UNDERSTANDING THE INTERPLAY BETWEEN GEOMETRY AND ULTRAFAST DYNAMICS IN LIGAND FIELD EXCITED STATES OF INORGANIC CHROMOPHORES By Eileen Dixon Foszcz A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of C hemistry - D octor of P hilosophy 2015 ABSTRACT UNDERSTANDING THE INTERPLAY BETWEEN GEOMETRY AND ULTRAFAST DYNAMICS IN LIGAND FIELD EXCITED STATES OF INORGANIC CHROMOPHORES By Eileen Dixon Foszcz After photoexcitation , the relaxation dynamics between excited states of a molecule are governed by bot h the energies and displacement of these states. For transition metal complexes in particular, ligand modification (via electron withdrawing substituents, electron donating substituents, aromatic substituents, etc) to alter the energetics of the excited states has been well studied. Recently, interest in the displacement of these surfaces from the ground state and the geometric ramifications of this displacement ha ve spurred many studies in several research groups. Here , ligand modifications are made to modify molecular distortions (i.e. displacement) , rather than the energetics. The research presented in this thesis focuses on intersystem crossing process es in electroni cally simple chromium(III) compounds. With only a few excited states accessible after visible excitation, interpretation of the excited state dynamics is significantly simplified. Ligand substitution and its effect on the kinetics of the system have been studied using ultrafast transient absorption spectroscopy with ~50 fs pulses. The first study presented in this work focuses on identifying the molecular vibrations occurring immediately after excitation and how those motions facilitate intersystem cross ing. The second study presented here focuses on modulating the energetics, not through ligand substitution, but with high (25 T) magnetic fields. Over the course of pursuing these measurements, various instrumental and software advances were necessary to both collect and analyze the data. These advancements, along with the findings from both studies, are the focus of the discussions herein. Copyright by EILEEN DIXON FOSZCZ 2015 v To all four of my parents: thank you for always encouraging me to dream and to keep reaching for the stars vi ACKNOWLEDGEMENTS I would like to thank my advisor, Professor James McCusker, for all of his support and guidance throughout my PhD career. Though the first idea for my PhD topic did not work out as planned, Jim was there with more ideas and a new plan to help get me throu gh this. His unwavering faith that I could build a new laser experiment and bolstering force when I needed it. I am eternally indebted to Dr. Warren Beck for his astu te observations in the midst of the many laser problems encountered over the duration of my tenure at MSU and making spot - on suggestions for what to try and where to go next. Without his ultrafast expertise, I am sure the McCusker lab would not be where i t is today. I would also like to thank Dr. Ben DeGraff and Dr. Boyd Goodson. Dr. DeGraff hired me for a summer and gave me my first exposure to transition metal compounds, quantum mechanics, and lasers. He also encouraged me to look at more options than just forensic chemistry and to consider graduate school, which were wise words indeed. Dr. Goodson was instrumental in my grad school application process. He even things I h have found my way to Michigan State for a PhD. I would like to thank my many lab mates and fellow MSU researchers for their help and friendship along the way. Allison thank you for teaching me everything you knew about the laser. I will always appreciate your head - nod - and - smile during my literature seminar to ease my nerves. Joel, thank you for laying so much of the ground vii work for this project and providing me with the compou nds so I didn't have to spend a lot of time in the synthesis lab. you being there to bounce ideas off of and that we can problem solve all of these complex issues together. I know the laser lab wil l be in fine hands when I leave here and you both will come up with even better, more ingenious ways to solve future problems than I could. I am especially grateful to you both for your help editing this lengthy document. Bryan, I have complete faith tha t you'll continue the chromium/nickel project with ease and you'll be a master of the laser. Preston, thanks for always being ready with a story to make us all laugh. I appreciate the secret messages with vials in the drawer and how you made sure I got m y waste containers taken care of on time. Lisa and Lindsey thanks for being there to make me relax and get out once in a while! Grad school would not have been the same without tagging alo ng for some of your shenanigans. I owe a very big debt of gratitude to Drew for being a (life and) science sounding board and an amazing help with all of my computational woes. I would Larry - than k you for being there to listen and for being the chill force in the lab when I needed to cool down. You know how to put things in perspective and help me see the forest for the trees. Dani - thank you for your motivating words, friendship, and for indulg ing my crafty side with non - science side projects. Though you were extra quiet proclaimed something surprising very loudly, which never failed to make me smile. Sara and Jon, th anks for making me laugh over lunch breaks; you'll never know how much I needed it some days. Michael, Dan, and Soumen, thank you so much for viii indulging my questions and loaning me optics when I needed them. And a special thank you to Michael for having s o much set up at the Mag Lab before I arrived both times and for teaching me so much about FROG and short pulses during my trips. To my family, I want to thank you all for being patient as I went through this process, for diligently asking me what I was w orking on when I came home to visit, for expertly smiling and nodding when you got hopelessly lost in my reply, and for learning definitely felt the love and support from a ll of you in my time here in Michigan. I'm so thankful that we've survived and I'll be living much closer to all of you in the next chapter of my life. Jeremy, you are the love of my life and my lifeline. You continually impress me with just how much of what is in this document that you understand and can relate to others. Your continued support through the rough patches, especially towards the end, has kept me from the breaking point. I could not be more excited to close this chapter of my life and start the next with you as my best friend, partner in crime, and husband. ix TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ ........... x i i LIST OF FIGURE S ................................ ................................ ................................ ........ xi i i KEY TO ABBREVIATIONS ................................ ................................ ......................... xv i i i 1 Introduction ................................ ................................ ................................ .............. 1 1.1 Photophysical Processes in Transition Metal Compounds ................................ 1 1.2 Tr ansient Absorption Spectroscopy ................................ ................................ ... 5 1.2.1 General Experimental Considerations ................................ ....................... 5 1.2.2 Conditions for Vibrational Coherence ................................ ...................... 10 1.3 Backgr ound on Vibrational Coherence ................................ ............................ 15 1.3.1 Early Experiments - Diatomics and Organics ................................ .......... 15 1.3.2 Vibrational Coherence in Transition Metal Compounds ........................... 16 1.4 Contents of this Dissertation ................................ ................................ ............ 18 REFERENCES ................................ ................................ ................................ .............. 20 2 Experimental Methods ................................ ................................ ........................... 2 4 2.1 Steady State Absorption Measurements ................................ .......................... 24 2.2 Tran sient Absorption Measurements ................................ ............................... 24 2.2.1 Wile E ................................ ................................ ................................ ...... 24 2.2.2 Road Runner ................................ ................................ ........................... 28 One Color Measurements ................................ ................................ ........ 33 Two Color Measurements ................................ ................................ ........ 35 White Light Probe Experiments ................................ ............................... 37 2. 2 .3 Pu lse Characterization Techniques ................................ ......................... 39 2.3 Co mplications with Shorter Pulses ................................ ................................ ........ 47 2.3.1 Prism Compres sion and Group Delay Dispersion ................................ ... 48 2.3 .2 Pump and Probe Overlap Angle ................................ .............................. 54 2.3.3 Detection Wavelength and its Effec ts on the Observed Oscillations ....... 56 2.4 Data Analysis Techniques ................................ ................................ ................ 57 2.4.1 Igor ................................ ................................ ................................ .......... 57 2.4.2 Linear Predic tive Single Value Decomposition ................................ ........ 58 2.5 Computational Methods ................................ ................................ ................... 59 2.5.1 Gaussian Modeling ................................ ................................ .................. 59 2.5.2 Computatio nal Details for Specific States ................................ ................ 60 Cr(acac) 3 : 4 A 2 Ground State ................................ ................................ ... 60 Cr(acac) 3 : 2 E Excited State ................................ ................................ ..... 60 Cr(acac) 3 : 4 T 2 Excited State(s) ................................ ................................ 60 Cr(TMHD) 3 : 4 A 2 Ground State ................................ ................................ . 61 APPENDICES ................................ ................................ ................................ ............... 63 Appendix A: Optics Details ................................ ................................ ..................... 64 Appendix B: White Light Generation Media ................................ ............................ 66 x Appendix C: LabVIEW Data Co llection and Work Up Programs ............................. 69 Appendix D: Pe rforming FFT Analysis in Igor ................................ ......................... 83 Appendix E: LPSVD P rogram Details ................................ ................................ ..... 85 Appendix F: FROG Algorithm Modifications and Their Employment ....................... 88 Appendix G: FFT Time Spa cing and Frequency Resolution ................................ . 100 Appendix H: Time - Depen dent Fast Fourier Transforms ................................ ....... 104 REFERENCES ................................ ................................ ................................ ............ 107 3 Cr(acac) 3 and Cr(TMHD) 3 - Pump Dep endent Vibrational Coherence ............. 11 2 3.1 Introduction ................................ ................................ ................................ .... 112 3.2 Previous Time - Resolved Data on Cr(acac) 3 ................................ .................. 117 3.2.1 Femtosecond Dynamics Observed with Transient Absorption and IR ... 117 3.2.2 Transient Absor ption Utilizing 50 fs Pulses ................................ ............ 123 3.3 Current Efforts to Explore the Ultrafast Dynamics of Cr(acac) 3 ...................... 127 3.3.1 One Color Pump Dependence ................................ ............................... 128 Experimental ................................ ................................ .......................... 129 600 nm Excitation Results ................................ ................................ ..... 134 560 nm Excitation Results ................................ ................................ ..... 136 510 nm Excitation Results ................................ ................................ ..... 138 Discussion ................................ ................................ ............................. 140 3.3.2 Two Color Pump Dependence ................................ ............................... 147 600 nm Excitation Results ................................ ................................ ..... 153 560 nm Excitation Results ................................ ................................ ..... 155 505 nm Excitation Results ................................ ................................ ..... 157 Discussion ................................ ................................ ............................. 159 3.4 Cr(acac) 3 Concluding Comments ................................ ................................ ... 167 3.5 Cr(TMHD) 3 Vibrational Coherence ................................ ................................ . 168 600 nm Excitation Results ................................ ................................ ..... 171 560 nm Excitation Results ................................ ................................ ..... 172 525 nm Excitation Results ................................ ................................ ..... 174 Discussion ................................ ................................ ............................. 175 3.6 Cr(TMHD) 3 Concluding Comments ................................ ................................ 181 3.7 Future Work ................................ ................................ ................................ ... 181 APPENDICES ................................ ................................ ................................ ............. 18 4 Appendix A: Supplemental Data ................................ ................................ ........... 18 5 Appendix B : Ground State Recovery in Cr(acac) 3 and Cr(TMHD) 3 ....................... 195 Appendix C : Gaussian Calculation Results ................................ ........................... 197 R EFERENCES ................................ ................................ ................................ ............ 231 4 Magnetic Field Dependence of Intersystem Crossing in Cr(III) Compounds .. 23 6 4.1 Introduction ................................ ................................ ................................ .... 236 4.2 Methods ................................ ................................ ................................ ......... 240 4.2.1 Optical Components ................................ ................................ .............. 240 4.2.2 Magnet C apabilities and Probe Design ................................ .................. 243 4.3 NHMFL Studies ................................ ................................ .............................. 245 xi 4.3.1 Dynamics of Cr(acac) 3 in Acetonitrile and Dichloromethane in High F ields ................................ ................................ ................................ .................... 245 4.3.2 Dynamics of Cr(TMHD) 3 in Di chloromethane in High Fields .................. 249 4.4 Concluding Comments ................................ ................................ ................... 251 APPENDICES ................................ ................................ ................................ ............. 254 Appendix A: Probe Design ................................ ................................ .................... 255 Appendix B: Exponential Fits for Cr(acac) 3 and Cr(TMHD) 3 ................................ . 256 REFERENCES ................................ ................................ ................................ ............ 261 5 Outlook and Future Work ................................ ................................ .................... 2 6 4 REFERENCES ................................ ................................ ................................ ............ 270 xii LIST OF TABLES Table 3.1: Summary of Observed Oscillations for Cr(acac)3 in MeCN Utilizing One Color Experiments ................................ ................................ ................. 140 Table 3.2: Summary of Oscillations Observed Utilizing Two Color Experiments on Cr(acac) 3 in MeCN ................................ ................................ ................. 160 Table 3.3: Summary of Observed Oscillations for Cr(TMHD) 3 in DCM Utilizing a Two Color Pump - Probe Setup ................................ ................................ ....... 1 76 Table 3. 4 : Summary of Observed Oscillations for Cr(acac) 3 in DCM Utilizing Two Color Experiments ................................ ................................ ................. 1 88 xiii LIST OF FIGURES Figure 1.1 Possible Photophysical Processes Between Excited and Ground Potential Energy Surfaces ................................ ................................ ........................ 3 Figure 1.2 Transient Absorption Pulse Schematic and Sample Data .......................... 6 Figure 1.3 Potential Energy Diagram of a T ransient Absorption Experiment .............. 8 Figure 1.4 Simplistic Depiction of Wavepacket Motion On an Excited State Potentia l Energy Surface ................................ ................................ ........................ 1 1 Figure 1.5 Coheren ce in Excited State Absorption Signals ................................ ....... 12 Figure 1.6 Loss of Ground State Absorption and Raman Contributions to TA Signals ................................ ................................ ................................ ................. 14 Figure 1. 7 Coherent Oscill ations in Chloroform ................................ ........................ 15 Figure 1. 8 Large Geometric Flattening of Cu(I) bis - 2,9 - dimethyl - 1,10 - phenanthroline Upon Photoexcitation ................................ ................................ ............... 1 7 Figure 2.1 Wile E Laser Table Layout ................................ ................................ ....... 2 5 Figure 2.2 Schematic of Road Runner Demonstrating the Variability in the Experim ents Available With This System ................................ ................. 29 Figure 2.3 One Col or Experiments on Road Runner ................................ ................ 33 Figure 2.4 Two Col or Experiments on Road Runner ................................ ................ 35 Figure 2.5 White Light Pro be Experiments on Road Runner ................................ .... 38 Figure 2. 6 Comparison of Traditional Autocorrelation and SHG FROG Techniques 4 2 Figure 2. 7 General PG FROG Configuration ................................ ............................ 43 Figure 2. 8 Example FROG Traces f or PG and SHG FROG Geometries .................. 44 Figure 2. 9 PG XFROG Experimental C onfiguration ................................ .................. 47 Figure 2.10 Group Delay Dispersion for Various Lengths of BK7 Glass ..................... 49 Figure 2. 11 Illustration of Angular Dis persion in a Prism Compressor ........................ 51 Figure 2. 12 Pulses With and Without Pri sm Compression on Road Runner .............. 54 xiv Figure 2. 13 The Effect of the Crossing Angle on the Resulting Pulse Width .............. 56 Figure 2.14 LPSVD A nalysis Program Output Graphs ................................ ................ 59 Figure 2.B1 White Light Generation Media a nd Their Stability in the Red ................... 67 Figure 2.B2 Stability of White Light Med ia During Delta A Calculation ........................ 68 Figure 2.C1 FROG Data Collection Pr ogram Front Panel ................................ ........... 71 Figure 2.C2 New Data Workup Program W ith Baseline Correction ............................. 7 5 Figure 2.C3 Examining Scan Stability With "Make Delta A's" Program ....................... 76 Figure 2.C4 Calculation of the Signal to Noise of the Data Set With Each Additional Scan ................................ ................................ ................................ ......... 77 Figure 2.C5 Simplified Representation of the Signal, Reference, and Lock - in Reference waves at the Phase Sensitive Detectors ................................ 79 Figure 2.C6 Rephasing Data Colle cted by Lock - in Amplification ................................ . 80 Figure 2.F1 Binner Program Main Panel ................................ ................................ ..... 88 Figure 2.F2 Binner Program Displaying Ba ckground Corrected FR OG Trace ............ 89 Figure 2.F3 Binned Trace Ready for the FROG Algorithm ................................ .......... 90 Figure 2.F4 The Frogger Program Jus t After Launching from MATLAB ..................... 91 Figure 2.F5 The FROG Algorithm At Convergence ................................ ..................... 92 Figure 2.F6 The PG_XFROG Program Showing the Results of a Conv erged Algorithm ................................ ................................ ................................ ................. 94 Figure 2.G1 Comparison of FFTs With and Without Zero Padding ........................... 101 Figure 2.H1 LabVIEW TD FFT Program ................................ ................................ .... 10 5 Figure 3.1 Tanabe - Sugano Diagram for a d 3 Metal Center ................................ ..... 113 Figure 3.2 Steady State Absorption and Emission Spectra for Cr( acac) 3 ............... 115 Figure 3.3 Potential Energy Surface Diagram for the Lowest Energy Ligand Field States and Their Corresp onding One - Electron Diagrams ...................... 116 Figure 3.4 Cr(acac) 3 TA Data Pumping with 120 fs 625 nm Pulses ........................ 118 Figure 3.5 Ultrafast IR Results Foll owing 400 nm Excitation of Cr(acac) 3 .............. 120 xv Figure 3.6 Results from 50 fs excitation at 600 nm for Cr(acac) 3 ............................ 124 Figure 3.7 Vibrational Modes Possibl y Facilitating Ultrafast ISC ............................ 125 Figure 3.8 Transient Absorption Data for Cr(TMHD) 3 in DCM ................................ 127 Figure 3.9 Overlay of Cr(acac) 3 Ground and Excited State Absorptions With the One - Color Pump and Probe Combinations ................................ .................... 130 Figure 3.10 IGOR and MATLAB Data Analysis Techniques Compared ................... 131 Figure 3.11 Cr(acac) 3 Vibrations Resu lting from 600 nm Excitation ......................... 135 Figure 3.12 Cr(acac) 3 Vibrations Resu lting from 560 nm Excitation ......................... 137 Figure 3.13 Cr(acac) 3 Vibrations Resu lting from 510 nm Excitation ......................... 139 Figure 3.1 4 FT Raman Spectrum for Cr(acac) 3 in the Solid State ............................ 142 Figure 3.15 566 and 461 cm - 1 Modes on the 2 E and 4 T 2 Surfaces ............................ 144 Figure 3.16 233 cm - 1 Mode in B oth the 2 E and 4 T 2 States ................................ ........ 145 Figure 3.17 Pump and Probe Spectra for Cr(acac) 3 Two Color Experiments ........... 149 Figure 3.1 8 Typical Data Set for Cr(acac) 3 in th e Two C olor Pump - Probe Setup ..... 150 Figure 3.1 9 Probe Wavelength Effects on the MeCN Solvent Response ................. 152 Figure 3. 20 Cr(acac) 3 600 n m Pump, 520 nm Probe Results ................................ ... 154 Figure 3.2 1 Cr(acac) 3 560 n m Pump, 520 nm Probe Results ................................ ... 156 Figure 3.2 2 Cr(acac) 3 505 n m Pum p, 520 nm Probe Results ................................ ... 158 Figure 3.2 3 4 T 2 299 and 510 cm - 1 Vibrational Motions ................................ .............. 161 Figure 3.2 4 Scissoring Mode at 254 cm - 1 on the 4 T 2 and 2 E Excited States ............. 162 Figure 3.2 5 Low Frequency Methyl Group Rotation at 70 and 104 cm - 1 ................... 163 Figure 3.2 6 Illustrations of Multimode and Progression Excit ation Schemes ............ 164 Figure 3.2 7 Raman Peaks From CH 2 Cl 2 Obser ved in Two Color Experiments ........ 169 Figure 3.2 8 Two Color Data Using DCM as a Solvent ................................ .............. 170 Figure 3.2 9 Cr(TMHD) 3 in DCM Following 600 nm Excitation ................................ ... 17 2 xvi Figure 3. 30 Cr(TMHD) 3 in DCM Following 560 nm Excitation ................................ ... 173 Figure 3. 31 Cr(TMHD) 3 in DCM Following 525 nm Excitation ................................ ... 175 Figure 3.3 2 Ground State Vibrational Modes in Cr(TMHD) 3 ................................ ..... 179 Figure 3. A1 Cr(acac) 3 in MeCN With 505 nm Excitation ................................ ........... 1 85 Figure 3. A2 Cr(acac) 3 in MeCN With 560 nm Excitation ................................ ........... 1 86 Figure 3.A3 Cr(acac) 3 in MeCN with 600 nm Excitation ................................ ............ 1 87 Figure 3.A4 Cr(acac) 3 in DCM Following Excitation at 525, 560, and 600 nm .......... 189 Figure 3. A5 Cr(TMHD) 3 in DCM Following 600 nm Excitation ................................ .. 192 Figure 3.A6 Cr(TMHD) 3 in DCM Following 560 nm Excitation ................................ .. 193 Figure 3.A7 Cr(TMHD) 3 in DCM Following 525 nm Excitation ................................ .. 194 Figure 3.B 1 Ground State Recovery Dynamics for Cr(acac) 3 in MeCN and DCM ..... 1 95 Figure 3.B 2 Ground State Recovery Dynamics for Cr(TMHD) 3 in DCM .................... 1 96 Figure 4.1 Schematic of Radical Ion Pair Energy Levels as a Function of Magnetic Field ................................ ................................ ................................ ....... 23 7 Figure 4.2 Proposed Zeeman Splitting of Cr(acac) 3 in Fields up to 25 T ................ 23 9 Figure 4.3 The 25 Tes l a Split Florida - Helix Magnet ................................ ................ 244 Figure 4.4 The Dynamics of Cr(aca c) 3 in MeCN in Fields From 0 T to 25 T ........... 2 45 Figure 4. 5 Cr(acac) 3 in MeCN with 1.1 ps Fit ................................ .......................... 2 46 Figure 4. 6 Acetonitrile Cross Correlation Signals from 0 to 25 T ............................ 24 7 Figure 4. 7 The Dynamics of Cr(acac) 3 in DCM in Fields From 0 to 25 T ................ 24 8 Figure 4. 8 Dynamics of Cr(TMHD) 3 in DCM at Fields From 0 to 25 T .................... 24 9 Figure 4.A1 Initial Probe Design ................................ ................................ ................ 256 Figure 4.A2 Improved Probe Design ................................ ................................ ......... 25 8 Figure 4.B1 FFT of the Oscillatory Component in the DCM Signal ........................... 25 9 Figure 4.B2 Cr(acac) 3 in DCM with 1.1 ps Fit ................................ ............................ 25 9 xvii Figure 4.B3 Dichloromethane Solvent Response in Fields from 0 T to 25 T ............. 260 Figure 4.B4 Cr(TMHD) 3 Exponential Fit ................................ ................................ .... 260 Figure 5.1 Cr(acac) 3 Derivatives Available for Future Coherence Studies .............. 2 6 5 xviii KEY TO ABBREVIATIONS LF ........................... ligand field MLCT ..................... metal - to - ligand charge transfer LMCT ..................... ligand - to - metal charge transfer CT .......................... charge transfer ES .......................... excited state GS .......................... ground state VR .......................... vibrational relaxation VC .......................... vibrational coolin g IVR ......................... intramolecular vibrational redistribution IC ............................ internal conversion FL ........................... fluorescence ISC ......................... inters ystem crossing BISC ....................... back intersystem crossing PH .......................... phosphorescence acac ........................ 2,4 - pentanedione or acetylacetonate TMHD ..................... 2,2,6,6 - tetramethyl - 3,5 - heptanedione bpy ......................... - bipyridine phen ....................... 1,10 - phenanthroline Tren(py) 3 ................ tris(2 - pyridylmethyliminoetyl)amine MeCN ..................... acetonitrile DCM ....................... dichloromethane MeOH ..................... methanol PF 6 ......................... hexafluorophosphate xix ClO 4 ........................ perchlorate TA ........................... transient absorption LPSVD ................... linear predictive single value decomposition M - L ......................... metal - ligand (bond) FWHM .................... full width at half max FROG ..................... frequency resolved optical gating OPA ........................ optical parametric amplifier YAG ........................ yttrium aluminum garnet CaF 2 ....................... calcium fluoride ND .......................... neutral density IRF ......................... instrument response function XC .......................... cross correlation OKE ........................ optical Kerr effect FROG ..................... frequency resolved optical gating XFROG .................. cross - correlation FROG GVD ....................... group velocity dispersion GDD ....................... group delay dispersion SHG ....................... second harmonic generation PG .......................... polarization gating WLG ....................... white light generation XPM ....................... cross - phase modulation SPM ....................... self - phase modulation FT ........................... Fourier transform FFT ......................... fast Fourier transform TD FFT ................... Time - dependent fast Fourier t ransform xx DFT ........................ density functional theory TD DFT .................. time - dependent density functional theory PCM ....................... polarizable continuum model CPCM ..................... conductor - like polarizable continuum model G03 ........................ Gaussian '03 G09 ........................ Gaussian '09 CAS SCF ................ complete active space self - consistent field ISRS ....................... impulsive stimulated Raman scattering GSR ....................... ground state recovery AMU ....................... atomic mass unit NHMFL ................... National High Magnetic Field Laboratory GPIB ....................... general purpose interface bus 1 1 Introduction This dissertation examines the ultrafast dynamics of tris(2,4 - pentanediono)chromium(III) , Cr(acac) 3 . The ultimate goal of this work is to find a "handle" in the ligand framework where substitutions will reliably and predictably alter the photophysics of the compound. Thus, an in - depth understanding of the geometry changes occurring in this molecule over the course of the ultrafast dynamics is imperative. The work in this thesis targets two experimental techniques to gain information about the ultrafast dynamics in these molecules : vibrational coherence and perturbation with a strong magnetic field. The molecules studied in this thesis are transition metal compounds based on an octahedrally coordinated Cr(III) metal center. Utilizing visible excitation, these compounds have nomi nally two excited states to sample prior to returning to the ground state . This greatly reduces the complications associated with interpreting kinetics in these systems compared to other transition metal compounds, examples of which include Ru(II), Fe(II) , and Cu(I) compounds ( vide infra ) . While the simple electronic picture of these Cr(III) complexes make s the m a ttractive candidates for study, ideally the concepts established here will be more broadly applicable in the field of transition metal photophys ics. 1.1 Photophysical Processes in Transition Metal Compounds The focus of this dissertation is on photophysical processes, or processes that occur after the absorption of light and do not cause a permanent change in the composition of the molecule. In gen eral, transition metal compounds contain a variety of absorption features arising from the ligand, metal center, or both, namely n - *, - *, d - d, and charge transfer, respectively. The d - d and charge transfer absorptions are of 2 primary interest, as the n - * and - * transition s are only modestly altered from their pure - organic counterparts. Metal centered d - d transitions, also called ligand field (LF) abso rptions, have relatively low ex tinction coefficients due to the symmetry forbidden nature of the tran sition between metal - based orbitals . As such, most of these transitions have peak intensities at 100 M - 1 cm - 1 or less. 1 Charge transfer transitions, however, involve the transfer of an electron from a metal orbital to a ligand orbital (metal - to - l igand charge transfer, or MLCT) or from a ligand orbital to a metal orbital (ligand - to - metal charge transfer, LMCT) . These transitions are no longer between orbitals on the metal center, so it is easier to obey the symmetry restriction for transitions, leading to strong extinction coefficients , ranging from 10 3 to 10 4 M - 1 cm - 1 . 2 Another important aspect of LF and CT absorptions is their presence in the visible part of the spectrum. As such, the majority of visible excitat ion studies on transition metal compounds utilize these transitions to initiate photop h ysical processe s. Light absorption occurs when the incident photon has sufficient energy to promote an electron to a higher energy orbital , or excited state (ES) . T he B orn - Oppenheimer approximation allows the movement of the nuclei to accommodate this electronic change to be neglected, since an electron 's motion is instantaneous compared to the rate of nuclear movement . 3 This means that the excited state is generated with the same geometry as the ground st ate (GS) structure. At this point, the excited molecule has a number of possibil i ties for dissipating this excess energy and returning to the ground state configuration. These processes are shown schematically in Figure 1 . 1 . The potential energy surfaces are labeled S 0 , S 1 , and T 1 , where the S denotes a state with a singlet multiplicity and the T denotes a state with a triplet 3 multiplicity. The vertical axis r epresents the energies of these electronic states, while the horizontal axis relates geometric parameters of the states. The process of absorbing a photon of energy h is represented by a vertical green arrow moving the system into the S 1 excited state. As the energy of this photon is high enough to excite Figure 1 . 1 Possible Photophysical Processes Between Excited and Ground Potential Energy Surfaces The ground and excited states are represented as pote ntial energy surfaces displaced along some generalized energies. Absorption of a photon is shown as the green arrow, while transitions between states of the same multiplicity (S 0 1 ) are shown in orange and transi tions between different multiplicities (T 1 1 ) are shown in red. The blue oscillating arrows represent vibrational relaxation , or movement to lower vibrational levels within an excited state surface. Radiative transitions are represented as solid arrows; nonradiative transitions are represented as dashed arrows. the v =7 vibrational leve l, vibrational relaxation (VR ) may occur to dissipate enough energy to relax to a Boltzmann distribution in the S 1 state . This V R process is typically thought of a vibrational motion of the molecule transferring energy to the surrounding solvent as heat (vibrational cooling, VC) or transferring vibrational energy to other 4 modes of the molecule (intramolecular vibrational redi stribution, IVR) . This is seen as the blue wavy arrow pointing to the bottom of each excited state surface. To return to the ground state from S 1 , the system may nonradiatively decay via internal conversion (IC) , again transferring this energy as heat to the surrounding solvent, or emit a photon as fluorescence (FL) to radiatively transition between these states. 4,5 Alternately, t he S 1 state may transition to the T 1 state through intersystem crossing (ISC) , which occurs by flipping the spin of an electron while maintaining the total energy of the system, hence the horizontal arrow. The system may then undergo V R on the T 1 surface before radiatively or nonradiatively returning to the ground state through phosphorescence or ISC , respectively. In this case, ISC i s a vertical transition which dissipates energy of the system to the surrounding solvent media. All of these processes are associated with a rate , and the overall photophysics of the system results from the kinetic competition between these rates. The geometric aspect of these transitions is represented by the reaction coordinate along the x - axis in Figure 1 . 1 . This reaction coordinate could be a number of geometr ic changes, from a bond length change to a torsional twisting of the ligands in the molecule or even a combination of modes, This vertical transition upon absorption of light places the system on the S 1 surface at unchanged despite the movement of an electron. 3 The Franck Condon governs the intensity of a transition , and results in the highest probabilities for transitions where the nuclei are stationary. 6 These stationary positions occur at the turning points, or edges , of the potential energy surface. is 5 that as the excited state relaxes to the geometry associated with the potential minimum, vibrational relaxation can facilitate the necessary reconfiguration. To look at that another way, identification of the vibrational modes facilitating a structure change or ultra fast relaxation event provides insight into which structural aspects of the molecule might affect the rate of these events and should be chemically manipulated . Identification of these vibrational modes, either as initially excited or po pulated through IVR, may be accomplished through a number of techniques. Because the excited state v ibrations are of interest, time - resolved techniques are needed. At the most basic level, a light source is requir ed to transition the molecule to the excited state , and then any UV - Visible, IR, Raman, etc., spectroscopic technique may be used to get information about these vibrations. 7,8 The approach employed in this dissertation uses visible light in a pump - probe experiment to investigate these vibrations. Utilizing laser pulses shorter than the period of the molecul ar vibrations of interest, the nuclear motions of excited state relaxation events may be monitored as a function of time. 1.2 Transient Absorption Spectroscopy 1.2.1 General Experimental Considerations Transient absorption spectroscopy (TA) is a pump - probe techniq ue that investigates excited state absorption as a function of time . The pump pulse pro motes a small fraction of the sample to an initial excited state , where at some time delay , the weak probe pulse interacts with the sample, and the transmitted intens ity of this probe pulse is recorded as a function of . In this way, kinetics of the excited state processes (IC, ISC, VR, etc.) may be inferred from the signal. Since the absorption changes are 6 referenced to the ground state absorption of the molecule, the signals are represented Since TA promotes only a fraction of the molecules in solution to the excited state, the signals recorded are actually a mix of ground state and excited state absorption signals, as seen in equ ation 1 .1 , below: ( 1 .1 ) path length of the cell, c GS percentage of ground state promoted to excited state by the pump pulse. 9 From this equation, it is easy to see that p osi tive signals result when the excited state extinction Figure 1 . 2 Transient Absorption Pulse Schematic and Sample Data The transient absorption laser pulses, left, shows how the pump pulse (orange) interse cts with the probe pulse (green) at a small angle inside the sample cell. The delay between the pulses is changed in order t o record the transient signal. Example data , right, showing a transient absorption signal (black dots) for [Fe(tren(py) 3 ](PF 6 ) 2 . The inset shows the ground state (black) and approximate excited state (blue) absorption spectra, and the excited state spectrum minus the ground state spectrum is shown in the solid red trace. The TA signal match the simulated difference spectrum quite w ell. The figure on the right is a dapted with permission from reference 10 . © (2008) American Chemical Society. 7 coefficient is greater than the ground state extinction coefficient. Negative signals, however, may result from the loss of ground state absorption, or ground state bleach, upon promotion of some molecules to the excited state. This is typically seen in spectral regions where the ground state extinction coefficient is greater than the excited state extinction coefficient. If the sample is emissive and the probe pulse stimulates emission from the excited state to the ground state, this will also produce a negative TA signal. 4,11 A TA signal of is zero is called an isosbestic point, and it only occurs where the ground state and excited state absorptions are identical. These concepts are illustrated in Figure 1 . 2 , where left panel shows the timing delay of the pump and probe pulses incident on the sample cuvette, and the right panel black dots, contains regions of positive, negative, and zero signal. The inset in Figure 1 . 2 shows the ground state and approximate excited state absorption spectra for [Fe(tren(py) 3 ](PF 6 ) 2 , a s pin crossover compound. 