3.564501386089 H 1.235608509279 7.997480977268 4.719861018369 H - 1.878242210992 - 0.462031959979 - 2.485188482221 H - 3.655169497737 0.796506326396 - 3.646370619576 H - 3.010451494002 4.036034527582 - 0.857801848527 428 H - 6.908845505599 5.762954753327 - 2.369908417979 H - 5.961317359144 3.833970835201 - 6.121876391863 H - 7.413545199064 - 5.354133291553 4.821571581955 H - 5.249716595098 - 4.327007468280 1.234096687036 H - 4.244217741622 - 2.432790767930 5.001843942099 H 8.383284394659 - 3.824648590197 4.696663376532 H 6.370961426890 - 2.410610490 444 1.152843235900 H 4.286710629138 - 2.496270029772 4.953192019262 H 8.447203180508 3.683354470720 - 4.696685930065 H 6.412370019721 2.298774893570 - 1.154188732454 H 4.327799064466 2.427747635047 - 4.953179615348 H - 1.138301440916 - 9.142483876020 - 4.697128285169 H - 2.778976391664 - 5.828617178078 - 2.475890611120 H 1.404997292357 - 5.831214538571 - 3.611323038423 H - 2.678478982704 5.873841350254 2.478755126727 H - 0.980012832427 9.158038405054 4.700618267069 H 1.505838915216 5.804659791231 3.610859934281 H - 7.322686054444 5.480103343963 - 4.82042915 1863 H - 5.175658451135 4.417245612862 - 1.233338344346 H - 4.204293395609 2.504457237289 - 5.000672714183 429 3 . [Ru(dmesb) 3 ](PF 6 ) 2 Ground State Atom X Y Z Ru 10.4621845479 0.9083771661 5.5159985485 N 11.471886981 1.5233678181 7.2677345918 N 9.4524422457 - 0.1667029052 6.9988092902 N 11.464732617 2.1146379866 4.1315185454 N 9.4087365629 2.7337911444 5.6769988282 N 9.4289 581285 0.129512613 3.9070936713 N 11.5503645293 - 0.8111989846 5.1775362343 C 12 .4906269437 2.421964272 7.3136704796 C 13.1007428137 2.7947098614 8.512131617 C 12.6536254606 2.2446903033 9.7385407602 C 11.5848509349 1.3205601003 9.6720204078 C 11.0140961769 0.9709336677 8.4415052051 C 13.2750957518 2.6197622284 11.03417 97248 C 13.8646322449 3.896793118 11.2078374207 C 14.4507361958 4.254982786 12.4335198766 C 14.4638694266 3.3416322469 13.5071127931 C 13.8837069892 2.0672200248 13.3447532837 C 13.2928792148 1.7101861563 12.1209410976 C 8.4374224938 - 1.0 404124018 6.7611298137 C 7.8148978921 - 1.7491887758 7.7884756291 C 8.2375957902 - 1.5778656609 9.1298005518 430 C 9.2997528407 - 0.6710657531 9.3546472434 C 9.893327113 0.0179491228 8.28995467 C 7.5999410491 - 2.3166589988 10.2485417636 C 6.2443223129 - 2.7218749268 10.1652201081 C 5.638174053 - 3.4177499186 11.2246298138 C 6.376776913 8 - 3.7270415021 12.3847448097 C 7.727027188 - 3.3326851212 12.4770171439 C 8.3323442977 - 2.6321312264 11.4203261828 C 12.494645 9369 1.6945480949 3.3488380558 C 13.1166915883 2.5376230383 2.4280511958 C 12.6766193903 3.876019256 2.2784583438 C 11.5975467487 4.290099749 3.0938493252 C 11.0049596518 3.4059600993 4.0037445051 C 13.3142374548 4.8018138002 1.3087028444 C 14.6814354109 4.6549513249 0.965672267 C 15.2882952992 5.531050869 0.0501630362 C 14.5386281293 6.5663294449 - 0.5441782824 C 13.1769389169 6.719676169 - 0.2131341335 C 12.5706617883 5.8475916863 0.7066372643 C 8.3637522229 2.9652675137 6.51 4583108 C 7.7291218934 4.2058323762 6.5871809959 C 8.1708515398 5.2789399774 5.7749523194 C 9.2623307764 5.0206778878 4.9132034613 431 C 9.8646442667 3.7564956469 4.8778402162 C 7.5184081711 6.6121861113 5.8240859889 C 8.2491220197 7.7902014938 5.5291383121 C 7.6284438798 9.0497829908 5.5786290722 C 6.2647145401 9.1556273896 5.9194347156 C 5.5276699046 7.9905561876 6.213297808 C 6.148964269 6.7311663817 6.1689690435 C 8.3756254687 0.7180946031 3.2565382432 C 7.7606531322 0.1511126713 2.154820706 C 8.2393772276 - 1.1087578147 1.6324688528 C 9.3296128799 - 1.693739025 2.2794579846 C 9.9408514937 - 1.090156839 3.4136968859 C 7.5993120613 - 1.7378471784 0.4490293937 C 7.6489214626 - 3.1419410822 0.2447183015 C 7.0482613744 - 3.7314363678 - 0.8802016501 C 6.3780805875 - 2.9328190267 - 1.8304431875 C 6.315661799 - 1.5380006831 - 1.638644813 C 6.9162767056 - 0.9484635856 - 0.5123423218 C 12.6101120345 - 1.259944397 5.9226521638 C 13.2717042409 - 2.4437785801 5.6513718754 C 12.8342790701 - 3.2771828356 4.5541131842 C 11.7393373127 - 2.8311752472 3.8116734475 C 11.0801858599 - 1.6060802243 4.1095960865 432 C 13.5298700472 - 4.5509738945 4.2393450081 C 12.8534157458 - 5.6212789828 3.5969848243 C 13.5195806511 - 6.8207473826 3.2950172581 C 14.8800870304 - 6.9839944305 3.6301561793 C 15.5637710208 - 5.9322814393 4.2725780903 C 14.8965842145 - 4.7324005704 4.5756855665 H 12.8304540144 2.8295501311 6.3703921802 H 13.9295217051 3.4916571805 8.4756777988 H 11.1873415856 0.8941481349 10.5839022459 H 14.8887672954 5.2421018367 12.5525826816 H 13.897831765 1.3538324999 14.1640597681 H 8.1312351241 - 1.16 25895255 5.730831835 H 7.025690893 - 2.4454591188 7.5312440988 H 9.64649907 - 0.4912216332 10.3638298585 H 4.5949335029 - 3.711504649 11.148588789 H 8.3062500592 - 3.5753356604 13.3635737683 H 12.8128772416 0.6682630129 3.4737025962 H 13.9196228641 2.1377587167 1.8202409955 H 11.2390149876 5.3091444189 3.0303657672 H 16.3402202419 5.4110461956 - 0.1937374878 H 12.5898298964 7.509310293 - 0.6737463852 H 8.0345310916 2.1384324105 7.1302334834 H 6.9129619332 4.3295107882 7.2889079917 433 H 9.6222356194 5.8016419447 4.2560329894 H 8.2062019113 9.9434705019 5.3596651677 H 4.4742373912 8.062384571 6.4693971287 H 8.0173918723 1.6546665483 3.6666123118 H 6.9043352031 0.6520223368 1.7197093261 H 9.7483772874 - 2.6182111525 1.8993865467 H 7.093 4272124 - 4.8096467696 - 1.0107221287 H 5.8059309252 - 0.910900048 - 2.3656875741 H 12.9235205742 - 0.628096156 6.7449346424 H 14.0959121047 - 2.74004422 6.2888950922 H 11.3859480005 - 3.4149133361 2.9698324504 H 12.9781596068 - 7.6288933416 2.8098571847 H 16.6134906713 - 6.0437655138 4.5320371318 H 5.9080868581 - 4.2668593093 13.2031630087 H 9.381199024 - 2.3604340002 11.5013654499 H 5.6508043709 - 2.4718595917 9.2903027125 H 5.7845447589 10.1297869106 5.9559260038 H 9.307473475 7.7336824436 5.2898472851 H 5.5576750423 5.8434279207 6.3752737725 H 15.0077300278 7.2424209604 - 1.253914183 H 11.5135381823 5.9668199323 0.9279362552 H 15.2816905743 3.8784017719 1.4315342477 H 14.9189264949 3.6 181818413 14.4543919266 434 H 12.874748957 0.7135765585 12.0091735996 H 13.8433615726 4.6236258193 10.4006853052 H 8.1343519219 - 3.7810471754 0.9774068461 H 5.9117835891 - 3.3891395846 - 2.6996833208 H 6.8732304997 0.13104946 - 0.3989168895 H 15 .3946579086 - 7.9 128213994 3.3983197283 H 11.7977654314 - 5.5307749031 3.3552505838 H 15.4510138817 - 3.928340199 5.0513912665 435 APPENDIX E . DATA PROCESSING AND ANALYSIS 1. Curve Fitting Nearly all of the ultrafast data collected on the systems described in this dissertation require curve fitting. The only exception to that would be stage molecules, which are meant to show little - to - no decay over the delay of the translation stage and are used to determine the goodness of alignment of the laser s ystem. Oddly enough, though, two of the three stage molecules also require population analysis when used on the longer - pulse system because their lifetimes actually cause a slight decay over the course of the 13 ns measured. These are [Fe(tren(py) 3 )] 2+ ~ 60 ns in MeCN) 1 and [Os(bpy) 3 ] 2+ 2 for which tren(py) 3 = tris((N - (2 - pyridylmethyl) - 2 - - bipyridine. But for the vast majority of complexes, even if the lifetimes are too long for the ultrafast systems to measure, there are other kinetic processes to be monitored, and these require exponential curve fitting. The Igor (WaveMetrics, Inc.) software is typically used for this, and the data presented in this wo rk use IgorPro v. 6.37 or IgorPro v. 8.00. This will open a dialogue ( E . 