10 This molecule represents a special instance where the " excited state spectrum " may be collected explicitly using steady state UV - Visible absorption through synthetic modifications to the ligand . By subtracting the ground state absorption spectrum (black) from the excited state absorption spectrum (blue), the transient absorption signal for this compound may be simulated. This simulated spectrum (red) is a close match to the actual transient absorption signal (black dots) in this case since there is no stimulat ed emission in this compound. The negative signals occur where the ground state absorbs more, the positive signal occurs where the excited state absorbs more, and there are two isosbestic points from the two crossing points in the ground state spectra. 8 E xcited state absorption may be monitored in a narrow spectral region (single wavelength) or over a broad spectral region (full spectra). The differences are illustrated in Figure 1 . 3 , which shows the interaction of the pump and probe pulses with three different states, GS , E S 1 , and E S 2 . The pump pulse, represented by either the solid red or blue arrows from G S to E S 1 , generate s a population on the E S 1 surface accord ing to its energy and the Franck Condon overlap describe d above. The subsequent absorption of a probe photon, represented by the dashed arrows from E S 1 to E S 2 , occurs following these same rules. Figure 1 . 3 Potential Energy Diagram of a Transient Absorption Experiment The solid arrows represent the action of the pump pulse to move an electron from the ground state, G S, to the first excited state, E S 1 . The probe pulse (dashed arrows) is a subsequent absor ption into a higher lying excited state, E S 2 . In the experimental scenario of the blue pump pulse, the molecule is initially excited into a higher lying vibrational level and the opportunity for vibrational cooling on 9 the E S 1 state exists. Supposing this happens on a timescale that is fast in relation to ground state recovery, this process should reveal itself in the excited state dynamics. At very early times, while the molecule is still in the initially prepared vibrationa l level, the red probe pulse will have sufficient energy to promote population into the E S 2 state. However, once the E S 1 state has vibrationally relaxed into lower vibrational level s , this red probe pulse no longer has enough energy to generate E S 2 popula tion. This thought experiment is entirely analogous to monitoring the TA signal at a single wavelength. The full spectra l data over the same time window would simultaneously reveal the absorption of all of the probe wavelengths depicted in Figure 1 . 3 at a given time delay. The actual process of collecting this data is described in detail in Chapter 2, however , a brief note will be made here that the detection methods necessarily bias single wavelength experiments for more accurate kinetic information (i.e. time constants for processes), while the full spectra data often proves invaluable for the assignment of t hose time constants to specific processes. For the TA experiments described in this thesis, the pump pulse is moved in relation to the probe pulse, and results in three distinct periods in the data: negative time, tim e zero, and positive time. Time dela ys where the probe pulse reaches the sample before the p ump pulse are referred to as negative time and display a value of zero in TA signals. In this scenario , the detector records only the ground state absorption of the probe wavelength , which is set to zero in TA data. Time zero occurs when the pump and probe pulses reach the sample at exactly the same time. And a t positive time , a decreased pump delay cause s the pump pulse to always reach the 10 sample before the p robe pulse , leading the probe to monitor absorption signals from the excited state. 1.2.2 Conditions for Vibrational Coherence Since the time duration of a Gaussian pulse and its spectral bandwidth are bound by a Fourier relationship: ( 1. 2 ) where p is the pulse duration and p is the bandwidth of the pulse, the shorter the time duration of the pulse, the larger the spectral bandwidth. 12 With short enough pulses, new features arise in the TA data. Once the pump pulse duration is less than the vibrational period for a particular vibrational mode in a molecule , that mode may now be excited ; this corresponds to the "impulsive limit" for excitation . 7,13 A nother way to think of this is the pump pulse may now have enough bandwidth to simultaneously excite multiple vibrational levels. 14 If these conditions are met, oscillatory features may be seen in the TA data which correspond to the motion of wavepack et s on the potential energy surface s . 15,16 This oscillatory feature results because "at a given time, the energy of the el ectronic transition is given by the vertical distance between two surfaces taken at the position of the wavepacket." 13 This means that as the wavepacket moves across the potential energy surface, the Franck Condon factors change to higher or lower lying vibrational states, causing the absorption intensity to fluctuate. This w avepacket motion is illustrated simplistically in Figure 1 . 4 , depicting the same two potential energy surfaces at different points in time. The far left case represe nts the wavepacket immediately after formation by the large bandwidth pump pulse. The 11 wavepacket moves across the excited state surface, with levels hitting the "turning point" of the vibrational level at different times (as can be seen in panels 3 and 4) . 3 The wavepacket (and thus the obser ved oscillations) remains intact until vibrational dephasing has destroyed the coherence between the states (panel 5). Figure 1 . 4 Simplistic Depiction of Wavepacket Motion On an Excited State Potential Energy Surface A view of two potential energy surfaces and the evolution of a wavepacket on the excited state surface with time is shown here from early time (left) to late time (rig ht). The broad bandwidth pump (represented by the colors on the various vibrational levels) creates a coherent superposition in multiple vibrational levels. This wavepacket moves across the surface until reaching the other edge (panel 2). The exaggerate d anharmonicity in this potential leads the vibrational levels to have different turning positions (panels 3 and 4) and causes the wavepacket to dephase (panel 5). While Figure 1 . 4 addresses the picture of simultaneous excitation of multiple vibrational levels, the work by Pollard and Mathies in the impulsive limit better explains the oscillatory signals originating fro m the ground and excited states, and even the solvent used in the experiment. Their models assume the pump - probe experiment consists of three field - matter interactions: two of which come from the pump pulse, and one that comes from the probe pulse. 17 For excited state absorption, seen in Figure 12 1 . 5 , below , the two pump interactions (blue arrows) each serve to create a w avepacket on the first excited state, v 1 , and these wavepackets move along the v 1 surface from the forces applied by the excited potential energy surface. At some time delay, the probe pulse (green arrow) promotes one of these wavepackets to excited state v 2 , producing an electronic coherence between v 1 and v 2 , where the two wavepackets propagate until they dephase. 17 Figure 1 . 5 Coherence in Excited State Absorption Signals The pump pulse interacts with the ground state twice (blue arrows) to create two wavepackets on the v 1 excited state surface. The horizontal arrows indicate the propagation of these wavepackets on the potential until the probe pulse (green arrow) moves one of the wavepackets up to excited state v 2 . The wavepackets cont inue to produce oscillations in the TA signal until they dephase. Figure adapted with permission from reference 17 . © AIP Publishing LLC . 13 The signals resulting from the ground state and solvent result from Raman processes, and are called impulsive stimulated Raman scattering (ISRS). Though the two processes are slightly different, they may generally be represented by Figure 1 . 6 . Here, the first pump interaction creates a wavepacket on excited state v 1 , whic h prop a gates on the potential energy surface until the second pump interaction moves this displaced wavepacket back down to the ground state. This pump created wavepacket on the ground state propagates on the ground state surface until the probe pulse exc ites it back to v 1 (loss of ground state), or creates a second wavepacket on excited state v 1 (resonance Raman). 17 If the pump pulse is nonresonant, as is the case for the visible pumps and solvents used in this thesis, the pump pulse interacts with a virtual level instead of an electronic excited s tate . The bandwidth of the pulse is sufficient to drive the vibrational mode on the ground state because it contains a pair of frequencies with a difference tuned to the vibrational mode in question. 18 An important feature of these diagrams is that displaced and moving wavepackets generate the oscillatory signal observed. If the wavepacket has neither significant displacement from its initial position nor substantial momentum , it will not appear in the signal. 17 For the situation depicted in Figure 1 . 6 , a very short pump pulse will generate a stationary ground state wavepacket and exhibit only signals from the probe - produced excited state wavepacket. Since a wavepacket can be formed on either the excited or the ground state potential en ergy surfaces (or both), these oscillations represent the Raman modes of those states. 19 It is also possible to impulsively stimulate Raman modes in pure solvent, which is completely transparent to visible light. An example of this is seen in Figure 1 . 7 14 Figure 1 . 6 Loss of Ground State Absorption and Raman C ontributions to TA Signals The two pump interactions (blue arrows) serve to create a displaced wavepacket on the ground state surface which propagates until the probe pulse (green arrow) promotes it back to the excited state v 1 . This diagram is explicitly for ground state bleach, but the Raman diagram is only slightly different. In that case, the probe pulse creates a new wavepacket on v 1 , such that wavepackets are moving on both v 0 and v 1 surfaces. Figure adapted with permission from reference 17 . © AIP Publishing LLC . below , where studies by Pau l Champion and coworkers show the utility of using 45 fs pulses to resolve the Raman modes of chloroform in a TA experiment . 20 The oscillatory TA data collected in the time - domain is seen in the top panel, while the frequency components of the signal are shown in panel B after processing the data with Linear Predictive Single Value Decomposition (LPSVD) (see Chapter 2 for more details). For comparison, the tradition al Raman spectrum of the compound is shown in panel C. The peaks in the power spectrum in panel B are located at 262, 362 - 368, and 668 cm - 1 , which are a good match for the traditional Raman peaks (panel C) at 262, 361 - 367, and 15 669 cm - 1 . 20 While this example demonstrates the efficacy of this method in nonresonant samples, it is equally suited to resonant samples. 15,20,21 Figure 1 . 7 Coherent Oscillations in Chloroform Panel A shows the TA data for the entire time - domain trace as well as an expansion of the 100 fs - 4 ps region of the data. Using a Fourier - transform based data analysis program on the data gives the results in B, which are compared to the traditional Raman spectrum in C. The accuracy of this method is reflected in the agreement between the TA retrieved oscillations and the Raman data. Figure r eproduced from reference 20 with permission . © John Wiley & Sons, Inc. 1.3 Background on Vibrational Coherence 1.3.1 Early Experiments - Diatomics and Organics An early pioneer in th e area of vibrational coherence was Dr. Ahmed Zewail and his team of researchers who sought to map out the transition state of reactive molecules 16 and visualize bond breaking reactions. His efforts in the field were reco gnized with the Nobel Prize in Chemistry in 1999 for " for showing that it is possible with rapid laser technique to see how atoms in a molecule move during a chemical reaction." 22 Since its application in analyzing di - and tri - atomics 23 25 , this area of study has progressed to systems of large organic molecules where processes such as proton transfer reactions 26 and cis - trans isomerizations may be monitored. 27 While these works are important, the types of excited states, the density of excited states, and relaxation cascades are typically quite different for organic molecules than transition metal complexes. 4 However, they do highlight the ability of this technique to probe geometric changes in the molecule on ultrafast timescales. 1.3.2 Vibrational Coherence in Transition Metal Compounds In the las t decade, there has been an increased push to apply this methodology to the study of transition metal compounds. These systems allow for the ligand structure to be subtly modified while minimally a ffecting the electronic structure of the molecule. 28 30 The coherence studies on transition metal compounds include systems like Zn(II) cytochrome c , Pt dimers, Ru(II) terpyridine - type compounds, Pt and Os halides, Cu(I) phenanthrolines, Fe(II) polypyridyls, Cr carbonyls, and Cr(III) acetylacetonate. 29 35,14 ,36,37 The se studies highlight the retention of coherence through excited state surface crossings, geometry distortions, ligand loss, and solvent interactions. The Ru(II) study , in particular, shows that vibrational coherence, due to the ligand distor tion in a halogenated terpyridine, survived both ISC and IC from the initially populated 1 MLCT state to a 3 MC (metal centered) state. 30 In [Fe(bpy) 3 ] 2+ , excitation into the 1 MLCT results in <250 fs relaxation through a large density of excited states to the 17 5 T 2 lowest energy excited state accomp anied by a 0.2 Å Fe - N bond length change. 14,10 The vibrat ional coherence observed by Chergui et al. was assigned to a N - Fe - N bending mode on the 5 T 2 state stimulated by this ultrafast Fe - N bond elongation during the excited state relaxation. 14 The studies on Cu(I) phen anthroline s reveal vibrational coherence that is damped out by a particularly large structural change . 29 In the ground state, Cu(I) is d 10 , preferring a tetrahedral - like coordination environment where the two phenanthroline ligands are 90° from each other. However, excitation into the 1 MLCT excited state produces a formally d 9 Cu(II) and a reduced phenanthroline ligand; the preferred structure of this compound is now a flattened, square planar - like geometry , portrayed in Figure 1 . 8 , below . 38,39 Tahara and coworkers have studied three different Cu(I) phenanthroline systems w ith varying degrees of ground state structural distortion, afforded by substituents in the 2,9 positions on the ligand, and have observed vibrational coherence in the excited state for all three of them. The coherence seems to Figure 1 . 8 Large Geometric Flattening of Cu(I) bis - 2,9 - dimethyl - 1,10 - phenanthroline Upon Photoexcitation The ground state structure is seen on the left, where the ligands are perpendicular to each other, whereas the excited state st ructure, containing a Cu(II) center and a reduced phenanthroline ligand, flattens the two ligands to achieve a geom etry closer to square planar. Reprinted with permission from reference 38 . Copyright ( 2007 ) American Chemical Society . 18 dephase on the same timescale as the flattening distortion in each of these molecule s, and the oscillatory signals are attributed to Cu - N stretching as the excited state is predicted to have shorter Cu - N bond lengths. 35 While the examples discussed here highlight the use of MLCT excitations, which affect the M - L bond lengths and cause some structural changes, they also convey the high density of excited states and how analysis of vibrational coherence b ecomes complicated in the presence of so many surface crossings. The work in this dissertation removes some of these problems by focusing on Cr(acac) 3 and a structurally similar derivative, where there are nominally three potential energy surfaces composi ng the entire photophysical picture; the quartet ground state, a spin - allowed quartet excited state, and one doublet excited state lower in energy than the initial quartet state. 40 Therefore, there is only one surface crossing in any of the excited state dynamics. Also, th e excitation for this system is a ligand field transition where an electron is moved from a nonbonding t 2g orbital to an anti - bonding e g * orbital, thus, the geometry of the excited state is expected to undergo a geometric distortion. 5 By st udying the vibrational motions of this molecule in the excited state, both before and during the surface crossing event, we hope to identify the vibrational modes and/or geometric distortions responsible for the ultrafast photophysics observed in the syste m. In this way, synthetic modifications to the ligand set may be able to alter the timescale of these processes and provide a source of kinetic control in this system. 1.4 Contents of this Dissertation All of the work in this dissertation focuses on the u se of TA to investigate ISC in Cr(acac) 3 and tris(2,2,6,6 - tetramethyl - 3,5 - heptanediono)Chromium(III), Cr(TMHD) 3 . 19 Before any vibrational coherence could be collected in this lab , the instrumentation and data collection protocols had to be developed and ref ined to give reliable results. Chapter 2 cover s these aspects , detailing the specific laser setups used to collect this data and the various new programs that had to be written and/or used in order to collect and analyze the data. Chapter 3 delves into t he photophysical background of Cr(acac) 3 and Cr(TMHD) 3 and details the results of experiments utilizing <50 fs excitation pulses to produce vibrational coherence in these sy s tems . Chapter 4 details the results of ultrafast experiments conducted in fields up to 25 Tesla at the National High Magnetic Field Laboratory in collaboration with Dr. Stephen McGill and Dr. Michael Bishop. Here we hope to use the perturbations of a large magnetic field on the excited states to alter the relaxation dynamics in Cr(aca c) 3 and Cr(TMHD) 3 . Chapter 5 gives an outlook on this work and its impact on science both within this research lab and in the broader scientific community. 20 REFERENCES 21 R EFERENCES (1) Miessler, G.; Tarr, D. A. Inorganic Chemistry ; Pearson Education, 2004. (2) James, R.; Moore, E. In Metal - Ligand Bonding ; The Royal Society of Chemistry: Cambridge, UK, 2004; pp 75 82. (3) McQuarrie, D. A.; Simon, J. D. Physical Chemistry: A Molecular Ap proach ; University Science Books: Sausalito, CA, 1997. (4) McCusker, J. K. Acc. Chem. Res. 2003 , 36 (12), 876. (5) Juban, E. A. The Ultrafast Dynamics of Chromium(III) Coordination Complexes, University of California Berkeley, 2006. (6) Drago, R. S. Phy sical Methods For Chemists , 2nd ed.; Surfside Scientific Publishers: Gainsville, FL, 1992. (7) Browne, W. R.; McGarvey, J. J. Coord. Chem. Rev. 2007 , 251 (3 - 4), 454. (8) Chem. Soc. Rev. 2005 , 34 (8), 641. (9) Brown, A. M. Excited - State Dynamics of Iron(II) - Based Charge - Transfer Chromophores, Michigan State University, 2011. (10) Smeigh, A. L.; Creelman, M.; Mathies, R. A.; McCusker, J. K. J. Am. Chem. Soc. 2008 , 130 (43), 14105. (11) Berera, R. ; van Grondelle, R.; Kennis, J. T. M. Photosynth. Res. 2009 , 101 (2 - 3), 105. (12) Paschotta, R. Field Guide to Laser Pulse Generation ; SPIE Press: Bellingham, WA, 2008; Vol. FG14. (13) Fragnito, H. L.; Bigot, J. - Y.; Becker, P. C.; Shank, C. V. Chem. Phys. Lett. 1989 , 160 (2), 101. (14) Consani, C.; Prémont - Schwarz, M.; ElNahhas, A.; Bressler, C.; van Mourik, F.; Cannizzo, A.; Chergui, M. Angew. Chemie Int. Ed. 2009 , 48 (39), 7184. (15) Pollard, W. T.; Fragnito, H. L.; Bigot, J. - Y.; Shank, C. V.; Mathies, R. A. Chem. Phys. Lett. 1990 , 168 (3 - 4), 239. (16) Dhar, L.; Rogers, J. A.; Nelson, K. A. Chem. Rev. 1994 , 94 (1), 157. (17) Pollard, W. T.; Lee, S. - Y.; Mathies, R. A. J. Chem. Phys. 1 990 , 92 (7), 4012. 22 (18) Weiner, A. M. Ultrafast Optics ; Boreman, G., Ed.; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2009. (19) Beck, W. F. In Encyclopedia of Chemical Physics and Physical Chemistry ; Moore, J. H., Spencer, N. D., Eds.; Institute of Physi cs Publishing, Ltd.: Bristol, England, 2001; pp 1743 1772. (20) Wang, W.; Demidov, A. A.; Ye, X.; Christian, J. F.; Sjodin, T.; Champion, P. M.; Champion, M. J. Raman Spectrosc. 2000 , 31 (1 - 2), 99. (21) Champion, P. M.; Rosca, F.; Wang, W. S.; Kumar, A. T. N.; Christian, J. F.; Demidov, A. A. In SPIE ; Scherer, N. F., Hicks, J. M., Eds.; 1998; Vol. 3273, pp 80 89. (22) Sciences, T. R. S. A. of. Press Release: The 1999 Nobel Prize in Chemistry http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1999 /press.html. (23) Mokhtari, A.; Cong, P.; Herek, J. L.; Zewail, A. H. Nature 1990 , 348 (6298), 225. (24) Zewail, A. H. J. Phys. Chem. A 2000 , 104 (24), 5660. (25) Polanyi, J. C.; Zewail, A. H. Acc. Chem. Res. 1995 , 28 (3), 119. (26) Takeuchi, S.; Tahara, T. J. Phys. Chem. A 2005 , 109 (45), 10199. (27) Schoenlein, R.; Peteanu, L.; Mathies, R. A.; Shank, C. Science (80 - . ). 1991 , 254 (5030), 412. (28) Schrauben, J. N. Electronic Structure and Excited State Dynamics of Chromium(III) Co mplexes, Michigan State University, 2010. (29) Hua, L.; Iwamura, M.; Takeuchi, S.; Tahara, T. Phys. Chem. Chem. Phys. 2015 , 17 (3), 2067. (30) Hewitt, J. T.; Vallett, P. J.; Damrauer, N. H. J. Phys. Chem. A 2012 , 116 (47), 11536. (31) Dillman, K. L.; Sh elly, K. R.; Beck, W. F. J. Phys. Chem. B 2009 , 113 (17), 6127. (32) Cho, S.; Mara, M. W.; Wang, X.; Lockard, J. V.; Rachford, A. A.; Castellano, F. N.; Chen, L. X. J. Phys. Chem. A 2011 , 115 (16), 3990. (33) Van Der Veen, R. M.; Cannizzo, A.; Van Mourik J. Am. Chem. Soc. 2011 , 133 (2), 305. (34) Zheldakov, I. L.; N. Ryazantsev, M.; Tarnovsky, A. N. J. Phys. Chem. Lett. 2011 , 2 (13), 1540. (35) Iwamura, M.; Watanabe, H.; Ishii, K.; Takeuchi, S.; Tahara, T. J. Am. Chem. So c. 2011 , 133 (20), 7728. 23 (36) Schrauben, J. N.; Dillman, K. L.; Beck, W. F.; McCusker, J. K. Chem. Sci. 2010 , 1 (3), 405. (37) Trushin, S. A.; Kosma, K.; Fuß, W.; Schmid, W. E. Chem. Phys. 2008 , 347 (1 - 3), 309. (38) Iwamura, M.; Takeuchi, S.; Tahara, T. J. Am. Chem. Soc. 2007 , 129 (16), 5248. (39) Shaw, G. B.; Grant, C. D.; Shirota, H.; Castner Jr, E. W.; Meyer, G. J.; Chen, L. X. J. Am. Chem. Soc. 2007 , 129 (7), 2147. (40) Juban, E. A.; McCusker, J. K. J. Am. Chem. Soc. 2005 , 127 (18), 6857. 24 2 Experimental Methods This chapter will detail the various instruments used to collect the data presented in this thesis. Modifications or alterations to these methodologies will be addressed specifically in cases where they apply. The molecules described in this thesis were previously prepared by Joel Schrauben and were used without further purification. 1 2.1 Steady State Absorption Measurements All UV - Visible spec tra were collected on a Varian Cary 50 UV - Visible Spectrometer. Typically sample solutions were prepared in 1 mm path length cells. corrected for a baseline offset by subtracting the value at 800 nm wh ere the sample absorbance should be zero. The flow cells would not fit in the cuvette holder intended for 1 cm cells and were manually held in front of the window. Static cells were held upright while they rested inside the cuvette holder. A comparison of spectra collected with the cell at different angles to the incident beam reveals minimal changes in the peak intensities, indicating that holding the cell does no t introduce spectral inaccuracies. 2.2 Transient Absorption Measurements Two separate femtose cond laser systems were used to collect the data be described in detail below. 2.2.1 Wile E This is the older of our two laser systems, producing approximately 120 fs pulses at the sample position. The system layout is depicted in Figure 2 . 1 . The 76 MHz 25 Figure 2 . 1 Wile E Laser Table Layout Cartoon depiction of Wile E. The red beam represents the 803nm l ight from the Mira and Regen. The white beam is the white light continuum generated in the CaF 2 disc. The green beam represents the tunable pump beam, which is double passed over the delay line to give a ~13 ns time window for the experiment. modelocked Ti:S apphire oscillator (Coherent: Mira 900 Basic) is pumped by 532nm light from a 5.4 W solid state Nd:YVO 4 diode la ser (Coherent: Verdi). The Ti:S apphire output power is approximately 5 nJ /pulse , and the output spectrum is centered at 803 nm w ith 13 nm full width at half maximum ( FWHM ) as characterized by an Ocean Optics spectrometer. The oscillator output is routed into a Ti: S apphire regenerative amplifier ( regen, Positive Light: Spitfire). The regen is pumped at 1 kHz by a 527 nm, 6.8 W Nd: YLF diode laser (Positive Light: Evolution) and has an output of ~750 /pulse at 800 nm. This beam is then split by a 70:30 beam splitter with the larger portion pumping an optical parametric amplifier (OPA, Quantronix: TOPAS) to create the visible pump beam; the remaining portion is used to create a white light continuum probe beam utilizing a continuously moving 6 mm CaF 2 disc, a stationary sapphire window, or a 26 stationary 4 mm YAG window (see Appendix B for more information on the white light spectra g enerated by these media) . The OPA output is sent through a telescope which expands the beam diameter to approximately twice its original size in order to mitigate di vergence over the long beam path. The beam is then double passed using two retroreflector s (CVI Melles Griot) through a 1.2 m delay line (Aerotech: LMAC - 095 actuator and a Soloist CP motion controller ) , which provides experimental delays out to approximately 13 ns. This is a major alteration to the experimental set - up from previous descriptions , and the hardware required extensive modifications to the LabVIEW program s that drive them , as detailed in A ppendix C . To offset this 13 ns delay, prior to white light generation the probe beam is rou ted as 800 nm light on the table for a distance that compensates for the delay line and the path length inside the OPA. It is converted to white light just prior to the sample in order to minimize dispersion and to maintain the integrity of the white ligh t probe . A small pick off (<10% reflectance) in the 800 nm probe just before white light generation produces the reference beam. The pump beam is attenuated to ~3 - 5 on using neutral density filters. The polarization of the probe b eam is set to magic angle (54.7°) with respect to the pump beam polarization at the sample position. In s ingle wavelength experiments, the probe wavelength is selected by inserting 10 nm band pass filters i n the white light probe beam after the sample. T he filtered probe light and the reference beams are detecte d by matched photodiodes (Thorlabs: PDA36A). T he intensity of the reference beam is attenuated with an iris to match the probe intensity at negative time. By balancing the photodiodes at negative time and employing differential lock - in detection, the change in absorbance may be recorded 27 directly. The lock - in amplifier (Stanford Research Systems: SR810) is synchronized to a c h opper (SR540) which modulates the pump beam at 445 Hz. The computer ele ments include a shielded BNC connector block (National Instruments: BNC - 2110), a shielded cable (National Instruments: SHC68 - 68 - EPM), and a data acquisition card (National instruments: NI PCIe - 6320) which performs the analog to digital conversion of the si gnal . The delay line movements and data collection process are coordinated using a custom LabVIEW program written in the McCusker group; further details are given in A ppendix C . The data from Wile E presented in this thesis are the averaged result of at least 6 scans, where each scan corresponds to the average intensity value when the delay line visits each time delay in the forward direction and then the reverse direction (i.e. down and back). Solvent signals were collected at each wavelength of intere st to establish time zero and the instrument response function (IRF). Fitting the cross correlation signals with a Gaussian function gives a FWHM of ~130 fs. A home - built data work up program (Appendix C) corrects the raw data to remove the lock - nal modification (scaling) and extract s the actual delta A values along with assigning standard deviation values to each data point . Full spectra on Wile E are collected using Ultrafast Systems (UFS) spectrometers (CAM - VIS - 2, grating #4, and CAM - NIR - 1). The UFS visible spectrometer collects ~600 nm spectral window with the current grating. Unfortunately, the dynamic range of the complementary metal oxide semiconductor (CMOS) detector necessitates a large amount of ND filtering on the probe beam before c oupling to the spectrometer, which is accomplished by focusing the beam into a 200 m fiber, 28 matching the spectrometer dispersion. However, even at the tightest focal spot, the fiber typically cannot capture the entire probe beam leading to an inhomogenei ty in data between data sets collected on different days . These challenges have led to a strong preference for the SPEX and its diode array (currently on Road Runner; see below for a full description) , and therefore full spectral data recorded over the du ration of this work were collected on the SPEX, regardless of laser system. 2.2.2 Road Runner Road Runner is our newest femtosecond laser system and produces 35 fs pulses out of the OPA. The laser system is depicted in Figure 2 . 2 ( below ) , and it is readily apparent from the number of optics on the table that there are many more possible beam paths for these experiments laid out on the table. The use of magnetic faceplate kinematic mirrors ( Thorlabs : KS1R) and dovetail optical rails ( Thorlabs RLA## 00 family , where ## denotes the length of the rail in inches ) ha ve helped to make this system highly variable in very little time and with minimal realignment. All of the pump/probe configurations will be detailed bel ow, but much of the data collection process remains the same and will be covered here first. The oscillator in this system (Coherent: Mantis) is also a modelocked Ti:S apphire laser. Unlike the Mira, however, the Mantis employs an o ptically p umped s emicond uctor pump laser (5 W, 532 nm) contained within the oscillator cavity to increase stability. The Mantis output ( power of ~ 5 n J /pulse at 80 MHz , with a spectrum centered 800 nm, >70 nm FWHM) is routed to the r egen erative amplifier (Coherent: Legend Elite) . The Legend also encompasses the pump l aser within the regen footprint; however , the pump source is still an Evolu tion ( 6 W output, Coherent) 29 pumping the Ti:S apphire rod at 527 nm a t a 1 kHz rep rate. The Legend 's 800 nm, 23 nm FWHM spectral output is 3 5 fs in pulse duration and typically 1. 2 0 mJ /pulse . The outp ut passes through at 70:30 beam splitter with 70% routed to an OPA (Coherent: OPerA Solo) to generate the visible pump beam and the other 30% is used as the probe Figure 2 . 2 Schematic of Road Runner Demonstrating the Variability in the Experiments Available With This System The solid red beam is 800 nm light which is always routed on these paths. The dashed red lines denote optional paths for di fferent probes (i.e. white light continuum or single color from the probe OPA). The many optics on the table reflect the flexibility of the system for multiple TA set ups. 30 beam, either to generat e a white light continuum via the 800 nm light or pumping t he probe OPA (Coherent : OPerA Solo) to generate a single color probe beam. The time delays are accomplished routing the pump beam through a 1.2 ns delay line (Aerotech ATS100 - 200 actuator, Aerotech BMS60_UFA motor, Aerotech Unidex 100 controller) . Although the probe beam is also routed through a delay line ( Aerotech ATS100 - 200 actuator , Aerotech 50SMB2 - HM motor, Aerotech Soloist MP controller) , this is used to compensate for pump path length changes in different experimental set ups , not to actively achieve pulse delays in real time during data collection . For all of the data collection configurations, the angle between the pump and probe beams as they focus into the sample is kept at a small angle (4 ° or less) to minimize temporal broadening of th e cross - correlation function. 2 Single wavelength measurements are achieved b y coupling the transmitted probe beam to a monochromator (Jarrell Ash: MonoSpec 18; 1200 groove/mm grating, blaze 500 nm) where the output is directly incident on a photodiode (Thorl abs, PDA55). The reference beam is generated from a pick off (microscope cover slide) in the probe beam path , and this beam is irised in order to achieve balanced detection. The reference and signal photodiodes are analyzed by t w o lock - in amplifiers (Stanford Research Systems: SR810). The first lock - in records delta A dire ctly by differential detection (A - B, where A is the signal photodiode and B is the reference) and the lock - in is synced to a chopper modulating the pump beam (SR540, 4 46 Hz). The second lock - in records only the reference photodiode signal (I 0 ) and is sync ed to the 1 kHz frequency of the regen timing box. In this way, drifts in I 0 over time may be corrected in the data during post - processing. The X and Y signals from the lock - ins (signal in phase and at /2 phase to 31 the reference signal , respectively) are taken from the back panel via BNC and sent to a data acquisition card in the computer (National Instruments: PCIe - 6320 ) by a BNC terminal box (National Instruments: BNC - 2110) coupled to a shielded cable (National Instruments: SHC68 - 68 - EPM ) connected t o the card. Data acquisition is accomplished using home - built LabVIEW programs which sync hronize the stage movements with the output s from the lock - ins. The data presented in this thesis represent the delta A values after averaging at least six scans. S ingle wavelength mea surements were collected using a LabVIEW data collection program slightly modified from the program on Wile E where "one scan" sends the delay line in the forward direction for the specified number of points and returns to the starting position. This was done to avoid washing out the oscillations in the data through (possible) errors in stage positioning in the reverse direction. Time - resolved spectra l data a re record ed by focusing the white light probe beam into a liquid light guide (E dmund Scientific, 4 mm core diameter) coupled to a SPEX 270M spectrometer equipped with an HC233 - 0900 image sensor (Hamamatsu) employing a diode array detector (C5964 NMOS , 1x512 pixel array ). The diffraction grating inside the SPEX has 300 grooves/mm, as blazed at 600 nm (part number 510 19 095 ), which gives a linear dispersion of 12.4 nm/mm. The resulting spectral range of the diode array detector is approximately 300 nm. The power supply box for the detector , which also provides the appropr iate interf ace for the computer, is connected to the PC card (National Instruments: NI 6052E) via a National Instruments SH68 - 68 - EP cable, both of which were provided by Hamamatsu with the detector. The spectrometer 32 entrance slits are typically set at 1 mm (~5 nm re solution) , but any differences will be explicitly mentioned with the data. Data are acquired using a home built LabVIEW program. The first s tep is to which are the scattered pump photons that make it into the liquid light guide wh ile the probe beam is completely blocked. This can be done either with the pump delay stage stationary , while sitting at the starting position (at negative pump - probe delay ) , or as a function of the delay position if the scatter exhibits a strong stage position dependence. The next step is to collect the background, or ground sta te absorption spectrum, at negative time . This is done wi th both the pump and probe beams incident upon the sample as the LabVIEW progra m subtracts out the dark counts while collecting the background trace. After collection of the background is complete, the delay line moves through the desired time points while the computer subtracts out dark counts and ratios the background and positive time signals to generate delta A directly. E data positions averaged together. Data work up has been described in detail in Allison 3 , but briefly the raw data file consists of a matrix of pixel vs time intensity values. The pixels must be converted to wavelength using a calibration file, and the absolute times (stage position in time) must be converted to real times ( corrected for time zero). Then this data may be plotted in a graphing program. For short time delays where spectral chirp is present in the raw data, spectra of the pure solvent are collected. The wavelength dependence of time zero in this solvent is fi t with a double exponential function, which is then used to correct the probe dispersion spectra data. 33 One Color Measurements Figure 2 . 3 One Color Experiments on Road Runner Only one OPA is used for this experiment and the resulting beam is split into both to tune the detection wavelength off of the central wavelength of the probe (pump) pulse. T his configuration utilizes only the pump OPA to generate both pump and probe beams. The OPA output beam is routed to a 90 ° periscope to flip the polarization to horizontal before passing through a folded prism compressor. The compressed beam is picked off and sent toward the pump de lay line where it is split by an anti - reflective 34 ( AR ) coated 30:70 (R:T) beam splitter ( CVI L aser ) into the pump and probe beams; this is depicted in Figure 2 . 3 ( above ). The pump beam, transmitted through the splitter, bounces off the retroreflector on the delay line and is routed towards the sample after passing through the chopper wheel. The probe beam is reflected off of the splitter and is routed through the probe delay line before a turning mirror sends it towards the sample. Both beam paths pass through an ND filter wheel ( Thorlabs NDC - 50C - 4, 0 - 4 OD), a laminated thin film polarizer (400 - 700 nm, Thorlabs ), an achromatic half waveplate (400 - 700 nm, CVI Melles Griot), and a plano - convex l ens (Newport, BK7 glass, 400 mm focal length) before striking the sample cuvette. As previously mentioned, t he angle of incidence for the pump and probe beams upon the sample is kept to a minimum, typically 4 ° or less. The thin film polarizers are used to clean up the magic ang le with respect to the pump polarization. This is checked using a cube polarizer in the sample position and monitoring the transmission on a power meter. After this polarization check, the variable ND filter wheels are adjusted to attenuate the pump powe /pulse , while the probe power is set to 1/10 th the pump power, /pulse . Single wavelength traces are then collected for both the molecule in solution and pure solvent. The pulse duration is characterized using cross correlation ( XC) in the pure solvent and methanol (MeOH) , and optical Kerr effect (OKE) or frequency resolved optical gating (FROG) in MeOH. Although m ethanol is known to give a shorter XC signal than commonly used solvents like acetonitrile (MeCN) or dichloromethane (DCM) , 4 it is preferred here because it gives much cleaner signals in the OKE and FROG experiments. MeCN and DCM show long tails in OKE and FROG, 35 making the pulse duration ambiguous. A full description of pulse characterization is given in section 2. 2.3 , below. Two Color Measureme nts Figure 2 . 4 Two Color Experiments on Road Runner The pump beam travels the same path as in the one color experiment but now the reflected beam from the beam splitter before the delay line is block ed. The probe beam travels through its own prism compressor to compress the beam before passing its delay line and being routed into the sample. 36 The term tw o color is used here to refer to the configuration where both OPAs are in use on the laser table. As you can see in Figure 2 . 4 above , the remaining 30% of the regen power transmitted through the beamsplitter at the regen output is steered into the probe OPA. The probe OPA output is then used as the probe and reference beams. The pump OPA output follows the exact same beam path as described in the one color experiment ; however , the beam reflected off of the beam splitter before the delay line has been blocked . which accommodates the beam movement between ports as the wavelength is tuned. After this mirror, the beam is r outed to a periscope set at 90 ° to flip the polarization before passing through the prism compressor. T he compressed beam is picked off and steered through the probe delay line before rejoining the path used for the probe in the one co lor experiment. The pickoff in the probe line is still used as the reference beam for balanced detection. The prob e polarization is checked using a cube polarizer in the sample position to ensure magic angle detection , and the powers are checked so that /pulse /pulse . If adjustment is needed, the appropriate ND filter is turned until the power is correct. The pulses are characterized using pure so l vent employing XC , OKE , and FROG techniques as discussed for the one c olor experiments above . As both prism compressors have to be optimized independently, it is rare that two color experiments would occur in isolation of one color experiments. Typically, the set - up starts as one color, where the pump prism compressor spac ing is optimized. Once this is set, the probe arm from the beam splitter is block ed, and the probe OPA is employed. For this reason, the above discussion 37 assumes that the pump polarization has already been cleaned up and set, and that only the probe pola rization needs to be checked. White Light Probe Experiments If a white light continuum probe is desired, the regen beam transmitted through the beam splitter is routed around the table near the regen and Mantis before passing next to the probe OPA and j oining the normal probe beam path on the probe delay line. This can be seen in Figure 2 . 5 below as the many red beams on the table. The routing on the table achieves the necessary delay to compensate for the pump beam passing into and through the OPA , as well as the distance added by the pump prism compressor. The probe beam still passes through the ND filter wheel, but a different linear polarizer ( Thorlabs : LPNIRE100 - B) and waveplate are used to set the polarization of the probe beam, since the one and two color experiments use visible (400 - 700 nm) optics. These 800 nm optics are already set up further down the beam path, so the visible optics are simply removed from their post holders and set aside. Th e one/two color probe beam lens is on a dovetail rail and the rail carrier screw is loosened so that the post may be removed from the rail and the lens set aside. The probe turning mirror ha s a magnetic faceplate mount, so the faceplate may simply be disc onnect ed and set aside to allow the beam to pass. After the 800 nm polarization optics, a n iris is set to trim the beam down to a 5 mm diameter before the beam is focused with a plano - convex lens into a continuously moving 4 mm CaF 2 window . These paramet ers are based off of a report for very stable and spectrally flat white light continuum using CaF 2 . 5 Since 38 Megerle and coworkers have indicated that the white light generation is best when the input polarization matches the polarization axi s of the CaF 2 in the mount, the waveplate Figure 2 . 5 White Light Probe Experiments on Road Runner The regen beam is routed around the table to match the pump beam path length before being steered onto the probe delay line and following the optic path toward the sample. The 800 nm light is converted into a continuum (represented by the white lines) near the sample position and focused into the sample using reflective optics. Here, the transmitted probe ma y be coupled into the SPEX, shown at the end of the table. is set for the best white light spectrum and the ND filter is adjusted to ensure a clean, single filament beam is produced. The generated continuum strikes a parabolic mirror 39 and a flat mirror i n a folded configuration which focuses and routes the probe beam to the sample (see Figure 2 . 5 ). The pump beam follows the same path previously described for th e two color experiments, but now the turning mirror on the rail is removed by loosening the rail carrier screw and removing the entire post holder from the rail, while the lens is pushed up the rail toward the white light set - up. With appropriate pump be am steering, this rail should ensure that the pump beam is the same pulse duration as that measured in a one color experiment and that the lens movement has not introduced any new dispersion to the pulse. As with the one and two color set - ups, the pump tu rning mirror creates an acute angle (~4 ° ) with the probe beam incident upon the sample. Since the probe polarization is determined by the best white light spectrum, the polarization of the pump and probe beams at the sample position must be checked and th e pump polarization should be rotated to achieve magic angle detection. The monochromator and the signal photodiode are initially moved over to this sample position to verify the pump/probe overlap as well as the pulse duration . Because the temporal respo nse with the white light probe is longer than for two color experiments, this is not the typical set up for collecting single wavelength traces on Road Runner. Instead, the primary use of this set - up is to collect full spectra l data , which is done by coup ling the probe beam into the liquid light guide and using the SPEX and full spectra LabVIEW programs as discussed above. 2.2.3 Pulse Characterization Techniques Due to the short nature of the pulses in this experiment, the IRF is determined using both the OKE signal produced by neat solvent and a typical XC. After extensive 40 trial and error with this short pulse system, we have discovered that the OKE signal is diagnostic of the pulse duration at the sample, while the XC signal gives a better depiction of the a ctual IRF of the system, accounting for optics after the sample as well (filters, etc). We believe this difference results from the origin of the recorded nonlinear signals, as detailed below. The XC signal is recorded by placing a nonresonant sample, suc h as the pure solvent for a particular experiment or MeOH, in the sample holder. TA signals at short delays are then recorded as they would be for regular samples. Because the solution is nonresonant, the only signals present in the data result from the direct overlap of the pump and probe pulses in the solvent. In order to record the OKE signal, a Glan - laser polarizer is placed after the sample, but before the monochromator. This polarizer, hereafter called the analyzing polarizer, is set perpendicular to the probe beam polarization. This is accomplished by monitoring the signal photodiode voltage on the oscilloscope while rotating the analyzing polarizer cube. The cube is set properly when the voltage reading is at a minimum. The reference photodiode is blocked completely and the data set is collected. The OKE experiment has the advantage of being much more sensitive to the simultaneous presence of the pump and probe pulses as it relies on the strong interaction of their electric fields with the solv ent molecules to produce a polarization change in the probe photons so that some light is transmitted to the detector. Argawal 6 succinctly describes this process as follows: "t he ordinary OKE process can be understood by two sequential processes: the pump pulse induces the anisotropic refractive index change in the medium and then the activated medium can change the 41 polarization direction of the probe pulse ." In this way, the detector only records a signal when both the pump and probe are temporally overlapped in the sample. Conversely, typical cross correlation measurements rely on simple two photon absorption even ts and are therefore less sensitive to the temporal overlap of the pump and probe. 4 , 7 The resulting data from OKE and XC measurements are fit with a Gaussian curve and the FWHM is extracted. The width of the p ump and probe pulses may then be calculated through the following equation: (2. 1 ) where pu is the pump pulse duration, pr is the probe pulse duration, and c is the measured (convolved) pulse response. 2 For both the XC and OKE responses, c is the FWHM of the Gaussian fit. Since this is a one color experiment and the pump and the probe should be (approximately) the same pulse duration, this equation simplifies to: (2. 2 ) and therefore, a simple rearrangement of the equation yields the pulse duration of the pump (probe) pulse. ( 2. 3 ) A more rigorous pulse characterization technique is FROG (Frequency Resolved Optical Gating) developed by Rick Trebino in the early 1990s. 8,9 The "frequency resolved" aspect of FROG is nothing more than collecting the full spectrum of the n onlinear response instead of passing the transmitted probe through a monochromator. 10 An algorithm is then used to extract the pulse shape and phase from 42 the 2D spectral and temporal data. A typical second harmonic generation (SHG) FROG setup is depicted in Figure 2 . 6 , which high lights the similarities to a traditional autocorrelation experiment. An incoming pulse of an unknown time duration is split into two pulses which are then focused by a lens and overlapped in a nonlinear crystal where the frequencies combine to produce a p hoton at twice the frequency of the incoming pulses. As the time delay between the pulses is changed, the upconverted light only appears when the two pulses are interacting in the sample, and as such provides a measure of the pulse duration. Figure 2 . 6 Comparison of Traditional Autocorrelation and SHG FROG Techniques Traditional autocorrelation (top) employing a second harmonic generation crystal (SHG) where the resulting signal is focused into a photodiode for detection. SHG FROG (bottom) simply replaces the photodiode with a spectrometer and appropriate detector (ca mera, diode array, etc.). Figure r eproduced with permission from reference 10 . © John Wiley and Sons 43 The conver sion from a traditional 1D experiment to a (2D) FROG experiment shown in Figure 2 . 6 applies to all pulse characterization methods: polarization gate ( PG), autocorrelation (SHG), third harmonic generation, transient grating, and self diffraction. The only difference between these methods is the nonlinear phenomenon used to generate the signal. The data in this thesis utilizes PG FROG, as it makes use o f the OKE setup with only a change in detection method to record both OKE and FROG signals, as seen in Figure 2 . 7 . PG FROG has several other advantage s over other methods, such as automatic phase matching between the pulses at the sample, unambiguous pulse and phase retrieval, and the resulting signals are the most intuitive of all the FROG configurations. 8 Also unlike SHG FROG, the experiment is largely invariant to the wavelength of the pulse; the analyzing pola rizer in use is a broadband Figure 2 . 7 General PG FROG Configuration The pulse in question is split by a beam splitter into both the gate and unknown pulse which are then crossed in a nonlinear medium (fused silica, carbon disulfide, methanol, etc) and the resulting signal passes through the analyzing polarizer and into the spectrometer. The unknown pulse polarization is rotated to 45° from the gate pulse polarization with the analyzing polarizer set to 90° from the pulse polarization. Figure reproduced from reference 10 with permission. © John Wiley and Sons polarizer rated for use across the visible region. SHG throughout the visible would require a thin nonlinear crystal (100 - 300 µm) at different angles depending on the wavelength of the pulse, and a UV detector to record the resulting signal. FROG 44 experiments characterizing white light continua have shown that crystal angle - dithering is necessary to achieve phase matching over t he bandwidth of the pulse, adding another level of complexity to the experiment. 10,11 The primary advantage of PG FROG is that you can readily see if the pulses are fully compressed or still contain some residual chirp and the kind of residual chirp (i.e. positive or negative) or pulse distortion. This is illustrated in Figure 2 . 8 , below , which shows example data traces for PG and SHG FROG setups under various pulse conditions. 8 In the case of negative or positive chirp, PG FROG gives a distinct Figure 2 . 8 Example FROG Traces for PG and SHG FROG Geometries The top row shows the spectral characteristics of the pump, with the time dependent in tensity (solid) and phase (dashed). The second row shows the frequency dependent intensity (solid) and phase (dashed). The third row, however, depicts the instantaneous frequency (blue) and the group delay vs. frequency (green). The bottom two rows show the FROG trace response for the given geometry and pulse characteristic. Note the symmetry of the FROG response in the SHG geometry for both negative and positive chirp, whereas PG FROG is able to readily distinguish these cases. Figure reproduced with permission from reference 8 ; some data from the original figure has been masked for simplicity. © AIP Publishing, LLC 45 response for each case, whereas SHG FROG gives identical results; this is the result of the unambiguous pulse and phase retrieval mentioned earlier. For SHG FROG, it would be possible to determine the sign of the chirp by adding a piece of glass to the beam path before the beam splitter (introducing positive chirp) and running the FROG trace again 8 , but this doubles the amount of work necessary to get to an answer readily available with PG FROG. Both PG and SHG FROG give clear indications when other issues are present in the pulse, such as self - phase modulation (SPM), or higher orders of phase distortions (cubic and quartic spectral phase). It is also readily apparent if double pulsing is occurring from one of the optics in the beam line, provided the distance between the main and artifact pulses is within the FROG collection window. These latter issues, SPM and higher order distortions, are not apparent in OKE traces, making FROG very beneficial to pulse characterization. To collect FROG traces in the one - color set up described above, the monochromator is simply removed after collecting the OKE trace and the transmitted probe beam is coupled into the SPEX by the liquid light guide. A modified LabVIEW program, originally written by Dr. Michael Bishop, snaps the background pump photons incident on the detector at negative time and subtracts that from all positive time points, very similar to the dark counts in full spectra (details given in Appendix C : LabVIEW Data Collection and Work Up Programs ). The scan is set up so the nonlinear response of MeOH is well surrounded by areas of zero signal: an "island in a sea of zeroes." 9 The program i nterpolates the pixel data to give a higher wavelength resolution and the resulting data file is written to a worksheet in a format amenable to the FROG analysis MATLAB programs, vide infra . 46 Once the FROG trace has been collected, it may be processed usin g an iterative Fourier transform (FT) and generalized projections algorithm. 8,9,11,12 The algorithm works to find both the intensity and phase of the pulse by solving for the electric field which best reproduces the collected FROG trace. 12 The resulting electric field must satisfy both data and nonlinear optical constraints; the data constraint pertains to the magnitude of the electric field in relation to the measured FROG tr ace, while the nonlinear optical constraint derives from the mathematical form of the signal field in the experiment. 8 The algorithm proceeds to minimize the electric field within one of these constraints, FTs the result, minimizes for the other constraint, FTs again, minimizes the electric field for the first constr aint and so on until convergence is reached. This point is determined by comparing the resulting FROG trace to the original FROG trace until the error is sufficiently low. The FROG analysis programs used in this thesis were obtained from Professor Trebin o's website 13 and used with minor modifications which will be detailed in Appendix F : FROG Algorithm Modifications and Their Employment . Altogether, three separate programs were needed, "binner", "frogger", and "PG_XFROG." The FTs performed in the algorithm go faster with NxN data matrices, so "binner" works to zero pad the data to create an NxN matrix. "Frogger" is responsible for loading the now binned trace and running the iterative FT algorithm on the data until a suitably reproduced tra ce is obtained. "PG_XFROG" is the program responsible for determining the electric field of an unknown pulse that is different from the gate pulse, vide infra . In addition to fully characterizing a pulse by gating it with itself, FROG can also be used to determine the pulse characteristics for an unknown pulse of a different 47 frequency than a known gate pulse. This is called XFROG (cross - correlation FROG), and is employed to characterize the probe pulse in the two - color experiments. Since the pump pulse remains the same after being characterized for the one - color set up, it is now used as the known gate with the new probe beam from the second OPA. The general schematic for PG XFROG is shown in Figure 2 . 9 . Figure 2 . 9 PG XFROG Experimental Configuration The orange beam represents the fully characterized reference pulse of one wavelength while the red beam represents the unknown pulse of a different wavelength. The optics are exactly the same as in PG FROG, save for the beam splitter, making this extremely easy to employ for the two - color experiments. Figure reprinted with permission from reference 14 . © Optical Society of America The data collection proceeds utilizing the same LabVIEW program as in PG FROG; however, electric field is determined using the "PG_XFROG" MATLAB program in this case. 2.3 Complications with Shorter Pulses One of the major differences between the set - up on Wile E and those on Road Runner is the prism compressor ; but why is it only needed on one system? This section aims to explain the new challenges that arise when the pulse duration gets shorter. Much of the time and effort getting Road Runner to the curr ent configuration stemmed from encountering and working through these challenges and so the big issues will be summarized here. 48 2.3.1 Prism Compression and G roup D elay D ispersion Any laser pulse duration is related to its spectral bandwidth through the uncerta inty relationship, which limits the minimum product of these two quantities based on the pulse shape. For Gaussian pulses, this limit is 0.441, and pulses whose duration is equal to the spectral limit are said to be transform limited . 15 Practically , what this means is that shorter pulse durations require more bandwidth than longer pulse durations. Translating this into tangible numbers for Wile E and Road Runner means that Wile E's 120 fs pulses only require 3.31 nm of bandwidth for a 520 nm transform limited pulse, while Road Runner's 35 fs pulses require 11.36 nm of bandwidth at 520 nm to be transform limited. This increased bandwidth will be subject to group velocity dispersion (GVD) when passing through a transmissive optic, which means "the group velocity of light in a transparent medium depends on the optical frequency or wavelength." 1 6 Each wavelength will experience a slightly different delay passing through the optic, and with large bandwidths, this equates to a large broadening in the pulse duration (proportional to the bandwidth) . This relationship between pulse duration and b roadening is shown in Figure 2 . 10 . Here, the effect of group delay dispersion (GDD) on an input pulse duration is plotted for four different lengths of BK7 glass. Th e GDD is simply the GVD multiplied by the length of the material. 15 BK7 glass is a common material in lenses, which are used in all of the experimental se tups described earlier in this chapter. Assuming 10 mm of BK7 glass accounts for all of the transmissive optics in the pulse train, 35 fs pulses broaden out to about 75 fs after passing through these optics. However, if input pulse is 120 fs, the 10 mm o f glass adds only a few fs to the total pulse duration. 10 mm of BK7 glass is a 49 fairly reasonable assumption given the optics in the beam path required for the experiment: a waveplate, thin polarizer, ND filter wheel, lens, and cuvette face. GVD is ther efore unavoidable via the current set - up. This is why special optics are needed on Road Runner to recompress the pulse s after this detrimental broadening. Figure 2 . 10 Group Delay Dispersion for Various Lengths of BK7 Glass The curves shown here represent the pulse broadening experienced by a 520 nm pulse as it passes through 1 mm (yellow), 5 mm (green), 10 mm (blue), or 20 mm (purple) of glass. The red curve shows th e ideal case, where there is no pulse broadening, i.e. no transmissive elements in the beam path. Figure based off of data in reference 15 . As mentioned above, GVD results from the wavelength dependence of the refractive index. This has two major effects on a pulse: angular dis persion and temporal dis persion , or chirp. 17 Positive chirp results in the blue wavelengths being slowed down as they travel through a medium, while negative chirp causes the red wavelengths to slow down . 15,9 Mo st transparent media causes positive chirp throughout the visible region. 16 50 Retaining the 35 fs pulse duration at the sample position requires the implementation of negative chirp to rev erse the pulse broadening from the optics in the pulse train. This is accomplished by capitalizing on the angular dispersion of a material, which causes blue wavelengths to exit the material at a sharper angle than redder wavelengths. 17 A prism compressor uses this phenomenon to negate the positive chirp induced while traveling to the sample. The prism compressor on Road Runner is in the folded geometry, mean ing that the pulse passes through each prism twice. The first prism acts to spread the wavelengths in space, while the inverted second prism cancels out the angular dispersion . A mirror placed after the second prism reflects the beam back through the pri sm s so the spatial dispersion is undone. 15 Overall, the redder wavelengths are forced to traverse more glass in the second prism than the bluer wavelengths , allowing them to "catch up." This is shown in Figure 2 . 11 , which demonstrates the introduction of negative chirp to a slightly positively chirped pulse. An optima lly aligned compressor will introduce enough negative chirp to the pulse that after it passes through the optics on the way to the sample, it is transform limited. 15 A folded prism compressor, while less complicated than a 4 - prism compressor, still has multiple tuning elements. The prisms must be rotated to the minimum angle of deviation each time the wavelength of the input pulse is changed. This ensures that the exit face of prism 1 is parallel to the entrance face of prism 2 and minimizes reflective losses. 18 The distance between the tips of prisms 1 and 2 is the coarse tuning for the geometry - induced negative GVD, while translating the prisms normal to their base into (and out of) the beam fine tunes the positive GVD without changing the beam paths. 15,18 The reflection of the beam at a slight angle after prism 2 does slightly alter the 51 Figure 2 . 11 Illustration of Angular Dispersion in a Prism Compressor The input pulse entering this 4 - prism pulse compressor has a large bandwidth but the pulse is relatively unchirped . The angular dispersion of the prisms creates ne gative chirp in the output pulse , where the red wavelengths are now lagging behind the blue wavelengths. To create a folded prism compressor, a mirror is inserted at the dotted line and the beam is reflected back through the first two prism s, following the light gray arrows . dispersion introduced by the prisms, but the advantages of a less complicated and more compact setup outweigh this disadvantage. 15 The prisms used on Road Runner are made from L a KL21, which is useful for pulses longer than 25 fs and at wavelengths greater than 380 nm. 15 Its dispersion characteristics also allow the compressor to be more compact than if SF10 prisms were imple mented; this is helpful given the space constraints on the optical table. These prisms are intended for use with horizontally polarized light, but the OPA output in the visible region is vertically polarized. In this case, the polarization is flipped by inserting a 90° periscope into the beam path. Unlike using a waveplate to accomplish this task, the periscope does not add chirp to the pulse. The step - wise procedure for setting up a folded prism compressor is nicely detailed in reference 15 , and will not be repeated here. However, the material dispersion 52 information in that document led to the creation of a worksheet that will easily calculate the optim al L a KL21 prism spacing for any wavelength if given the right starting information. This worksheet is now used every time the lase r is tuned and has been extremely helpful in speeding up the process of compensating for positive chirp . The worksheet calcu lates the prism spacing based on a few formulas, presented below, and the concept that the GVD intrinsic to the optical beam path for the experiment should be introduced in equal and opposite magnitude by the prism compressor. 15 ( 2. 4 ) ( 2. 5 ) ( 2. 6 ) ( 2. 7 ) Here, c B is pulse duration limit described earlier, which is dependent on the pulse shape (0.441 for Gaussian pulses), is the central wavelength of the pulse, is the spectral FWHM of the pulse in nm, c is the speed of light, out is the output pulse duration , l is the prism spacing, D 1/e2 is the beam diameter at 1/e 2 , and n ( along with its first and second derivatives ) is intrinsic to the prism material, available in the paper. Equations 2. 4 and 2. 5 allow the user to quantify the GVD introduced by optics in the system co mpletely in terms of observables. Once the GVD of the system is known f or the wavelength of interest, equation 2. 6 may be solved to determine the appropriate prism spacing for that wavelength. The worksheet only needs four values from the us er to 53 determine the prism spacing: 1/e2 , and the uncompressed pulse duration ( out ). A spectrum of the OPA output provides and , while the uncompressed pulse duration may be measured by removing the steering mirrors into and out of the prism compressor , allowing the beam to bypass the compressor altogether and still remain on the original beam path for a one color experiment. The final variable, D 1/e2 , is easily measur ed using the set of irises set up for aligning the beam into the prism com pressor. By placing a power meter after iris 2 and measuring the power as the iris diameter is decreased, the user may generate a Gaussian plot of the beam size which is easily fit to give the FWHM of the beam . While this is not the proper measurement of D 1/e2 , the beam out of the OPA is slightly divergent and the FWHM at this position gives a good estimate of D 1/e2 , which is actually the width at 13.5% of the intensity. 19 The efficacy of the prism compressor is illustrated in Figure 2 . 12 , below , where the unco mpressed pulse is shown in blue, and the compressed pulse is shown in red. By fitting both of these data sets with Gaussians (seen as the smooth, solid blue and red curves), the pulse duration may be extracted. The fits here show that the uncompressed pu lse duration is ~100 fs, while the prism compressor has shortened the pulse duration to 47 fs. Using the spec tral information for the pulse ( c = 505.1 nm, = 10.5 nm ), the transform limit is 35.7 fs, so the prisms could be adjusted further to yield a better compressed pulse. This adjustment is done iteratively, where the prism spacing is changed in one direction, the beam steering is adjusted to pass through the cent er of all the irises, and the OKE is collected again. If the pulse duration increases, 54 the prisms are moved the opposite direction. Typically, if the value for the beam diameter is correct, the worksheet will get the prism spacing right on the first try . Figure 2 . 12 Pulses With and Without Prism Compression on Road Runner The red and blue do t s are experimental data from OKE traces collected on Road Runner in the one color set up at 505 nm. The blue d ots, representing the uncompressed pulse OKE response, have been fit (blue solid Gaussian fit line) to a pulse width of 101.8 fs. The red dots, representing the compressed pulse OKE response, have been fit (red solid Ga ussian fit line) to a pulse width of 47.1 fs. The transform limit for this pulse is 37.2 fs, suggesting that the compressor could be further optimized . 2.3.2 Pump and Probe Overlap Angle As Ziolek et al. have shown, the pump and probe intersection angle plays a large role in the cross - correlation width of the pulses. 2 The interested reader is referred to their paper for a full discussion of the pulse parameters and their effects on the measured FW H M of the cross - correlation, but the main points will be summarized here. In any pu mp - probe experiment, the probe beam diameter should be less than the pump beam diameter , and the optics are set up so that the beams cross at a relatively small 55 exper imental conditions. The authors chose values from their current experimental setup for their modeling, namely: 2 mm path length cell, 400 nm pump and probe pulses, pump beam diameter of 2 mm, and probe beam diameter of 0.2 mm. The top half of Figure 2 . 13 shows the results from modeling the cross - correlation of two 75 fs pulses at various intersection angles. The cross - correlation FWHM is largely unaffected by angles under 5 degrees, while the FWHM is roughly 50% larger by changing the angle to 10 degrees. The bottom half of the figure is the same modeling for two 20 fs pulses; the results of changing the angle are much more drastic. Here, even an angle of 5 degrees has affected the cross - correlation of the pulses. 2 While this study has expl icitly modeled pulses of the same wavelength, the importance of maintaining a small intersection angle for experiments utilizing short pulses is clear. This is why the set up for Road Runner places the sample a fair distance from the turning mirrors, sinc e a smaller angle could be achieved if the distance to the sample was increased. As it is, the pump mirror cuts into the periphery of the probe beam ever so slightly in its current placement; any closer and the central part of the beam would be clipped. 56 Figure 2 . 13 The Effect of the Crossing Angle on the Resulting Pulse Width Modeled cross - correlation functions for pump and probe pulses centered a t 400 nm, pump beam diameter 2 mm, probe beam diameter 0.2 mm, crossing at various angles in a 2 mm path length cuvette of acetonitrile. The top plot shows the results for input pulses of 75 fs, while the bottom models the response for 20 fs input pulses. Figure reproduced from reference 2 with permission . 2.3.3 Detection Wavelength and its Effects on the Observed Oscillations Single wavelength collection on Road Runner is accomplished by passing the transmitted probe beam through a monochromator utilizing slits to give ~2 nm FWHM bandpass. Typically the monochromator is tuned to the blue and red edges at the FWHM of the raw O PA output spectrum. This tuning away from the central wavelength of the probe spectrum has been shown to a ffect the observed frequencies in works by Champion and coworkers. 20,21 In general, their observations showed that when the detuning from the central wavelength was minimal, lower wavenumber modes were 57 enhanced in the signals, while larger detuning resulted in enhancement of higher wavenumber modes. These observations were made fo r one - color experiments, and it s appli cability to two - color data will be discussed in more detail in Chapter 3 in the context of actual data. 2.4 Data Analysis Techniques 2.4.1 Igor Igor Pro (WaveMetrics, Lake Oswego, OR, USA) version 6.3 was used for the analysis of single wavelength and full spectra d ata contained in this thesis. The procedure for data processing and plotting full spectra data has been covered in previous McCusker group theses and will not be expanded upon here. 3,22 For single wavelength traces, built - in functions were used to fit the data. The Gaussian function was used to fit both XC and OKE traces; for the solvent traces (i.e. MeCN or DCM, but not MeO H) , the time where the Gaussian returned to baseline was noted and used as the minimum starting point for fitting data on the molecule of interest. Mono - or bi - exponential fits with x offsets were used to fit data on the molecule of interest. Occasionall y coherence data was fit with a tri - exponential function, which had to be added as a new user function, as this successfully minimized the residual. The residuals from the exponential fits are further processed by the fast Fourier transform ( FFT ) routine to give the FFT magnitude of the frequencies. These output frequencies are in Hz, and are converted to cm - 1 for this thesis. To increase the resolution of the FFT, the data may be zero padded; see Appendix G : FFT Time Spacing and Frequency Resolution for more details. Any data presented in this thesis using zero paddi ng will be mentioned explicitly. 58 2.4.2 Linear Predictive Single Value Decomposition The Linear Predictiv e Single Value Decomposition (LPSVD) analysis presented in this thesis was accomplished using MATLAB script s acquired from Dr. Warren Beck after being modified by Dan Roscioli and originally written by Dr. Andrey Demidov and Dr. Paul Champion. The purpose of this program is to fit the data and extract the exponential components as well as the frequencies of the oscillations. An important difference here is that the damping times and the phases of these frequencies are also presented, which Igor is unable to do. The LPSVD results are presented in four graphs: the truncated data set overlaid on the full data set , the truncated data with the combined exponential and oscillatory fit, the residual of the truncated data after the exponential components have be en extracted along with the oscillatory fit, and the power spectrum from the FFT of the fit. These are shown in Figure 2 . 14 below . The program also outputs a table of all the frequency components as well as the exponential components used to fit the data. The user has complete control over how many oscillations are used to fi t the data, however, there are always at least two exponential components in the fit. One thing to note is that the power spectra from the LPSVD analysis are always smoother than those calculated in Igor for the same data set. This is because the LPSVD p ower spectrum comes from the FFT of the fit function, not the raw data. Further details on using the LPSVD pro gram are presented in Appendix E : LPSVD Program Details . 59 Figure 2 . 14 LPSVD Analysis Program Output Graphs This is the graphing window which shows the results of the LPSVD analysis. The top left graph shows the raw data (red) and the truncated data (green) and uses numbers to show the points truncated: 62 in the beginning and 0 at the end in this case. The top right graph shows the data points of the pure oscillation (gre en) and the fit using 3 oscillations (blue). The bottom left graph is the truncated data (green) and the fit composed of both oscillatory and exponential components (blue). The bottom right graph is the power spectrum resulting from the FFT of the oscill atory fit curve. 2.5 Computational Methods 2.5.1 Gaussian Modeling The starting geometries for all calculations were built using GaussView. 23 G eometry optimizations, frequency calculations, and single point calcula tions were performed using either the Gaussian '03 (G03) or Gaussian '09 (G09) software packages . 24,25 All calculations made use of the unrestricted B3LYP hybrid functional, composed of the LYP functional develop ed by Lee, Yang, and Parr and the Becke three parameter hybrid functional (B3) . 26 28 A ll calculations employed the 6 - 311G** basis set. 29 32 G 03 calculations were carried out on the Michigan State University Chemistry 60 department computational ser ver, Hydra, while G09 calculations were carried out on the High Performance Computational Center (HPCC) servers at Michigan State University. 2.5.2 Computational Details for Specific States O ver the course of this thesis work, the G09 software package became available to researchers at Michigan State University which is why some wo rk was completed in G03 , while so me was completed in G09 . This section aims to clarify how each state (ground or excited) was optimized for the molecules of interest in this thesis. Cr(acac) 3 : 4 A 2 Ground State G round state optimizations of Cr(acac) 3 in G03 were started using the crystal structure data . For these geometry optimizations, the ground state geometry wa s constrained to D 3 symmetry by freezing the dihedral angles for all methyl group protons. The system was optimized in both DCM and MeCN solvent continu a , using the polarizable continuum model ( pcm ) and conductor - like pcm (c pcm ) models, respectively. 33 Frequency calculations from these optimized geometries showed no negative frequencies, indicati ng a global minimum had been reached. Cr(acac) 3 : 2 E Excited State This optimization was started from the previously optimized 4 A 2 ground state in an MeCN continuum using G03 . The methyl group dihedrals remained frozen, while the total spin multiplicity of the system was changed to 2 from 4. The frequency calculations resulted in all positive frequencies for this geometry. Cr(acac) 3 : 4 T 2 Excited State(s) The frequencies of the Franck Condon 4 T 2 excited state s were obtained using G 09. Because the Cr(acac) 3 ground state structure had previously been optimized in 61 G03, it was re - optimized from the final G03 structure using G09. The calculations would not pass while retaining D 3 symmetry, so the structure was allowed to reduce to C 1 symm etry. This optimized ground state was then subjected to time - dependent density functional theory 34,35 to determine the ten lowest excited state energies . From these results , the three lowest energy states were chosen to for further study . Because the point group of the molecule is C 1 sym metry , it can no longer support the 4 T 2 degeneracy, and so must split into three A terms . 36 These lowest three states are believe to be the spli t 4 T 2 state ; this will b e discussed more in Chapter 3. Each of these three states were then subjected to frequency calculations at the current geometry to give the frequencies of the 4 T 2 state in the Franck Condon geometry. The frequency result files we re expected to have , and all three did indeed exhibit, negative frequencies since this is not the stable geometry of the excited state. Attempts were also made to optimize the structure of each of these states using G09, but the optimization routine was h aving difficulty finding a global minimum under the conditions used ; thus, this information is not currently available for this thesis. Cr(TMHD) 3 : 4 A 2 Ground State The starting geometry for Cr(TMHD) 3 came from the Cr(acac) 3 crystal structure, whereupon t he methyl groups were changed to tert - butyl groups , and the molecule was symmeterized (i.e. the tert - butyl groups were positioned at identical angles off of the acac backbone). The structure was then optimized in G03 employing the PCM model and DCM for the solvent. While t he resulting geometry was formally C 1 symmetry, it was very close to C 3 symmetry; attempts to lock the dihedral angles of the tert - butyl 62 groups and optimize the structure under higher symmetry conditions were unsuccessful. The frequency results from the optimized geometry showed only positive frequencies. As mentioned for the Cr(acac) 3 4 T 2 excited states, the optimized ground state structure was submitted for re - optimization in G09. Unfortunately, this geometry optimization is not finding a global minimum, potentially due to the large variability in the rotation of methyl groups present in this molecule. Due to these complications, no data is currently available about the frequencies in the excited states of Cr(TMHD) 3 , for eit her 2 E or 4 T 2 state s . 63 APPENDICES 64 Appendix A: Optics Details All visible light mirrors (pump line and visible probe) are protected silver mirrors from Thorlabs unless otherwise noted. Part # PF10 - 03 - P01 Desc. Ø1" ( 25.4 mm) round, Protected Silver Mirror. IR (800 nm) mirrors are protected gold mirrors from Thorlabs ; Part # PF10 - 03 - M01 Desc. Ø1" (25.4 mm) round, Protected Gold Mirror . Prisms Newport Part # 06LK10 Desc. Brewster Angle Dispersing Prism, Ultrafast, LaKL21, 15 mm , 370 - 2000 nm Prism mount Thorlabs Part # KM100PM Desc. Kinematic mounting platform. Prism clamping arm Thorlabs Part # PM3 Desc. Small Adjustable Clamping Arm, 6 - 32 Threaded Post 50:50 Beam Splitter CVI Melles Griot Part # BTF - VIS - 50 - 2501M - C - reflective coating. Thickness: 1 mm 70:30 Beam Splitter CVI Laser Optics Part # BTF - VIS - 30 - 2501M - C Desc. St - reflective coating. Thickness: 1 mm Variable ND filter wheels (both unmounted and mounted wheels) are from Thorlabs . Part # NDC - 50C - 4 - A an d NDC - 50C - 4M - A Desc. ( Un ) mounted Continuously Var iable ND Filter, Ø50 mm, OD: 0 - 4 .0, A nti - R eflective C oating: 350 - 700 nm , UV Fused Silica Substrate . Thickness: 2 mm Half wave plate CVI Melles Griot Part # ACWP - 400 - 700 - 06 - 2 Desc. Air - spaced Achromatic half waveplate, air spaced quartz and MgF 2 components, coated for 400 - 700 nm light, 12 mm clear aperture, Thickness: 1 mm Visible Economy Linear Polarizers Thorlabs Part # LPVISE100 - A - BK7 protective windows, 4 00 - 700 nm, polarizing film between windows. Thickness: 3.5 mm 800 nm Economy Linear Polarizer Thorlabs Part # LPNIRE100 - B Desc. 1" Linear Polarizer ; N - BK7 p rotective w indows, 600 - 1100 nm , polarizing film between windows. Thickness: 3.5 mm Lenses a re typical BK7 glass out of the Newport lens kits available in the laser lab. Lenses are typically plano - convex with the plano side facing the incoming beam and centered so that the beam is still on its original linear path. 65 Glan - Laser Polarizer CVI M elles Griot Part # CPAD - 10.0 - 425 - 675 Desc. Glan - Laser double escape window linear polarizer; air spaced calcite prisms, (modified version of Glan - Taylor so less reflective loss es), anti reflective coating for 425 - 675 nm light. 