1) in which y 0 and x 0 are the offsets of the y - and x - represents the lifetime. If multiexponential kinetics are observable, then this equation may be modified, as shown in eqn. ( E . 2) : 436 ( E . 2) function). This follows the form: ( E . 3) Width here is equal to twice the standard deviation of the Gaussian function. This type of curve is used for a variety of purposes in the ultrafast laser lab, including in the calculation of the pulse duration, Gaussian deconvolution, finding the beam width, and many others. When fitting the kinet ics of a complex with IgorPro, in the dialog u e box under the to begin with a monoexponential function and increase the number of exponentials in the fit o nly as needed. Choose the y and x data from the drop - l the data will be fit, including any negative - time points. It is best if the cursors are placed around the data that displays the kinetics ( Fig. E . 1 ). The cursors are accessed by pressing ctrl+i on Windows or command+i on iOS whe n the graph is selected. Both cursors can be placed on the graph, or just one. If using the cursors, in for the ) into the Start or E nd window if only using one. 437 Figure E . 1 . Example of data (red diamonds) fit in Igor Pro 8 with a monoexponential function with an x - offset (black trace). The constants are provided in a box on the graph, and residuals are displayed as black diamonds above. The solvent scan (black diamonds, below) is provided for reference. The cursors can be seen in the gray box below the graph. In the residuals an oscillation is visible, particular before ~6 ps. This indicates that another exponential may be required to fit the data well. (Data shown are of the complex CRT - S3 - exc = 430 nm, pr obe = 620 nm.) Once the data to be fit has been selected, initial guesses for the coefficients can be made in required when performing a user - defined fitting function Residuals can be added (as in Fig. E . 1 duals, as can the fit Fig. E . 1 . 438 The residuals are a measure of the goodness of fit of the model to the data. Ultimately, they residuals. In Fig. E . 1 , there is a well - defined oscillati begin above 0, decrease to less than 0, and increase again to >0, at which point they eventually function. When this is done ( Fig. E . 2 ), in fact, the residuals are more evenly dispersed around 0, and no well - defined oscillations are observable any longer. Furthermore, the error bars on both the amplitudes and lifetimes are reasonable; often if a biexponential is fit to data that is well - described by one exponential, the error bars are many orders of magnitude greater than the average value. Figure E . 2 . Data of CRT - S3 - 173 in MeCN (red diamonds) fit in IgorPro with a double exponentia l function with an x - offset (black trace). The residuals (black diamonds, above) are more evenly solvent trace, for reference. 439 1.1 Writing and Saving Procedures For the data presented in C hapters 2 , 3 , and 5 , an Arrhenius model was used to calculate values of activation energy (E a ) and frequency factor (A) from variable - temperature transient absorption spectra. The Arrhenius equation , eqn. ( E . 4 ) , ( E . 4) for which k nr represents the ground state recovery rate, k B temperature, can be lineariz ed, such that ( E . 5) for which the y - intercept is ln(A) and the slope is given by E a /k B . While a simple linear fit is easily done in Igor, the Arrhenius function is not one that comes pre - loaded to the software. For this, and other functions that may need to be called on semi - regularly or more, Igor allows users to write functions and to sav e them for use at a later time. In order to demonstrate writing a user - defined function in Igor, the linearized Arrhenius u that are not to be held constant. For instance, if eqn. ( E . 5) is t would be entered as the fit coefficients so that Igor can do all the calculating. Because the x - data coefficients are described, mo appear as: f(InverseT) = ln(A) ((Ea/0.69503)*InverseT) ( E . 6) 440 This is the Igor repr esentation of eqn. ( E . 5) , where 0.69503 k B in cm - 1 . When the function is e Curve Fitting window, with the newly - written function selected. Ensure that the correct waves are chosen for the x and y data, then function. The bottom of - ng can begin with variable; if the curve returned is wildly inaccurate, it is likely that the guesses were not close to the right order of magnitude. With the on the graph, as well as a box with the values of the variables. Once the function has been run once on a set of data, it is not necessary to make initial guesses as to the coefficients any longer . This is only needed if fitting a new set of data, or if the curve fit poorly the first time. If there is a user - defined function that would be convenient to have readily available for use in Igor in the future, Igor allows for curves to be saved for exac tly that purpose. Write the dialogue will open that is similar to the Command window but will have text in it. This text should resemble Scheme E . 1 below. Select all of the text, then copy and paste 441 box with the text that defines the curve fitting fun ction. The function should now appear in the Curve Fitting options. Function arrhenius(w,InverseT) : FitFunc Wave w Variable InverseT //CurveFitDialog/ These comments were created by the Curve Fitting dialog. Altering them will //CurveFitDialog/ make the function less convenient to work with in the Curve Fitting dialog. //CurveFitDialog/ Equation: //CurveFitDialog/ f(InverseT) = ln(A) - ((Ea/0.69503)*InverseT) //CurveFitDialog/ End of Equation //CurveFitDialog/ Independent Variables 1 //CurveFitDia log/ InverseT //CurveFitDialog/ Coefficients 2 //CurveFitDialog/ w[0] = A //CurveFitDialog/ w[1] = Ea return ln(w[0]) - ((w[1]/0.69503)*InverseT) End Scheme E . 