10 mm clear aperture. T hickness: 22 mm Beam Splitter cube Thorlabs Part # PBS251 420 - 680 nm , N - Rotation Stages Thorlabs Part # RP01 Desc. Manual rotation mount with continuous 360 ° rotation. Single - Axis Translation Stage with Standard Micrometer Thorlabs Part # PT1 Desc. 3" x 4" Stage ; 1" Translation Stage with Standard Micrometer, 1/4" - 20 Taps . Dovetail Optical Rails Thorlabs Part # RLA0300, RLA1200, RL A2400 Desc. Compact optical rails made for use with snap on rail carriers to provide rigid mechanical assemblies. Rails contain 4/20 holes over the length of the rail, but may Dovetail Rail Clamps Thorlabs Part # RC1, RC2 Desc. Clamps made for use with dovetail rails. Used to couple optics to the rail. RC1 Rail Clamps Thorlabs Part # CL6 Desc. Wedged Table Clamp for RLA Series Rails Amplified Silicon photodiodes are PDA36A on Wile E, and PDA55 on Road Runner. (PDA55 is no longer a valid part, they have been superseded by the PDA36A model; however, in practice these have been found to have worse signal amplitudes for the same incident light intensity.) 66 Appendix B: White Light Generation Media This lab typically uses CaF 2 for the generation of white light, but the stability of this medium for wavelengths red of 650 nm is not very good. The biggest benefit to CaF 2 f or white light generation (WLG) is its ability to generate a spectrum that extends below 400 nm. 37 However, on the occasion that the red part of the spectrum is of more use for the experiment, another medium should be used. Figure 2 . B 1 shows the intensity of white light transmitted through a solution of a [Ru(bpy) 3 ] 2+ derivative, tris(4,4' - diphenyl - 2,2' - bipyridine) ruthenium(II) bis( hexafluorophosphate ) [ Ru(dpb) 3 ](PF 6 ) 2 , collected as the "I 0 " for full spectra , for four different media . Two different CaF 2 plates were tested, 4 mm and 6 mm thick, to examine the effect of thickness on stability , along with a sapphire plate, and a 4 mm thick yttrium aluminum garnet (YAG) plate . The pump wavelength for this continuum g eneration is 800 nm, which is the standard wavelength used in this lab for WLG, although the spectrum generated is known to have a dependence on the pump wavelength. 37,38 The steep drop in white light intensity around 520 nm is most likely due to the onset of [ Ru(dpb) 3 ] 2+ absorption, rather than a result of the material itself. Aside from the 4 mm CaF 2 plate, all of the media seem to generate approximately the same spectrum: a broad peak around 550 nm, followed by higher intensity, narrower peak around 710 nm. The sharp upswing around 760 nm is caused by the pump wavelength; and increase in the intensity of the white light spectru m in the vicinity of the pump wavelength has been seen in the literature before. 38 67 Figure 2 . B 1 White Light Generation Media and Their Stability in the Red These traces are the transmitted background through a sample of Ru(dpb) 3 2+ during the set up for full spectra with various white light generation media ; the absorption spectrum for this compound is shown in gray for reference. All traces from the white light media have been normalized relative to their intensity between 700 and 730 nm. More critical than just the background spectrum of these media though, is how they behave during a delta A calculation. Negative time spectra for the media are shown in Figure 2 . B 2 . These traces more effectively highlight this instability in the red for these different media, as the delta A calculation at negative time should be zero. The non - zero wiggles, however, sh ow where the spectrum is highly variable and the background is not properly removed from the signal. These wiggles also appear in the positive time data, effectively obscuring significant dynamics in this region. As YAG has the best stability and therefo re the least amount of wiggles, this medium is best suited for applications where wavelengths above 600 nm are of interest. 68 Figure 2 . B 2 Stability of White Light Media During Delta A Calculation Under the same experimental conditions as, these are typical traces for negative time, highlighting the highly variable parts of the spectrum as non - zero amplitude. The YAG window (green) clearly shows the most stable performance in this part of the spectrum. 69 Appendix C : LabVIEW Data Collection and Work Up Programs Wile E's Updated Data Collection Code While t he majority of the data collection code remains unaltered from previous McCusker group members who helped to write it , the specific implementation of the code needed an update in order to successfully communicate with the Soloist controller for the LMAC delay line. The primary difference being that the Soloist is looking for a reference number to be sent and retrieved at certain intervals and this number is altered a fter each new command, so it needs to be in a constantly running and updating structure. This necessitated the implementation of a while loop around the existing code; once the program was running, all values within the while loop would be read and scanne d for changes while values outside the while loop would be ignored. This also led to changing from a case structure to manage the different processes (home the stage, go to the starting position, start the scan, etc) to an event structure that triggered off of a button value change for each event. The advantage of the event structure is that a default case executes continuously while the while loop is running but no other event is happening. For the Soloist, this default event is sending and retrieving updated values from the controller, including the reference number. Despite these changes, the overall function of both the single wavelength and full spectra data collection programs is largely intact. The full spectra program greatly benefitted from the addition of a built - in wait time vi which chose the appropriate wait time for the distance the stage was traveling. This meant that in a scan where late time points were added with a larger step size, that wait time did not have to be applied to the shorter steps taken in the early part of the scan. 70 For scans consisting of a large amount of points, these changes to wait times really added up. The proper wait times for step sizes were determined using the SCOPE utility included in the Soloist softwar e. By monitoring the position error in time after having the delay line move commonly used step sizes, an average wait time for each step size was calculated. A vi was written with simple true/false logic to choose the correct wait time for a given step size or step size range. Immediately after the scan is started, an array is made for all of the delay line positions that will be sent to the controller during the scan. The wait time vi take s that array, computes the step size between every point in tha t array, and writes an array of the appropriate wait times. These arrays are both read off of an index value as the scan proceeds so that the appropriate wait time is always loaded with its corresponding new position value. All Data Collection Programs All of the data collection programs for both laser systems have been updated to accept a starting position in time, rather than steps, mm, or some other distance the particular delay line is looking for in a command. The advantage of entering the scan pa rameters directly in time (fs for Road Runner and ps for Wile E) is that the user can quickly and easily get the data they are after while the LabVIEW program does the appropriate unit conversions before sending the move command to the stage controller. A n optimized structure to compile all of the delay positions required in a scan has helped remove redundancies when higher density early time points or low density late time points are added to the scan. The user simply inputs the information on the front panel for the starting position, step size, and number of points for higher density or late 71 time points and the LabVIEW program sorts all of the positions from closest to furthest and removes any duplicates from the array. FROG Data Collection Figure 2 . C1 FROG Data Collection Program Front Panel The program collects the spectrum vs. time data a nd plots the 2D data in the lower left plot, while the integrated intensity vs. time is shown in the lower right plot. The upper plot shows the spectrum at a given time point. Further details are given in the text. This LabVIEW program was originally written by Dr. Michael Bishop at the National High Magnetic Field Laboratory 39 , but was modified to work with the Aerotech controller an d delay line on Road Runner, as well as the SPEX and Hamamatsu diode array. In this way, no new instruments had to be acquired in order to collect FROG traces. The program front panel is seen in Figure 2.C1, and t he details of the program are given below . 72 The "destination folder" specifies the user's desired file path, while the "file identifier" text box is the name of the file. Dr. Bishop added a background feature to append the timestamp to the end of this filename, and the full file path and filenam e are displayed in "file pathname string." Under the "delay line setup" column, the user specifies the start position (in time; just as in the regular data collection program), the step size, and the number of steps. In the "spectrometer setup" column, t he user may adjust the diode array exposure time, the number of scans to average (more on this in a bit), and the start and stop "pixel" cutoffs. Typically, the exposure is left at 0.6 s, as this is the normal setting for full spectra data collection as w ell. The " scans to average " feature is not operational right now, but may be fixed in the future if mo re signal averaging is desired; the current data sets seem to be fine without it. The cutoff designations apply to "pixels" after the program runs an in terpolation routine to increase the spectral resolution of the detector. While the diode array actually contains only 512 pixels, resulting in ~0.7 nm/pixel resolution, the interpolation routine decreases this number to 0.2 nm/pixel . Here the "blue W cut off" tells the program the pixel to start with and "red W cutoff" specifies the length of pixels to keep after "blue W cutoff." The values for "com port" and "scan mode" are never changed and default to the values shown when the program opens. The "spect rum x - axis" button toggles the x - axis of the top graph between pixel number and wavelength when setting up the baseline intensity on the spectrometer. Once the FROG scan has started, the x - axis of the top graph changes to the interpolated pixels (truncate d by the blue and red cutoff numbers). 73 When the run button up in the toolbar is pressed, the first while loop controlling the baseline spectrum is started. The stage moves to the starting position (or optionally runs the initialization routine if the "in itialize delay" button is depressed on the front panel) and the diode array pixels are read into the computer. At this point, the pump beam should be open to the sample, and this baseline reading is similar to the "dark counts" of full spectra collection ; it will be subtracted off of all of the FROG spectra as they are collected at each time step in the scan. This data displays in the upper graph, updating in real time for any changes the detector sees. For the best signal - to - noise in the FROG trace , the pump and probe beams are allow ed to the sample and the ND filter wheel after the sample is rotated until the leakage intensity of the probe beam is about 0.2. Then the probe is closed, and the spectrum is allowed to read a few iterations of the pump only background intensity before the "start scan" button is pressed. "Start scan" ends the baseline spectrum while - loop and saves the last baseline reading as a "DC" file in the designated data folder. The next while loop starts, which runs the FROG data co llection routine. This while loop is active until either the "stop scan" button is depressed or a spectrum i s collected at all of the desired time delays. When the spectra are collected, they are passed into a sub - vi controlling the interpolation of the data, and the resulting data and associated wavelengths are truncated as specified on the front panel and then plotted in the bottom two plots. The bottom left plot is the full 2D data set, while the bottom right plot is the intensity after summing over a ll of the w avelengths at each time point. At the end of the scan, this 74 summed intensity data is sent to a pulse parameters sub - vi which evaluates the FWHM of the pulse and updates the "Int. Pulse FWHM (fs)" field. After the scan is done (or the "stop sc an" button has been pressed), the program saves two files, a .frg file and a .txt file. The .frg file contains a header with the information the FROG MATLAB script is looking for when reading the data ( vide infra ), and below is all of the 2D data from the scan where the each column is a different time delay and the rows pertain to wavelength. The .txt file contains the time points and wavelengths for the data set explicitly in the first two columns, followed by the 2D data set. Hitting the stop button lo cated in the toolbar will avoid saving any of the data files. Data Worku p Programs Over the course of this work, it became apparent that new data workup programs were necessary to fully examine the data. These new programs will be detailed here. The first update was simply adding a function to the existing single wavelength data workup program to remove a baseline offset. The main purpose of this workup program is to calculate the delta A values for the scan, but it needs to remove the scaling applied to the raw data values by the lock - in amplifier 40 , shown in equation 2 . 8 , first. ( 2. 8 ) H ere , the signal is the raw difference intensity value (signal photodiode minus reference photodiode voltage), the sensitivity comes from a set ting on the lock - in front panel , and 10 V is the applied scaling factor . The workup program removes this scaling while calculating the delta A values according to equation s 2. 9 and 2. 10 : ( 2. 9 ) ( 2. 10 ) 75 The baseline offset correction is applied to the output values prior to this delta A calculation so that "output" here really represents "output - offset" . The front panel of the program is shown in Figure 2 . C2 , where the "# pts to ave" box indicates the number of negative time points to include in the offset removal. The "offset" box indicates the calculated average of these points which has been removed from the scaled data. The other inputs on the front panel relate to the delta A calculation and time zero correction, which have been previously described i n Appendix A of Allison Brown's thesis. 3 Figure 2 . C2 New Data Workup Program With Baseline Correction The new functionality here is the "# pts to ave" box which allows the user to select how many points to average for removing the baseline offset. The "offset" box displays the averaged value removed from the data. The UFworkup program described above calculates delta A values for the average of all of the scans. As the coherenc e experiments required more scans with a much higher data point count than previous data collections, a new program was written to calculate the delta A value for each scan collected in order to look for intensity drifts or changes over the course of data collection. This new program functions in the same manner as the above mentioned program, but it reads each scan's data, removes a 76 baseline offset for that particular scan, calculates the delta A, and saves all of the worked up scans in a new data file as individual columns . These scans can then be plotted in Igor to look for instabilities in the data set, allowing the user to remove unstable scans from the average before working up that data further . The program front panel, seen in Figure 2. C3 , looks exactly the same as the UFworkup program, however the "offset" listed here is the offset average for the last scan in the data set. Figure 2 . C3 Examining Scan Stability With "Make Delta A's" Program On the left is real data acquired on DCM in obviously unstable laser conditions. The traces go from red (scan 1) to blue (scan 14) and time zero is obviously shifting along with an intensity change. These instabilities are not always obvious in the average of all the scans, which makes this program immensel y useful given the long scan times required in the coherence data collection. In a similar program, the signal - to - noise value of the data set with each additional scan examines the effect of extended collection times on the quality of the data. Since a typical coherence scan consists of 495 data points with an 800 ms wait time for the delay line to settle between each move, the scans take ~11 minutes each. Originally d ata sets were collecting an average of 80 scans or more, but as this took over 14 hours, it was possible laser drift or instability was doing more to harm the signal - to - noise average than the increased data set length was helping. Figure2. C4 shows the fro nt panel of the program, along with the results from a data set. The "start pt" box indicates 77 where in the data the solvent peak ends so that the signal - to - noise ratio is calculated for the molecule's signal only. The graph s imply plots the averaged sign al - to - noise value with each additional scan. For the data set shown here, the signal - to - noise drops after scan 18, indicating it may be beneficial to truncate scans 19 - 84 from the averaged data set . Further examination using the "Make Delta A's" program would reveal whether these scans should be truncated from the data set or not. The signal - to - noise program, Figure 2 . C4 Calculation of the Signal to Noise of the Data Set With Each Additional Scan The signal - to - noise program applied to a data set for Cr(acac) 3 dissolv ed in MeCN. The initial signal - to - noise value in the stable region before scan 18 is not very high, but it drops in half by the end of the data set. when applied to these previous data sets of 80 scans , helped determine the optimum scan number for data collection of pure solvent or solutions. Based on the data sets analyzed, 14 scans was ad equate to reach a stable signal - to - noise value for solvent, 78 while a minimum of 28 scans was adequate for solutions. This helped speed up the dat a collection process while ensuring high data integrity. The last new program for data workup resulted from discussions with Dr. Michael Bishop while collecting data at the National High Magnetic Field Laboratory. The data collection programs he had writ ten for those experiments collected both the signal and phase values from the lock - in, which was different from existing protocols in the McCusker group. Dr. Bishop explained that the phasing may differ between molecules and by assuming the phase to be th e same for all data sets, some of the signals may be smaller than they could be. This is a direct result from the phase sensitive detection occurring in the lock - in amplifier ; the chopper input supplies a reference frequency for the signal, but the lock - i n generates a sine wave which is applied to the signal by the phase sensitive detector s. A simplified diagram of this phase relationship can be seen in Figure 2 . . By "phasing" the lock - in, the user is tuning the phase of the lock - in generated sine wave to achieve the best match with the phase of the signal. The phase difference between the signal and lock - in reference sine waves is nal and phase outputs of the lock - as shown in equations 2. 11 and 2. 12 . 40 ( 2.11 ) ( 2.12 ) signal in the X channel will decrease. By rephasing the data, however, this shifting may be reve rsed and all of the signal will be displayed in the X channel. That is the purpose 79 of the program "Rephase the Data" shown in Figure 2 . . Along with rephasing the da ta, the phase can also be completely removed by applying the following relation: ( 2. 1 3 ) Equation 2. 1 3 gives the magnitude of the signal vector, which is not dependent on phase. 40 Figure 2 . C5 Simplified Representation of the Signal, Reference, and Lock - in Reference waves at the Phase Sensitive Detectors The reference box wave (red) represents the ch opper frequency into the lock - in, while the middle wave (blue) represents the signal being modified by the chopper frequency. The bottom wave (green) represents the sine wave generated by the lock - in; the phase of this wave is adjusted to maximize the sig nal out of the phase sensitive detectors. 80 Figure 2 . C6 Rephasing Data Collected by Lock - in Amplification The program works with either raw data traces (i.e. pre - delta A workup) or worked up data traces and their corresponding signal phase file. The names of the files of interest are specified in the respective boxes, along with the scan number to read. "App trace may be seen in the top graph, while the phaseless data is seen in the bottom graph. See the text for more details. The program is constructed to handle either raw or worked up "X" data; if raw data is supplied, the data is passed in as rows which is the format the subsequent calculations are expecting. If the data has been worked up, the data file will be in column form, and so a transpose must be applied by pressing the "Amp Transpose" button. To specify the data files, the combination of the file path, amp name, and 81 phase name boxes is required. For this example, the path is " C: \ Users \ Eileen \ []Research[] \ Data \ Cr(tbut)3 \ 15Aug26 \ 15Aug26a " where the amplitude is con tained in file "15Aug26a" (a raw data file), and the phase is in the file "15Aug26aSig ph." The amp name and phase name strings are appended to the file path, so no further information needs to be entered into the amplitude name box. However, if the work ed up trace was desired, amp name should read "wu" and the amp transpose button should be pressed. The time axis spacing is taken from the amplitude file, so the phase data will plot using that x - axis, no matter which amplitude file is chosen (raw or worked up). The "amp row" and "phase row" specify which row (or column if the amplitude is transposed ) to plot in the top graph. For this example, a total of 15 scans were taken, but since the raw data file includes a row of the stage position in steps and then a row of the stage position in time, there are actually 17 total rows in the data file. LabVI EW starts the index at zero instead of one, so 16 in the "amp row" box refers to the last row in the amplitude data file. The signal phase file, however, does not contain stage positions, so the last scan number is generally used. Note: this currently as sumes that the phase is identical for all scans and this may need to be modified in future versions of the program. The signal and phase values are ported into a built - in LabVIEW function that converts real (X) and imaginary (Y) components into polar comp onents, r and . The "applied phase" slider value on the front panel is converted from degrees to radians, and this phase shift is added to the raw value before the r and " " (now phase shifted) values are converted back into real and imaginary componen ts and re - plotted. Since 82 this program runs in a while loop, the top graph plotting the rephased data updates in real time as the phase shift is changed. The red phase trace may be scaled by updating the "phase scaling" box, making it easier to see the be st phase shift. Also for convenience, the phase is fit with a linear function and the residual of that fit is shown on the front panel, along with the maximum phase value; with proper rephasing, both of these values should be minimized. The bottom plot displays the phaseless data , computed according to Equation 2. 13 above. Once the user is satisfied with the rephased data, the original signal, rephased signal, new phase values, and phaseless data are saved to a worksheet with "_[phase shift]" appended to the amplitude file name; [phase shift] is the degree phase shift applied at the time the while loop was stopped. It is important to note that this information only saves when the square "stop" button (located below the applied phase slider) is pressed, not when the stop button in the toolbar is pressed. This was done as a convenience when the wrong data rows or filenames were chosen before the program started running so that "junk" files would not be saved. 83 Appendix D : Performing FFT Analysis in Igor For the coherence data where a FFT is desired, several additional steps are necessary. First, the data is fit using the exponential x - offset functions , and the residual of the fit is added to the graph. This may be done automatically by navigating t o the ing the drop down by s the oscillatory feature for the FFT process after the population dynamics have been removed from the data. The cursors are pl aced on the residual trace at the first and last points of the oscillatory feature to select this range for the FFT routine. Typically, the data imported to Igor uses time in fs or ps, but the FFT routine needs to have the time in s. The simplest way to do this is to inputting the appropriate values for the X axis start and delta between points in seconds. Since the section of data within the cursors is all that will undergo the FFT process, the start point is the x value of the first cursor and the delta is the tie spacing between points, typically 5E - 15 seconds . From here, the FFT may be done by access ing ich launches to those displayed in the top graph. The FFTs shown in this thesis are magnitude FFTs, where the cursors were used to denote the input range (if the input range does not satisfy the FFT requirements, a blue box will appear around the values; simply subtract - ax is is frequency in Terahertz (THz) and y - axis is the FFT magnitude. A separate excel sheet has been set 84 up to convert the THz numbers to wavenumbers (cm - 1 ) and these values are noted on the graphs. 85 Appendix E : LPSVD Program Details The main script, ru nsvd9.m, prompts the user to select the appropriate raw data file to open, plots the data in a separate graphing window, and then prompts the user to confirm that this is the appropriate data set. This script is looking for data files that contain only tw o columns: time, formatted to account for time 0, and data in delta A form. This means that the current data files acquired from the data work - up LabVIEW program have to be opened and the errors column must be removed from the file before it is resaved. After confirming that this is the correct data, the program asks if the time scale needs to be converted from microns, if the data need to be flipped on the time scale, and if the data need to be shifted. These first two prompts (unit conversion and flip ping) must have resulted from the specific way Champion and coworkers collected their data, but they are not employed with the data in this thesis. Data shifting may be use d to adjust time 0 if necessary; however , this is usually adjusted before the data is opened in the program. After the adjusted and shifted data is re - plotted in the graphing window, the program asks the user how many starting points to cut. This has typically been pre - determined from working up the data in Igor, but the user may take a guess as the values may easily be changed. The starting point is chosen after the solvent XC signal goes away. The program then asks for the number of ending points to cut, which is always set to zero for the data in this thesis. After entering the s tarting and ending points to cut, the truncated trace is presented in green over the raw data trace in red in the graphing window and the user is prompted to confirm that these points are 86 acceptable. If the user enters no, the starting and ending points a re chosen over again; if yes, then the script moves on and these points may not be changed without starting this analysis over from the very beginning. With the truncation point set, the script is now ready to run the single value decomposition (SVD) fit ting routine. The user is now prompted for the number of oscillations to use in the fit. For the data in this thesis, this number started at two and was increased to five or six. The results were then compared and the best fit with the fewest oscillatio ns was chosen as the optimal fit. The next prompts set values for the optimization routine; the starting and ending orders of the Hankel matrix and the step size. Acceptable order values range from four to 394 depending on the data set. Here the startin g order is always four and the ending order begins at 100 but is adjusted by watching the optimization routine. If the optimized result comes from the 95 th iteration, the routine is run again with an increased ending order to ensure that this is not a loc al minimum. The step size used here is 1 and larger steps sizes were not tried. The program is now set to begin the SVD routine, and asks the user if they would like to control the fit. If answered no, the routine runs automatically stepping through th e Hankel orders incrementally; if yes, the routine stops after every order and waits for the user to press any key before moving on to the next order. A prompt after this deals with the speed of MATLAB to speed up the calculations. This option removes the two graphs presenting the data and the current fit line (i.e. the truncated data with and without exponential components and the the power 87 power spectrum of every order and the other two graphs are populated when the routine finishes the last Hankel order. As the routine optimizes the fit, a table in the main MATLAB window updates the user on the current Hankel order and the order with the best fit so far. This best fit order number is the one used to determine if a higher ending order is necessary, as mentioned above. Once the SVD routine has finished, the program prints a calculation results section in the main MATLAB window. Here the values for the data shift, starting and ending truncation points, data points in the set, oscillations fit, and the optimal order of the Hankel matrix are presented. Below that is the table of the oscillatory and exponential components of the optimal fit. The table contains both positive and negative frequencies of the oscillatory components, owing to the double - sided nature of the FFT; only the positive f requencies will be reported here. The user is then prompted to print the graphing window, save all of the graphs and the results table, along with the options to remove frequencies and try the whole procedure again. The latter brings the user back to the truncation stage of the routine, where the starting and ending points may be adjusted as well as the number of oscillations in the fit. The option to remove frequencies has never been used, but it allows the user to adjust the left and right edges of the frequency window, in principle to determine the contributions of the major frequencies in that window. 88 Appendix F : FROG Algorithm Modifications and Their Employment FROG Scripts The scripts needed to work up FROG traces were written to use MATLAB's gr aphical user interface (GIU). For this reason, these are more intuitive to work with for users intimately familiar with LabVIEW. The first script the user needs to open is "binner". This launches the GIU for the binning program, who's main function is t o turn the data into an NxN array in order to speed up the FT process in the FROG algorithm. 9 Along with the binned trace dimensions, the user has complete control over extracting a subset from the total 2D plot to bin, how much background subtraction to perform , and where to center the traces prior to binning. Figure 2.F1 Binner Program Main Panel This is the binner program 13 after the raw data trace has been loaded into the program. The top tabs, "calibration", "extract", "Background", "Centering", "Filter", and "Binning", relate to the different functions of the program. See text for more details. As see n in Figure 2.F1 , the binner program displays the full 2D trace of the data, displayed in a colorized intensity plot where black and/or red represent low intensity 89 values and blue an d/or white are high intensity values. The vertical axis here corresponds to the spectral domain and so the trace to the right of the 2D plot corresponds to the pulse intensity vs. frequency. Similarly, the bottom axis for the 2D plot is time, and so the trace display e d below the colorized plot is the pulse intensity vs. time. Figure 2.F2 shows the data after background subtraction has been completed. Figure 2 . F2 Binner Program Displaying Background Corrected FROG Trace By subtracting the constant polar izer leakage from the recorded trace, the isolated pulse can be cleanly seen. This data is now ready for binning. The background subtraction was performed by iterating between subtracting a constant delay and subtracting a constant frequency. The "delay points" and "frequency points" boxes indicate how many rows/columns to average before subtracting that value from all of the data. Typically, subtracting a constant frequency h as the largest impact because of the slight polarizer leakage of the probe beam. Once the pulse intensity is well isolated (i.e. near zero background outside of the pulse envelope), it is ready for binning. 90 On the binning tab , the user has the option to select the bin size, binned width % (whether to zero pad the trace while binning), and which axis to fit while binning the other to create an NxN array. These parameters are more thoroughly described in the "read me" file that downloads with the code, an d most have been left unchanged from the default values. 13 The "axis fit" was set to wavelength for the data in this thesis because the wavelength axis typically had more data points in the original data set than the time axis. Empirically, this gave better binned trace results as well. A trace that has been binned along the wave length axis can be seen in Figure 2.F3 , below . The Figure 2 . F3 Binned Trace Ready for the FROG Algorithm The background corrected trace has now been binned alon g the time axis, extending the time axis from ~ - 150 to 105 fs to ~ - 400 to 400 fs. A slight change in the range of the wavelength axis has occurred as well to ensure the data length was a power of 2. resulting binned trace is now ready to be saved and t hen imported into the program that will run the iterative FT algorithm, "frogger". 91 "Frogger" is set to load with an example data set and fit results in all of the graph panels, as can be seen in Figure 2.F4 . The user then opens a binned FROG trace to wor k up. The program makes an initial guess as to the electric field and plots that in the retrieved pulse graph. There are also graphs displaying the temporal intensity and phase of the pulse, as well as the spectral intensity and phase of the pulse. The remaining two plots show the error between the binned FROG trace and the retrieved FROG spectrum, as well as the values for the different minimization parameters. Figure 2 . F4 The Frogger Program Just After Launching from MATLAB This is the frogger GIU window where all of the information and errors for the retr ieved pulse will be displayed. After loading the data set , the proper pulse characteristics must be chosen. As discussed above, the electric field derives from the specific nonlinear respons e occurring to give the recorded signal, so the proper nonlinearity must be chosen for the result to make physical sense. The drop down menus for the "domain" and "algorithm" options are reduced to just one choice after PG is selected as the nonlinearity. The 92 program is now ready to solve for the elec tric field of the pulse and the algorithm is started by hitting the "run" button. Figure 2 . F5 The FROG Algorithm At Convergence The reconstructed trace closely resembles the binned FROG trace (top left) except for some intensity around the center of the pulse, which is highlighted in the Difference plot. The intensity of the temporal and spectral profiles of the pulse are shown with solid lines, while the phase is shown as a dotted line. The error value s are changing out in the 4th decimal place with each iteration, showing that a minimum in the fit has been reached. The agreement of the reconstructed trace indicates this is a valid solution for the electric field. The results , seen in Figure 2.F5 , are easily saved for all of the values shown (spectral intensity and phase, temporal intensity and phase, reconstructed trace, etc) and the user may select which minimization to save, the Z error determined pulse information, the G error determined pulse information, or the current iteration's pulse information. For this thesis, the Z error was saved because the algorithm is set to a Z minimization routine. The "frogger" GUI code is not able to handle XFROG data, so a different script must be used to ana lyze that data. 93 XFROG Script The code provided by Prof. Trebino on his website includes a folder called "Demo" that contains a program called "PG_XFROG_Auto." This program encompasses both the binning and electric field retrieval steps. Since the user has more control using the GIU "binner" program from the FROG workup, the sub - routine "PG_XFROG" responsible for the electric field retrieval in "PG_XFROG_Auto" was re - worked to be a stand - alone program and accept the file format from the "binner" output. Other modifications were made to ensure the output graphs plotted in a single window to make data comparison easier between the original and retrieved XFROG traces. The results of a converged XFROG analysis are shown in Figure 2.F6 . 94 Figure 2 . F6 The PG_XFROG Program Showing the Results of a Converged Algorithm The graph windows displays many of the same parameters seen in the "frogger" GUI, but it does not display the phase information. Also the gate pulse intensity in the time domain has been added for reference. W he n the MATLAB script has finished, it prints the final G error, the time - bandwidth product for the pulse, and the pulse FWHM in both fs and nm. One major advantage of the PG_XFROG program is that it only plots the various spectra once the algorithm has reached convergence, so the entire process tends to be faster than running the " frogger " program on a similar pulse. Program modifications to the default folder location when more data is needed have also speed up the process. The program remembers the path where the XFROG trace originated and prompts the user to select a gate pulse from that same folder. Since the binned traces and FROG results d ata are typically saved in the same location as the original FROG and XFROG data, this makes sense. The program also now only displays files with the proper 95 extension for the data it needs (i.e. a binned XFROG trace ends in .bin, but the gate pulse file e nds in .Ek). The updated PG_XFROG code is included below with comments in green. PG_XFROG.m function PG_XFROG(frog1, guess_flag) % PG_XFROG.m % % This is a script for the automated retrieval process. This example % is a PG XFROG problem, with a measured g ate from a GRENOUILLE 8 - 50. % If PG FROG is being used, simply change the gate pulse to itself. Of % course, another geometry will also have to change the form of the % gate, and the FROG algorithm that the program call s . % % See also: PG_XFROG, binner _cmd_demo, calibrate, qFROG_TX, % frog_wtol_x, frog_wtol % By Jeff Wong (GaTech) - 2011 - 08 - 09, 2022 % === START === warning off fprintf(1, 'Start PG XFROG \ n' ); % Find the name of measurement made by GRENOUILLE if nargin < 1; [fdat,pname1]=uigetfile( '*.bin.frg' , 'Get XFROG Data File' ); frog1=[pname1 fdat]; end [PathDir,FileName,Ext]=fileparts(frog1); SaveName=strcat(PathDir,FileName); % "frog1" is the "name_cal_bin" composed in "PG_XFROG_auto" gren_name = regexp(frog1, '_' , 'split' ); gren_dir = gren_name{2}; temp_cmd = sprintf( 'dir(''%s/*Temporal*'')' ,gren_dir); temp_list = evalin( 'base' ,temp_cmd); gren_path = sprintf( '%s/%s' , gren_dir, temp_list.name); clear gren_name gren_dir temp_cmd te mp_list if nargin < 2; guess_flag = 1; end 96 %Gives all of the variables a "***1" name so you know it's from the first %pulse loaded in. if strcmpi(frog1, '' ) % Load trace1 from GUI [Asig1,tau1,freq1,dtau1,f01,df1,NumD1,NumL1,filename1] = froglo ad(); else [Asig1,tau1,freq1,dtau1,f01,df1,NumD1,NumL1,filename1] = frogload(frog1, 'delay' ); end % Start timer tic; % Initialize constant w1=2*pi*freq1; N = length(tau1); G1 = Inf; Et1B = []; % BG Subtraction, aggressive BG sub traction may result in non - physical % trace that the algorithm can not retrieve. %flag20=input('Do you want to run background subtraction? (y/n) ','s'); %if flag20 == 'y' %Asig1 = Asig1 - 0.008; %Asig1 = nonegatives(Asig1); %end % Take the square root of Asig for Magn itude Repel Asig1 = sqrt(Asig1); %% Define the initial guess method dt1 = mean(diff(tau1)); lam01 = ltow(w1); % UI input if input method is not provided from the parent. method = { 'Gaussian' , 'Random' }; if ~(guess_flag) fprintf(1, 'Please select initial guess from menu... \ n' ) guess_flag = menu( 'Select Initial Guess' , 'Gaussian' , 'Random' ); end fprintf(1, 'Using method: %s \ n' , method{guess_flag}); % Choose between Gaussian and Random. Modification can be made if you have % other p r e ferences. sw itch guess_flag 97 case 1 % Start with Gaussian [Et1,t1, Ewdum,wdum]=pulsegenerator(N, @fgaussian, 75, dt1, lam01, [0], 0, [0,0,0]); case 2 % Start with Random [Et1,t1, Ewdum,wdum]=pulsegenerator(N, @rand, 75, dt1, lam01, [0], 0, [0,0,0]); end %% Read the GATE Pulse from GRENOUILLE % Only required because this is a n XFROG example. Ignore this part if you % are working with normal FROG. You do NOT have a known gate pulse if working % with normal FROG. [t_x, Et_i,Et_p] = readqfrog(pname1); Et2 = sqrt(Et_i) .