1. - defined function. This code can be saved for use at a later date. 442 2. Gaussian Deconvolution To better understand the electronics of the excited states of a complex, spectroscopists wi ll on occasion use a method known as Gaussian deconvolution of ground state absorption spectra. This is the process of taking a simple UV - Vis and using a summation of Gaussians to recreate the original spectrum. This technique was used throughout this diss ertation in an attempt to better define pump and probe wavelengths. It has been noted previously, and should be noted again, that Gaussian deconvolution only provides one possible set of Gaussians that might describe the spectrum. Deconvolution is arbitrar y and simply a mathematical function, so it should only be used as a first approximation. Igor currently has two programs for multipeak fitting: 1.4 (old version) and 2. These can egin by using the old version, and then the method for the new version will be described after. First, the data should be plotted versus energy units, not wavelength. This allows the Gaussians to be accurately determined. From the Multipeak Fitting menu in Igor, choose Multipeak Fitting 1.4 (old version). This will bring up a dialog box, as seen in Fig. E . 3 . It is often useful to change the x - axis on the graph so that it reads from high energy (left) to low energy (right), as a typ ical UV - Vis spectrum would. To do this, double - click on the x - axis on the graph, then select the last tab at the top labeled 443 Figure E . 3 . (Left) The absorption spectrum of [Ru(dpb) 3 ](PF 6 ) 2 in MeCN plotted against energy. (Right) The multipeak fitting panel for version 1.4 in Igor. When fitting an absorption spectrum for the first time, it is often useful to limit the range of the x - axis, which will also limit the number of peaks Igor attemp ts to find. Additionally, in moving to higher energies, there is a much greater density of states which will inherently increase the degree of overlap between absorption peaks. Obviously this will make it harder to fit the spectra in these areas. For examp le, in Fig. E . 3 , the band centered at ~28000 cm - 1 significantly overlaps with the high - intensity feature at ~32000 cm - 1 . The identity of the lower energy transition was desired for the analysis of [Ru(dpb) 3 ] 2+ , so the higher energy band was included in the analysis for accuracy. However, the exact parameters of the feature at ~32000 cm - 1 will be viewed with skepticism as any higher - energy bands are discounted from this analysis. In the peak fitting panel, choose the x - and y - w aves from the spectrum that should be fit. 444 offset by some amount, so the y - axis may need to be expanded. This is also necessary as Igor may calculate a Gaus sian with a negative amplitude (which is physically impossible but demonstrates the point that this process is a mathematical construct). It is often very useful to generate the Gaussian curves in a table in Igor and sum them in a separate wave, so that th e summation can be added to the plot. This will allow for better visual confirmation of the goodness of fit, as opposed 2 value supplied by Igor ( Fig. E . 4 ). For example, the spectrum provided may appear as if only four Gau ssians are needed to describe the data, as shown in Fig. E . 4 . But the summation of these bands clearly demonstrate that this is a poor fit clearly missing features, particularly low - amplitude, high - bandwidth features that underlie nearly the entire spectrum. Figure E . 4 . Ground state absorption spectrum (black diamonds) of [Ru(dpb) 3 ](PF 6 ) 2 in MeCN. Igor initially finds four main Gaussians (red traces) but when summed together (blue trace), the spectrum is clearly not well - represe nted. It is evident from Fig. E . 4 that more than four Gaussians are required to reconstruct the 445 ground state absorption spectrum. Therefore, the number should be increased in the Multipeak and type in the number of Gaussians desired. The initial guess for the added Gaussian is likely to ext to each) while doing the initial fitting, and then slowly relaxing the fit parameters individually to allow Igor to find the best estimate. This should be done reiteratively while increasing the number of Gaussians until the best representation of the data is achieved ( Fig. E . 5 ). Figure E . 5 . Steady state absorption spectrum (black diamonds) of [Ru(dpb) 3 ](PF 6 ) 2 in MeCN reconstructed (blue trace) by Gaussian deconvolution. Seven bands were required to fit these data. Alternatively, the newer version of Multipeak Fitting in Igor (version 2) may be used. This will initiate a dialog box ( Fig. E . 6 ) that requires the x - and y - waves to be selected, as well as the Fig. E . 7 ) that - guess as to the number and shape of the peaks, as well as the summat ion spectrum in overlaid on 446 Figure E . 6 . (Left) Ground stat e absorption data of [Ru(dpb) 3 ](PF 6 ) 2 in MeCN. (Right) Multipeak fitting dialog box for version 2 in Igor. 447 Figure E . 7 . Multipeak Gaussian fitting of the absorption spectrum of [Ru(dpb) 3 ](PF 6 ) 2 in MeCN using version 2 of the software. The original data are held in the middle panel (black diamonds) along with the summation of Gaussians (blue trace) that is composed of the individual Gaussians calculated in the bottom panel. Above is shown the residuals. without changing any parameters, a new spectrum that modestly represented the data was achieved with only four peaks and a baseline ( Fig. E . 7 ). It is evident, however, that this convolved spectrum does not fully represent the grou nd state absorption spectrum in its entirety. While it may be subtle, the red feature ~18000 cm - 1 is underestimated, there is poor fitting of the blue shoulder of the low - energy MLCT transition (~23000 cm - 1 ), as is true of the blue shoulder of the higher e nergy MLCT band at ~29000 cm - 1 . This would appear to imply at least three bands are missing from the analysis. To do this using the version 2 software, drag a box around the area that appears to be missing a peak. Right click in the box and select x - axis). Click and hold on the spectrum and drag the cursor down, creating a positive Gaussian. 448 al spectrum that now has an without adding further Gaussians ( Fig. E . 8 ). Figure E . 8 . Ground state absorption spectrum of [Ru(dpb) 3 ](PF 6 ) 2 in MeCN (black diamonds) overlaid with the convolved Gaussian fit (blue trace) in the center panel made up of the sum of the individual curves in the = 0. The greatest amplitude features are near the highest energy portion of the spectrum, which is to be expected (see text for details). Seven Gaussians were required to reconstruct these data. Ultimately, both versions of the software provided seven Gaussians for the best fit. Additional curves may always be added, but they likely become extraneous. The summary of the curves are given in Table E . 