* exp (1i * Et_p); % Find range of GREN time - axis N = floor((max(t_x))/dtau1); t_x_new = ( - N:N)*dtau1; % Resample the GREN Et2_new = interp1(t_x, Et2, t_x_new, 'cubic' ); % Pad zeros, so that they have the same length Et2_new = padarray(Et2_new, [0, round((length(tau1) - length(t_x_new))/2)]); if (length(Et2_new) > length(tau1)) Et2_new(end) = []; else Et2_new(end+1) = 0; end % Rename and clean up variables Et2 = Et2_new; clear Et2_new t_x_new ; % Plotting, optional. To check the gate pulse is not under - sample scrsz=get(groot, 'ScreenSize' ); figure( 'OuterPosition' ,[scrsz(3)*0.33 scrsz(4)* 0.33 scrsz(3)*0.66 scrsz(4)*0.66]); subplot(2,3,3);plot(tau1, abs(Et2).^2);title( 'Gate Pulse' ); clear Ewdum wdum Et2 = center(Et2, 'max' ); %% Retrieval 98 % Define the gate (it is known in this example), PG geometry is used here, % and therefore using |E|^2 % Change the gate according to your system. Gate = quickscale(magsq(Et2)); % The retrieval algorithm goes here. Change accordingly. [Et1B, Et1, Esig1, G1, Z1, EW1] = qFROG_TX(Asig1, Et1, tau1, w1, w1, Gate, G1, Et1B); % Should generate a sub pa nel of graphs from "DisplayXFROG.m" that update as the algorithm is % running. Original XFROG, Retrieved XFROG, Retrieved E(t), Retrieved % E( \ lambda), and G Error (of final) % Finish the retrieval problem. % Et1B is the output that will be used later on. %% Plotting % Generate the retrieved FROG trace Ew1B = fftc(Et1B); Asig1 = Asig1.^2; Asig1r = abs(fft_FROG(CalcEsig(Et1B,quickscale(abs(Et2).^2)))).^2; % Convert everything from angular frequency (w) into lambda (lam) [Asig1_lam, lam] = frog_wtol(Asig1,w1,t1); [Asig1r_lam, lam] = frog_wtol(Asig1r,w1,t1); [ELam1B, lam] = equally_spaced_spectrum_lam(Ew1B,w1); %Plot the 2D data %Original Data ax(1)=subplot(2,3,1); subplot(2,3,1);imagesc(t1,lam,Asig1_lam);set(ax(1), 'Tag' , 'FROG Trace,dum' );title( 'Measured Trace' ); h1 = get(ax(1), 'children' ); %Retrieved Data ax(2)=subplot(2,3,4); subplot(2,3,4);imagesc(t1,lam,Asig1r_lam);set(ax(2), 'Tag' , 'FROG Trace,dum' );title( 'Retrieved Trace' ); h2 = get(ax(2), 'children' ); linkaxes(ax); %use the same li mits for both images % Plot the retrieved pulse's 1D data % Should appear in the same window as the 2D plots! subplot(2,3,2);plot(t1, quickscale(abs(Et1B)));title( 'Probe Temporal' ); subplot(2,3,5);plot(lam, quickscale(abs((ELam1B))).^2);title( 'Probe Sp ectral' ); 99 %% Save output %Use if you want to manually name the file: %datadump = input('Type a name for the saved data set. ','s'); %Auto - name the file using the input XFROG trace name datadump = frog1; %out_name = strcat(datadump,'.mat'); %save(out_name) %Save the Temporal trace data Ekname=[SaveName, '.Ek.dat' ]; esave(t1,Et1B,Ekname); %Save the Spectral trace data Speckname=[SaveName, '.Speck.dat' ]; esave(ltow(w1),Ew1B,Speckname); %Save the Reconstructed trace data AReconName=[FileName, '.A recon.dat' ]; fname = fullfile(PathDir, AReconName); Xfrogtracesave(Asig1r_lam,lam,t1,[],fname); %Save the original trace data AName=[FileName, '.A.dat' ]; fname = fullfile(PathDir, AName); Xfrogtracesave(Asig1_lam,lam,t1,[],fname); TBP1 = calcTBPrms(Et1B,t 1,Ew1B,w1); FWHM_fs = fwhm(magsq(Et1B),t1); FWHM_nm = fwhm(magsq(fftc(Et1B)),ltow(w1)); fprintf(1, 'G1: %e \ n' , G1); fprintf(1, 'TBP1: %f \ n' , TBP1); fprintf(1, 'FWHM fs: %f \ n' , FWHM_fs); fprintf(1, 'FWHM nm: %f \ n' , FWHM_nm); % Stop timer toc clear sb1 sb2 clear Asig1 Asig1r Asig1_lam Asig1r_lam end 100 Appendix G : FFT Time Spacing and Frequency Resolution The resolution of the frequency domain is related to the number of points collected in the time domain. So to increase the resolution of the FFT for the same time point spacing (frequency range), more points need to be collected. 41 For the FFTs presented in this thesis, the time spacing is 5 fs and the time range is typically 2 ps or more of positive time. With these conditions, each scan takes approximately 13 minutes to collect, and a data set is typically 40 scans or more; adding on more points to each scan is not a trivial time investment. One alternative to adding more data points is to use zero padding. Zero padding refers to the practice of adding a st r ing of zeros to the end of the information to the time domain, but it results in interpolatio n of the data in the frequency domain. 42 An independent check of the frequencies recovered from an FFT of the non - zero padded residual with the zero padded residual ( Figure 2.G1 ) confirms the increase in frequency resolution while leaving the overall spectrum unchanged. 101 Figure 2 . G1 Comparison of FFTs With and Without Zero Padding This graph shows the FFTs of MeCN, where overlaid are the unpadded data (blue), the data with 420 points of zero padding (red), and 840 points of zero padding (green). The dominant peaks in the blue curve are maintained in the red and green traces, however their features are much sharper and more resolved. A M ATLAB script has been written to zero pad any oscillatory residual by a user determined amount, typically a factor of 10 12 or more. The script is explicitly placed below with comments (green) to help guide the user through the process. ZeroPadding.m %%M ATLAB script to zero - pad the data % Zero padding => adding zeros to the end of the "residual" (coherence without exponential components) data in order to boost frequency resolution %% Clear out the old graphs hold off clf(subplot(2,1,1)); clf(subplot(2,1,2)); clf; %% Bring in the data file flag1= 'n' ; while flag1== 'n' 10 2 [fdat,pname]=uigetfile( '*.*' , 'Get data file' ); %returns fdat as file name selected and pname as path (folder) for the file filename=fdat; %set 'filename' equal to the name and extension of the file fdat=[pname fdat]; % sets 'fdat' as full path to file (think window's address bar) fid=fopen(fdat); % figure out file format and proceed with conversion dat=fscanf(fid, '%f %f' ,[2,inf]); % read data from text file and write to 'dat' % data needs to be tab delimited; reads in as rows fclose(fid); % closes the open file data=dat'; % transpose the data array; makes it into columns Time=data(:,1); % column 1 is the time data Resid=data(:,2); % column 4 is the IRF total signal subplot(2,1,1),plot(Time,Resid) % plot the raw IRF file xlabel( 'Time, s' ) ylabel( 'Delta A' ) title( 'Raw Data' ); hold on flag1=input( 'I s it the data file you wanted? (y/n) ' , 's' ); % did you pick the wrong file? If so, fix it. end ; %% Zero pad the Residual and the Data for time zero ZP=input( 'How much t o zero pad the data? ' ); nptsResid=length(Resid); % tell me the length of the raw time column ZPlength=(ZP - nptsResid); nptsTime = nptsResid + ZPlength; % new array length DeltaT = Time(3) - Time(2); % calculate the time spacing % Build the new Resid data time array and fill it with corrected time values Timeinit=Ti me(2); FinalTime=((Timeinit - DeltaT)+((ZP - 1)*DeltaT)); Time0=(Timeinit - DeltaT); TimenewT = (Time0:DeltaT:FinalTime); % initialize the new time array (as ROW) TimenewT(1)=0; %make the first value 0, regardless of step size to point 2. Timenew=TimenewT'; % make into a column % Build the new data array and fill it in with zeros ResidT=Resid'; 103 PadDataT = padarray(ResidT, [0 ZPlength], 0, 'post' ); % initialize a new padded data array (as ROW) PadData=PadDataT'; % make into a column subplot(2,1,2), plot(Timenew,PadData); %plot new zero - padded time and data arrays xlabel( 'Time, s' ) ylabel( 'Delta A' ) title( 'Zero - Padded Data' ); hold on nptsTimeNew=length(Timenew); flag11=input( 'Do you want to save the ouput data? (y/n) ' , 's' ); if flag11== 'y' [newfile,pname]=uiputfile( '*.*' , 'Save the data as' ); %you set the file name for the new file and tell it where to save fdat=[pname newfile]; %specifies the new filename fid=fopen(fdat, 'w' ); %tells it to open the file you made for writing dout=[TimenewT; PadDataT]; %sets up the data to write to the file in matrix form The ' ; ' terminates a row and data is in ROWS % THIS COMBINATION OF PASSING IN ROWS AND USING A SEMICOLON WORKS!!!!! fprintf(fid, 'Time (s) \ t Delta A \ n' ); %sets up the c olumn headers; 'n tells it to go to the next line fprintf(fid, '%1.16f \ t %1.16f \ n' ,dout); %writes in the data in the formats specified; transposes the matrix you made above fclose(fid); %closes the file end 104 A ppendix H : Time - Dependent Fast Fourier Transforms Traditional FFT methods assume that the oscillatory signals are stationary with time. This may not always be the case, especially if electronic state changes are happening in the midst of these vibrations, as is the case with this research. To investigate whether the vibrational energy could be seen shifting from one mode to another in time, a time - dependent fast Fourier transform (TD FFT) program was written in LabVIEW ( Figure 2 . ) . Investigation into t his data ana lysis method was inspired by Dr. Photochemistry and Photophysics of Coordination Compounds in Traverse City, MI. However, there have been papers on this subject in the literature for many years. Also known as the "short - time Fourier transform", TD FFT applies a window function to the data, FTs the data within the window, and moves the window placement in tim e (i. e. the x - axis) and repeats the process. In this way, a 2D set of data is constructed analyzing the frequency content of the signal in time. 43 The window chosen for this analysis can have a large impact on the resulting signals; for the current TD FFT program, a Gaussian window is used, though the disad vantages of such a window are nicely addressed by Kraszewski et al. 44 In future iterations of this program, the windo w function should be a variable on the front p anel, but for now , it is a built - in property of the program and not easily changed. 105 Figure 2 . H1 LabVIEW TD FFT Program The homebuilt program to analyze the frequency content of the signal with time. The 1D plot on the left is the input data, while the 2D plot on the right is the resulting TD FFT data. Here, it appears that low frequency modes become stronger at later tim es, suggesting IVR may be populating these modes . The directions posted to the left on the front panel give pretty explicit directions on the use of the program, but the most important content in that list is the proper format for the data file. The data file must be in columns, with time in seconds and the data pre - processed to remove exponentials. The TD FFT program has no fitting routine for the exponential components in the data, and the FFT of the data with exponentials is unreliable; these comp onents must be removed beforehand. This is easily done by using the residuals from the IGOR FFT analysis and saving the data in the proper format as a text (tab delimited) file. The two other relevant controls are the "Gaussian FWHM, fs" and "Move Gaussi an in Time, fs" which control how wide the Gaussian window is and how far it is moved with each FFT iteration, respectively. Typically, only the Gaussian FWHM is adjusted when examining data , as this seems to have the largest effect on the data. The larg er the window width, the finer the resolution of the 106 frequencies, but the time axis has more uncertainty. Conversely, a narrow window will give much better resolution along the time axis, while the frequencies will be more uncertain. The "map selector" c ontrol under the z - axis values for the TD FFT plot allows the user to control the color scheme of the resulting plot. 45 The program starts when the user hits the run button in the toolbar and finishes when the Gaussian window has fully moved across the data set. At the completion of the windowing routine, LabVIEW saves the results in a data file with the name "[data file]_[Gaussian FWHM]_[Gaussia n move]" where the names in [ ] correspond to the values on the front panel. In this way, each Gaussian FWHM tried saves as a new uniquely named data file. The z - axis scaling may be changed by the u ser to highlight oscillations that are otherwise difficult to see. In the current version of the program, changing the "map selector" value only updates the graph's color scheme the next time the program is run. Unfortunately, results from this program w ere not as concrete as originally thought and they will not be discussed in the context of this thesis. One issue is highlighted in the example shown in Figure 2 . : t he exponential fit leaves the residual below baseline at long times, possibly causing the low frequency artifact at late times in the TD FFT analysis. 46 Obviously, altering the fit and running the TD FFT analysis on the new residual should remove the ambiguity of th is feature - artifact or IVR - and the finer points of this program and its analysis are still in development. It is interes ting to note, however, that the TD FFT results form a sort of counterpart to the damping times calculated for the LPSVD analysis. T he degree of correlation, however, is highly dependent on the window values chosen for the TD FFT analysis. 107 REFERENCES 108 R EFERENCES (1) Schrauben, J. N. Electronic Structure and Excited State Dynamics of Chromium(III) Complexes, Michigan State University, 2010. (2) Ziolek, M.; Naskrecki, R.; Lorenc, M.; Karolczak, J.; Kubicki, J.; Maciejewski, A. Opt. Commun. 2001 , 197 (4 - 6), 467. (3) Brown, A. M. Excited - State Dynamics of Iron(II) - Based Char ge - Transfer Chromophores, Michigan State University, 2011. (4) Rasmusson, M.; Tarnovsky, A. N.; Åkesson, E.; Sundström, V. Chem. Phys. Lett. 2001 , 335 (3 - 4), 201. (5) Megerle, U.; Pugliesi, I.; Schriever, C.; Sailer, C. F.; Riedle, E. Appl. Phys. B 2009 , 96 (2 - 3), 215. (6) Agarwal, A.; Kamada, K.; Shimizub, Y.; Ohta, K.; Shimizu, Y.; Ohta, K. Nonlinear Opt. 1999 , 21 , 335. (7) Juban, E. A. The Ultrafast Dynamics of Chromium(III) Coordination Complexes, University of California Berkeley, 2006. (8) Trebi , M. A.; Richman, B. A.; Kane, D. J. Rev. Sci. Instrum. 1997 , 68 (1997), 3277. (9) Trebino, R. Frequency - Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses ; Trebino, R. , Ed.; Kluwer Academic Publishers: Boston, 2000. (10) Trebino, R.; Bowlan, P.; Gabolde, P.; Gu, X.; Aktürk, S.; Kimmel, M. Laser Photonics Rev. 2009 , 3 (3), 314. (11) Imran, T.; Figueira, G. In International Conference on Applications of Optics and Photonics ; Costa, M. F., Ed.; 2011; Vol. 8001, pp 80010U 1 80010U 7. (12) Sukhoivanov, I. A.; Guryev, I. V. Photonic Crystals ; Springer Series in Optical Sciences; Springer Berlin Heidelberg: Berlin, Heidelberg, 2009; Vol. 152. (13) Wong, T. C.; Treb ino , R. Rick Trebino: Atlanta 2013 . (14) Ratner, J.; Trebino, R. In Frontiers in Optics 2011/Laser Science XXVII ; OSA: Washington, D.C., 2011; pp 2 3. (15) Newport Corporation. Application Note 29: Prism Compressor for Ultrashort Laser Pulses ; Newport Co rporation: Irvine, CA, 2006. (16) Paschotta, R. RP Photonics Encyclopedia ; RP Photonics Consulting GmbH, 2015. 109 (17) Mines, T. C. S. of. Dispersion and Ultrashort Pulses http://ticc.mines.edu/csm/wiki/images/f/f0/UFO05 - Dispersion.pdf. (18) Fork, R. L.; M artinez, O. E.; Gordon, J. P. Opt. Lett. 1984 , 9 (5), 150. (19) Photonics, I. O. &. Technical Note . IDEX Optics & Photonics 2015, pp A158 A162. (20) Rosca, F.; Ionascu, D.; Kumar, A. T. N.; Demidov, A. A.; Champion, P. M. Chem. Phys. Lett. 2001 , 337 (1 - 3), 107. (21) Wang, W.; Demidov, A. A.; Ye, X.; Christian, J. F.; Sjodin, T.; Champion, P. M.; Champion, M. J. Raman Spectrosc. 2000 , 31 (1 - 2), 99. (22) Smeigh, A. L. Ultrafast Dynamics Associated with Transition Metal - Based Sensitizers for Titanium Dioxide Based Solar Cells, Michigan State University, 2007. (23) Dennington, R.; Keith, T.; Millam, J. M. Semichem Inc.: Shawnee Mission, KS 2009 . (24) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgom ery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Is hida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, Ö.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al - Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gon zalez, C.; Pople, J. A. Gauss ian, Inc.: Wallingford, CT 2004 . 110 (25) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X. ; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, Jr., J. A.; Peralta, J. E.; Ogliaro , F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gauss ian, Inc.: Wallingford, CT 2009 . (26) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988 , 37 (2), 785. (27) Becke, A. D. J. Chem. Phys. 1993 , 98 (7), 5648. (28) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994 , 98 (45), 11623. (29) McLean, A. D.; Chandler, G. S. J. Chem. Phys. 1980 , 72 (10), 5639. (30) Wachters, A. J. H. J. Chem. Phys. 1970 , 52 (3), 1033. (31) Hay, P. J. J. Chem. Phys. 1977 , 66 (10), 4377. (32) Raghavachari, K.; Trucks, G. W. J. Chem. Phys. 1989 , 91 (2), 1062. (33) Tomasi, J.; Mennucci, B.; Cammi, R. Chem. Rev. 2005 , 105 (8), 2999. (34) Furche, F.; Ahlrichs, R. J. Chem. Phys. 2002 , 117 (16), 7433. (35) Scalmani, G.; Frisch, M. J.; Mennucci, B.; Tomasi, J.; Cammi, R.; Barone, V. J. Chem. Phys. 2006 , 124 (9), 094107. (36) Cotton, F. A. Chemical Applications of Group Theory , Third Edit.; John Wiley & Sons: New York, 1990. (37) Nagura, C.; Suda, A.; Kawano , H.; Obara, M.; Midorikawa, K. Appl. Opt. 2002 , 41 (18), 3735. (38) Bradler, M.; Baum, P.; Riedle, E. Appl. Phys. B 2009 , 97 (3), 561. (39) Bishop, M. M. Tallahassee 2014 . (40) Systems, S. R. MODEL SR810 DSP Lock - In Amplifier Manual ; Stanford Research Systems, 2005; Vol. 8. (41) Cerna, M.; Harvey, A. F. Appl. Note 041 2000 , No. July, 1. 111 (42) Smith, J. O. Spectral Audio Signal Processing , 2011th ed.; W3K Publishing, 2011. (43) Zhan, Y.; Halliday, D.; Jiang, P.; Liu, X.; Feng, J. J. Neurosci. Methods 2 006 , 156 , 322. (44) Biomed. Opt. Express 2014 , 5 (9), 3023. (45) http://forums.ni.com/t5/LabVIEW/Darren - s - Occasional - Nugget - 07 - 17 - 2014/m - p/2925132 (accessed Sep 10, 2015). (46) Book, L. D.; Arnett, D. C.; Hu, H.; Scherer, N. F. J. Phys. Chem. A 1998 , 102 (98), 4350. 112 3 Cr(acac) 3 and Cr(TMHD) 3 - Pump Dependent Vibrational Coherence 3.1 Introduction The main advantage of selecting tris(2, 4 - pentanediono)chromium(III) (Cr(acac) 3 ) for studies of relaxation processes is that it is electronically simple. The limited number of excited states compared to other transition metal systems like [Ru(bpy) 3 ] 2+ and [Fe(tren(py) 3 )] 2+ greatly reduces the c omplexity of the ultrafast dynamics. 1 3 Aside from the electro nic simplicity of Cr(III) compounds, Cr(acac) 3 was chosen in particular for being photochemically inert . Sheridan et al. contribute this stability to the pseudoaromaticity of the planar, 6 - member, chelate ring, as it is orders of magnitude slower than [Cr (C 2 O 4 ) 3 ] 3 - at racemization and photoaquation. 4 The wealth of previous knowledge on Cr(III) compounds in the literature 5,6 also make this an attractive starting point for the se studies. The Tanabe - Sugano diagram for Cr(III) compounds in an octahedral field can be seen in Figure 3 . 1 , below . 7 This diagram lays out the energetics of the ligand field transitions (electron transitions within the d - orbital manifold on the metal center ) as a function of ligand field strength (energetic splitting between d - . The ground state of the molecule is 4 A 2 , which can be seen as the green line at the x - axis; a ll of the spin allowed transitions are shown in green, while the spin forbidden transitions are shown in blue. Absorption of a photon corresponds to a vertical transition on this diagram, and if the exact ligand field strength for the compound is known, the ener gies of the ligand field states may be calculated explicitly. As it is, this diagram is formulated for a ratio of C/B equal to 4.50, which is likely for most Cr(III) compounds. 7 Cr(acac) 3 has a ligand field strength of approximately 2.2 when estimated 113 from transition energies for the 4 T 2 and 2 E states, vide infra. At this position, the lowest spin allowed transition is into the 4 T 2 state, while the lowest energ y excited state is the 2 E. At higher excitation energies, population of the two 4 T 1 states is possible. Figure 3 . 1 Tanabe - Sugano Diagram for a d 3 Metal Center This diagram plots the energies of the exc ited states (vertical axis) as a function of the ligand field strength (horizontal axis). 7 The quartet states, representing the spin allowed transitions from the 4 A 2 ground state are shown in green while the doublet (spin forbidden transitions) are shown in blue. Figure adapted from information in reference 8 . The slopes of the excited state energies as a function of ligand field strength is rather telling about their orbital population. A line with relatively little change in energy t raconfigurational change (i.e. a spin flip of an electron 114 within an orbital). A strongly sloped line, however, is indicative of an interconfigurational change, or electron movement between the t 2g and e g * orbital sets which are split in accordance with th e ligand field strength. The ground state absorption and emission spectra for Cr(acac) 3 were previously collected in our group, and the results are shown in Figure 3 . 2 . 3,9,10 The ground state absorption is shown in black , with the green trace scaling up the visible region of the spectrum by 50. The emission spectrum, collected at 90 K in an optical glass, is shown in blue. The band assignments for these features were previously described in detail by Schrauben 9 , and will be briefly summarized here. The lowest energy absorption in the visible region, centered at 560 nm, corresponds to the 4 T 2 ligand field absorption. The shoulder seen at 380 nm is caused by 4 ( 3 IL) absorption, where the 4 ( 3 IL) state represents an admixture of quartet charge transfer and triplet intraligand chara cter. Also buried under this transition is the 4 T 1 ligand field state. The intense absorption around 335 nm is caused by a ligand to metal charge transfer (LMCT) transition. The absorptions above this band are ascribed to - * transitions on the basis of the Ga(acac) 3 reference compound absorption. The gallium analogue, with its full d - manifold, cannot exhibit d - d transitions or CT transitions, leaving only intraligand absorptions as the cause of the absorptions. The emis sion, with a maximum at 775 nm, results from the 2 E excited state. The breadth of these ligand field transitions is also telling about the geometric change in the molecule associated with these states. Considering a potential energy surface diagram, a b road absorption or emission feature corresponds to two surfaces whose minima are shifted relative to one another. This shifting causes an increase in 115 the Franck Condon overlap for multiple vibrational energy levels, resulting in a broader transition. Con versely, a very narrow transition indicates two potential energy surfaces that are nested, resulting in adequate Franck Condon overlap at just a few vibrational energy level s . Figure 3 . 2 Steady State Abs orption and Emission Spectra for Cr(acac) 3 UV - visible absorption spectrum for Cr(acac) 3 shown in black (scaled x50 in green), the Ga(acac) 3 reference compound absorption in red, and Cr(acac) 3 90 K emission data in blue. Figure 3 . 3 shows these concepts applied to the absorption and emission spectra of Cr(acac) 3 . The broad absorption band indicates that the 4 T 2 minimum is shifted from the 4 A 2 ground state minimum. The 2 E, with its very narrow emission spectrum, should have a mi nimum at or very near that of the ground state . This shifting could be caused by any number of things, but here it is simplistically assumed to correlate with the metal - ligand bond distance. 116 Figure 3 . 3 Po tential Energy Surface Diagram for the Lowest Energy Ligand Field States and Their Corresponding One - Electron Diagrams The minima of the potential energy surfaces here is taken as the metal - ligand bond length, where the 4 T 2 surface is displaced owing to th e population of the e g * orbital. The 2 E state corresponds to a simple spin flip within the t 2g orbital manifold and is expected to be the same geometry as the ground state. Given the Tanabe - Sugano diagram and the observed absorption and emission data for this compound, one - electron pictures for the ligand field states may be developed. These are overly simplified representations of these states, but they can still be quite instructive. The ground state d 3 configuration places one electron in each of the t 2g orbitals, as seen in Figure 3 . 3 . The 4 T 2 energy exhibits a large change as the ligand field strength is increased, indicating an electron is moving from the filled t 2g set to the e g * set of orbitals. This population of an anti - bonding orbital should introduce a change in the metal - ligand bond length, considering the e g * orbitals are oriented directly along the metal - ligand bonds. This bond length change would shift the potential energy surface for the 4 T 2 relative to th e ground state (along the Cr - O bond length coordinate) and result in a broad absorption feature. The 2 E, however, is largely indifferent to the change in the ligand field strength, indicating the transition does not transfer electrons between the t 2g and e g * sets. This state is depicted as a single electron spin flip within 117 the t 2g set which should leave the Cr - O bond length unchanged. The highly nested potentials would give rise to a very narrow emission spectrum, which is observed experimentally. 3.2 Previ ous Time - Resolved Data on Cr(acac) 3 3.2.1 Femtosecond Dynamics Observed with Transient Absorption and IR Previously collected TA data on Cr(acac) 3 employed a pump wavelength of 625 nm, which corresponds to generating a vibrationally cool 4 T 2 state. Observed ki netics are shown in Figure 3 . 4 . The full experimental details are given in ref. 10 ; white light generated in a CaF 2 plate was used as the probe. The top half of Figure 3 . 4 shows the full spectra collected from 460 nm to 6 90 nm, where early time traces are shown in red and the late time traces are shown in blue. With time the spectrum decreases in intensity, narrows, and red shifts. The kinetics of this amplitude change are shown in the bottom half of Figure 3 . 4 , where single wavelength traces at 480 and 680 nm are fit with a monoexponential decay of ~1 ps. 10 118 Figure 3 . 4 Cr(acac) 3 TA Data Pumping with 120 fs 625 nm Pulses The top spectrum shows the full spectra col lected after pumping at 625 nm and probing with a white light continuum. The traces go from black (negative time) to red (early time) down to dark blue (late time). The spectrum decreases in intensity, narrows, and red shifts with time. The bottom displ ays the single wavelength kinetics for the same sample conditions. See text for more details. Figure reproduced with permission from reference 10 . © (2005) American Chemical Society . 119 By r ecording the low temperature (77 K) ns TA signal across this same spectral range, a plot of the full thermalized 2 E state could be obtained . An overlay of this data with the 5 ps trace from the fs TA data confirms that the 2 E is fu ll vibrationally cooled by 5 ps. Since it is highly unlikely that the absorption spectra from the 4 T 2 and 2 E excited states are highly similar, the 1 ps time constant was assigned to vibrational cooling on the 2 E surface. The red shifting and narrowing of the full spectra data support this assignment as vibrational cooling ; a vibrationally hot molecule will have a greater amount of Franck Condon overlap with vibrational levels in an upper state than after cooling to lower vibrational levels has occurred, causing a narrowing of the spectrum . 10 The intersystem crossing ( ISC ) from the initially populated 4 T 2 state to the 2 E was hypothesized to precede vibrational relaxation on the 4 T 2 surface and happen within the 120 fs IRF of the system. 3,10 The ultrafast dynamics following photo - excitat ion of Cr(acac) 3 have also been studied by directly monitoring the recovery of ground state vibrations using an IR probe. This work was performed by Kunttu and coworkers 11,12 using pump wavelengths of 345 and 400 nm and monitoring the C - O and C=C bond vibrations at 1579 cm - 1 and 1521 cm - 1 , re spectively. Unlike the previously discussed TA experiments exciting the 4 T 2 ligand field state in Cr(acac) 3 , these experiments excite the 4 ( 3 IL)/ 4 T 1 state (400 nm pump) and the 4 LMCT state (345 nm pump). The data clea rly show a bi - exponential decay compo se primarily of a short ~ 15 ps component with smaller contributions from a longer ~800 ps component. The authors assign this long time component to ground state recovery from the 2 E, which is consistent with the TA picture presented by Juban et al. 3,10 They initially assign the 15 ps component to internal conversion ( IC ) from the 120 4 T 2 to the ground state and emphasize that this constitutes 70 - 85% of the decay signal. 11 Re - examination of this data in conjunction with ground state vibrational cooling data has lead to a new interpretation of this data. Using an IR pump with an IR probe, Kunttu and coworkers observed two time constan ts for ground state vibrational decay: a 300 - 700 fs component and a 10 - 12 ps component. 12 The long time component was assigned to vibrational cooling on the ground state surface, while the 300 - 700 fs component was tentatively assigned to intramolecular vibrational redistributio n (IVR) on the ground state. Figure 3 . 5 Ultrafast IR Results Following 400 nm Excitation of Cr(acac) 3 Utilizing a 400 nm pump, the C - O and C=C vibrations were monitored over a time window of several hundr ed picoseconds. The data were fit with a bi - exponential function, revealing time constants of ~15 ps and ~800 ps. See text fo r more details. Figure reprinte d with permission from reference 11 . © (2007) American Che mical Society. By using a global fitting routine for all of the data they had collected, the rates of IC ( 4 A 2 4 T 2 ) and BISC ( 4 T 2 2 E ) were further clarified. The optimized IC rate i s 121 1.56 ps, very similar to the vibrational cooling time constant observ ed above in ultrafast TA, and the earlier ~15 ps component i s probably a convolution of this 1.5 ps IC and 12 ps ground state vibrational cooling. The authors do acknowledge, however, that their simulations indicate a greatly reduced contribution of the f ast component to ground state recovery dynamics following 600 nm excitation. At 100 ps, only 32% of the decay has occurred via the fast process, while the 400 nm pump shows 71% of the decay occurring via the fast process (345 nm shows 85%). 12 This observation lend s credence to the absence of a fast component in the TA spectrum following a 625 nm pump pulse in Juban's data. This dependence on excitation energy for the fast decay process indicates the presence of a B ISC process that is dependent on vibrational cooling within the 2 E. By examining the decay of the ex cited state absorption, the 7 - 10 ps decay was assigned to the 2 E vibrational cooling. 12 The authors hypothesize that with sufficient pump energy, the system is thermally activated to BISC to the 4 T 2 manifold where it can relax to the ground state in 1.5 ps (while the ground state vibrationally cools in 10 - 12 ps). After the vibrational cooling on the 2 E surface has occurred, the population is trapped on the 2 E until the ground state population is recovered in 700 - 900 ps. 12 Recent computational modeling by Ando et a l. 13 suggest s that this strong coupl ing between the 2 E and the 4 T 2 state is actually facilitated by potential energy surface crossings and spin orbit coupling between the 2 T 1 and the 4 T 2 state s . The results show that the 2 T 1 and 4 T 2 states cross near the Franck Condon region, and simulation s suggest population transfer between these states happens around 200 - 250 fs , even before the molecule has reached the distorted 4 T 2 structure . Since the 2 T 1 and 122 2 E states are so close in energy and geometry, ultrafast IC between these states is assumed t o proceed after the 2 T 1 is populated. 13 The optimiz ation of the 4 T 2 geometry confirms a distorted structure with four longer Cr - O bond lengths resulting from the e g * (d x 2 - y 2 ) population, and the dihedral angle between the oxygen atoms on two of the acac ligands is significantly increased from 90° to 120°. Simulations of th e path between the Franck Condon (ground state) geometry and the distorted 4 T 2 geometry indicate the low frequency modes (displacements in the primary coordination sphere, particularly the Cr - O bond length) are primarily responsible for driving this distortion. 13 These data make clear the need for advanced understanding of the processes occurring between excitation and 1 ps. The works of Juban and Kunttu agree that ISC from the quartet manifold ( 4 LMCT, 4 ( 3 IL)/ 4 T 1 , or 4 T 2 ) to the 2 E occurs within 100 fs. They also agree that the 2 E decays back to the ground state in about 800 ps. 3,10,12 (This ground state recovery timescale has been measured as 950 ps in MeCN; see Appendix A for details.) The intervening processes are a little murkier, wi th each experiment having its own advantages. The IR probe results in narrower spectra, where the vibrational cooling is easier to see , but the initially formed excited state is no longer a ligand field transition . The TA results look at electronic absor ptions which are broader, but kinetic complications are minimized by exciting into the lowest energetically allowed transition. Further investigations into the geometric factors driving the ultrafast ISC process could shed more light on these processes. 123 3.2.2 T ransient Absorption Utilizing 50 fs Pulses Previous experiments in our group, in collaboration with the Beck laboratory , employed 50 fs pump and probe pulses. As discussed in Chapter 1, the increased bandwidth with sh orter pulse duration can produce a wavepacket. The results of these experiments are seen in Figure 3 . 6 , where clear oscillations are seen in the data, lasting into multi - hundreds of femtoseconds, superimposed on the population dy namics. This data was collected by pumping the low energy side of the 4 T 2 absorption at 600 nm (15 nm FWHM) and monitoring the transient signals with a 600 nm probe (i.e. a one color experiment), which was either detected without spectral filtering or by using a monochromator with a 4 nm bandpass to monitor the probe at 592 nm and 608 nm. 14 The data show n here was collected at 592 nm, and the excited state absorption can be - monoexponential fit of the data and once the population dynamics (the fit) have been removed, the oscillatory residual is much clearer. This is seen in the bott om panel of Figure 3 . 6 , where the black line here represents a cosinusoidal fit to the data composed of vibrations at 164 and 75 cm - 1 . 14 124 Figure 3 . 6 Results from 50 fs excitation at 600 nm for Cr(acac) 3 The top graph shows the entire kinetic trace resulting from 600 nm excitatio n and a 600 nm prob e, both 50 fs in duration. The bottom plot is an expansion of the short time region where clear oscillations are seen in the data. The black line in both plots represents the fit of the data. See text for more details. Figure repr od uced from reference 14 with permission of The Royal Society of Chemistry . This vibrational coherence was assigned as wavepacket motion on the excited state , due to the low oscillator strength of the ground state absorption and the longer timescales for ground state recovery from the excited states. 14 The coherence signal originates near time zero, and the damping times for the two oscillations are 70 fs (1 6 4 cm - 1 vibration ) and 1.6 ps (75 cm - 1 vibration ) . In light of the previously resolved TA 125 dynamics, the 70 fs time constant was loosely associated with the ISC process, indicating the coherence is originated on the 4 T 2 surface, but is maintained though the ISC crossing onto the 2 E surface. 14 Figure 3 . 7 Vibrational Modes Possibly Facilitating Ultrafast ISC The symmetric breathing mode, left, and the scissoring mode, right, from ground state frequency calculations in Cr(acac) 3 . Figure reproduced from reference 14 with permission of The Royal Society of Chemistry . Ground state DFT calculations were carried out in an attempt to identify these vibrational modes, as they may play an important role in the reaction coordinate of this ISC process. Two modes , at 184 cm - 1 and 256 cm - 1 , were selected as likely candidates for the 164 cm - 1 mode observed. The population of an e g * orbital upon formation of the 4 T 2 state is predicted to lower the se frequencies by weakening the Cr - O bonds. These modes, seen in Figure 3 . 7 , involve displacements within the primary coordination sphere of the compound. Along with these modes, it was noted that nearly all of the low energy vibrational modes i nvolved motions of the methyl groups or deformation of the ligand backbone. 14 To test if the methyl gr oup motion was a key factor in the ISC process, the authors synthesized a derivative using 2,2,6,6 - tetramethyl - 3,5 - heptanedione 126 (Cr(TMHD) 3 ), which retains the overall structure of Cr(acac) 3 while exchanging the methyl groups for tert - butyl groups on the li gand backbone. The structure of the ground state absorption spectrum and the emission spectrum are largely the same, however the maxima are slightly red shifted from the same features in Cr(acac) 3 . 9,14 Despite this small perturbation to the zero point energies of the electronic states, the TA signals show dramatic differenc es from Cr(acac) 3 . The excited state dynamics of this molecule were analyzed using the same methods as the 120 fs resolution TA studies on Cr(acac) 3 described above. Pumping on the low energy side of the 4 T 2 state, both full spectra and single wavelengt h data were collected. These results are shown in Figure 3 . 8 , where the full spectra data exhibit more than just the narrowing and red shifting of the spectrum as was observed with Cr(acac) 3 . Instead, Cr(TMHD) 3 shows a distinct decrease in the intensity on the blue side of the spectrum, while the redder wavelengths grow in. The dynamics are confirmed by the single wavelength traces, which show this decay and rise occurring on the same timescales. The spectra become invariant a fter 12 ps, indicating the signal is originating from the 2 E state and it is vibrationally cooled at that point . The ~1.8 ps dynamics observed are assigned to the ISC from the 4 T 2 to the 2 E state , and encompass the vibrational cooling on the 2 E as well . This assignment is further substantiated by performing Gaussian deconvolution on the excited state spectra. This fitting procedure efficiently models the profiles of the full spectra traces by assuming two Gaussians, centered at 465 nm and 525 nm, start w ith relatively equal intensities at 300 fs, but the blue Gaussian decays as the red Gaussian grows with time. The large magnitude change in the ISC timescale for Cr(TMHD) 3 , coupled with the vibrational 127 analysis of Cr(acac) 3 suggest that the methyl groups on the acac backbone play a large role in the ultrafast dynamics observed in Cr(acac) 3 . 9,14 Figure 3 . 8 Transient Absorption Data for Cr(TMHD) 3 in DCM The full spectra data, evolving in time from the red to blue colored trace, clearly show a decay on the blue edge of the spe ctrum and a concomitant rise on the red edge of the spectrum. Single wavelength data, right, confirm these processes occur with the same time constant, ~ 1.8 ps. Figure reproduced in part from reference 14 with permission of The Royal Society of Chemistry . 3.3 Current Efforts to Explore the Ultrafast Dynamics of Cr(acac) 3 The work in this thesis seeks to fu rther these coherence studies on both Cr(acac) 3 and Cr(TMHD) 3 . The experimental details are given in Chapter 2, which describes the setup for the 35 fs laser system acquired after the collaboration with Dr. Beck. This system has the flexibility to do one color or two color experiments, which will be detailed separately below. 128 3.3.1 One Color Pump Dependence The previous coherence data on Cr(acac) 3 , while instructive, resulted from creating population in the 4 T 2 state near the minimum of the potential energy s urface (i.e. vibrationally cool). 14 The 4 T 2 absorption, however, is well isolated from other electron ic states (see Figure 3 . 2 ), allowing for clean excitation of this state from 490 nm to 700 nm. In practice, the usable range is limited by the oscillator strength at these wavelengths, but the excess vibrational energy in this ex cited state may still be reasonably varied by ~ 4200 cm - 1 . The previous ly observed dynamics (1.1 ps cooling on the 2 E surface) have already been shown to be invariant with pump wavelength 10 , so the focus of this discussion will be on the oscillatory features of the data. The experimental setup for the one color experiment has been described in detail in Chapter 2, but it is worth noting this data was collected with a few modifications. The most noteworthy being that the p robe beam contained a waveplate and Glan - Laser cub e polarize r, while the pump beam did not contain these optics . T he prism compressor was optimized without these optics on the probe line (i.e. GDD on the pump and probe were the same), but they were reinserted before the data was collected in order to ach ieve magic angle polarization . Consequently, the pump and probe are not simultaneously optimally compressed. Despite these issues, the nominal pulse widths, as characterized by cross - correlation only, are 60 fs. A cube polarizer after the sample was or iented to allow for maximum probe transmission, while rejecting the pump photons at magic angle polarization. This cube polarizer after the sample helped to mimic the experimental conditions during the collaboration with the Beck laboratory 14 , and has proven to be a useful technique in Paul Champion's studies. 