1 for comparison between the two methods. Version 2 of the software tends to be more user - friendly in that it generates the residuals and the summation curve 449 automatically. But either can be used for this technique with comparable results. In fact, the cent ral energy of each of the bands are very similar, particularly for the four lowest - 0 < 100 cm - 1 ). The greatest differences are in the higher energy bands, and in peak 4. The higher energy transitions are explained using the density of state s logic outlined above. Peak 4 is defined by the v.2 software to have a width of 3000 cm - 1 , which consequently causes the amplitude of the four bands nearest in energy to it to have drastically smaller amplitudes relative to those calculated by the v. 1.4 software. This serves to illustrate the fact that Gaussian deconvolution, even when performed by the same curve fitting software (Igor Pro), can result in two different sets of peaks, proving the point that these data should only be viewed as a first appro ximation of the excited states. Table E . 1. Fit parameters for Gaussian deconvolution in Igor by both version 1.4 and 2. Software Version Fit Parameters Peak 1 Peak 2 Peak 3 Peak 4 Peak 5 Peak 6 Peak 7 v. 1.4 A (M - 1 cm - 1 ) 57900 41900 28400 10100 10300 21800 1000 x 0 (cm - 1 ) 33600 31900 28700 23700 22400 20800 17800 width (cm - 1 ) 1700 1100 2800 1800 900 1300 900 v. 2 A (M - 1 cm - 1 ) 81000 11800 22100 11700 9200 18700 900 x 0 (cm - 1 ) 32400 29300 27900 24000 22400 20800 17700 width (cm - 1 ) 1800 1100 1700 3000 900 1200 900 3. Full Spectral Data Single - wavelength experiments are a powerful method for very accurately determining 450 lifetimes associated with photophysical processes. However, if a sample is entirely new, it is often necessary to begin by collecting full spectral data. This allows for a full picture understanding of the time - dependence of the spectra, not just the kinetics at one specific probe wavelength. Full spectra are essential if photochemistry is believed to be occurring in the sample under irradiation, such that new chemical speci es are being formed. The set - up of this experiment has in essence already been described in Chapter 2 , which utilizes a pump and a white light probe; the difference comes down to detection. Instead of using a photodiode which tr eats all colors as one signal, a polychromator must be used which is capable of detecting signal from many different probe wavelengths at the same time. This can be in the form of a photodiode array (PDA) or a charge - coupled device (CCD). PDAs are often ci ted as having a sensitivity range better suited for transient absorption signals whereas CCD detectors are more frequently used in emission experiments, however some have shown that both are capable of producing equally high - quality data. 3 The detector must be well - calibrated prior to use, and this is typically done with the use of a Hg/Ar lamp which has well - defined emission peaks. This procedure has previously been described by J. N. Miller. 4 When collecting full spectral data, if a window of ~1 ns or less is collected, a solvent scan should also be included so that the wavelength - dependent dispersion, or chirp, can be accounted for (see Ap pendix F for a more thorough description of chirp). This requires running the solvent under the same conditions as the sample (i.e., density of points). The number of points and number of scans can be different between the two, however. Additionally, becau se of the nature of the chirp - correcting procedure, the time points must be evenly spaced, and it is important to collect an extraneous number of points in the negative time, and again with points after the signal being measured. Chirp - correction applies a polynomial function to the solvent response, then linearizes 451 the data based on that polynomial. Therefore, any pixels on the edges are smeared greatly, so these should not be points that are used in the calculation of the kinetics. It is also imperative t o collect full spectral data under unchanging conditions, meaning any ambient light or stray laser scatter must stay constant during the collection period. 3.1 Data Work Up Procedure This work - up procedure (known as ChirpCorr_v6 - 4.ipf) was previously writ ten by A. L. Smeigh 5 with modifications from A. M. Brown. 6 For ease of discussion, line numbers are added to the beginning of each line and should not be included when input into the Igor Command Window. The procedure must be called on before any of the code in Scheme E . 2 can be applied. The code to be entered in the Command Window is given in black. Actions that must be taken by the user are given in red. 1 Load ChirpCorr_v6 - 4.ipf 2 In Excel, or wherever the averaged full spectra data can be opened in a table, an array of the contain the time points, and the first column shows the wavelengths . Correct the time points - zero is not critical, but it must remain constant between the solvent and sample data sets. Ensure the wavelengths are correct given the number of pixels and the calibration of the spectrometer. Scheme E.2. Code for IgorPro for full spectral transient absorption data work up. The code is provided in black, where the comments are presented in red. Italicization indicates that the value given is a placeholder and should only be taken as an example. 452 or rows. Save this as a worked up file; it will be called on by Igor for processing. 3 loadSpectrum(" FolderName "," FileName ", "solvent") 4 The quotation marks are required when name the folder and file names that are titled whatever they are in the computer being used. This will open a dialog box and allow the user to choose the correct file. Here, the final averaged solvent scan that was worked up as outlined above is chosen. The third input in this command is the name that the window with the spectra will be given. 5 SetScale/I x 315.065,611.959,"Wavelength (nm)", solvent; SetScale/I y - 0.1 34,1.5,"Time (ps)", solvent 6 This redefines the x - and y - axes of the solvent window. The values given should be the bluest and reddest wavelengths from the worked up solvent file for the x - axis, just as the most negative and most positive time points are given for the y - axis. The names given in quotations are the axis titles. The spectrum displayed should have time in the y - axis and wavelength in the x - axis. 7 DTSpectrum(solvent, "solvent_trans") 8 The copies the spectrum in solvent and pastes it into a ne w window transposed. See Fig. E . 9 . 9 ShowInfo 10 edit 11 Lines 10 and 11 should bring up the cursors and open a new table, respectively. Use the cursors to follow the center of the solvent trace. In the table, type the wavelength in the first wave, and the time in the second wave. Do this for as much of the solv ent trace as possible. It is likely that the shape will change as redder wavelengths are reached. For tricks on finding 453 the center of the solvent trace, see Appendix E Section 4.2 below. 12 Display wave1 vs wave0 13 This will display a plot that should be time versus wavelength. The general shape should arc from the bottom left toward the top right. 14 CurveFit dblexp_XOffset, wave1 /X=wave0 /D 15 This fits the time versus wavelength data with a double - exp onential function. If this function does not describe the data well, a polynomial of the 4 th or 5 th order can be used. The fit coefficients it returns are, in order: y 0 , A 1 1 , A 2 2 , and x 0 . See Fig. E . 10 . 16 17 This duplicates the spectrum so the chirp - correction will not alter the original data. 18 solvent_cc=solvent_trans(x+Chirp( y 0 , A 1 , 1 , A 2 , 2 , x 0 , y))(y) 19 The coefficients obtained from the exponential fit of t he solvent trace are used here. The rest of the code should be copied exactly. This should then correct the solvent_copy data so Fig. E . 11 ), not spread over 1 - 1.5 ps as was th e case before. 20 loadSpectrum(" FolderName "," FileName ", "sample") 21 SetScale/I x 315.065,611.959,"Wavelength (nm)", sample; SetScale/I y - 0.134,1.5,"Time (ps)", sample 22 DTSpectrum(sample, "sample_trans") 23 Lines 20 - 22 are the same for the sample as they were for the solvent. After transposing the sample data, a table should be made with the sample_trans data. Select all of the TA data by clicking on the first wave name, then pressing control+a on PC or comma nd+a for Macs. 454 Copy the data into the clipboard by pressing control+c (PC) or command+c (Mac). 24 LoadWave/J/D/A=sample_SW/E=1/K=0 "Clipboard" 25 This will paste what was previously copied into a new table. 26 27 From the sample_SW matrix, sel ect the time points and copy them. 28 LoadWave/J/D/A=time_sample/K=0 "Clipboard" 29 4 , 495 ) 30 This corrects for any baseline offset that is present in the data. The name of the sample waves to be corrected are named, followed b y the first point collected (always = 0), followed by the number of negative time points that can safely be counted as background meaning no signal has begun by this time point at any wavelength. The last number is the total number of points in the wavelen gth vector. 31 32 Copy the data from sample_SW and paste it into the sample_copy matrix. 33 34 sample_cc=sample_copy(x+Chirp(( y 0 , A 1 , 1 , A 2 , 2 , x 0 , y))(y) 35 These should be the exact coefficients used in line18 above. The spectrum of the sample data should now also be chirp - corrected. 455 36 37 Copy the wavelengths from the sample_final table. 38 LoadWave/J/D/A=wavelength_ 39 Copy all of the TA data from sample_final. 40 41 140 ) 42 This plots the final, chirp - corrected spectral data against the wavelength vector. The fi nal input number is the number of time points. The chirp - correction can often leave the spectra looking very jagged, particularly around time - zero ( Fig. E . 12 ). It is useful, then to apply a smoothing function. From the sample_FS vs. wavelength_sample0 plot, choose Analysis smoothing number to 30. T his number should never be greater than 30 or else it implies waves (_smth will be appended to the names) can be plotted against the wavelength vector. 456 Figure E . 9 . positive feature and dark blue is a negative feature. The center of the signal is taken to be time zero time - - 0.4 ps at the bluest wavelengths to nearly 0.3 ps at ~550 nm. Figure E . 10 . Plot of the time and wavelength points (black diamonds) from the full spectral solvent scan fitted with a double exponential (red trace) that is used for the chirp correction. 457 Figure E . 11 . Full spectral solvent trace after the chirp correction has been applied. Here, the center - correction is e vident in the smearing of the pixels, which is why it is important to collect extra time points before and after the signal. Figure E . 12 . Full spectral data of [Ru(dpb) 3 ](PF 6 ) 2 in EtOH. These data have been chirp - corrected 458 3.2 Solvent Fitting One of the more challenging procedures in the full spectral data work up is the determination o f the center of the solvent trace for any given wavelength. Fig. E . 13 will be taken as an example; these are the same data shown in Fig. E . 9 , but in different colors. The first step is to choose a color s cheme with a high degree of separation between the different signs. To do this, Fig. E . 13 is se the contrast, allowing for better understanding of the spectra. The best contrast with this color table is when the most positive and most negative values are roughly equal. Next, identify the shape of the solvent response. For approximately 400 - 530 nm, the shape of the signal appears to be roughly the same. Going from negative to positive time, the signal dips, goes very positive, dips below negative again, and then has a very small positive feature. Looking specifically at 450 nm, the negative signal b egins at - 0.14 ps (where it begins to go darkest), and the signal appears to be complete by 0.18 ps. The center of this signal must then be 0.04 ps. This happens to be where the brightest yellow turns into red (positive goes to negative), which may not int uitively be where one would call the center of the signal. 459 Figure E . 13 . The data plotted in Fig. E . 9 but recast in a different color scheme and modulated so the positive and negative color scales were roughly equal. This helps increase the contrast. The black line in the center of the yellow signal helps guide the eye and is user - drawn. Another method can be combined with the procedure above or may be used on its own. It involves drawing a line at the approximate center of the most distinguishable feature (here, the yellow stripe), and using that as a guide for the eye. To do this, type ctrl+t or command+t from the solvent window. This will open a Toolbar on the side of the window. If the topmost option is selected, click on the tab below it, which shows grayed geometric shapes. Then click the tab with the line. Go to the center of the most identifiable feature, at the bottommost wavelength. Clic k once and drag the cursor away. A black line should be following the cursor. Use this to place a series of small black lines to draw a curve through the center of the feature. This line can be seen in Fig. E . 13 . Then, use the cur sors to follow this line in order to determine the wavelength - time correlations for the chirp - correction. 