15 As with any 129 brand new experiment to a lab, there is a bit of a learning curve while ful ly optimizing the experimental conditions and this was no different. The procedure for collecting coherence data has since been optimized, but the one color data will still be presented here. Experimental The pump wavelengths chosen for this study were 5 10, 560, and 600 nm. Since these are one color exper iments, the probe beam shares the same spectral profile as the pump beam. For all of the pump wavelengths, the monochromator ( 10 nm bandpass) was tuned to the left edge of the pump spectrum, as shown in Figure 3 . 9 , below . The pump wavelengths vary the vibrational energy by ~3000 cm - 1 , while having minimal spectral overlap with each other , i.e. pumping distinctly different vibrational levels with eac h pump wavelength . The experiments were performed in a 1 mm path length cuvette where the absorbance of Cr(acac) 3 in acetonitrile (MeCN) at the pump wavelength of interest was ~0.5. T he results presented are the combination of two data sets at each pump wavelength . The data were worked up and analyzed according to procedures detailed in Chapter 2 and appendices, which w ill not be repeated here. A typical data set consists of at least 4 0 scans, where scans showing instability or shifting (laser drift) o ver time were removed prior to data averaging. The resulting data set was processed in two programs, I GOR Pro and MATLAB, where traditional fast Fourier Transforms (FFT) and linear predictive single value decomposition (LPSVD) were performed, respectively . 16 18 While these two programs give comparable results in terms of the frequencies recovered ( vide infra ) , LPSVD results are cleaner and will be reported throughout the 130 rest of this analysis. The best LPSVD fit was determined by e xamining the residual of the fit and evaluating the RMS value of the fit. For the data presented in this thesis, the best fit occurred when the RMS value stabilized and the residual no longer showed oscillatory features (data not shown). Figure 3 . 9 Overlay of Cr(acac) 3 Ground and Excited State Absorptions With the One - Color Pump and Probe Combinations The ground state absorption for the 4 T 2 state in Cr(acac) 3 (black) overlaid with the 600, 560, and 510 n m pump spectra (solid orange, turquoise, and green lines, respectively). The probe spectra after the monochromator (dashed lines), are centered approximately at the left edge of the FWHM of the pump spectrum. The blue curve is the excited state absorptio n at 1.5 ps, and is shown for reference. These IGOR and LPSVD workup procedures are shown in Figure 3 . 10 on a typical data set for Cr(acac) 3 . The graph s on the left half of the figure represent the analysis process in IGOR, wh ereas the right graph s represent the analysis process in MATLAB using LPSVD. By comparing the frequency results of both methods, it is easy to see that the LPSVD spectrum suffers from less noise, and is better at picking up low intensity frequencies (i.e. 64 cm - 1 ). 131 Figure 3 . 10 IGOR and MATLAB Data Analysis Techniques Compared The top left graph shows the IGOR data analysis method, where the exponential components are fit explicitly (red line) and the fit residual is Fourier transformed (bottom left graph.) The major peaks are picked out from the noisy baseline and labeled. The top right graph shows the data (blue) and the LPSVD fit (red) which is comprised of cosinusoidal components with individual dampi ng times. It is this fit that is converted into the power spectrum (bottom right graph), hence its much smoother appearance. The FT spectra show pretty close agreement, despite the difference in methodology. 132 Data for the molecule and the pure solvent are collected under identical experimental conditions for all pump/probe combinations in order to differentiate the impulsively stimulated Raman modes of the solvent from mode s corres ponding to the molecule of interest . F requencies occurring in both the p ure solvent and molecule 's power spectra are neglected. For the LPSVD data shown in Figure 3 . 10 , the 374 cm - 1 mode corresponds to the C - CN bending mode in MeCN, which matches the Raman frequency of 380 cm - 1 quite well. 19 The LPSVD fit of pure MeCN under these conditions (not shown) gives 384 cm - 1 , which matches within experimental error. The frequency resolution and range of the FT spectrum using either method is taken from the time - domain data passed in to the analysis. The frequency r esolution, f , is defined by the following equation: ( 3. 1 ) where N is the number of points acquired in the time - domain signal, is the time spacing between points, and the product of N · is the length of time containing the time - domain signal. 20 For all of the experimental data collected, was 5 fs, while N varied depending on the breadth of the solvent signal around time zero . For both methods, the frequency analysis was started after the nonresonant solvent response (see Chapter 1) around time zero had ended; the frequency resolution o f most data sets is 15 cm - 1 . The frequency range of the results is similarly related to the time - domain signal. The last frequency is given by: ( 3. 2) 133 such that the frequ ency range of the data goes from 0 to f F. 20 Typical values of N were 400 and over, such that the 0 - 3300 cm - 1 range is reliably covered by all data sets. The frequency range of excited vibrational modes, however, comes from the pulse characteristics. As discussed in Chapter 1 (section 1.2.2), there are two schools of thin king on this: t he first is that the pulse must have enough spectral bandwidth to coherently excite at least two vibrational levels , 21,22 and t he second is that all vibrational modes which have periods more than two times the pulse duration will be excited. 23,24 To illustrate the difference between these two scenarios, co nsider a 35 fs laser pulse centered at 520 nm. For a transform limited pulse, the bandwidth would be 11.4 cm - 1 , meaning the total energy spread of the pulse at FWHM is 421.6 cm - 1 . Under the first condition for quantum beating , modes less than ~211 cm - 1 c ould be excited by this pulse. Alternately, examining the impulsive excitation limit, modes with periods of 70 fs and longer will be excited by this pulse, corresponding to modes less than ~477 cm - 1 . These two ranges bear some obvious differences, but if the energy spread of the pulse at intensities lower than FWHM is considered , the two ranges may be reconciled. The absolute limit of frequencies one could expect to observe corresponds to 1/pulse duration - 952.3 cm - 1 in this case - but often this limit is not reached. 25 It should be noted here that the solvent vibration is stimulated nonresonantly by a similar mechanism. This process, as discussed in chapter 1, is called impulsive sti mulated Raman scattering (ISRS) and requires only that the pump pulse be short in rel ation to the vibrational period . T he bandwidth of the pulse is therefore sufficient to contain multiple pairs of frequencies with a frequency difference matching the vibrational mode of interest , which drives the vibration. 26 134 600 nm Excitation R esults Pumping at 600 nm creates a relatively vibrationally cool population on the 4 T 2 surface, as dis cussed earlier in section 3.2.2 . The recorded data are shown in Figure 3 . 11 , where the results and analyses of two data sets are shown in a stacked plot. The top plot in each set displays the raw data, along with the LPSVD fit to the data. The F T of this fit is displayed in the power spectrum below, reflecting the frequency components in the fit. These experimental conditions closely match those used in the previous coherence study 14 ; however , the LPSVD analyse s of the recorded signals show that the oscillatory feature consists of more than two vibrational modes . The power spectr a shown in Figure 3 . 11 contain peaks at 183, ~ 2 26 , 284, ~460 , and 486 cm - 1 after neglecting the 377 cm - 1 mode from the solvent. The pulse characteristics for these data sets reveal that these 470 cm - 1 components may be outside of the frequenc ies expected considering both the quantum beat and impulsive excitation pictures. The first data set was collected using 60 fs pulses centered at 599 nm with a bandwidth of 27.6 nm. This leads to an expected frequency range of 386 and 274 cm - 1 , respectiv ely. The second data set was collected with a 48 fs pump pulse centered at 600.5 nm with a bandwidth of 20.9 nm. The expected frequency range here is 290 and 348 cm - 1 , respectively. All of these limits suggest that the higher frequency modes at ~470 cm - 1 should not be excited and yet they are clearly resolved in the power spectra. This suggests that the se "limits" are not strict and that strong modes at higher frequencies may still be excited. 135 Figure 3 . 11 Cr(acac) 3 Vibrations Resulting from 600 nm Excitation The top and third plots show the data (blue dots) and the LPSVD fit of the data (red l ine) collected pumping at 600 nm and probing at 592 nm for two data sets. The FT of the LPSVD fit is displayed below the data, where frequencies Cr(acac) 3 (blue) and MeCN (red) are shown explicitly. The two data sets exhibit very close agreement in the results, especially for peaks at ~226, and 460 cm - 1 . 136 560 nm Excitation R esults Pumping at the ground state ab sorption maximum , which is also the energy for the best Franck Condon overlap to the excited state , unfortunately results in data with some oscillatory features, but they are not as pronounced as the 600 nm pump data sets. The data, shown in Figure 3 . 12 , below , exhibits only a few vibrations outside of the solvent mode. These vibrations, at 87, ~190 , 223 , and 568 cm - 1 , echo the low frequency vibrations obser ved utilizing the 600 nm pump. Examining t he pulse characteristics again reveals that the 568 cm - 1 mode is well outside of the anticipated range of frequencies excited during the wavepacket formation. The data in the top two graphs in Figure 3 . 12 were recorded utilizing 59 fs pulses centered at 560.3 nm (17 nm FWHM), leading to anticipated frequencies of 270 and 283 cm - 1 , respectively. The extreme limit from the pulse duration is 565 cm - 1 , putting this frequency just on the edge of the limit. It is therefore regarded as an artifact and will not be further analyzed. The low frequency component present in the Cr(acac) 3 data also appears in the MeCN LPSVD fit, indicating it may be an artificial component in the data. As a result, this frequency will not be investigated fu rther in the discussion section below. The second data set reveals frequencies that would be expected given the pulse characteristics of the pump. The better compressed 51 fs pulses were centered at 561.1 nm, with a spectral bandwidth of 15.8 nm. This l eads to expected frequency ranges of 251 and 324 cm - 1 , respectively. The recovered frequencies of 189 and 223 cm - 1 fit well within this range. The frequency at 373 cm - 1 is attributed to MeCN, despite the overly broad feature from the solvent LPSVD fit di rectly. 137 Figure 3 . 12 Cr(acac) 3 Vibrations Resulting from 560 nm Excitation The top and third plots show the data (blue dots) and the LPSVD fit of the data (red l ine) collected pumping at 56 0 nm and probi ng at 5 5 2 nm for two data sets. The FT of the LPSVD fit is displayed below the data, where frequencies Cr(acac) 3 (blue) and MeCN (red) are shown explicitly. The two data sets show limited frequencies with only one common mode at 190 cm - 1 . 138 510 nm Excita tion Results Th is excitation wavelength creates the most vibrationally hot wavepacket on the 4 T 2 surface. This set of pump and probe wavelengths also affords the highest signal to noise, as the ground state absorption is much lower than the excited state absorption here. Also, the exponential decay from vibrational cooling can clearly be seen in the data sets, presented in Figure 3 . 13 . The higher signal to noise here allows for clearer oscillatory features, and the power spectr a of the LPSVD fits are in close agreement. A rather broad mode is seen at ~180 cm - 1 , followed by a sharper peak at 456 cm - 1 . The bottom data set contains a higher frequency component at 551 cm - 1 that is reminiscent of the 568 cm - 1 peak present following 560 nm excitation. As discussed for 560 nm excitation, this 551 cm - 1 mode , along with the narrow 883 cm - 1 mode, is outside of the range of frequencies expected in the wavepacket. For the top data set, the excitation pulse was 12.8 nm at FWHM centered at 510.7 nm with a measured pulse duration of 60 fs. The expected frequency ranges for this data set is 245 and 279 cm - 1 , respectively. This 883 cm - 1 mode is clearly outside of these ranges, and will be considered an artifact in the data. As for the s econd data set, the expected frequency ranges are slightly different due to the shorter pulse duration. For this 510.8 nm pulse (11.5 nm FWHM), the pulse duration was measured as 46 fs, which leads to 220 and 370 cm - 1 for the anticipated frequency ranges, respectively. Given the agreement of the LPSVD fit with the data this is clearly a necessary component, however it will not be analyzed further in the discussion section. 139 Figure 3 . 13 Cr(acac) 3 Vibrati ons Resulting from 510 nm Excitation The top and third plots show the data (blue dots) and the LPSVD fit of the data (red l ine) collected pumping at 56 0 nm and probing at 5 5 2 nm for two data sets. The FT of the LPSVD fit is displayed below the data, where frequencies Cr(acac) 3 (blue) and MeCN (red) are shown explicitly. The two data sets exhibit strong matching in the breadth and frequency of the modes at ~178 and 456 cm - 1 . 140 Discussion The results from both data sets at each pump wavelength are summar ized in Table 3 . 1 , below . Each row represents the LPSVD results for the corresponding excitation wavelength , and the frequencies are group ed i n columns by equivalent modes. The damping times, listed in parentheses in the table, will be analyzed in the next section detailing the two color experiments, but are listed here for reference. This table highlights the presence of the ~184 cm - 1 mode at all excitation wavelengths. The next mode, ~225 cm - 1 , i s present only at 560 and 600 nm excitation, while the ~459 cm - 1 mode is present only for excitation on the edges of the 4 T 2 absorption. The final common mode, ~559 cm - 1 is present only at 510 and 560 nm excitation. Vibrations in the far right column, sa ve for the mode at 486 cm - 1 , have been discounted as artifacts in the individual discussions above and will not be discussed further. As the 486 cm - 1 mode is past the limit of the expected frequencies and has no counterpart in any of the other data sets, it will be ignored for the remainder of the discussion. Table 3 . 1 : Summary of Observed Oscillations for Cr(acac) 3 in MeCN Utilizing One Color Experiments As Champion and coworkers have stated, "[femtose cond coherence spectroscopy] can be thought of as a true time - domain analog of Raman spectroscopy, whereby the Fourier transform of the time - domain signal maps directly on to the 141 traditional Raman spectrum." 15 In this regard, the ground state Raman spectrum of Cr(acac) 3 is a nice starting point for estimating the frequencies that might be present in the excited states of this molecule, especially considering the similar geometry of the 2 E state to the ground state which has been predicted to exhibit very similar vibrations to the ground state . 6 The resonance Raman spectrum of Cr(acac) 3 has been collected a number of times over the years with similar results. 14,27 29 One set of t hese results is shown in Figure 3 . 14 , and contain s ground state frequencies very close to those observed in the present excitat ion study. The peak at 457 cm - 1 has the highest intensity, followed by 232 (shoulder) and 562 cm - 1 at much weaker intensities. The peak at 188 cm - 1 is not present in the data set shown in Figure 3 . 14 , however it has been observe d in other resonance Raman spectra . 14 It has been noted that one advantage to this coherence spectros copy technique is the ability to observe low wavenumbers modes that are either weak or absent in traditional Raman spectroscopy. 30 To further clarify these modes and their origins, DFT frequency calculations were performed at the UB3LYP/6 - 311G(d,p) level emplo ying a CPCM solvent continuum to model surrounding acetonitrile bath for the optimized ground and 2 E states, and the 4 T 2 state at the Franck Condon (FC) geometry. These frequency results, listed in Appendix C : Gaussian Calculation Results , were compared to the experimental frequencies listed in Table 3 . 1 . Details of these calculations are given in Chapter 2, however it should be noted that the molecule was optimized without symmetry restrictions and the resulting point group is formally C 1 , but it is very close to higher symmetry point groups through 142 Figure 3 . 14 FT Raman Spectrum for Cr(acac) 3 in the Solid State The experimentally collected spectrum for Cr(acac) 3 in the solid state is shown here for a Fourier Transform Raman spectrometer. Figure adapted with permission from reference 27 . © (2015) Elsevie r. slight methyl group rotations. In the C 1 point group all of the vibrations are Raman active, allowing the results to be directly applicable to the experimental results. For the 4 T 2 calculations, the C 1 point group cannot support the degeneracy of this state, and so it is split into three separate states. The energie s of these states in the TD DFT calculation do closely resemble the A 1 and E set that is predicted with a descent in symmetry. 31 The frequency results from these FC states contain negative frequencies consistent with these being unoptimized Franck Condon structure s . The 2 E calculation, despite a similar degeneracy issue, did not suffer from this complication. Since it is the lowest energy doublet, a "ground state" DFT calculation could be performed by merely 143 changing the spin on the optimized ground state structure from a quartet to a doublet and re - optimizing the structure. Considering the previous TA results which sh ow the ISC from the 4 T 2 to the 2 E is sub - 100 fs, the strong agreement of the observed frequencies to the ground state Raman modes, and the low oscillator strength of ground state absorption compared to absorption out of the 2 E, these vibrations are assigne d to the excited state. In agreement with earlier results, oscillations are present out to the end of the time - domain window at 2 ps, which indicates that the coherence is retained through the ISC process. Considering the large amount of vibrational over lap between the 4 T 2 and 2 E surfaces, this efficient crossing (and retention of coherence) is not surprising. The calculations indicate that vibrational modes at 232, 457, and 562 cm - 1 are present in both the 4 T 2 and 2 E states. T he 184 cm - 1 mode , however, is distinctly 2 E in character as it has no energetic match for any of the 4 T 2 calculations. The calculated 188 cm - 1 2 E mode looks exactly like the ground state 184 cm - 1 mode pictured in Figure 3 . 7 , which comes as no surprise giv en the predicted frequency matching. This mode is a symmetric breathing of the acac ligands way from the Cr center, resulting in lengthened Cr - O bonds. The other modes appearing on both surfaces may facilitate the ultrafast ISC and require further exami nation. The correlation between 4 T 2 and 2 E modes at 559 cm - 1 is straightforward. For all of the modeled excited states, the motion is the same; the C - CH 3 bond is left rigid and a swinging of the methyl group causes the attached carbon to shift out of t he plane of the acac backbone, and the oxygen is displaced out of plane in the opposite direction. The other side of the ligand performs this same motion, but out of phase. Figure 3 . 15 144 overlays the two extremes of this motion f or comparison. This mode matching between the states is also seen at 459 cm - 1 , where all of the ligands exhibit a symmetric stretch across the acac backbone. This vibration is likely strongly coupled to the formation of the 4 T 2 state, where the bonding c haracter of the Cr - O bonds is reduced due to population of the e g * orbital. Figure 3 . 15 566 and 461 cm - 1 Modes on the 2 E and 4 T 2 Surfaces Th e 566 cm - 1 mode (left) corresponds to a torsion of the methyl g roup which forces the attached carbon atom to shift up or down from the plane of the ligand backbone. The methyl group on the opposite side of the ligand performs the same motion, but in the opposite direction. The 461 cm - 1 mode is a symmetric stretch ac ross the acac backbone. Further inspection of the ~225 cm - 1 mode reveals that 4 T 2 - ES 1 and - ES 2 are moving in an asymmetric version of the torsional scissor mode shown in Figure 3 . 7 , where one ligand is mostly stationary and th e other two scissor out of phase from each other with the methyl groups undergoing a large amplitude wag . The 2 E mode at this frequency involves a similar methyl group wag, however this time it leverages the C=O arm of the acac in and out of the plane. T hese motions can be seen explicitly in Figure 3 . 16 . In both cases, the large methyl group displacement alters the Cr - O bond lengths 145 for both of these modes. I t is conceivable that vibrational energy may transfer from one mode t o the other during the state change since they both involve methyl wagging motions, but the connection is less obvious than the 559 and 459 cm - 1 modes above. Figure 3 . 16 233 cm - 1 Mode in both the 2 E and 4 T 2 States For the 2 E (left), the arms of the acac ligand rotate about the C=CH bond on the backbone, with the arms moving out of phase from each other. For the 4 T 2 mode (right), the plane of the backbone remains intact but the ligands scissor out of phas e with each other. Ando et. al. discussed the importance modes involving Cr - O bond stretching in their theoretical study of the ultrafast ISC process. While simulating the reaction path to move from the Franck Condon 4 A 2 geometry to the distorted 4 T 2 ( optimized) geometry, they saw that this path was mainly described by low frequency modes corresponding to displacements in the primary coordination sphere. And as these modes move the geometry closer to the 4 T 2 minimum, it intersects a surface crossing wi th the 2 T state at nearly degenerate energy near the Franck Condon region before the geometry has had much opportunity to change. 13 Both the DFT results of this work and Ando's 146 computational results agree that almost all of the low wavenumber modes involve Cr - O bond stretching. Revisitin g the information in Table 1 armed with this mode coupling information is enlightening. For the 600 nm pump, where there is little excess vibrational energy in the excited state, only the 225 and 459 cm - 1 modes are able to couple the two states. This cou pling is expected to be highly efficient when the vibrational motion and energy is the same between the 4 T 2 and 2 E states, as is the case for the 459 cm - 1 mode. The coupling should still be quite good at 225 cm - 1 , where the same atoms are moving but with slight variations between the 4 T 2 and 2 E states. When the excess vibrational energy in the system is increased by pumping at 560 nm, both the 225 and 568 cm - 1 modes are present , despite lacking the bandwidth to create a wavepacket in the 568 cm - 1 mode. P resumably, the 459 cm - 1 mode should be present as well, since it is seen in the 510 nm pump data. The signal to noise of the data collected while pumping at 560 nm was particularly low for both data sets despite coinciding with the ground state absorptio n maximum. It i s very likely that the small amplitude of the oscillatory residuals obscured some of the components in the signal, this 459 cm - 1 mode being one of them. As with the 459 cm - 1 mode, the 559 cm - 1 vibration provides an efficient coupling betwe en the 4 T 2 and 2 E surfaces due to the identical motion in both states. The presence of these high frequency modes indicates that they are strongly coupled to the Franck Condon excitation. This is especially true for the 510 nm pump, where only the 559 an d 459 cm - 1 modes are seen, despite being well outside of the pulse bandwidth for wavepacket formation . All of these modes are alike in their deformation of the Cr - O bond, which is expected to be different in the 4 T 2 optimized structure, and so their 147 prese nce and coupling to each other are logical. The 184 cm - 1 mode, present at all pump wavelengths, may be a result of IVR in the 2 E state as it is lower in energy than all of the other vibrational modes initiated on the 4 T 2 surface. Since this mode corresp onds to the symmetric breathing mode of the molecule, involving Cr - O bond length changes, it would be an efficient way to reverse the bond elongations in the 4 T 2 state and return to the original bond lengths on the 2 E surface. This one - color data set ha s provided some valuable insights into the coupling between the 4 T 2 and 2 E surfaces, but the data was not without its issues. For all of the data sets, the signal to noise was relatively low, and especially low for the 560 nm pump data. The pulses were n ot optimally compressed, which may have prevented deeper modulations from being observed. Residual chirp in the pump pulse has been known to wash out coherence oscillations , and negative chirp , in particular , has been used as a method to i ncrease ground s tate vibrational coherence. 32 36 And in the one color experiment, the prob e pulse is restricted to wavelengths within the pump spectrum, sometimes leading to probing where there is little excited state absorption signal (and further d egrading the signal to noise). The two color experiments improve on a lot of these drawbacks. 3.3.2 T wo Color Pump Dependence For the two color experiments, the experimental set up followed the description in Chapter 2, where the output from each OPA was passed through a separate prism compressor which was optimized f or each beam. These data were collect ed after acquiring thinner, minimally dispersive optics which were matched between the pump and probe beams, removing the cube polarizer after the sample, and utilizing both OKE 148 and FROG (see Chapter 2) for pulse characterization. As a result, t he nominal pulse duration at the sample for the pump was 49 fs for 505 nm pump pulses and 33 fs for 560 and 600 nm pump pulses. The probe pulse, centered at 520 nm was more difficult to compress and was generally 45 fs at the sample position. It was thought that t he two color experiments might decrease the time duration of the nonlinear processes occurring around time zero. The one color experiments, with their phase and energy matching between the pump and the probe pulses derived from the same laser source, wer e prime candidates for cross - phase modulation (XPM) and self - phase modulation (SPM) while the pulses overlapped in the sample. 37,38 These processes should be minimized after moving to the two color experiments since the energy matching w ill be removed and the phase matching should be less. While the pulse compression should help minimize the nonresonant solvent response , reducing the XPM and SPM is thought to have a bigger effect. The nonresonant solvent response lasted until ~ 150 fs ( vide supra ) in the one color experiments , prohibiting signatures of the 4 T 2 state from being directly observed. If this window is minimized, the 4 T 2 signatures might become more apparent. For this study, pump wavelengths of 505, 560, and 600 nm were use d, for the same purpose as described in the one color data set vide supra . The sample absorbance at each pump wavelength was typically 0.3 - 0.5 for a 1mm path length cell. The major difference was the probe wavelength, which was set at 520 nm for all pu mp wavelengths. This coincide s with the 2 E excited state absorption maximum and should help increase the signal to noise in the data . Figure 3 . 17 contains this spectral 149 information, displaying the spectrum for ea ch pump and probe wavelength superimposed on the ground and excited state absorption spectra. Figure 3 . 17 Pump and Probe Spectra for Cr(acac) 3 Two Color Experiments The ground (black) and excited state ( solid blue) absorption spectra of Cr(acac) 3 are shown in relation to the pump wavelengths (solid maroon, green, and red) used in this study. The probe wavelength recorded was tuned with a monochromator and the probe spectra are shown in dashed lines (purp le, blue, and green). Also i n this study, the monochromator tuning was changed to assess the benefit of probing at the blue or red (FWHM) edge of the probe spectrum or at the maximum of the spectrum , utilizing slits set to 5 nm bandpass . Champion and coworkers have seen this tuning play a vital role in enhancing the low or high wavenumber modes observed in their one color experiments, 15 and so the concept was applied here. This tuning is responsible for the three probe spectra present in Figure 3 . 17 ; they all derive fro m the same 520 nm probe OPA pulse which is then filtered after passing through the monochromator before being recorded by the photodiode. 150 Data for both Cr(acac) 3 and MeCN were collected under identical conditions at every pump/probe combination in the st udy. The resulting data sets were worked up according to the procedures previously described for the one color data. Data for MeCN consisted of an average of at least 14 scans while data for Cr(acac) 3 was typically an average of 24 scans or more. The lo wer scan numbers compared to the one color experiments came from analyzing the signal to noise of the data as a function of each additional scan; these parameters proved optimal for achieving high signal to noise while minimizing data collection times (se e Chapter 2 for more details). Figure 3 . 18 Typical Data Set for Cr(acac) 3 in the Two Color Pump - Probe Setup The full data set is seen in the bottom portion of the graph with the fit (red) of the long tim e amplitude components. The residual of the fit is seen in the top portion of the graph. The nonresonant solvent response ends around 135 fs, which is largely the same as the one color experiments. Figure 3 . 18 shows a typical data set from these two color experiments. The nonresonant solvent response does not appear to be any shorter for these experiments, despite the better pulse compression. Here, the fit is started at 135 fs, which is a slight improvement from the one col or results, but not as significant as was hoped. This could 151 mean that the timescale for XPM (or SPM) is intrinsically slow, so even though it may be reduced between the pulses, the process still takes the same amount of time. This is unfortunate, as it c ould still obscure processes from the 4 T 2 surface. Before summarizing the results from this study, it is worth pointing out that for a given pump/probe combination, tuning the monochromator setting changed the shape of the nonresonant solvent response. This can be seen in the top half of Figure 3 . 19 , where the solvent traces for one pump wavelength and three monochromator settings are displayed. Kovalenko et. al . have previously assessed these pulse shapes as arising from an el ectronic and Raman contribution to the signal. As monochromator wavelength is tuned, these components have different contributions and the shape of the peak changes. 39 This effect is particularly pronounced because the energy difference between the 514 nm probe and the 524 nm probe (371 cm - 1 ) almost matches the 380 cm - 1 Raman mode of MeCN. The solvent traces collected with 600 nm excitation show the largest effect of this Raman contribution. This is because the C - H (2250 cm - 1 - 1 ) stretching modes can interact with the 600 nm pump to produce anti - Stokes absorption at 510 and 528 nm 39 , which is very close to the monochromator settings. The coupling of these two effects creates very large amplitude oscillations in the solvent signal, as can be seen in the bottom half of Figure 3 . 19 . The oscillations are out of phase by 180°, which is expected when monitoring at wavelengths that span the vibration of interest. This effect was previously observed in CH 2 Br 2 by Nelson and coworkers, who were monitoring the t ransmitted 615 nm probe at 609 and 620 nm using a monochromator. 40 They attribute this antiphase relationship to a "wagging" of the probe spectrum "back and forth between the red and blue as the 152 Figure 3 . 19 Probe Wavelength Effects on the MeCN Solvent Response For the same pump probe overlap, the monochromator after the sample was tuned to the blue edge (green), maximum (red), and red edge (blue) of the probe spectrum. This energy difference is enough to constructively interact with and enhance the solvent vibrations. This is the reason for the 180° phase shift seen in the residuals. See text for more details. probe pulse arrives at the sample alternately in phas e or out of phase with the coherent vibrational motion induced by the excitation pulse." 40 This does not create challenges 153 for the data collection and assessment; it merely emphasizes the solvent vibration more than in the one color experiments. 600 nm Excitation Results The results from 600 nm excitation are shown in Figure 3 . 20 , below , where it is obvious that there are many more vibrations present than with the one color data sets. While the one color data rarely picked up oscillations below 150 cm - 1 , this is clearly a non - issue for the two color setup. Here, modes at ~ 30 , 76 , 85, 10 4 , and 12 3 cm - 1 can be seen , along with highe r energy vibrations at ~ 1 90 , 260, 330, 380, and 510 cm - 1 . The peak around 380 cm - 1 is assigned to the M eCN Raman mode and is ignored. The spectrum of the pulse used here, 22.2 nm FWHM at 599.8 nm, corresponds to a total energy of 617 cm - 1 . In the qua ntum beat picture then , wavepackets can be reasonably expected for the frequencies at or below 309 cm - 1 . The pulse duration was measured at 27 fs by FROG, and leads to a limit of 617 cm - 1 in the impulsive limit of excitation. Using the quantum beat limit leaves the 503 cm - 1 mode out of range, but considering the impulsive limit, this mode is reasonable. Given these two methods, the range of recovered frequencies is reasonable given the pulse characteristics. 154 Figure 3 . 20 Cr(acac) 3 600 nm Pump, 520 nm Probe R esults Shown on the left are the raw data sets ( blue dots ) and the LPSVD fits ( red ) for each pump - probe combination . The FT power spectra of the fit are shown on the right. All of the fits contain a t least four components, typically less than 380 cm - 1 . 155 560 nm Excitation Results The data resulting from 560 nm excitation are shown below in Figure 3 . 21 . As with the 600 nm excitation results, low frequency modes (less t han 100 cm - 1 ) are seen in at three probe wavelengths. The data also exhibit common peaks around 190, 250, 450, and 500 cm - 1 . The MeCN Raman mode at 380 cm - 1 was only visible when probing at 512 and 524 nm. This could be a result of the wagging mechanism described above, which clearly shows that the solvent oscillations are washed out when probing at 519 nm. Frequencies above the solvent mode are seen when probing at both 524 and 512 nm. The pulses used here were compressed to 35 fs, making it possible to excite modes at 477 cm - 1 and under. The spectral excitation limit is closer to 332 cm - 1 (560 nm, 2.8 nm FWHM), which excludes the modes at ~455 and 505 cm - 1 . Clearly, this spectral excitation limit is too small to be reasonable given these results. U sing the impulsive limit, only the ~ 50 5 cm - 1 mode is outside of the range, but given the breadth of the transition, this falls within a reasonable range. 156 Figure 3 . 21 Cr(acac) 3 560 nm Pump, 520 nm Probe Results The data (blue dots) and the LPSVD fit (red) are shown on the left for each pump/probe combination while the FT of the LPSVD fit is shown on the right. The frequencies resemble those seen following 600 nm excitation, including the broad low freque ncy components. 157 505 nm Excitation Results The results following high energy excitation into the 4 T 2 state may be seen in Figure 3 . 22 , where only the data probing at 514 nm show strong oscillations. This may be a direct result of both the increased pulse length and the decreased bandwidth. The pulses were only compressed to 52 fs here, and the bandwidth of the pulse was 8.8 nm FWHM centered at 504.6 nm. These characteristics lead to excitation bandwidths of 321 cm - 1 and 171 cm - 1 , respectively. This accounts for the majority of the recovered frequencies lying below 260 cm - 1 , and the noticeable absence of even the solvent mode at 380 cm - 1 . The consistent appearance of the 450 cm - 1 mode for 524 and 514 nm probes indicates that e ither there is enough bandwidth to excite this mode, or it is strongly coupled to the other modes that are excited in the wavepacket formation. This would also apply to the 507 cm - 1 mode present when probing at 519 nm. Despite the decreased frequency ran ge available for wavepacket formation, the data exhibit similar frequencies at ~60, 183, and 220 cm - 1 . 158 Figure 3 . 22 Cr(acac) 3 505 nm Pump, 520 nm Probe Results Data (blue dots) and LPSVD fits (red) for each pump/probe combination are shown on the left, while the FT of the LPSVD fit is shown on the right. The oscillatory amplitude in the data is less, leading to few frequencies in the power spectrum. Recovered frequencies agree well with results from lo wer energy exci t ation s . 159 Discussion The results of this two color study have been summarized in Table 3 . 2 , along with the frequencies and damping times of a second data set (see Appendix A, Figures 3.A1 - A3 for data) . The first column shows the pump/probe wavelength being monitored and the oscillations are grouped by common frequencies in the columns to the right. The two rows surrounded by the pump/probe heading represent the two data sets collected for that combinat ion. The last column in Table 3 . 2 shows the high frequency modes that appeared in some of the LPSVD analyses; they will not be discussed in this section, however, it is possible that they too are strongly coupled to the Franck Co ndon modes of the molecule as they are beyond the expected frequency range for wavepacket formation. As mentioned in the discussions of the data above, there are several new modes visible below 1 90 cm - 1 for these data sets , with average frequencies of 2 9, 70 , and 111 cm - 1 . Other new modes are seen at ~2 50, 308 , and 50 7 cm - 1 . The 1 90 cm - 1 and 45 6 cm - 1 modes , previously observed in the one color data above , are present here, too. For the same reasons discussed previously for the one color data, t hese fr equencies are all attributed to vibrational coherence on the excited states of the system. By comparing these results to the ground state resonance Raman spectrum of Cr(acac) 3 , ( Figure 3 . 14 ) it is clear there are ground state fr equencies at 125, 231, 252, and 457 cm - 1 . 14,27 29 It is hard to say whether the low frequency modes are present in the ground state as none of the resonance Raman s tudies contain frequencies below 125 cm - 1 . 160 Table 3 . 2 : Summary of Oscillations Observed Utilizing Two Color Experiments on Cr(acac) 3 in MeCN Turning to the DFT frequency calculation results ( Appendix C : Gaussian Calculation Results ), it is apparent that the frequencies at ~50 7 and 30 8 cm - 1 must come from the 4 T 2 state as there are no corresponding frequencies in the 2 E results. The 2 E (ground state) contains large gaps in the frequencies in these regions, jumping from 453 to 566 cm - 1 (452 - 569 cm - 1 ) and from 268 to 344 cm - 1 (257 - 349 cm - 1 ), leaving no doubt that these come from the 4 T 2 state. The remaining modes at ~2 50 , 111, and 68 cm - 1 are seen in both the 4 T 2 and 2 E frequency results. Since the motions of the modes at 456 and 190 cm - 1 have previously been discussed and assigned in the context of the one color data, they will not be covered again here. One of the biggest differences from the data collected using one color e xperiments is the presence of vibrations belonging to the 4 T 2 state. These modes , 299 and 510 cm - 1 , can be seen in Figure 3 . 23 , where both exhibit large displacements 161 of the methyl groups on the acac backbone. T he 299 cm - 1 mode induces asymmetric wagging of the methyl groups, which simultaneously shifts the whole acac backbone left to right about the metal center. This causes the Cr atom to shift positions to accommodate thi s sliding of the acac ligands. The 51 0 cm - 1 mode looks quite similar to the breathing mode across the ligand backbone previously seen at 461 cm - 1 , however Figure 3 . 23 4 T 2 299 and 510 cm - 1 Vibrational Motion s The 299 cm - 1 (left) vibration indu ces asymmetric wagging of the methyl groups, which also shifts the entire acac ligand about the Cr center. The 510 cm - 1 (right) is primarily a symmetric stretch across the acac backbone, but the ligand does not remain planar, as the central carbon and hyd rogen shift up and down out of the plane as the methyl groups stretch and compress. the acac backbone does not remain planar during this motion. Instead, the central carbon and hydrogen atom on the backbone oscillate up and down out of the plane as th e methyl groups stretch and compress. The mode at ~245 cm - 1 is almost the same motion on both the 4 T 2 and 2 E surfaces. This mode is essentially the 254 cm - 1 scissor mode seen in Figure 3 . 7 above. A side by sid e comparison of the 2 E and 4 T 2 motions is shown in Figure 3 . 