460 4. Singular Value Decomposition As is true for all spectroscopic techniques, pump - probe spectroscopy has inherent artifacts that require thorough unde rstanding and potential correction. 7 Many of these signals come from the fact that peak powers of ultrafast pulses are on the order of 10 9 W. It should come as no surprise then that the majority of the high - intensity artifacts are observed at time zero, the point at which the pump and probe pulses meet both spatially and temporally within the sample. During negative time (when the probe pulse propagates through the sample prior to the pump pulse) and positive time (vice versa), the se signals are less likely to occur. Unfortunately, low signal/noise ratios and wavelength - dependent noise are two time - independent problems that also occur. In all of these situations, little to no knowledge a priori of the molecular dynamics makes it nea rly impossible to discern real signal from spectral artifacts. Since 1982, singular value decomposition ( SVD ) has been a mathematical approach for analyzing spectral data in order to separate real signals from instrumental artifacts. 8 To implement this tool in our lab, the underlying mathematical principles of SVD were used to write MATLAB scripts. SVD was built on the principles of linear algebra, and begins by assuming that every matrix A ( ) can be decomposed according to eqn. ( E . 7) : A = USV T ( E . 7) in which U ( ) is an array of the left orthonormal eigenvectors of AA T , S ( n, n ) is a diagonal matrix of decreasing eigenvalues of AA T , and V ( t, n ) is an array of the right orthonormal eigenvectors of A T A. 9 n th columns of U and V. Columns of U and V in turn are the spectral and kinetic traces of A, respectively. For ultrafast TA spectroscopy, SVD is a power ful tool that can allow the spectroscopist to determine the origin of spectral and kinetic features in full spectra data. The first way in which this 461 is done is by determining which values of S are significantly greater than the noise. Although components in the noise do correlate to real spectral and/or kinetic features they are typically insignificant to the point that assignment is unnecessary. 9 The number of vectors of U and V that are significant directly correlate to the comp onents of S that are separate from the noise. U and V are then plotted against wavelength and time to give the respective spectral and kinetic traces of the data. 4.1 Using the MATLAB Code MATLAB is a powerful calculating tool which has the added benefit of already coming equipped with the SVD coding. MATLAB (MathWorks) R2012a was used for the results presented herein. While the MATLAB - based code was used, some additional modifications were made in order to make the data more understandable to the user, th us resulting in the code provided in Scheme E . 3 . For ease of reading, line numbers are given to the left of the code, but these should not be included in the actual script. Any font in green is a comment meant to explain what f unction the line(s) of code is performing. Both scripts given below are functions such that only the input variables need be known ahead of time. The format of the function is: brackets denote what outputs will be given once the function is performed (thes e can be changed from the Command Line and do not require the script to be rewritten), the name in blue denotes the name of the function being used, and parentheses indicate the inputs required to perform the function. Inputs can be placed directly into th e command line when calling on the function, or they can be defined as variables previously, in which case the variable needs only be called on. For the inputs, startw is the first wavelength from the full spectral data, endw is the final wavelength, and w int is the interval between each wavelength. Similarly, startt is the first time point collected, endt is the final time point, and tint is the interval between each time point. A is the two - dimensional array of full 462 spectral data. This data can be baselin e - corrected and/or chirp - corrected; the effect of these corrections should be viewed on a case - by - case basis as different data sets will require different handling prior to SVD analysis. 1 function [U,S,V,time,wavelength] = mccSVD(startw,endw,wint,startt ,endt,tint,A) 2 3 %% The SVD function 4 5 %The purpose of this function is to perform SVD on the full spectral data, 6 %A, input by the user. This function does not plot the significant 7 %singulars, it only gives the user the information about wh ich components 8 %are significant. For the plotting of those vectors, please use 9 %mccSVDsings.m. 10 11 wavelength = [startw:wint:endw]'; %build the wavelength vector based on the 12 %starting and ending points, as well as the interval distance 13 time = [startt:tint:endt]'; %build the time vector based on the starting 14 %and ending points, and the time interval 15 16 %% Displaying the SVD results 17 Scheme E. 3. Code for MATLAB function mccSVD which performs SVD on a two - dimensional array of full spectral data. 463 18 %This panel has two subplots and a table. The topmost plot is the raw 19 %data. Then SVD is performed and the middle plot displays the reconstructed 20 %full spectral data. The table on the bottom shows in various ways the 21 %significance of the components. This will be discussed further below. 22 A(A==inf) = 0; %search data for points at infinity and set them to zero 23 A(isnan(A)) = 0; %search data for non - numerals and set them to zero 24 fspanel= figure (' Name','Full Spectra','NumberTitle','off',... 25 'Units','normalized','Position',[0 1 0.4 1]); %build a pane for figures 26 subplot('Position',[0.09 0.71 0.87 0.24]); %uppermost plot will contain 27 %raw 3D data 28 surf(time,wavelength,A,'EdgeColor','none') ; 29 title('Raw Data','FontSize',12); 30 xlabel('Time','FontSize',10); 31 ylabel('Wavelength (nm)','FontSize',10); 32 zlabel('Change in Absorbance','FontSize',10); 33 [U S V] = svd (A); %performing SVD 34 A_svd = U*S*V'; %recombining the decomposed vectors 35 subplot('Position',[0.09 0.37 0.87 0.26]); %middle plot will contain 3D 36 %data recombined from SVD vectors 37 surf(time,wavelength,A_svd,'EdgeColor','none'); 38 title('SVD of Raw Data','FontSize',12); 39 xlabel('Time','FontSize',10); 464 Scheme E.3. (cont 40 ylabel('Wavelength','FontSize',10); 41 zlabel('Change in Absorbance','FontSize',10); 42 43 %Columns 1 and 2 of Significance table contain autocorrelation values for 44 %singular vectors of U and V. The equations for the autocorrelation come 45 %from Henry and Hofrichter, Methods Enzymol. 210, 129 - 192. 46 47 ncol = length(U); 48 nrow = ncol; 49 u = zeros(1,ncol); 50 for icol = 1:ncol; 51 u(icol)=0; 52 for irow=1:nrow - 1; 53 u(1,icol) = u(icol)+(U(irow,icol)*U(irow+1,icol)); 54 end 55 end 56 Significance = zeros(10,4); %building array that will be used in the table 57 Significance(:,1) = u(1,1:10)'; 58 ncol = length(V); 59 nrow = ncol; 60 v = zeros(1,ncol); 61 for icol = 1:ncol; 465 Scheme 62 v(icol)=0; 63 for irow=1:nrow - 1; 64 v(1,icol) = v(icol)+(V(irow,icol)*V(irow+1,icol)); 65 end 66 end 67 Significance(:,2) = v(1,1:10)'; 68 69 %Column 3 of Significance table contains F - ratios from F - test. This is 70 %essentially comparing the standard deviation of reduced data set and the 71 %raw data set, with the standard deviation of just one data set. For more 72 %information on F - tests pl ease see F_test.m. 73 74 p = length(A); 75 fb = 2*length(time) - 1; %for the Between groups ratio 76 fw = 2*(p - 1); %for the Within groups ratio 77 for q = 1:10; 78 z1 = U(:,q)*S(q,q)*V(:,q)'; %recompose data using q singulars 79 mean_c = mean(z1); %fin d the mean of each of the columns of z 80 z_m = mean(mean(z1)); %find the overall mean of z 81 Sb = sum(p*(mean_c - z_m).^2); 82 between_groups = Sb/fb; %Between groups value 83 z_b = z1(:,q) - mean_c(1,q); %difference of z column value and average column 466 value 84 Sw = sum(sum(z_b.^2)); 85 within_group = Sw/fw; %Within groups value 86 Significance(q,3) = between_groups/within_group; %F - test ratio 87 end 88 89 90 %Column 4 of Significance table is value of S corresponding to rank. 91 for n = 1:10; 92 Significance(n,4) = S(n,n); %building a vector of the diagonal values of S 93 end 94 95 %The following commands insert the Significance array as a table into the 9 6 %third subplot area of the panel. 97 uitable('Data',Significance,'ColumnName',{'U','V','F - ratio',... 98 'Value of S'},'RowName',{'1','2','3','4','5','6','7','8','9','10'},... 99 'Units','normalized','Position',[0.4 0.04 0.59 0.24],'FontSize',12); 1 00 annotation('textbox',... 101 [0.0253055555555555 0.0421052631578947 0.363583333333333 0.23625730994152],... 102 'String',{'','The number of significant singular','values is given by the number of','singular values in columns U or V','and >0.99, in col umn F - ratio >10.'},... 467 103 'FontSize',12,... 104 'FitBoxToText','off'); 105 106 end The first line of code in the mccSVD script is calling on the function to be performed. There are lines of comments (which will be ignored for the present discussion), followed by the wavelength and time vectors being built in lines 11 and 13, respectively . Then non - numbers such a data set that can be handled by the SVD function. Ultimately, setting these values to zero does not change the analysis as these p 24 - 25 used to create a panel which will display the results desired. The upper third of this panel will show the surface plot of the raw full spectral data, A vs. wavelength and vs. time, t he axis titles of which are defined in the next lines (29 - 32). After the labels are given, SVD is performed in line 33, with the recombined A_svd value being calculated in the next line and plotted as the middle third in the previously - built figure panel. The next section of code (lines 47 - end) describes the statistical analysis performed on the weighting factors. First, autocorrelation is performed on both the U and V eigenvectors, which provides a measure of S/N for the specific elements of U and V. 9 The size of the autocorrelation matrix is defined in lines 47 - 48 for U and 58 - 59 for V; defining the array size first reduces the amount of processing time required to perform the calculation. Two for - loops are used with eqn. ( E . 8) to determine the autocorrelation values for U and V, C(U i ) and C(V i ), respectively: 468 ( E . 8a) ( E . 8b) Here, the j notation calls on the element of the i th co lumn of the array being selected. These values for each of the first 10 elements of U and V are placed into the first and second columns of the Significance table in the bottom third of the figure panel. From lines 74 - 87, the F - ratios are calculated and pl aced in the third column, which are a measure of the statistical comparability of the SVD data set and the raw data set. The F - test , eqn. ( E . 9 ) 10 to be more precise determines exactly ( E . 9a) ( E . 9b) ( E . 9c) how many singulars of U and V are statistically required to describe the data set well. It is therefore presumed that all others will only contribute to minor changes or will increase the noise. In eqn. ( E . 9a) a ratio is taken of the variance between groups to the variance within groups. This is essentially looking at the error from one data set as a reference (f Within Groups ) and comparing it to a second data set and its error (f Between Groups ). In eqns . ( E . 9b and E . 9c) , K is the number of data sets being evaluated, Y ij would represent the j th element of the i th being the mean of the sample), with N being the overall sample size and n being the number of elements in the group. The F - test and autocorrelations are performed to be independent measures of the statistical significance of the component being observed. They are compared, then, to S which is the weighting factor built into SVD. Line s 90 - 93 take the first ten S values and place them into the fourth column of the Significance table. The final ~10 lines of the code are used to generate the table itself. 469 Once SVD has been performed, it is often useful to compare the raw spectra with the SVD - analyzed spectra to ensure that the procedure is being done properly. From there, the Significance Table is an incredibly useful way of estimating the number of singulars that are required to describe the data well. This can be somewhat arbitrary as th e autocorrelation values may agree with the S values that there are two significant components, for example, but the F - test may determine only one singular is necessary. It is often best to overestimate the number of needed parameters and add one (to accou nt for noise). Once that value has been determined, it will become r in the next code that is used ( Scheme E . 4 ), the function mccSVDsings. This code takes the SVD results from mccSVD above and uses it to plot U vs. wavelength a nd V vs. time so as to best allow the user to decide visually the number of singulars needed to describe the data. It should be noted that the only way mccSVDsings can input U, S, V, time, and wavelength are if these are outputs from the mccSVD function. 