24 , where the differences are easily seen. The 4 T 2 vibration scissors all of the methyl groups on the 162 Figure 3 . 24 Scissoring Mode at 254 cm - 1 on the 4 T 2 and 2 E Excited States The 4 T 2 excited states show a completely symmetric scissoring mode at 253 cm - 1 where all of the methyl groups swing toward the oxygens in unison. This motion is slightly modified on the 2 E surface, where only one acac ligand swings the methyl groups toward the oxygens while the other two swing the methyl groups away from the oxygen. There is also some slight deformation of the acac ring in the 2 E vibration, specifically in the centr al carbon and hydrogen atoms. backbone in phase together, as denoted by the displacement vectors pointing towards the oxygen atoms on all ligands. For the 2 E vibration, however, two of the ligands swing their methyl groups away from the Cr metal cente r as the third ligand swings them toward the metal center. The overall motion remains the same, but the phase between the ligands is different. Closer inspection of the ground state 254 cm - 1 mode shown in Figure 3 . 7 shows the sa me phase relationship as the 2 E vibration shown here. The remaining low frequency modes at ~68, 111 cm - 1 are composed of methyl group rotations about the C - C bond on the acac backbone. Typically, one set of methyl groups on a single acac ligand is rota ting while the others are almost stationary. This is illustrated in Figure 3 . 25 , where the methyl groups are eclipsed at the extremes of the 163 rotation. The ~30 cm - 1 mode, while seen at multiple pump/probe combinat ions, will not be discussed here given the resolution of the experiment. It is possible that it is real, but the 15 cm - 1 resolution from the time domain delay spacing and the total time delay window in relation to the period of the vibration (less than tw o full periods over the entire time window) make this frequency suspect. Figure 3 . 25 Low Frequency Methyl Group Rotation at 70 and 104 cm - 1 The methyl groups on one ligand rotate approximately 180° about the C - C bond as evidenced by the ghost atoms (the opposite extreme of the rotation) in an eclipsed geometry to the original position. This is seen for both the 4 T 2 and 2 E excited states. Now that the of the oscillations has been assigned, a closer e xamination of their pump wavelength dependence is possible. Consistent with the one color results, the ~190 and 45 6 cm - 1 modes are seen at all pump wavelengths. The new frequencies at ~ 70 , 250, and 50 7 cm - 1 are also seen at all pump wavelengths. Only th e frequencies at ~111 and 298 cm - 1 seem to have a subtle pump wavelength dependence, where the 111 cm - 1 is prevalent at 600 and 560 nm excitation, while the 30 8 cm - 1 mode is seen for both 505 nm and 600 nm excitation. Almost all of the vibrations show up at every pump 164 wavelength, indicating that overall, there is not a strong pump dependence despite the large increase in extra vibrational energy to the system. This lack of pump wavelength dependence can be understood as the excitation of vibrational ove rtones at higher pump wavelengths. Takeuchi et al. explored this concept in their studies of 10 - hydrozxybenzo[h]quinoline. 41 They point out that oscillatory period depends on the energy difference between the coherently excited Figure 3 . 26 Illustrations of Multimode and Progression Excitation Schemes The two shaded Gaussians represent two different excitation pulses with differ ent center wavelengths while the narrow lines represent vibrational modes which could be excited by these pulses. Scenario A, multimode excitation, results in completely different frequencies being excited when the pump wavelength is changed. Scenario B, progression excitation, merely excites overtones of the same vibration at a higher pump energy. Figure reprint ed with permission from reference 41 . © (2005) American Chemical Society. 165 vibrations. Therefore, two scenarios are possible when changing excitation wavelengths. The pump pulse could create a wavepacket of different vibrational modes , where the oscillatory period corresponds to the difference between these two mode s. Or, the pump pulse could create a wavepacket on an overtone or combination progression where the spacing between the levels correspond s to the vibrational mode. For their study, t hey varied the pump energy by 1800 cm - 1 , but saw the same four bands in the 200 - 700 cm - 1 re gion of the Fourier Transform spectrum , which they concluded came "from a coherent excitation of the overtone/combination regression relevant to each vibrational mode." 41 This is believed to be the case for Cr(acac) 3 as well, where increasing the vibrational energy by >3000cm - 1 had no effect on the observed oscillations. This trend simply became clearer with the better signal to noise afforded in the two col or experiments. Also, the presence of modes outside of the pump pulse bandwidth indicates a strong coupling between these modes throughout the 4 T 2 excited state. The better signal to noise of these data sets allows for a more confident analysis of the associated damping times (see Table 3 . 2 ). Since the wavepackets are generated between two electronic states (see Chapter 1), electronic coherence is possible, but these dephasing times are typically sub - 70 fs. 42,43 The majority of the damping times observed here are longer than this, so the oscillations are assigned as vibrational coherence. Pure vibrational dephasing times occur on the ps timescale, ranging from 2 - 10 ps depending on the molecule and the vibration. 22,41 Vibrational de phasing times on a sub - ps timescale, indicate the mode is modulated in some way, such as undergoing a surface crossing in this case. 166 With these benchmarks in mind, the damping times in Table 3 . 2 are broadly reclassified as sub - 1 ps, longer than 1 ps, or a mixture for each vibrational mode (column). The two modes associated with the 4 T 2 state, 308 and 507 cm - 1 , exhibit damping times in the sub - 1 ps range, save for one instance for the 308 cm - 1 mode. The LPSVD fit for this data (600 nm pump, 519 nm probe) was altered to examine the robustness of this damping time, but despite changing the number of oscillations in the data or where the fitting routine started, this damping remained 1 ps or greater. It is attractive to believe th e 308 cm - 1 mode has a sub - 1 ps damping time as it is associated with the 4 T 2 state which undergoes ISC in less than 120 fs. Treating the 1 ps damping time as an outlier leaves an average dephasing time of ~78 fs for this mode, which is consistent with the previously published vibrational coherence data for Cr(acac) 3 . 14 The damping time of the 507 cm - 1 is clearly modulated by the ISC event, however th e damping time is not as fast as the 308 cm - 1 also associated with the 4 T 2 . Here, the average damping time is ~350 fs; roughly four times the damping time of the 308 cm - 1 mode. Interestingly, the 190 cm - 1 also shows sub - 1 ps damping times, save for two o utliers. Removing these two points yields an average damping time of 425 fs. Given the uncertainty of this damping time (78 cm - 1 ) and the presence of 4 T 2 vibrations at ~170 and 206 cm - 1 , it is possible that this is a mode on the 4 T 2 surface and not exclu sive to the 2 E. The remaining modes, which have been attributed to vibrations on both the 4 T 2 and 2 E states have a mixture of damping times ranging from 48 fs to 7 ps. It is difficult to say if these dephasing times are modulated by the surface crossin g or not. Most 167 likely these modes are created with the initial wavepacket, but are not intimately involved in the ISC process, which accounts for the large range in dephasing times. Liebel et al. describe the behavior of vibrations around surface cross ings as either tuning modes or coupling modes. Tuning modes are necessary to guide the wavepacket to the surface crossing while coupling modes are the modes spanning this surface crossing. The result is coupling modes are strongly affected by the surface crossing but the tuning modes are not. 44 Under this description, the observed modes at 190, 308, and 507 cm - 1 could be coupling modes responsible for driving the ISC process . The remaining modes seem likely to be tuning modes, whose movement of the methyl groups or expansion of the Cr - O bond lengths serve to move the wavepacket to the surface crossing. 3.4 Cr(acac) 3 Concluding Comments Using sub - 50 fs pump pulses a t different energies throughout the 4 T 2 absorption, many important vibrational modes were identified. All of these involved motions in the primary coordination sphere of Cr(acac) 3 , with a majority relying on motions of the methyl groups in particular. Tw o modes were explicitly assigned to the 4 T 2 state - 308 and 507 cm - 1 - and identified as coupling modes between the states based on their rapid damping times . The mode at 190 cm - 1 , reminiscent of the mode observed in the study by Schrauben et al. , also ex hibits a short damping time indicative of involvement in the ISC process. Modes at 70, 111, 233, 250, 456 , 566 cm - 1 showed similar motions between the 4 T 2 and 2 E states and could be facilitating the rapid ISC between the states owing to their energetic an d vibrational matching. The static nature of the observed vibrations at all pump wavelengths, particularly those outside of the pump pulse 168 bandwidth, indicates that these modes are strongly coupled to the 4 T 2 absorption and the subsequent energy redistrib ution driving the system towards the surface crossing. 3.5 Cr(TMHD) 3 Vibrational Coherence Since the Cr(acac) 3 results point to a heavy reliance on the methyl group motion to facilitate the ultrafast ISC and previous TA studies on Cr(TMHD) 3 show this ISC is drastically slowed when the methyl groups are replaced with tert - butyl groups ( vide supra ), two color pump dependence studies were carried out on this system as well. Following the same two color experimental setup described for Cr(acac) 3 , data sets were collected for Cr(TMHD) 3 in dichloromethane (DCM). Unfortunately the solubility in MeCN was low and sufficient optical densities could not be achieved at the desired pump wavelengths. As a control, solutions of Cr(acac) 3 in DCM were checked at select pump /probe combinations and the results ( Appendix A: Supplemental Data , Figure 3.A4 and Table 3.4 ) agreed with that for solutions in MeCN. Therefore, the results for Cr(TMHD) 3 may be compared directly with those of Cr(acac) 3 in MeCN . A significant difference, however, is the increased stimulated Raman scattering in DCM. Not only are there more Raman peaks observed in the pure solvent spectra, their amplitude, particularly at 292 cm - 1 , is much higher than most of the Raman peaks fr om Cr(TMHD) 3 ( vide infra ) . A typical spectrum from pure DCM is seen in Figure 3 . 27 , where the three peaks agree well with the literature values of 285, 703, and 3053 cm - 1 collected in the solid state. 45 These modes hav e been assigned to the CCl 2 scissor mode, the symmetric CCl 2 stretch, and the asymmetric CH 2 stretch, respectively. 19 There must be substantial coupling between these modes, as the pump characteristics never have enough energy to excite the mode at 3053 cm - 1 and ye t it is an important 169 component of the LPSVD fit of the solvent response for many pump - probe combinations . Figure 3 . 27 Raman Peaks From CH 2 Cl 2 Observed in Two Color Experiments The signal to noise for th ese solvent peaks is especially high compared to MeCN. The peaks agree with the literature values for DCM which are listed at 285, 703, and 3053 cm - 1 . The two color experiments were carried out for largely the same pump/probe combinations as Cr(acac) 3 , except the bluest pump wavelength was shifted to 525 nm due to laser instability. This still affords 2380 cm - 1 of additional vibrational energy across the 600, 560, and 525 nm excitation range. Also, since the 519 nm probe did not prove exceptionally u seful in the Cr(acac) 3 studies, these data were recorded only at 515 and 525 nm probes. Data sets again consisted of at least 14 scans for the solvent and at least 24 scans for Cr(TMHD) 3 (and Cr(acac) 3 ). The absorbance was between 0.4 and 0.5 at the pump wavelength using a 1 mm path length cuvette. Typical results for DCM and Cr(TMHD) 3 scans are shown below in Figure 3 . 28 . A strong rise in the transient absorption signal with time can be seen when p robing at 525 nm for all pump wavelengths. The data collected while probing at 515 nm shows much less of an 170 amplitude change. These results are consistent with the full spectral data for Cr(TMHD)3, presented in Figure 3 . 8 above . The subsequent discussion will focus on the oscillatory features of this data only. Figure 3 . 28 Two Color Data Using DCM as a Solvent The top graph shows a typical data set for Cr(TMHD) 3 in DCM. The oscillations are much more apparent here, but as can be seen in the bottom graph of pure DCM, they are largely due to the solvent. 171 600 nm Excitation Results Similar to Cr(acac) 3 , the 600 nm pump creates a relatively vibratio nally cool 4 T 2 state, while the 516 and 525 nm p robes monitor signals near the maximum of the 2 E excited state spectrum. The data its corresponding LPSVD fit are shown in Figure 3 . 29 . For reference, the pure DCM power spectra are plotted with the data for that probe wavelength. These DCM peaks are easily the largest peaks in the spectrum, particularly the 282 cm - 1 mode, and so the vertical scales have been truncated on the power spectra to make the Cr(TMHD) 3 peaks more visible. There is a distinct possibility the ISRS in DCM is so pronounced because the pump bandwidth is 575 cm - 1 , leading to an immense number of frequency combinations available to drive the 282 cm - 1 mode. Here, there are common modes at ~200 and 485 cm - 1 , bu t the spectra also exhibit peaks at 72, 122, 339, and 559 cm - 1 . The features are broader and less defined that the signals seen in Cr(acac) 3 , perhaps suggestive of the underlying phy sical process, or the result of the strong Raman contribution from the so lvent in the data. The LPSVD program tries to find and optimize subtle oscillations superimposed on a very large signal, which makes the subtle oscillations difficult to distinguish from noise. The pump pulse characteristics (36 fs, 600.2 nm with 20.7 nm FWHM) lead to a excitation limit of 287 cm - 1 in the quantum beat picture and 463 cm - 1 in the impulsive limit. For the quantum beat picture, this precludes the direct formation of wavepackets for the modes at 339, 492, and 559 cm - 1 . T he impulsive limi t relaxes this restriction some, but t he presence of modes above these limits suggests these vibrations are strongly coupled to the Franck Condon transition. 172 Figure 3 . 29 Cr(TMHD) 3 in DCM Following 600 nm E xcitation Results from exciting on the low energy side of the 4 T 2 absorption in Cr(TMHD) 3 while probing near the 2 E absorption maximum. The peaks are broader than those seen for Cr(acac) 3 in MeCN, and the predominant feature is the 282 cm - 1 DCM mode . Th e 516 and 525 nm probes share common modes at 200 and 485 cm - 1 . 560 nm Excitation Results The 560 nm pump is slightly to the blue side of the 4 T 2 absorption maximum in Cr(TMHD) 3 because of the s mall red shift observed for both the ground state absorptio n and stead state emission features compared to Cr( acac ) 3 ( vide supra ) . The vibrational modes observed probing at 51 2 nm and 526 nm are seen in Figure 3 . 30 , below , and have fairly well resolved peaks . Once again, the ISRS in DCM is very strong and 173 dominates the signal. The peaks at 88, 136, 210, and 323 cm - 1 echo those observed following 600 nm excitation. Figure 3 . 30 Cr(TMHD) 3 in DCM Following 560 nm Excitation Results from exciting near the 4 T 2 absorption maximum and probing near the 2 E absorption maximum for Cr(TMHD) 3 . The results from probing at 515 nm show peaks with a lot more definition, while the 525 nm probe results exhibit less definition when compared to Figure 3 . 29 . The spectral characteristics of the pump pulse (557.9 nm center, 18.2 nm FWHM) give an energy window of 585 cm - 1 , while the 32 fs pulse duration sets the impulsive limit at 515 cm - 1 . While the qua ntum beat picture suggests the modes observed at 323 and 383 cm - 1 cannot be excited with the initial wavepacket (292 cm - 1 174 limit) , the impulsive limit disagrees. As the ~330 cm - 1 mode was also observed at 600 nm excitation, it is probable that this mode is coupled with the formation of the initial wavepacket. 525 nm Excitation Results The data collected utilizing 525 nm excitation was subject to more pump scatter than other data sets because of the direct spectral overlap of the pump and probe wavelength s . This baseline offset was removed prior to LPSVD analysis and the results , as shown in Figure 3 . 31 , below , resemble other data sets without this issue. The vibrational modes observed with a 524 nm probe very strongly resemble the 524 nm probe data following 560 nm excitation. The vibrations present with the 514 nm probe, however, suggest the presence of higher frequency modes. Here the pulse duration is 40 fs, reducing the window of impulsively ex cited frequencies to modes at 417 cm - 1 or less. The quantum beat picture limits the prepared wavepacket to frequencies less than 221 cm - 1 (525 nm center wavelength, 12.2 nm FWHM). For either case, the frequencies at 513 and 1141 cm - 1 are outside of this window. Obviously the mode at 1141 cm - 1 , which is beyond even the maximum limit given by the pulse duration (834 cm - 1 ), is an artifact from the fit. The mode at 513 cm - 1 , however, supports frequencies observed at other pump wavelengths where the pulse re strictions are not so severe. It is likely that this mode is real and strongly coupled to the formation of the wavepacket in the Franck Condon region. 175 Figure 3 . 31 Cr(TMHD) 3 in D CM Following 525 nm Exci tation Results from p umping on the higher energy side of the 4 T 2 absorption in Cr(TMHD) 3 while monitoring the excited state absorption near the 2 E maximum. The data show low frequency modes similar to those observed following 560 nm excitation . The decre ased pulse bandwidth reduces the DCM contributions and leads to better resolution of the other frequencies present. Discussion The results from the data sets at the pump/probe combinations listed above have been compiled in Table 3 . 3 . The left column gives the pump/probe information, where the data is ordered from high energy pump/probe to low energy pump/probe. The oscillations for each combination are shown in rows, where like frequ encies are in the same column; t he dampin g times for these vibrations are listed in parentheses next to 176 the vibration. The oscillations at ~158, and 260 cm - 1 will not be addressed in this analysis because of their inconsistent presence at pump/probe combinations . This leaves common modes at ~ 67 , 1 19, 207, 334, 399, and 495 cm - 1 for further analysis . Table 3 . 3 : Summary of Observed Oscillations for Cr(TMHD) 3 in DCM Utilizing a Two Color Pump - Probe Setup The ground state resonance Raman spectru m for this compound is known and contains peaks at very similar frequencies to the Cr(acac) 3 structure. 46 This is not surprising given the structure s of the compound s and the frequencies discussed for Cr(acac) 3 . Of the Cr(acac) 3 vibrations discussed above, the ~70 and 111 cm - 1 modes - involv ing only the rotation of the methyl groups about the C - C bond - would be most significantly affected by the change from a methyl to tert - butyl group. Unfortunately, the Cr(TMHD) 3 Ra man spectrum stops at 150 cm - 1 and these changes, if present, are not visible. As with Cr(acac) 3 , DFT calculations were performed to gain more insight into the excited state vibrations for this compound; full computational details are given in Chapter 2 . The ground state was successfully optimized utilizing Gaussian '03 software 47 by freezing the dihedral ang les of the methyl groups within the tert - butyl groups on the ligand backbone. This optimized structure was ported into Gaussian 177 '09 48 for re - optimization of the ground state before performing the TD - DFT and excited state frequency calculations. However , the ground state structure has not optimized after over a month of computational time. This is most likely due to the unrestricted methyl groups, where their many degrees of freedom generate a very shallow potential minimum which prevents the program from finding a global minimum. The results from the Gaus sian '03 ground state frequency calculation (UB3LYP, 6 - 311g(d,p), pcm dichloromethane continuum model) are given in Appendix C : Gaussian Calculation Results . These calculations were done for IR intensity and not Raman intensity, but in C 1 symmetry, all of the vibrations are Raman active. This allows the fr equencies and their motions to be more generally applied to these results. Comparing these computational results to the experimental Raman spectrum gives a close match for fre quencies up to 450 cm - 1 . 46 Between 450 and 775 cm - 1 , the agreement between the calculation and the experimental spectrum is not very good; there are large gaps where no frequencies are listed and yet an experimental pea k is observed . However, past 775 cm - 1 the agreement becomes quite good again. These computational results serve as a good starting point, but should be reinvestigated to obtain better agreement with the experimental Raman spectrum. Applying these result s to the common frequencies in Table 3 . 3 , it becomes clear that all of these vibrations have a close match in the ground state frequencies except for the 67 cm - 1 mode, which falls in a large gap in the frequencies. Excited state calculations should be performed explicitly, but tentatively this 67 cm - 1 mode is assigned to a vibration in the 4 T 2 state. The remaining frequencies, despite their close match to ground state modes, are assigned to vibrational coherence i n an excited state. The 178 extinction coefficient for the ground state absorption maximum in Cr(TMHD) 3 is only modestly higher than that for Cr(acac) 3 , precluding the observation of vibrational coherence from the ground state surface. Following the same arg uments laid out for Cr(acac) 3 , the narrow emission spectrum indicates that the 2 E state is nested with the ground state potential energy surface and their frequencies are most likely similar. Upon inspection of the vibrational modes of the ground state, i t becomes clear that the tert - butyl groups experience the same types of motions as the methyl groups, albeit to a lesser extent. This is entirely consistent with the tert - butyl groups being bulkier overall. And while the individual methyl groups still ro tate a fair amount, this motion is offset by their attachment to the tertiary carbon before linking into the ligand backbone. It also appears that there may be less deformation of the primary coordination sphere, though the magnitude of the Cr - O bond le ng th change is difficult to gaug e from the vibrational motions alone. The ground state vibration modes at 118, 195, 332, 397, and 50 8 cm - 1 can be seen explicitly in Figure 3 . 32 , below . The vibration at 11 8 cm - 1 res embles the out of phase scissor - type mode previously seen in Cr(acac) 3 , where the downward bend on one ligand's tert - butyl groups coincides with the neighboring tert - butyl groups flexing backwards. While this motion translated into an outwa rd flexing of the ligand backbone for acac, particul arly the oxygen atoms , this motion is greatly diminished for TMHD. The 195 cm - 1 mode rotates the entire tert - butyl group while also leveraging the ligand backbone up and down out of the plane. This mode causes some of the largest Cr - O bond length changes for all of the vibrations discussed here. 179 Figure 3 . 32 Ground State Vibrational Modes in Cr(TMHD) 3 Cr(TMHD) 3 ground state vibrational modes of the fiv e commonly observed vibrations in the two color coherence data. The amplitudes of the tert - butyl group motions are on par with the methyl group motions, however, the motions do not translate as efficiently into ligand backbone deformations as they did for acac. 180 The mode at 332 cm - 1 is a symmetric stretch across the ligand backbone, similar to the motion observed at 461 cm - 1 in Cr(acac) 3 . As with the other modes for Cr(TMHD) 3 , however, the magnitude of the ligand displacement is reduced compared to Cr(a cac) 3 . The vibrational mode at 397 cm - 1 consists of a pucker, where the methyl groups in plane with the ligand backbone flex up, the central carbon on the ring is forced down, and the oxygens swing up. The final vibration at 508 cm - 1 is another symmetric stretch across the ligand backbone, where the central carbon and proton are nearly stationary while the Cr - O bonds undergo a larger bond length change than in the 332 cm - 1 mode. Assuming that the Cr - O bond lengths will try to lengthen to accommodate th e population of an anti - bonding orbital upon formation of the 4 T 2 , it is tempting to think that the modes at 195 and 50 8 cm - 1 will be the most important of those listed above as they appear to elicit the largest Cr - O bond length changes . Their presence at all of the pump/probe combinations listed in Table 3 . 3 bolsters this argument. The damping times for these modes are also indicative of their role in the ISC process. The mode at 399 cm - 1 , corresponding to the puckering of the acac backbone, exhibits damping times over 1 ps except for one case following 525 nm excitation. It is likely that this mode, without significant Cr - O bond length changes or tert - butyl group displacement, is unaffected by the surface crossing and relaxes with the traditional dephasing time. The mode at 332 cm - 1 exhibits a mix of damping times, indicating that it is modulated by, but not directly driving, the ISC process. The remaining modes at 67, 119, 207, and 495 cm - 1 exhibit damping times less than 60 0 fs for the majority of the LPSVD results. This strong modulation implies that these modes are driving the ISC event, and similar to 181 Cr(acac) 3 , these modes involve large movements of the tert - butyl groups which change the Cr - O bond distance or the flexin g of the ligand backbone directly. As the motions are somewhat similar to those observed in Cr(acac) 3 , but the timescale for ISC is so much slower, this implies that the magnitude of the motions is the driving factor. In this case, the tert - butyl groups mitigate the amount of Cr - O bond displacement. This strengthens the argument laid out by Ando et al. that Cr - O bond length changes drive the system towards the ISC event. 3.6 Cr(TMHD) 3 Concluding Comments Despite increasing the excess vibrational energy by over 2300 cm - 1 , there does not seem to be a pump dependence to the oscillations retrieved from the data for Cr(TMHD) 3 . Of the vibrational modes that were observed, only a low frequency mode at ~ 67 cm - 1 was readily assigned to 4 T 2 vibrational motion. How ever, excited state frequency calculations were not available for this compound, limiting the analysis of these vibrations. By inspecting the ground state frequencies, it can be seen that the deformation of the primary coordination sphere appeared to be l ess, and the Cr - O bond lengths were not as affected in the active vibrations. This is consistent with the previous conclusions for Cr(acac) 3 that this deformation is vital to the ultrafast ISC and is greatly facilitated by large amplitude motions of the m ethyl groups and Cr - O bonds . 3.7 Future Work Any subsequent researchers should strongly investigate alternative procedures to optimize the ground and excited states of Cr(TMHD) 3 using DFT methods. This would allow for a direct comparison to the frequencies established for Cr(acac) 3 . Another possibility would be to optimize the structures using complete active space self - 1 82 consistent field theory ( CAS SCF ) in collaboration with Dr. Ben Levine (Michigan State University) and to model the excited state wavepacke t motion using these methods. The wavepacket motion/path modeling performed by Ando et al. was done using CAS SCF methods. Under the assumption that DFT methods will work to optimize the pertinent structures for Cr(TMHD) 3 , the frequency calculations shou ld be re - run to calculate the Raman intensity, not the IR intensity. These results could then be compared to the ground state Raman spectrum, which would be a better indicator of their accuracy. Experimentally, it could be enlightening to collect full s pectra data utilizing a white light continuum probe to monitor the coherence in these systems. Provided the IRF and the resolution on the diode array is good enough, the phases between probe wavelengths may be investigated and the "classic turning points" of the potential(s) identified. 21,22 This may reveal better wavelengths for probing the 4 T 2 oscillations, particularly in the case of Cr(TMHD) 3 where a bit of a spectral signature is detected blue of the 2 E excited state absorption. The data collected on Cr(TMHD) 3 may become clearer if the Raman modes from DCM were subtracted from the data prior to performing the LPSVD analysis. This would remove som e of the largest amplitude features that are not relevant to the molecular vibrations of interest, leaving room for a finer analysis of the smaller amplitude frequencies present. This may reveal the presence of the 164 and 256 cm - 1 modes at more pump/prob e combinations so that they may be added to the analysis. It may also prove enlightening to zero pad the data prior to LPSVD analysis to increase the resolution in the frequency - domain. Chergui and coworkers have related 183 slight decreases in the oscillat ory frequency with increasing excitation energy to the (an)harmonicity of the potential energy surface they are probing. 21 With the current r esolution of this experiment at 15 cm - 1 , this kind of information is not available. 184 APPENDI CES 185 Appendix A: Supplemental Data Cr(acac) 3 Two Color Data in MeCN Figure 3 . A 1 Cr(acac) 3 in MeCN With 505 nm Excita tion These data exhibit common modes at ~190, 250, and 460 cm - 1 , consistent with the other data set from 505 nm excitation. These modes correspond to both the 2 E and 4 T 2 states. The pulse duration here was 45 fs, and the spectral bandwidth 10.8 nm. 186 Figure 3 . A 2 Cr(acac) 3 in MeCN With 560 nm Excitation The 517 nm probe exhibits a very broad spectrum, indicating the damping times are heavily modulated (truncated) b y the electronic state change. The pulse duration was 32 f s, and the spectrum of the pulse was 17.7 nm FWHM, centered at 558.5 nm. 187 Figure 3 . A 3 Cr(acac) 3 in MeCN with 600 nm Excitation The data collected when probing at 525 nm show clearer oscillations than have been observed for most pump probe combinations. The common modes include the sharp feature at 188 cm - 1 , and a broader peak at 512 cm - 1 , corresponding to the 2 E and 4 T 2 , respectively. The pulse duration was 36 fs, and the spectrum of the pulse was 23.6 nm at FWHM, centere d at 600.3 nm. 188 Cr(acac) 3 Two Color Data in DCM Table 3.4: Summary of Observed Oscillations for Cr(acac)3 in DCM Utilizing Two Color Experiments The strong Raman active modes in DCM result in peaks of the same magnitude as molecular vibrations of interest for the Chromium compounds. Given that these "artifacts" are so strong, they may be able to completely obscure other vibrational modes at much lower intensities. Despite these issues, the common modes found for Cr(acac)3 in DCM are a pretty clo se match to those found in MeCN. The one exception is the presence of a mode around 356 cm - 1, but this may have been obscured by the 380 cm - 1 mode of MeCN previously. This strong agreement allows for direct comparisons between the Cr(TMHD) 3 data in DCM a nd the Cr(acac) 3 data collected in MeCN. The data summarized in Table 3.4 are presented below. 189 Figure 3 . A4 Cr(acac) 3 in DCM Following Excitation at 525, 560, and 600 nm A summary of these results is presented in Table 3.4, above. At all excitation wavelengths, the peaks are much sharper compared to the data collected in MeCN. The stronger DCM modes at 282 and 707 cm - 1 may be obscuring other oscillations in the data, but overall the agreement to MeCN results is quite good. 190 Figure 3.A4 , ( cont' d ) 191 Figure 3.A4 ( Cont' d ) 192 Cr( TMHD ) 3 Two Color Data in DCM Figure 3 . A5 Cr( TMHD ) 3 in DCM Following 600 nm Excitation The data (blue dots) and the LPSVD fit (red line) are shown in the plots on the left, while the power spectra of the fits are s hown on the right. The DCM power spectra are shown explicitly to emphasize the strength of these modes. Except for the mode at 326 cm - 1 , the two data sets show a strong agreement. The pulse duration was 35 fs and the spectrum was centered at 598.1 nm (2 1 nm FWHM). 193 Figure 3 . A6 Cr(TMHD) 3 in DCM Following 56 0 nm Excitation The data (blue dots) and the LPSVD fit (red line) are shown in the plots on the left, while the power spectra of the fits are shown on the right. Here there is strong mode agre ement at 110 and 196 cm - 1 modes, while other frequencies at 141, 265, 334, and 396 cm - 1 are present. The pulse spectrum was centered at 560.4 nm (18.1 nm FWHM) and was measured as 37 fs by FROG. 194 Figure 3 . A7 Cr(TMHD) 3 in DCM Following 525 nm Excitat ion The data (blue dots) and the LPSVD fit (red line) are shown in the plots on the left, while the power spectra of the fits are shown on the right. The modes at 1111 and 914 cm - 1 are beyond the pump pulse capabilities and are treated as artifacts of the fits. The spectra have a common mode at ~145 cm - 1 , while also exhibiting overlapping peaks at ~415 cm - 1 . The pulse spectrum was centered at 525.7 nm (12.1 nm FWHM), and measured 36 fs by FROG. 195 Appendix B : Ground State Recovery in Cr(acac) 3 and Cr( TMHD) 3 Previous data on Cr(acac) 3 and Cr(TMHD) 3 were not able to fully quantify the ground state recovery timescale s in these compounds because of instrument limitations. The experimental setup for these data sets used a delay line capable of delays out t o ~1 ns. The timescale for ground state recovery for both of these compounds was guesstimated to be about 1 ns, but this could not be proven. With the installation of a 13 ns delay line on Wile E (see Chapter 2), these ground state recovery timescales co uld be characterized. Figure 3 . B1 Ground State Recovery Dynamics for Cr(acac) 3 in MeCN and DCM The ground state recovery dynamics for Cr(acac) 3 in DCM (blue) and MeCN (green) are shown here along with their fits. The two time constants are statistica lly different, which indicates a solvent dependence on ground state recovery despite the ligand field nature of the excited state. These data were collected by pumping at 560 nm and probing at 520 nm. In Figure 3.B1 above , t he ground state recovery (GSR) dynamics of Cr(acac) 3 in DCM and MeCN are overlaid after normalizing to the excited state maximum. The timescale for GSR in DCM averaged 1.15 ns for two data sets probing at five different 196 wavelengths. The timescale for GSR in MeCN, however, averaged 950 ps over two data sets probing at four different probe wavelengths. The ligand field nature of the excited state should keep the excited electron well shielded from the solvent, so it is not intuitive that there should be a solvent dependence. Yet these time constants are statistically different and indicate this solvent dependence requires further exploration. The GSR dynamics for Cr(TMHD) 3 in DCM are shown in Figure 3.B2 for a 560 nm pump and 530 nm probe . The average l ifetime for this data set is 870 ps after probing at four different wavelengths. The shorter timescale for GSR compared to Cr(acac) 3 in DCM is entirely consistent with the red - shifted emission maximum discussed above. Since the potentials are nested, a d rop in their energy difference shou ld lead to a higher rate of non radiative decay and thus a shorter lifetime. 49 Figure 3 . B2 Ground State Recovery Dynamics for Cr(TMHD) 3 in DCM The data shown here were collected using a 560 nm pump and a 530 nm probe. A monoexpone ntial fit to the data yields a lifetime of ~870 ps, averaged over the data set. 197 Appendix C : Gaussian Calculation Results Cr(acac) 3 Ground State Optimization # opt ub3lyp/6 - 311g(d,p) scrf=(cpcm,solvent=acetonitrile) scf=(maxcycle=1000) 0 4 Cr 0.00034300 - 0.00139100 0.00022800 C - 2.48659800 - 1.20198400 1.01090300 C - 2.51317700 - 2.17477400 0.00101500 C 2.75419400 - 0.19455000 - 1.01258100 C 2.28874100 - 1.54527800 1.01296500 C 3.14212400 - 1.08304200 0.00061100 C - 1.20774800 2.48041500 - 1.01332400 C 0.19776000 2.75304600 1.01018200 C - 0.62920600 3.26103800 - 0.00 206000 C - 1.54613100 - 2.29000200 - 1.00825900 O 1.58496700 0.30407700 - 1.13972600 O 1.05992000 - 1.21967700 1.13903100 O - 1.58553000 - 0.30555600 1.13924700 O - 1.05719700 1.21810800 - 1.13935100 O 0.52768300 1.52556900 1.13780800 O - 0.52762200 - 1.52957400 - 1.13565800 C 2.81026700 - 2.50026700 2.05551200 H 3.86069900 - 2.74664300 1.90707600 H 2.67950200 - 2.05719300 3.04665800 H 2.21661600 - 3.41828200 2.03175300 C 3.75319800 0.23686200 - 2.05519400 H 4.73568600 - 0.20684000 - 1.900 20700 H 3.38282500 - 0.04275500 - 3.04541700 H 3.84170300 1.32662400 - 2.03971800 C - 1.67130600 - 3.37597400 - 2.04557900 H - 2.55331700 - 3.99662800 - 1.89405300 H - 1.71516600 - 2.92147500 - 3.03920500 H - 0.77728300 - 4.00506600 - 2.01771000 C - 3.57937000 - 1.16755500 2.04800800 H - 4.32147700 - 1.95035500 1.89752900 H - 3.13603300 - 1.27560400 3.04176300 H - 4.07224800 - 0.19184200 2.01893000 C 0.76663900 3.68269500 2.05100400 H 0.46358000 4.71728400 1.89623700 H 0.44094600 3.35524000 3.0422 4300 H 1.85809800 3.61882300 2.03260300 C - 2.08171300 3.13011100 - 2.05495400 H - 2.17858700 4.20473300 - 1.90672400 H - 1.66245300 2.93839500 - 3.04654600 198 H - 3.07371300 2.67071400 - 2.02991200 H - 0.83430200 4.32199000 - 0.00239700 H 4.16391200 - 1.43468700 0.00077300 H - 3.33102300 - 2.88107500 0.00055100 Optimization information found in file: " CrAcac3_D3_Opt_G09_UB3LYP_6311gdp_cpcmMeCN6 .log" 199 Cr(acac) 3 Ground State Frequencies Stoichiometry C15H21CrO6(4) Framework group C1[X(C15H21CrO6)] Deg. of freedom 123 Full point group C1 NOp 1 Largest Abelian subgr oup C1 NOp 1 Largest concise Abelian subgroup C1 NOp 1 Standard orientation: --------------------------------------------------------------------- Center Atomic Atomic Coordinates (Angstroms) Number Number Type X Y Z --------------------------------------------------------------------- 1 24 0 0.000343 - 0.001391 0.000228 2 6 0 - 2.486598 - 1.201984 1.010903 3 6 0 - 2.513177 - 2.174774 0.001015 4 6 0 2.754194 - 0.194550 - 1.012581 5 6 0 2.288741 - 1.54527 8 1.012965 6 6 0 3.142124 - 1.083042 0.000611 7 6 0 - 1.207748 2.480415 - 1.013324 8 6 0 0.197760 2.753046 1.010182 9 6 0 - 0.629206 3.261038 - 0.002060 10 6 0 - 1.546131 - 2.290002 - 1.008259 11 8 0 1.584967 0.304077 - 1.139726 12 8 0 1.059920 - 1.219677 1.139031 13 8 0 - 1.585530 - 0.305556 1.139247 14 8 0 - 1.057197 1.218108 - 1.139351 15 8 0 0.527683 1.525569 1.137808 16 8 0 - 0.5276 22 - 1.529574 - 1.135658 17 6 0 2.810267 - 2.500267 2.055512 18 1 0 3.860699 - 2.746643 1.907076 19 1 0 2.679502 - 2.057193 3.046658 20 1 0 2.216616 - 3.418282 2.031753 21 6 0 3.753198 0.236862 - 2.055194 22 1 0 4.735686 - 0.206840 - 1.900207 23 1 0 3.382825 - 0.042755 - 3.045417 24 1 0 3.841703 1.326624 - 2.039718 25 6 0 - 1.671306 - 3.375974 - 2.045579 26 1 0 - 2.553317 - 3.996628 - 1.894053 27 1 0 - 1.715166 - 2.921475 - 3.039205 28 1 0 - 0.777283 - 4.005066 - 2.017710 29 6 0 - 3.579370 - 1.167555 2.048008 30 1 0 - 4.321477 - 1.950355 1.897529 31 1 0 - 3.136033 - 1.275604 3.041763 32 1 0 - 4.072248 - 0.191842 2.018930 33 6 0 0.766639 3.682695 2.051004 200 34 1 0 0.463580 4.717284 1.896237 35 1 0 0.440946 3.355240 3.042243 36 1 0 1.858098 3.618823 2.032603 37 6 0 - 2.081713 3.130111 - 2.054954 38 1 0 - 2.178587 4.204733 - 1.906724 39 1 0 - 1.662453 2.938395 - 3.046546 40 1 0 - 3.073713 2.670714 - 2.029912 41 1 0 - 0.834302 4.321990 - 0.002397 42 1 0 4.163912 - 1.434687 0.000773 43 1 0 - 3.331023 - 2.881075 0.000551 --------------------------------------------------------------------- D2PCM: C - PCM CHGder 2nd derivativ es, FixD1E=F FixD2E=F DoIter=F DoCFld=F I1PDM=0 Calling FoFJK, ICntrl= 100127 FMM=F ISym2X=0 I1Cent= 0 IOpClX= 1 NMat=1 NMatS=1 NMatT=0. Full mass - weighted force constant matrix: Low frequencies --- - 3.8391 - 0.0027 0.0031 0.0037 4.4112 9.5376 Low frequencies --- 26.3456 28.8051 40.3304 Diagonal vibrational polarizability: 217.8675780 234.2381222 209.7730361 Harmonic frequencies (cm** - 1), IR intensities (KM/Mole), Raman scattering activities (A**4/AMU), depolariz ation ratios for plane and unpolarized incident light, reduced masses (AMU), force constants (mDyne/A), and normal coordinates: Frequency # Frequency (cm - 1 ) Reduced Masses Force Constants IR Intensity 1 26.2166 3.9858 0.0016 3.2651 2 28.7735 4.1205 0.0 02 3.5714 3 40.3279 4.2434 0.0041 7.9486 4 48.1097 2.5121 0.0034 0.686 5 51.4403 3.0963 0.0048 0.2003 6 52.0062 3.2187 0.0051 0.1854 7 68.0942 1.2427 0.0034 3.4372 8 82.9715 1.1281 0.0046 3.0263 9 83.5244 1.1379 0.0047 3.1226 10 86.4019 1.079 0.004 7 0.4086 11 97.0658 1.0474 0.0058 0.1293 12 99.6314 1.0642 0.0062 0.0177 13 161.3313 2.8076 0.0431 0.0395 14 163.2805 2.6929 0.0423 0.0835 15 164.5812 2.6541 0.0424 0.1353 16 173.5317 6.2745 0.1113 1.1729 17 175.0744 6.5556 0.1184 1.1163 18 185.029 7.202 0.1453 0.0002 201 19 188.0776 5.6957 0.1187 0.8625 20 223.9761 6.158 0.182 0.2097 21 224.1975 5.902 0.1748 0.1204 22 235.5933 7.1114 0.2326 0.0559 23 241.6162 5.701 0.1961 3.5632 24 242.2123 5.6188 0.1942 3.7896 25 253.0701 3.3816 0.1276 1.0896 26 254.305 3.4075 0.1298 1.2306 27 257.0314 3.1887 0.1241 0.0274 28 349.2832 7.4674 0.5368 2.4538 29 354.041 10.2077 0.7539 65.3938 30 354.5317 10.3433 0.766 65.7619 31 422.213 4.6867 0.4922 6.9978 32 422.4446 4.6587 0.4898 10.8648 33 423.1174 4.622 5 0.4876 22.5902 34 449.3861 6.292 0.7486 183.5549 35 449.6824 6.3023 0.7509 181.7024 36 452.7984 5.7575 0.6955 0.5265 37 569.8092 2.8991 0.5546 0.2625 38 570.2753 2.8987 0.5554 0.2501 39 571.7161 2.9212 0.5626 0.0112 40 589.5869 4.6479 0.9519 63.14 08 41 590.3822 4.6536 0.9557 63.2337 42 605.68 5.0519 1.0919 95.1482 43 675.0585 4.1237 1.1072 59.9826 44 675.2989 4.1233 1.1079 59.0579 45 680.3143 4.1274 1.1255 0.1896 46 683.0274 2.9449 0.8095 14.8856 47 683.2657 2.9289 0.8056 13.3149 48 683.918 5 2.9324 0.8081 14.0529 49 800.055 1.1368 0.4287 30.3761 50 800.2164 1.1371 0.429 26.8039 51 803.0105 1.1356 0.4315 28.2682 52 947.3801 4.8275 2.5528 72.3929 53 948.3212 4.8154 2.5515 12.7933 54 948.4176 4.8179 2.5533 12.5415 55 962.6191 2.9726 1.62 29 16.188 56 962.6887 2.9758 1.6249 15.8991 57 963.2125 2.888 1.5787 0.3454 Full frequency results available in file: " CrAcac3_D3_freq_G09_UB3LYP_6311gdp_cpcmMeCN .log" 202 Cr(acac) 3 Time Dependent Single Point Calculation # td=(nstates=10) ub3lyp/6 - 311g( d,p) scrf=(cpcm,solvent=acetonitrile) scf=(tight,maxcycle=1000) 0 4 Cr - 0.00030800 - 0.00092400 - 0.00048000 C 2.51039100 - 1.15225700 - 1.01089300 C 2.55555700 - 2.12397200 - 0.00089000 C - 2.75017800 - 0.25067700 1.01120400 C - 2.25505300 - 1.59415900 - 1.01216100 C - 3.11840600 - 1.14902700 - 0.00058000 C 1.15508400 2.50520800 1.01338700 C - 0.25387800 2.74788400 - 1.01179700 C 0.56105300 3.27326900 0.00148700 C 1.59257800 - 2.25563600 1.01043400 O - 1.59205700 0.27321600 1.13804700 O - 1.03367300 - 1.24178700 - 1. 