1 function [singpanel] = mccSVDsings(r,U,S,V,time,wavelength) 2 3 %Build a panel which will contain surface plot of the reduced data set, as 4 %well as plots of the significant singular vectors of U versus wavelength, 5 %and V versus time. 6 7 %r is the previously - determined number of significant components (from 8 %mccSVD.m). Scheme E. 4. Code for the MATLAB function mccSVDsings which takes the SVD results from mccSVD and plots the user - determined most important singulars. 470 9 s = U(:,1:r)*S(1:r,1:r)*V(:,1:r)'; %reconstruction of data set from significant vectors 10 11 s ingpanel=figure('Name','Reduced Plots','NumberTitle','off',... 12 'Units','normalized','Position',[0.6 1 0.4 1]); 13 subplot('Position',[0.09 0.71 0.87 0.26]); 14 surf(time,wavelength,s,'EdgeColor','none'); 15 title('Reduced SVD Data','FontSize',12); 16 xlabel('Time','FontSize',10); 17 ylabel('Wavelength','FontSize',10); 18 zlabel('Change in Absorbance','FontSize',10); 19 20 subplot('Position',[0.09 0.37 0.87 0.26]); 21 plot(wavelength,U(:,1:r)); 22 title('Left Singular Values','FontSize',12); 23 xlabel( 'Wavelength (nm)','FontSize',10); 24 ylabel('Change in Absorbance','FontSize',10); 25 legend('show'); 26 27 subplot('Position',[0.09 0.05 0.87 0.26]); 28 title('Right Singular Values','FontSize',12); 29 plot(time,V(:,1:r)); 30 xlabel('Time (ps)','FontSize',10); 471 31 ylabel('Change in Absorbance','FontSize',10); 32 legend('show'); 33 34 end Line 9 is the first line of code that is not either the command or comments. Here, the data set is being reconstructed with r number of singulars, as is defined by the user. In line 11 a panel is built that will house three spectra. The top third is the surface plot of the reconstructed data showing r number of U vectors. Similarly, the bottom third is V vs. time and displays r number of V components. With these spectra in hand, it much more simple to visually determine the number of relevant singulars. A case study for following this method is outlin ed below. 4.2 Analyzing SVD Results The current procedure for SVD involves often frequent examination of the raw data and comparison with the mathematical constructs produced. Seemingly extraneous vectors of U and V are intentionally plotted in order to de termine the origin of these less significant traces. This also provides a method to determine the traces that are meaningful, and those that are not. The full spectrum, A, is then reconstructed using first one vector each of U and V, then two, and so on un til the spectrum is unchanged (not shown). A spectrum that remains essentially unchanged confirms that the components being factored into A are part of the noise and are thus insignificant. To determine the validity of the MATLAB scripts, SVD has been car ried out on full spectral data for [Ru(dpb) 3 ](PF 6 ) 2 - diphenyl - - bipyridine) in ethanol 472 (EtOH), the raw data for which are presented in Fig. E . 14 . The assignments for these features are based off of those given by Damrauer and McCusker. 11 Overall, the main trace grows in quickly (~ps) to a long - (GSB) is centered at ca. 470 nm that is due to loss of the ground state u pon population of the MLCT excited state. The positive signal on the blue edge of the ground st - * absorption of the reduced dpb ligand. Similarly, excited state absorption (ESA) nm) are of * - * absorption of the reduced dpb ligand, and the broad, featureless band at even lower energy is assigned as a ligand - to - metal charge transfer (LMCT) transition. A spectral trace in orange in Fig. E . 14 is observed to the pump and probe pulses overlap maximally and induce energy transfer events in the solvent, and as such can be disregarded as artifact. 473 Figure E . 14 . Raw full spectra data of [Ru(dpb) 3 ] 2+ in EtOH when pumped at 480 nm. Before time - zero (red and orange traces), no real signal is observed due to the probe hitting the sample before the pump can excite it. After time - zero, the long - lived transient grows in resulting in the final Upon performing SVD on this data set, the weighting factors of the first three values of S (hereon denoted S 1 , S 2 , S 3 ) are found to be 16.5, 2.6, and 2.0, respectively. From this, one might be inclined to assume that only one component is needed to accurately describe the data. The spectral component, U 1 ( Fig. E . 15 region 410 - 520 nm. V 1 , the kinetic trace, in Fig. E . 16 shows a rise (indicative of an absorptive feature) that never returns to baseline. This trace is clearly the long - lived transient that is p redominant in Fig. E . 14 . When A 1 is reconstructed from U 1 , S 1 , and V 1 in Fig. E . 17 , the resultant spectrum obviously does not replicate the original data. In this way, we have determined that one componen t is not sufficient to exactly describe the original data. 474 Figure E . 15 . The first spectral component, U 1 , of [Ru(dpb) 3 ] 2+ in EtOH (S 1 = 16.5). This trace represents the long - lived transient for this complex. Figure E . 16 . The first kinetic component, V 1 , of [Ru(dpb) 3 ] 2+ in EtOH (S 1 = 16.5). This trace represents the temporal behavior of U 1 , and shows a single picosecond grow - in followed by a long (>40 ps) static signal. 475 Figure E . 17 . The recombined spectra for the first spectral and kinetic components, A 1 . While these data do generally describe the full data set, there are obviously more features that must be included. The same analysis is performed on U 2 ( Fig. E . 18 ), which displays only ESA. The largest signal seems to be a remnant of the noise from the near ultraviolet (UV) region in U 2 . This is like ly - * absorption that occurs in the dpb radical ligand. Interestingly, V 2 ( Fig. E . 19 ) only shows one real signal centered at time - zero, whereas the rest of the kinetics are dominated by essentially large - amplitude noise that is shorter than the instrument response function (IRF) of the system, which is on the order of 250 fs. It is possibl e that V 2 is showing the immediat - * absorption as it deactivates into the MLCT manifold. When A 2 is reconstructed using U 1 , U 2 , S 1 , S 2 , V 1 , and V 2 , a spectrum that is much more reminiscent of the original data is produced ( Fig. E . 20 ). However, the spectral features toward the red edge of the spectrum are clearly not well reproduced by A 2 , implying the need for at least three elements each of U, S, and V. 476 Figure E . 18 . The second spectral component, U 2 , of [Ru(dpb) 3 ] 2+ in EtOH (S 2 = 2.6) is shown in green compared to the first (in red). This trace is predominantly ESA at higher energy and is - * absorption of the reduced dpb ligand. Figure E . 19 . The second kinetic component, V 2 , of [Ru(dpb) 3 ] 2+ in EtOH (S 2 = 2.6) is shown in green compared to the first (in red). This trace shows only a large spike centered around time - zero, implying the spectral features associated with it (U 2 ) are very shor t - lived (i.e.,