13861400 O 1.59244200 - 0.27296500 - 1.13882000 O 1.03070900 1.24006900 1.13942600 O - 0.55733200 1.51354900 - 1.13973900 O 0.55942800 - 1.51518500 1.13762100 C - 2.75559300 - 2.56196600 - 2.05314100 H - 3.80027300 - 2.83128500 - 1.90369700 H - 2.63502100 - 2.11777700 - 3.04507400 H - 2.14173900 - 3.46658200 - 2.02787000 C - 3.75886500 0.16076100 2.05253300 H - 4.73145500 - 0.30442200 1.89779900 H - 3.38310200 - 0.10881600 3.04349900 H - 3.87109500 1.24831000 2.03492000 C 1.74163700 - 3.33634200 2.0 5011000 H 2.63570200 - 3.93932200 1.89776800 H 1.77902000 - 2.87839200 3.04241500 H 0.86040800 - 3.98338400 2.02621000 C 3.60152600 - 1.09663800 - 2.04868600 H 4.35932300 - 1.86460600 - 1.89947500 H 3.15968900 - 1.21297900 - 3.04217600 H 4.07505700 - 0.11139200 - 2.01954500 C - 0.84060600 3.66520400 - 2.05352700 H - 0.56068100 4.70621400 - 1.89785100 H - 0.50510600 3.34549600 - 3.04405700 H - 1.93039300 3.57719000 - 2.03797700 C 2.01458100 3.17333100 2.05543800 H 2.08786400 4.24998200 1.90 802800 H 1.59990200 2.97165200 3.04695800 H 3.01654100 2.73607800 2.02972400 203 H 0.74350100 4.33827900 0.00205300 H - 4.13239200 - 1.52242600 - 0.00075400 H 3.38655200 - 2.81471000 - 0.00025000 204 Excitation E n ergies and Oscillator S trengths Excited State 1: 4.017 - A 2.5101 eV 493.94 nm f=0.0003 =3.785 82A - > 97A - 0.10661 82A - > 98A 0.12034 83A - > 97A - 0.12427 83A - > 98A - 0.10244 85A - > 97A - 0.18763 86A - > 98A 0.18125 87A - > 97A 0.42861 88A - > 98A 0.41403 92A - > 97A 0.48325 92A - > 98A 0.13908 93A - > 97A - 0.146 11 93A - > 98A 0.46682 This state for optimization and/or second - order correction. Total Energy, E(TD - HF/TD - KS) = - 2080.48803091 Copying the excited state density for this state as the 1 - particle RhoCI density. Excited State 2: 4.0 15 - A 2.5813 eV 480.31 nm f=0.0003 =3.781 82A - > 98A - 0.12051 83A - > 97A - 0.11879 84A - > 97A 0.11665 85A - > 98A - 0.12355 86A - > 97A 0.12545 87A - > 97A 0.11609 87A - > 98A 0.32020 88A - > 97A 0.32094 88A - > 98A - 0.12297 90A - > 97A - 0.54057 92A - > 97A 0.28338 92A - > 98A 0.29719 93A - > 97A 0.30226 93A - > 98A - 0.28981 Excited State 3: 4.015 - A 2.5826 eV 480.07 nm f=0.0003 =3.781 82A - > 97A 0.11805 83A - > 98A - 0.12174 84A - > 98A - 0.11430 85A - > 97A 0.12087 86A - > 98A 0.12766 87A - > 97A - 0.31374 87A - > 98A 0.11819 88A - > 97A 0.12136 88A - > 98A 0.33060 90A - > 98A 0.53738 205 92A - > 97A - 0.29109 92A - > 98A 0.28822 93A - > 97A 0.28558 93A - > 98A 0.30993 Excited State 4: 4.755 - A 3.0057 eV 412.49 nm f=0.0008 =5.403 91A - > 94A - 0.35382 92A - > 95A 0.34933 92A - > 96A 0.14591 93A - > 95A - 0.14191 93A - > 96A 0.34296 88B - > 92B - 0.32515 89B - > 93B - 0.32094 90B - > 91B 0.59269 Excited State 5: 4.776 - A 3.0243 eV 409.96 nm f=0.0003 =5.452 91A - > 95A 0.31915 91A - > 96A 0.14710 92A - > 94A - 0.41585 92A - > 95A 0.17266 92A - > 96A - 0.20962 93A - > 95A - 0.21009 93A - > 96A - 0.17876 88B - > 91B 0.45354 88B - > 92B - 0.21096 88B - > 93B 0.11572 89B - > 91B 0.23667 89B - > 92B 0.11580 89 B - > 93B 0.21098 90B - > 92B - 0.35724 90B - > 93B - 0.13355 Excited State 6: 4.776 - A 3.0246 eV 409.92 nm f=0.0003 =5.452 91A - > 95A - 0.14831 91A - > 96A 0.31849 92A - > 95A - 0.20 430 92A - > 96A - 0.17698 93A - > 94A - 0.41175 93A - > 95A - 0.18375 93A - > 96A 0.21529 88B - > 91B - 0.23702 88B - > 92B 0.11197 88B - > 93B 0.20996 89B - > 91B 0.45342 89B - > 92B 0.21100 89B - > 93B - 0.12155 206 90B - > 92B 0.13167 90B - > 93B - 0.35762 Excited State 7: 4.035 - A 3.1045 eV 399.37 nm f=0.0000 =3.821 82A - > 97A - 0.10100 83A - > 98A - 0.1 0052 85A - > 98A - 0.16317 86A - > 97A - 0.16415 87A - > 98A 0.37111 88A - > 97A - 0.37409 92A - > 97A - 0.15861 92A - > 98A 0.52252 93A - > 97A - 0.52728 93A - > 98A - 0.15657 Excited State 8: 4.019 - A 3.2177 eV 385.32 nm f=0.0012 =3.787 78A - > 97A - 0.12726 84A - > 97A 0.15064 87A - > 98A - 0.20992 88A - > 97A - 0.20215 90A - > 97A - 0.78989 92A - > 97A - 0.18306 92A - > 98A - 0.26080 93A - > 97A - 0.24807 93A - > 98A 0.18744 Excited State 9: 4.019 - A 3.2206 eV 384.98 nm f=0.0011 =3.787 78A - > 98A 0.12700 84A - > 98A - 0.15218 87A - > 97A 0.20333 88A - > 98A - 0.20384 90A - > 98A 0.79209 92A - > 97A 0.25339 92A - > 98A - 0.18727 93A - > 97A - 0.18227 93A - > 98A - 0.25326 Excited State 10: 4.278 - A 3.7921 eV 326. 95 nm f=0.0329 =4.326 91A - > 94A 0.18210 92A - > 95A - 0.27472 92A - > 96A - 0.11494 93A - > 95A 0.11407 93A - > 96A - 0.27568 87B - > 91B 0.12887 88B - > 92B 0.24758 89B - > 93B 0.24781 207 90B - > 91B 0.78576 90B - > 96B 0.15191 SavETr: write IOETrn= 770 NScale= 10 NData= 16 NLR=1 NState= 10 LETran= 190. ********************************************************************** Time - Depe ndent Single Point Information found in file: " CrAcac3_D3_TDsp3_G09_UB3LYP_6311gdp_cpcmMeCN .log" 208 Cr(acac) 3 2 E State O ptimization # opt=modredundant ub3lyp/6 - 311g(d,p) scrf=(cpcm,solvent=acetonitrile) scf=(fermi,maxcycle=1000) 0 2 Cr 0. 00000000 0.00000000 0.00000000 C 0.73268400 2.66145500 0.99687500 C 0.00000000 3.32125300 0.00000000 C - 1.93854500 - 1.96525000 - 0.99687500 C - 2.67122900 - 0.696204 00 0.99687500 C - 2.87629000 - 1.66062700 0.00000000 C 2.67122900 - 0.69620400 - 0.99687500 C 1.93854500 - 1.96525000 0.99687500 C 2.87629000 - 1.66062700 0.00000000 C - 0.73268400 2.66145500 - 0.99687500 O - 0.80079800 - 1.40278100 - 1.12639000 O - 1.61524300 0.00787900 1.12639000 O 0.81444500 1.39490200 1.12639000 O 1.6 1524300 0.00787900 - 1.12639000 O 0.80079800 - 1.40278100 1.12639000 O - 0.81444500 1.39490200 - 1.12639000 C - 3.74835600 - 0.43525700 2.01885600 H - 4.64227700 - 1.0334960 0 1.84341500 H - 3.35903400 - 0.65235600 3.01816400 H - 4.01198800 0.62604200 2.00154700 C - 2.25112200 - 3.02854300 - 2.01885600 H - 3.21617300 - 3.50358200 - 1.84341500 H - 2.24447300 - 2.58283100 - 3.01816400 H - 1.46382600 - 3.78750400 - 2.00154700 C - 1.49723400 3.46380100 - 2.01885600 H - 1.42610500 4.53707800 - 1.84341500 H - 1.11 456000 3.23518600 - 3.01816400 H - 2.54816200 3.16146300 - 2.00154700 C 1.49723400 3.46380100 2.01885600 H 1.42610500 4.53707800 1.84341500 H 1.11456000 3.23518600 3.01816400 H 2.54816200 3.16146300 2.00154700 C 2.25112200 - 3.02854300 2.01885600 H 3.21617300 - 3.50358200 1.84341500 H 2.24447300 - 2.58283100 3.01816400 H 1.46382600 - 3.78750400 2.00154700 C 3.74835600 - 0.43525700 - 2.01885600 H 4.64227700 - 1.03349600 - 1.84341500 H 3.35903400 - 0.65235600 - 3.01816400 H 4.011 98800 0.62604200 - 2.00154700 209 H 3.81400400 - 2.20201600 0.00000000 H - 3.81400400 - 2.20201600 0.00000000 H 0.00000000 4.40403200 0.00000000 D 3 2 29 30 F D 3 2 29 31 F D 3 2 29 32 F D 3 10 25 26 F D 3 10 25 27 F D 3 10 25 28 F D 6 4 21 22 F D 6 4 21 23 F D 6 4 21 24 F D 6 5 17 18 F D 6 5 17 19 F D 6 5 17 20 F D 9 7 37 38 F D 9 7 37 39 F D 9 7 37 40 F D 9 8 33 34 F D 9 8 33 35 F D 9 8 33 36 F Optimization information found in file: " Cr Acac3_D3F_2E_opt_UB3LYP_6311gdp_fermi_cpcmMeCN .log" 210 Cr(acac) 3 2 E State F requencies Stoichiometry C15H21CrO6(2) Framework group D3[O(Cr),3C2(.CH),X(C12H18O6)] Deg. of freedom 20 Full point group D3 Largest Abelian subgroup C2 NOp 2 Largest concise Abelian subgroup C2 NOp 2 Standard orientation: --------------------------------------------------------------------- Center Atomic Atomic Coor dinates (Angstroms) Number Number Type X Y Z --------------------------------------------------------------------- 1 24 0 0.000000 0.000000 0.000000 2 6 0 0.732684 2.661455 0.996875 3 6 0 0.000000 3.321253 0.000000 4 6 0 - 1.938545 - 1.965250 - 0.996875 5 6 0 - 2.671229 - 0.696204 0.99687 5 6 6 0 - 2.876290 - 1.660627 0.000000 7 6 0 2.671229 - 0.696204 - 0.996875 8 6 0 1.938545 - 1.965250 0.996875 9 6 0 2.8 76290 - 1.660627 0.000000 10 6 0 - 0.732684 2.661455 - 0.996875 11 8 0 - 0.800798 - 1.402781 - 1.126390 12 8 0 - 1.615243 0.007879 1.126390 13 8 0 0.814445 1.394902 1.126390 14 8 0 1.615243 0.007879 - 1.126390 15 8 0 0.800798 - 1.402781 1.126390 16 8 0 - 0.814445 1.3949 02 - 1.126390 17 6 0 - 3.748356 - 0.435257 2.018856 18 1 0 - 4.642277 - 1.033496 1.843415 19 1 0 - 3.359034 - 0.652356 3.018164 20 1 0 - 4.011988 0.626042 2.001547 21 6 0 - 2.251122 - 3.028543 - 2.018856 22 1 0 - 3.216173 - 3.503582 - 1.843415 23 1 0 - 2.244473 - 2.582831 - 3.018164 24 1 0 - 1.463826 - 3.787504 - 2.001547 25 6 0 - 1.497234 3.463801 - 2.018856 26 1 0 - 1.426105 4.537078 - 1.843415 27 1 0 - 1.114 560 3.235186 - 3.018164 28 1 0 - 2.548162 3.161463 - 2.001547 29 6 0 1.497234 3.463801 2.018856 30 1 0 1.426105 4.537078 1.843415 31 1 0 1.114560 3.235186 3.018164 32 1 0 2.548162 3.161463 2.001547 33 6 0 2.251122 - 3.028543 2.018856 211 34 1 0 3.216173 - 3.503582 1.843415 35 1 0 2.244473 - 2.582831 3.018164 36 1 0 1.463826 - 3.787504 2.001547 37 6 0 3.748356 - 0.435257 - 2.018856 38 1 0 4.642277 - 1.033496 - 1.843415 39 1 0 3.359034 - 0.652356 - 3.018164 40 1 0 4.011988 0.626042 - 2.001547 41 1 0 3.814004 - 2.202016 0.000000 42 1 0 - 3.814004 - 2.202016 0.000000 43 1 0 0.000000 4.404032 0.000000 --------------------------------------------------------------------- Density matrix has only Abelian symmetry. D1 PCM: C - PCM CSMder 1st derivatives, ID1Alg=0 FixD1E=F DoIter=F I1PDM=0. D2PCM: C - PCM 2nd derivatives, FixD2E=F I1PDM=0. Density matrix has only Abelian symmetry. Full mass - weighted force constant matrix: Low frequencies --- - 15.8024 - 15.6578 - 14.2954 3.8237 12.3267 23.4380 Low frequencies --- 39.8430 43.0139 55.5326 Diagonal vibrational polarizability: 195.5380719 489.3866137 122.3142559 Harmonic frequencies (cm** - 1), IR intensities (KM/Mole), Raman scattering activities (A**4/AMU), depolarization ratios for plane and unpolarized incident light, reduced masses (AMU), force constants (mDyne/A), and normal coordinates: Frequency # Frequency (cm - 1 ) Reduced Masses Force Constants IR Intensity 1 14.1955 4.2528 0.0005 3.007 9 2 24.5212 3.7339 0.0013 2.195 3 54.3444 2.2111 0.0038 3.4837 4 70.849 1.3973 0.0041 5.4499 5 70.8913 1.4021 0.0042 0.2125 6 79.6604 2.5257 0.0094 0.1138 7 82.2029 2.1936 0.0087 1.5807 8 82.9877 1.262 0.0051 1.2146 9 89.3912 1.594 0.0075 0 .3768 10 90.2828 1.3524 0.0065 5.7928 11 101.3376 1.1325 0.0069 0.9342 12 102.3798 1.1402 0.007 0.3256 13 151.6753 3.7085 0.0503 1.007 14 167.0352 3.506 0.0576 0.4526 15 172.0613 2.6805 0.0468 0.7639 16 177.3487 4.6637 0.0864 1.3013 17 177. 3705 3.6402 0.0675 0.8746 18 188.4336 7.7021 0.1611 0.0011 19 189.35 6.3673 0.1345 0.8031 212 20 219.6094 6.7574 0.192 0.087 21 230.2767 6.7763 0.2117 0.0049 22 233.0061 6.8219 0.2182 0.0331 23 244.4329 5.2855 0.1861 3.27 24 244.6959 5.7798 0.203 9 3.3914 25 255.7133 3.3177 0.1278 1.7567 26 256.1452 3.2932 0.1273 2.0242 27 268.9053 2.9619 0.1262 0.0048 28 344.361 7.3168 0.5112 4.0771 29 354.1519 10.5116 0.7768 44.8675 30 370.2263 9.0198 0.7284 4.8262 31 422.6002 4.684 0.4929 32.3346 32 422.9382 4.6181 0.4867 8.4591 33 423.0541 4.6963 0.4952 10.2498 34 447.317 6.1315 0.7229 173.9364 35 449.8913 6.3237 0.7541 191.9691 36 453.9905 5.71 0.6934 0.2541 37 566.6775 2.9154 0.5516 0.8817 38 568.6168 2.8961 0.5517 0.1133 39 570.5 048 2.9114 0.5583 0.0166 40 582.802 4.4088 0.8823 42.3951 41 593.2067 4.6246 0.9588 79.7196 42 598.2976 4.7755 1.0072 86.377 43 671.0597 4.0643 1.0784 58.6495 44 671.1865 4.0664 1.0793 57.7572 45 678.5575 4.1407 1.1233 0.2269 46 683.2759 2.90 45 0.799 4.8433 47 683.495 2.9445 0.8105 15.2602 48 684.0093 2.9464 0.8122 15.7981 49 787.3624 1.1392 0.4161 18.0136 50 789.6423 1.1393 0.4186 39.2743 51 790.1191 1.1395 0.4191 33.4402 52 947.5512 4.7727 2.5247 61.3333 53 947.646 4.7191 2.496 9 13.6225 54 949.0658 4.7691 2.5453 8.5107 55 961.8511 2.9736 1.6209 11.4881 56 963.0219 2.8851 1.5765 0.837 57 963.1202 2.9258 1.599 15.9825 Full frequency results in file: " CrAcac3_D3F_2E_ freq _UB3LYP_6311gdp_fermi_cpcmMeCN .log" 213 Cr(acac) 3 4 T 2 ES 1 Franck Condon Frequencies ------------------------------------------------------------------- Center Atomic Forces (Hartrees/Bohr) Number Number X Y Z -------------------------------- ----------------------------------- 1 24 0.000217328 0.000566690 - 0.000060671 2 6 0.002415059 0.001581506 - 0.004022550 3 6 - 0.000527525 0.000501772 - 0.000014982 4 6 - 0.001869549 0.002368515 0.004047175 5 6 0.000038657 - 0.002924625 - 0.003909978 6 6 0.000691220 0.000234374 - 0.000041111 7 6 0.002866799 0.000526434 0.003 818593 8 6 - 0.002488045 0.001454008 - 0.003791447 9 6 - 0.000116839 - 0.000707959 - 0.000004651 10 6 - 0.000982843 - 0.002796053 0.003762642 11 8 - 0.013075614 - 0.003607814 0.004388731 12 8 - 0.011792550 - 0.005396529 - 0.003987986 13 8 0.011063766 - 0.007713992 - 0.004350367 14 8 0.003064149 0.012419743 0.004142903 15 8 0.001278428 0.012619253 - 0.004092329 16 8 0.009263793 - 0.009022700 0.004004488 17 6 - 0.001117564 - 0.000363875 0.000284871 18 1 - 0.000227560 - 0.000297635 - 0.000246556 19 1 0.000010000 0.000061109 0.000042998 20 1 0.000027094 - 0.000021160 0.000018128 21 6 - 0.001160519 - 0.000474187 - 0.000280050 22 1 - 0.000371727 0.0000828 59 0.000262364 23 1 0.000057098 - 0.000039153 - 0.000042005 24 1 0.000020059 0.000042424 - 0.000033654 25 6 0.000925469 - 0.000649822 - 0.000264050 26 1 0.00 0121028 - 0.000389801 0.000254464 27 1 0.000011898 0.000053341 - 0.000035508 28 1 - 0.000035182 - 0.000002755 - 0.000038806 29 6 0.000932462 - 0.000818866 0.000281981 30 1 0.000409686 - 0.000050204 - 0.000258184 31 1 - 0.000070118 - 0.000018446 0.000051761 32 1 0.000011968 0.000031689 0.000022363 33 6 0.000258634 0.001145552 0.0 00256157 34 1 - 0.000150502 0.000328834 - 0.000230743 35 1 0.000039138 - 0.000043670 0.000040543 36 1 - 0.000033357 - 0.000025274 0.000034304 37 6 0.000137372 0.001156944 - 0.000273131 38 1 0.000253025 0.000274713 0.000237793 39 1 - 0.000054616 - 0.000029863 - 0.000042001 40 1 0.000019552 - 0.000043103 - 0.000029141 41 1 0.000003893 0.000030583 0.000003624 214 42 1 - 0.000028629 - 0.000022083 0.000007375 43 1 - 0.000034840 - 0.000020771 0.000086646 ------------------------------------------------------------------- Cartesian Forces: Max 0.013075614 RMS 0.003155708 NDeriv= 129 NFrqRd= 0 NDerD0= 0 MskFDP= 0 MskDFD= 0 MskDF0= 0 Re - enter D2Numr: IAtom= 43 IXYZ=3 IStep= 2. Maximum difference in off - diagonal FC elements: I= 25 J= 1 Diffe rence= 4.3062875163D - 04 Max difference between analytic and numerical forces: I=127 Difference= 3.1412442524D - 05 Full mass - weighted force constant matrix: Low frequencies --- - 770.2123 - 758.1657 - 40.3135 - 34.5176 - 34.0272 - 11.6055 Low freque ncies --- - 4.0443 - 0.6309 0.5555 ****** 5 imaginary frequencies (negative Signs) ****** Diagonal vibrational polarizability: 1123.2614067 483.0419417 486.7422454 Harmonic frequencies (cm** - 1), IR intensities (KM/Mole), Raman scat tering activities (A**4/AMU), depolarization ratios for plane and unpolarized incident light, reduced masses (AMU), force constants (mDyne/A), and normal coordinates: Frequency # Frequency (cm - 1 ) Reduced Masses Force Constants IR Intensity 1 - 770.212 1 3.5559 4.738 2825.685 2 - 758.166 13.4877 4.5679 2752.145 3 - 25.427 4.6021 0.0018 8.6182 4 - 14.0682 4.1445 0.0005 1.5664 5 - 7.2951 4.2034 0.0001 1.7158 6 33.1099 3.555 0.0023 0.4775 7 35.8004 3.6454 0.0028 0.285 8 42.5759 3.1836 0.0034 0.0368 9 72.6 455 1.1267 0.0035 2.5713 10 86.8611 1.1163 0.005 2.7793 11 90.67 1.1433 0.0055 2.813 12 91.4955 1.0418 0.0051 0.5979 13 98.9477 1.0288 0.0059 0.252 14 103.5755 1.0468 0.0066 0.218 15 125.5881 5.8989 0.0551 8.7518 16 128.4504 6.4766 0.063 8.0457 17 144.2863 6.1342 0.0752 3.1472 18 158.5739 2.8659 0.0425 0.3185 19 159.7143 2.8313 0.0426 0.4816 20 161.8606 7.5122 0.116 0.0427 21 162.7888 2.9246 0.0457 0.5364 22 206.9017 8.4444 0.213 15.6084 215 23 207.979 8.3433 0.2126 15.7512 24 209.4458 7.8057 0.2 017 2.6394 25 234.9917 4.1769 0.1359 0.0586 26 235.3882 4.2719 0.1395 0.1305 27 253.0619 2.878 0.1086 0.0021 28 299.4995 4.8586 0.2568 82.6918 29 300.4866 4.8515 0.2581 81.3317 30 321.2731 5.4221 0.3297 13.907 31 362.814 3.6976 0.2868 88.8394 32 36 3.4545 3.7129 0.289 88.8225 33 415.556 5.8394 0.5941 36.7146 34 425.5819 6.2081 0.6625 34.0675 35 426.3067 6.1958 0.6634 34.382 36 461.1155 5.6699 0.7103 0.0144 37 548.2537 4.2837 0.7593 44.8762 38 549.8997 4.3197 0.7696 46.1517 39 567.4792 2.8379 0 .5384 0.0426 40 568.2269 2.8369 0.5397 0.0291 41 569.301 2.8521 0.5446 0.0127 42 588.2433 4.3817 0.8933 84.7496 43 657.9989 3.6229 0.9242 162.4704 44 658.6434 3.6413 0.9307 163.9383 45 675.3655 3.0149 0.8102 3.1003 46 676.3566 3.0247 0.8152 1.779 4 7 676.8748 2.8251 0.7626 7.3374 48 681.0294 4.203 1.1485 0.011 49 799.167 1.1488 0.4323 16.3954 50 800.1284 1.1471 0.4327 18.4035 51 802.1226 1.1397 0.4321 23.8632 52 919.6471 4.8073 2.3955 178.0899 53 920.2345 4.7792 2.3845 176.7851 54 947.4635 4.8 488 2.5646 82.088 55 954.3888 3.5973 1.9305 3.6474 56 954.6977 3.5716 1.918 4.0252 57 960.875 2.8609 1.5563 0.0492 Full frequency results in file: " 51_CrAcac3_D3_TDFCes1_G09_UB3LYP_6311gdp_cpcmMeCN_6 .log" 216 Cr(acac) 3 4 T 2 ES 2 Franck Condon Frequencies ------------------------------------------------------------------- Center Atomic Forces (Hartrees/Bohr) Number Number X Y Z ------------------------------------------------------------- ------ 1 24 0.002378924 0.003251585 - 0.000125624 2 6 0.003297386 - 0.000529046 - 0.004638033 3 6 - 0.000261477 0.000652969 - 0.000759144 4 6 - 0.003043454 0.001790016 0.005169513 5 6 0.001223040 - 0.003560672 - 0.004790014 6 6 0.000893076 0.000741812 0.000814783 7 6 0.001667462 0.001436193 0.002849101 8 6 - 0.002368265 0.000123681 - 0.002665600 9 6 0.000359961 - 0.000128694 0.000761663 10 6 - 0.003070238 - 0.002036140 0.003250030 11 8 - 0.015756385 - 0.002624575 0.003505891 12 8 - 0.013885247 - 0.005775883 - 0.002535077 13 8 0.013048719 - 0.005439235 - 0.004991930 14 8 0.004856216 0.010013476 0.006046515 15 8 0.000594712 0.0106731 80 - 0.005496622 16 8 0.010169353 - 0.008400324 0.003644157 17 6 - 0.001152161 - 0.000304599 0.000122600 18 1 - 0.000226804 - 0.000269466 - 0.000246249 19 1 - 0.00 0005337 0.000048930 0.000003428 20 1 - 0.000004928 0.000008795 0.000042759 21 6 - 0.001391795 - 0.000631347 - 0.000300639 22 1 - 0.000440339 0.000071142 0.000331388 23 1 0.000078318 - 0.000045506 0.000001903 24 1 0.000029888 0.000029835 - 0.000048804 25 6 0.000843927 - 0.000432346 - 0.000153884 26 1 0.000096143 - 0.000300291 0.0 00193629 27 1 0.000005100 0.000040201 - 0.000018417 28 1 - 0.000005673 0.000033618 - 0.000063414 29 6 0.001101258 - 0.000999390 0.000464650 30 1 0.000474636 - 0.000076790 - 0.000326880 31 1 - 0.000132988 0.000008316 0.000020638 32 1 - 0.000014388 0.000062871 0.000015818 33 6 0.000293525 0.000906871 0.000339578 34 1 - 0.000118906 0.000244809 - 0.000169114 35 1 0.000024594 - 0.000093505 0.000038422 36 1 - 0.000018368 - 0.000069958 0.000034601 37 6 0.000059283 0.001160461 - 0.000515366 38 1 0.000240170 0.000265702 0.000234281 39 1 - 0.000078194 - 0.000111726 - 0.000035857 40 1 0.000008956 - 0.000106078 - 0.000020841 217 41 1 0.000124921 0.00004 0870 - 0.000086416 42 1 - 0.000033842 0.000125419 - 0.000101427 43 1 0.000139221 0.000204816 0.000204008 ------------------------------------------------------------------- Cartesian Forces: Max 0 .015756385 RMS 0.003302774 NDeriv= 129 NFrqRd= 0 NDerD0= 0 MskFDP= 0 MskDFD= 0 MskDF0= 0 Re - enter D2Numr: IAtom= 43 IXYZ=3 IStep= 2. Maximum difference in off - diagonal FC elements: I= 2 J= 1 Difference= 2.0907428113D - 02 M ax difference between analytic and numerical forces: I= 2 Difference= 8.1943078482D - 05 Full mass - weighted force constant matrix: Low frequencies ---- 2167.0242 - 161.0212 - 44.4312 - 35.6243 - 33.1860 - 19.0162 Low frequencies --- - 13.9655 0.4136 1.6321 ****** 4 imaginary frequencies (negative Signs) ****** Diagonal vibrational polarizability: 121.4717556 331.6327864 334.5315922 Harmonic frequencies (cm** - 1), IR intensities (KM/Mole), Raman scattering activities (A**4/AMU) , depolarization ratios for plane and unpolarized incident light, reduced masses (AMU), force constants (mDyne/A), and normal coordinates: Frequency # Frequency (cm - 1 ) Reduced Masses Force Constants IR Intensity 1 - 2167.0204 9.6516 26.704 840.9415 2 - 1 55.5764 7.2931 0.104 10.3866 3 - 33.4224 4.5187 0.003 8.8939 4 - 21.1479 4.4563 0.0012 2.2749 5 25.6469 4.3414 0.0017 1.2007 6 35.6952 3.3622 0.0025 0.321 7 43.3537 3.196 0.0035 0.0445 8 46.0268 3.6624 0.0046 0.6558 9 71.0852 1.1242 0.0033 2.3538 10 83.7103 1.1009 0.0045 2.4267 11 89.4854 1.1596 0.0055 4.4456 12 92.3799 1.0469 0.0053 0.8112 13 100.498 1.0433 0.0062 0.5425 14 102.5824 1.1037 0.0068 1.5461 15 109.1961 4.8863 0.0343 13.2648 16 132.5392 5.8602 0.0607 8.9201 17 153.1845 3.7319 0.051 6 1.4269 18 155.8156 2.7387 0.0392 2.1365 19 16.2099 2.8071 0.0425 0.2804 20 164.3605 5.0298 0.0801 0.6217 21 174.7507 6.7929 0.1222 7.461 22 206.7838 6.8947 0.1737 23.1944 218 23 209.8929 7.4473 0.1933 0.6547 24 217.9602 7.5137 0.2103 7.7766 25 233.63 66 4.6196 0.1486 1.4119 26 253.144 2.8657 0.1082 0.164 27 280.1321 3.5158 0.1626 48.1992 28 295.997 4.4539 0.2299 78.5832 29 309.1275 5.0038 0.2817 19.6423 30 328.3854 3.9003 0.2478 21.9234 31 392.3375 4.1394 0.3754 63.2157 32 414.8776 5.8495 0.5932 38.1312 33 421.9145 5.7992 0.6082 7.8017 34 433.1555 6.055 0.6693 47.7396 35 461.8671 5.6687 0.7125 0.1112 36 510.849 4.663 0.717 121.469 37 535.146 4.3532 0.7345 42.5631 38 555.4657 3.4754 0.6318 72.5056 39 567.9235 2.8386 0.5394 0.2575 40 569.45 68 2.8362 0.5419 0.0522 41 576.7309 3.2418 0.6353 55.4134 42 584.0202 4.146 0.8332 79.4147 43 664.7032 3.29 0.8565 72.3566 44 672.2625 3.5303 0.94 47.3913 45 673.1968 3.0149 0.805 24.3398 46 676.9728 3.0583 0.8258 22.6162 47 681.4291 4.2205 1.1547 4 .4245 48 747.1275 2.061 0.6778 14.0182 49 776.9436 2.5291 0.8995 105.8726 50 800.4544 1.137 0.4292 32.6154 51 805.1386 1.3409 0.5121 95.6439 52 871.7398 2.0637 0.924 35.3473 53 940.3703 4.3966 2.2907 33.5854 54 947.2403 4.8463 2.562 83.5445 55 953. 8618 3.959 2.1223 2.068 56 960.8199 2.8633 1.5574 0.3778 57 980.5215 2.4589 1.3929 75.642 Full Frequency results in file: " 55_CrAcac3_D3_TDFCes2_G09_UB3LYP_6311gdp_cpcmMeCN_5 .log" 219 Cr(acac) 3 4 T 2 ES 3 Franck Condon Frequencies ------------------------ ------------------------------------------- Center Atomic Forces (Hartrees/Bohr) Number Number X Y Z ------------------------------------------------------------------- 1 24 - 0.002714742 - 0.004122521 - 0.000046339 2 6 0.001273674 0.003402512 - 0.003651481 3 6 - 0.002002891 0.000147989 0.002004351 4 6 - 0.000471955 0.002280159 0.002714019 5 6 - 0.001173742 - 0.002052645 - 0.002977726 6 6 0.000224649 - 0.000397955 - 0.000889704 7 6 0.003821955 - 0.000607484 0.004959694 8 6 - 0.002416109 0.0026 52568 - 0.005125266 9 6 - 0.000582462 - 0.001039620 - 0.000849988 10 6 0.001811188 - 0.003290638 0.003764545 11 8 - 0.009869092 - 0.002481289 0.005043911 12 8 - 0 .009164719 - 0.006905889 - 0.006292110 13 8 0.009556618 - 0.007819743 - 0.003235689 14 8 0.003341828 0.015558780 0.002819062 15 8 - 0.000212497 0.016186610 - 0.003503943 16 8 0.008010197 - 0.011638298 0.005236608 17 6 - 0.001194472 - 0.000309581 0.000560539 18 1 - 0.000232299 - 0.000302876 - 0.000256546 19 1 0.000089193 0.000106273 0.000041419 20 1 0.000089781 0.000003765 0.000012518 21 6 - 0.000793084 - 0.000421883 - 0.000330429 22 1 - 0.000236286 0.000054277 0.000172324 23 1 0.00009589 2 - 0.000011605 - 0.000039231 24 1 0.000064244 0.000029645 - 0.000033363 25 6 0.001217859 - 0.000774003 - 0.000528429 26 1 0.000174105 - 0.000481838 0.000342459 27 1 - 0.000031012 0.000121419 - 0.000012076 28 1 - 0.000074887 0.000021090 - 0.000039261 29 6 0.000615834 - 0.000608687 0.000078306 30 1 0.000277686 - 0.000037786 - 0.0001740 59 31 1 - 0.000044624 - 0.000008678 0.000024810 32 1 - 0.000011830 - 0.000006058 0.000036324 33 6 0.000362339 0.001480663 0.000269225 34 1 - 0.000161883 0.00 0421436 - 0.000312476 35 1 0.000051306 - 0.000061137 - 0.000006253 36 1 - 0.000024340 - 0.000030006 0.000050165 37 6 0.000077979 0.001249978 - 0.000102095 38 1 0.000235523 0.000292337 0.000249253 39 1 - 0.000046878 - 0.000009059 0.000001033 40 1 - 0.000010788 - 0.000017260 - 0.000052051 220 41 1 - 0.000123419 0.000003585 0.000100512 4 2 1 - 0.000023074 - 0.000120268 0.000093455 43 1 0.000225238 - 0.000456281 - 0.000116018 ------------------------------------------------------------------- Cartesian Forces: Max 0.016186610 RMS 0.00333 3712 NDeriv= 129 NFrqRd= 0 NDerD0= 0 MskFDP= 0 MskDFD= 0 MskDF0= 0 Re - enter D2Numr: IAtom= 43 IXYZ=3 IStep= 2. Maximum difference in off - diagonal FC elements: I= 31 J= 1 Difference= 1.9636044146D - 02 Max difference between anal ytic and numerical forces: I= 2 Difference= 8.7459572511D - 05 Full mass - weighted force constant matrix: Low frequencies --- - 154.6618 - 44.7489 - 36.1738 - 33.0693 - 18.4061 - 16.6625 Low frequencies --- - 2.0377 0.1448 12.2391 ****** 3 im aginary frequencies (negative Signs) ****** Diagonal vibrational polarizability: 387.0160192 158.1267646 349.7548627 Harmonic frequencies (cm** - 1), IR intensities (KM/Mole), Raman scattering activities (A**4/AMU), depolarization ratios fo r plane and unpolarized incident light, reduced masses (AMU), force constants (mDyne/A), and normal coordinates: Frequency # Frequency (cm - 1 ) Reduced Masses Force Constants IR Intensity 1 - 149.8352 7.9434 0.1051 4.6834 2 - 33.6827 4.5904 0.0031 8.7123 3 - 16.7687 4.3651 0.0007 2.1972 4 21.5635 4.2386 0.0012 1.1522 5 35.2963 3.4715 0.0025 0.5718 6 41.6333 3.219 0.0034 1.2271 7 44.1268 3.3063 0.0038 1.0272 8 74.6448 1.1373 0.0037 3.9609 9 86.007 1.1202 0.0049 2.8663 10 89.8131 1.1436 0.0054 3.0747 11 90.9557 1.0399 0.0051 0.4093 12 96.6092 1.0251 0.0056 0.0106 13 103.6217 1.1244 0.0071 1.8828 14 105.6699 4.4387 0.0292 14.6871 15 131.2359 6.0376 0.0613 1.7702 16 153.7542 2.9864 0.0416 2.2314 17 155.5129 3.9665 0.0565 0.5409 18 160.6081 2.7243 0.0414 0.5672 19 163.6143 4.5172 0.0712 0.7203 20 173.5606 6.4944 0.1153 4.6642 21 208.6461 7.5508 0.1973 2.2309 22 211.2271 6.3978 0.1682 15.3486 221 23 218.5326 0.7052 0.1887 7.7177 24 246.8184 3.6346 0.1305 4.5719 25 253.5211 2.8914 0.1095 0.0402 26 285.1337 3.5959 0.1722 26.9849 27 297.0941 4.4466 0.2312 81.2436 28 308.5585 5.1356 0.2881 23.5642 29 344.5261 5.1444 0.3598 14.3617 30 392.5418 4.2013 0.3814 53.6338 31 414.4057 5.9082 0.5978 35.9193 32 419.2758 5.5708 0.577 5.9365 33 430.8188 6.1 042 0.6675 23.482 34 461.8454 5.668 0.7124 0.218 35 496.9239 5.921 0.8614 203.2983 36 534.991 4.114 0.6938 28.6242 37 546.7318 4.2293 0.7448 84.8744 38 567.7088 2.8237 0.5362 0.0652 39 569.3938 2.8479 0.544 0.0481 40 571.7911 2.9901 0.576 15.3764 4 1 584.2736 4.1885 0.8424 80.0203 42 662.9227 3.5202 0.9115 95.1469 43 671.9139 3.4653 0.9218 43.6442 44 675.5913 2.8823 0.7751 8.6461 45 676.5269 3.0854 0.832 24.9282 46 668.2721 4.2163 1.153 2.2582 47 731.177 2.3692 0.7463 35.3519 48 775.6787 2.896 8 1.0269 92.1412 49 798.7288 1.1506 0.4325 38.9857 50 803.7035 1.3577 0.5167 101.9407 51 848.4491 1.5321 0.6498 22.6894 52 938.8627 4.4646 2.3187 43.4268 53 947.2227 4.8478 2.5627 83.4048 54 954.1186 4.0522 2.1734 2.4758 55 960.7874 2.8662 1.5589 0. 4556 56 975.6518 2.5425 1.4259 45.1092 Full frequency results in file: " 54_CrAcac3_D3_TDFCes3_G09_UB3LYP_6311gdp_cpcmMeCN_5 .log" 222 Cr(TMHD) 3 Ground State Optimization # opt ub3lyp/6 - 311g(d,p) scrf=(solvent=dichloromethane,pcm) scf=(tight,maxcycle=1000 ) 0 4 Cr - 0.00626800 - 0.00228800 - 0.00119800 C - 2.56845500 - 1.04887500 - 1.01880800 C - 3.31517300 - 0.43775700 0.00184800 C 1.68029200 2.19006500 1.02112400 C 0.36821600 2.74488400 - 1.00632400 C 1.28371700 3.07623600 0.00618900 C 1.07442200 - 2.55639900 1.00285500 C 2.19819200 - 1.67442300 - 1.02214300 C 2.04565900 - 2.63497300 - 0.00866600 C - 2.74967400 0.34378400 1.02283800 O 1.27020800 0.98911900 1.12676700 O - 0.20607800 1.61342300 - 1.11372000 O - 1.30219000 - 0.97026000 - 1.127 90600 O 0.22390700 - 1.61509000 1.11070000 O 1.48523200 - 0.62489300 - 1.13068900 O - 1.50543400 0.59193500 1.13215700 C - 0.03543300 3.75552000 - 2.09845500 C 2.67608900 2.60759800 2.12161700 C - 3.61408600 0.98734200 2.12541900 C - 3.23940100 - 1.89128000 - 2.12195200 C 3.27144500 - 1.81723600 - 2.11960200 C 0.95074600 - 3.63785000 2.09471400 H 2.70938500 - 3.48050700 - 0.00935700 H 1.70161900 4.06662400 0.00638000 H - 4.38102600 - 0.57626300 0.00210200 C 4.18062900 - 0.56967500 - 2.0511 4800 H 4.91999400 - 0.60388200 - 2.85672800 H 3.59063200 0.34169600 - 2.15238400 H 4.71777500 - 0.52688700 - 1.09897000 C 2.54132800 - 1.84576100 - 3.48134600 H 3.27205400 - 1.87601400 - 4.29506000 H 1.90280200 - 2.73024900 - 3.56580000 H 1.91604000 - 0.96028600 - 3.59986000 C 4.13589600 - 3.08102800 - 1.98211400 H 4.68884900 - 3 .09752700 - 1.03903600 H 3.53823000 - 3.99411200 - 2.04837400 H 4.86800200 - 3.10705400 - 2.79414500 C 1.98360000 - 4.76881200 1.96977600 H 1.88423900 - 5.31050400 1.02528 900 H 3.00839800 - 4.39602100 2.04854000 223 H 1.83200400 - 5.48870200 2.77914000 C 1.12347600 - 2.93944700 3.46255300 H 0.40567600 - 2.12587000 3.57114100 H 0.96838400 - 3.66016500 4.27087400 H 2.13044800 - 2.52442400 3.56699800 C - 0.47186700 - 4.23439900 2.00003600 H - 0.62760000 - 4.95684800 2.80664900 H - 1.22358000 - 3. 44848100 2.07994900 H - 0.61767200 - 4.75288000 1.04764100 C - 3.39333300 2.51543500 2.05950700 H - 3.93829800 3.00595000 2.87149900 H - 2.33339400 2.75482100 2.150926 00 H - 3.75641100 2.92449100 1.11188500 C - 3.10605600 0.45475200 3.48442400 H - 3.64908900 0.94014000 4.30077300 H - 3.26368300 - 0.62477000 3.56702100 H - 2.04044800 0.65462400 3.60036100 C - 5.11552000 0.68694000 1.99309700 H - 5.52818400 1.06962200 1.05570900 H - 5.32345200 - 0.38485900 2.05004900 H - 5.65418300 1.1 7153800 2.81230000 C - 4.76706200 - 1.99139900 - 1.98566900 H - 5.06310500 - 2.46505500 - 1.04572900 H - 5.24837000 - 1.01153700 - 2.04546500 H - 5.16307900 - 2.60286100 - 2.8014390 0 C - 2.89092800 - 1.24051100 - 3.47969600 H - 1.81030200 - 1.15724000 - 3.59931900 H - 3.29260800 - 1.84698200 - 4.29684400 H - 3.32254400 - 0.23808500 - 3.55707800 C - 2.62985200 - 3.31013300 - 2.06305600 H - 3.03085700 - 3.92141200 - 2.87687200 H - 1.54446400 - 3.26521300 - 2.15693500 H - 2.87247900 - 3.80336400 - 1.11707300 C - 1.56423400 3.95 991400 - 2.00077200 H - 1.90371600 4.62256900 - 2.80230400 H - 2.08541200 3.00592200 - 2.08743600 H - 1.83917400 4.41531600 - 1.04465300 C 0.31131000 3.12641000 - 3.46671600 H - 0.02287200 3.78457800 - 4.27417800 H 1.39104400 2.98335800 - 3.57100700 H - 0.17351500 2.15605100 - 3.57708300 C 0.66646300 5.11739700 - 1.97617500 H 0.42697900 5.61833300 - 1.03433400 H 1.75318700 5.02451500 - 2.05178800 H 0.33405300 5.76892500 - 2.78927500 C 1.96555500 2.42783600 3.48223600 224 H 1.60162200 1.405 91900 3.59267000 H 2.66124200 2.64763700 4.29745400 H 1.11252600 3.10712800 3.57212000 C 3.88609000 1.64933900 2.04415100 H 4.58690700 1.86846800 2.85512800 H 3.56048200 0.61211600 2.12901800 H 4.41848600 1.76572300 1.09545800 C 3.17047900 4.05739600 1.99650600 H 3.70002400 4.22920600 1.05549200 H 2.35007200 4.77652500 2.06798700 H 3.86846800 4.27195900 2.81076700 Optimization information found in file: " CrTBut3_opt_UB3LYP_6311gdp_tight_CH2Cl2 .log" 225 Cr(TMHD) 3 Ground State Frequencies Stoichiometry C33H57CrO6(4) Fr amework group C1[X(C33H57CrO6)] Deg. of freedom 285 Full point group C1 Largest Abelian subgroup C1 NOp 1 Largest concise Abelian subgroup C1 NOp 1 Standard orientation: --------------------------------------------------------------------- Center Atomic Atomic Coordinates (Angstroms) Number Number Type X Y Z ---------------------------------------- ----------------------------- 1 24 0 - 0.006103 - 0.002530 - 0.001252 2 6 0 - 2.550578 - 1.091745 - 1.018463 3 6 0 - 3.307402 - 0.493123 0.002232 4 6 0 1.643222 2.218033 1.020770 5 6 0 0.321827 2.750462 - 1.006585 6 6 0 1.231592 3.097477 0.005914 7 6 0 1.117482 - 2.5381 31 1.002742 8 6 0 2.226194 - 1.637366 - 1.022197 9 6 0 2.089929 - 2.600516 - 0.008806 10 6 0 - 2.754694 0.297576 1.023245 11 8 0 1.253711 1.010423 1.126265 12 8 0 - 0.233211 1.609592 - 1.113704 13 8 0 - 1.285948 - 0.992164 - 1.127415 14 8 0 0.251433 - 1.611316 1.110432 15 8 0 1.495606 - 0.600221 - 1.130614 16 8 0 - 1.514895 0.566459 1.132164 17 6 0 - 0.099874 3.754303 - 2.098035 18 6 0 2.632 421 2.652020 2.120725 19 6 0 - 3.629488 0.927127 2.125602 20 6 0 - 3.207312 - 1.945479 - 2.121326 21 6 0 3.301654 - 1.761938 - 2.119593 22 6 0 1.011709 - 3.621541 2.094419 23 1 0 2.767765 - 3.434813 - 0.009577 24 1 0 1.632601 4.094853 0.006097 25 1 0 - 4.370829 - 0.649287 0.002577 26 6 0 4.190065 - 0.499533 - 2.050529 27 1 0 4.929955 - 0.521260 - 2.856047 28 1 0 3.585118 0.402029 - 2.151488 29 1 0 4.726332 - 0.448237 - 1.098273 30 6 0 2.572170 - 1.801889 - 3.481377 31 1 0 3.303383 - 1.819713 - 4.295014 32 1 0 1.948353 - 2.696776 - 3.566280 33 1 0 1.932329 - 0.926811 - 3.599596 34 6 0 4.186858 - 3.011401 - 1.982578 226 35 1 0 4.739760 - 3.019331 - 1.039347 36 1 0 3.60438 7 - 3.934214 - 2.049510 37 1 0 4.919495 - 3.024873 - 2.794430 38 6 0 2.063515 - 4.734985 1.969820 39 1 0 1.973596 - 5.278279 1.025300 40 1 0 3.081875 - 4.344990 2.048891 41 1 0 1.923852 - 5.457341 2.779133 42 6 0 1.172135 - 2.920361 3.462340 43 1 0 0.440898 - 2.118781 3.570629 44 1 0 1.028636 - 3.643591 4.270548 45 1 0 2.172034 - 2.488693 3.567301 46 6 0 - 0.400672 - 4.241855 1.999173 47 1 0 - 0.544709 - 4.966565 2.805915 48 1 0 - 1.165517 - 3.468618 2.078408 49 1 0 - 0.537263 - 4.762990 1.046854 50 6 0 - 3.432806 2.458523 2.060031 5 1 1 0 - 3.985556 2.940214 2.872033 52 1 0 - 2.376773 2.714621 2.151645 53 1 0 - 3.802117 2.862044 1.112438 54 6 0 - 3.113452 0.402383 3.484647 55 1 0 - 3.664333 0.879005 4.300895 56 1 0 - 3.254052 - 0.679505 3.567026 57 1 0 - 2.051156 0.619016 3.600953 58 6 0 - 5.125997 0.603100 1.992753 59 1 0 - 5.544493 0.979744 1.055494 60 1 0 - 5.316932 - 0.471894 2.049001 61 1 0 - 5.672435 1.078639 2.812109 62 6 0 - 4.733157 - 2.070979 - 1.985191 63 1 0 - 5.021417 - 2.548834 - 1.044941 64 1 0 - 5.230789 - 1.099348 - 2.045745 65 1 0 - 5.118796 - 2.689538 - 2.800579 66 6 0 - 2.869516 - 1.289428 - 3.479219 67 1 0 - 1.790407 - 1.188101 - 3.598733 68 1 0 - 3.260866 - 1.902853 - 4.296172 69 1 0 - 3.317835 - 0.294391 - 3.557041 70 6 0 - 2.574188 - 3.353953 - 2.061928 71 1 0 - 2.964847 - 3.972051 - 2.875615 72 1 0 - 1.489675 - 3.290972 - 2.155677 73 1 0 - 2.808653 - 3.850907 - 1.115838 74 6 0 - 1.632048 3.931423 - 1.999609 75 1 0 - 1.983640 4.588109 - 2.800818 76 1 0 - 2.136223 2.968301 - 2.086285 77 1 0 - 1.914647 4.381602 - 1.043241 78 6 0 0.257399 3.132164 - 3.466756 79 1 0 - 0.088784 3.784761 - 4. 273674 80 1 0 1.339461 3.008413 - 3.571587 227 81 1 0 - 0.210077 2.153375 - 3.577480 82 6 0 0.577851 5.128385 - 1.975325 83 1 0 0.329368 5.624900 - 1.033472 84 1 0 1.666072 5.054683 - 2.050680 85 1 0 0.234180 5.774102 - 2.788376 86 6 0 1.925801 2.460038 3.481698 87 1 0 1.579068 1.432147 3.592141 88 1 0 2.618225 2.691286 4.296518 89 1 0 1.061586 3.124948 3.572252 90 6 0 3.858222 1 .714124 2.042299 91 1 0 4.555639 1.944666 2.853029 92 1 0 3.550047 0.671542 2.126909 93 1 0 4.388157 1.839742 1.093401 94 6 0 3.102426 4.109960 1.995657 95 1 0 3.628558 4.290833 1.054418 96 1 0 2.270136 4.815259 2.067701 97 1 0 3.797146 4.335993 2.80 9612 --------------------------------------------------------------------- D1PCM: PCM CHGder 1st derivatives, ID1Alg=0 FixD1E=F DoIter=F I1PDM=0. D2PCM: PCM 2nd derivatives, FixD2E=F I1PDM=0. Full mass - weighted force constant matrix: Low frequencies -- - - 5.0145 - 0.4812 - 0.4373 - 0.4069 4.1410 6.9898 Low frequencies --- 18.4737 20.4902 23.0544 Diagonal vibrational polarizability: 116.4688699 116.7047242 105.3680123 Harmonic frequencies (cm** - 1), IR intensities (KM/Mole ), Raman scattering activities (A**4/AMU), depolarization ratios for plane and unpolarized incident light, reduced masses (AMU), force constants (mDyne/A), and normal coordinates: Frequency # Frequency (cm - 1 ) Reduces Masses Force Constants IR Intensity 1 18.2755 3.3669 0.0007 0.227 2 20.4312 3.6713 0.0009 0.3943 3 23.0143 3.4814 0.0011 0.4944 4 25.2674 3.6597 0.0014 0.0755 5 25.9923 3.8296 0.0015 0.1586 6 27.4391 3.7309 0.0017 0.0776 7 29.9929 3.264 0.0017 0.4019 8 31.9933 3.4654 0.0021 0.8365 9 33.4997 2.8659 0.0019 0.0009 10 35.6147 2.8771 0.0022 0.1619 11 38.5039 2.8689 0.0025 0.1735 12 41.9633 2.867 0.003 0.1688 13 100.8995 3.5794 0.0215 0.0181 14 101.1567 3.5947 0.0217 0.0168 228 15 101.8567 3.5771 0.0219 0.0169 16 105.6548 3.5855 0.0236 0.0005 17 117.5628 3.6654 0.0298 0.0088 18 118.0998 3.7118 0.0305 0.0002 19 128.2623 4.7313 0.0459 0.7587 20 128.6817 4.628 0.0452 0.8362 21 144.9243 5.5638 0.0688 1.8776 22 147.696 4.1286 0.0531 0.5747 23 148.6459 4.149 0.054 0.5084 24 162.4987 4. 0419 0.0629 0.0046 25 173.6687 3.6551 0.065 0.0005 26 194.9265 3.6374 0.0814 0.4016 27 195.9064 3.724 0.0842 0.4301 28 225.207 1.1404 0.0341 0.0763 29 226.4832 1.1203 0.0339 0.0669 30 231.2644 1.1144 0.0351 0.1208 31 232.8817 1.1647 0.0372 0.038 32 234.9977 1.1466 0.0373 0.1526 33 238.1153 1.1911 0.0398 0.058 34 243.5331 3.2124 0.1123 0.872 35 244.3063 3.0345 0.1067 0.8628 36 245.2233 3.1794 0.1126 0.0366 37 257.5745 1.9962 0.078 2.7301 38 260.7001 1.3002 0.0521 0.3092 39 263.1375 1.4323 0.05 84 0.2531 40 268.9919 1.4946 0.0637 0.1721 41 273.8445 1.0972 0.0485 1.9672 42 276.6702 1.1605 0.0523 1.6744 43 280.8726 1.0609 0.0493 0.9038 44 287.4233 2.4105 0.1173 0.0712 45 289.2685 2.6036 0.1284 0.0166 46 290.0132 1.7499 0.0867 1.3807 47 291. 3943 1.8141 0.0908 1.2234 48 300.9694 2.3285 0.1243 0.6676 49 301.6888 2.5719 0.1379 0.4976 50 307.561 1.9257 0.1073 2.7508 51 308.8207 2.954 0.166 4.672 52 313.1395 1.5352 0.0887 1.7888 53 315.1697 1.2367 0.0724 0.1306 54 316.6857 1.1976 0.0708 0.4 43 55 318.6556 1.7092 0.1023 0.4894 56 320.5557 1.1025 0.0667 0.2236 57 323.6215 1.0909 0.0673 0.1217 229 58 327.0698 1.1273 0.071 0.26 59 332.8058 3.038 0.1983 10.9424 60 333.4395 2.8544 0.187 10.7044 61 335.4487 2.7995 0.1856 1.0575 62 339.9574 3.342 0.2276 3.1423 63 340.8428 3.5224 0.2411 5.9462 64 350.8306 2.8121 0.2039 3.2993 65 357.3407 4.0279 0.303 38.2188 66 358.3249 3.9609 0.2996 37.169 67 380.6851 2.3223 0.1983 0.0307 68 382.2625 2.3148 0.1993 0.0137 69 384.2575 2.3252 0.2023 0.0055 70 394.9038 2.527 0.2322 1.7213 71 397.4567 2.6327 0.245 5.6323 72 398.811 2.6079 0.2444 5.0955 73 425.1591 3.085 0.3286 3.5672 74 426.791 3.096 0.3323 2.1907 75 430.5251 3.0104 0.3288 0.6984 76 436.1022 3.2217 0.361 47.3761 77 437.4707 3.2119 0.3622 43.9997 78 449.1244 3.3607 0.3994 15.7752 79 486.7284 3.4449 0.4808 5.9195 80 487.1537 3.4635 0.4843 10.0042 81 488.1145 3.5823 0.5029 30.2129 82 508.8166 2.9875 0.4557 84.4536 83 509.1458 2.9671 0.4532 73.5988 84 509.7069 2.9579 0.4528 60.3285 85 616.446 5.7066 1.2777 4.3061 86 616.6079 5.7072 1.2785 3.1649 87 628.87 6.4745 1.5086 29.6565 88 633.4348 5.4608 1.291 140.5741 89 633.8612 5.506 1.3034 141.1427 90 640.5657 5.4596 1.3199 0.0798 91 734.4712 6.859 2.18 0.1044 92 734.7538 6.8622 2.182 7 0.1532 93 735.55 6.8851 2.1948 0.0461 94 741.9074 5.099 1.6536 18.7563 95 742.2771 5.0825 1.6499 8.4784 96 742.3258 5.0709 1.6464 7.2031 97 783.9681 1.5679 0.5678 2.0078 98 785.2257 1.6209 0.5888 1.475 99 785.5607 1.6237 0.5904 0.9113 100 814.210 6 2.6838 1.0483 29.194 230 101 815.0004 2.5271 0.989 29.2484 102 815.5555 2.5401 0.9954 29.7115 103 823.3595 2.7219 1.0872 0.9982 104 823.8905 2.723 1.089 1.0276 105 824.1743 2.7198 1.0885 0.5062 106 876.2946 2.4966 1.1295 78.2135 107 877.0469 2.496 1.1 312 64.2808 108 877.2474 2.493 1.1304 31.2945 109 933.0998 1.7754 0.9108 0.1305 110 933.245 1.7823 0.9146 3.304 111 933.3714 1.7826 0.915 1.8531 112 934.329 1.7924 0.9219 2.196 113 935.8002 1.7873 0.9222 0.7332 114 936.0061 1.7861 0.9219 2.8752 115 941.9181 1.7369 0.9079 4.6597 116 942.9179 1.7442 0.9137 4.792 117 943.4478 1.7425 0.9138 3.5097 118 944.4368 1.6413 0.8625 0.5298 119 945.1549 1.6301 0.858 0.2779 120 946.539 1.6459 0.8688 0.8523 121 965.4229 1.2038 0.661 0.0405 122 966.9366 1.203 9 0.6632 0.0504 123 967.0493 1.2036 0.6632 0.0345 124 967.2392 1.2081 0.6659 0.1307 125 967.4571 1.2004 0.662 0.0356 126 968.9027 1.2015 0.6645 0.0557 127 981.8449 4.6293 2.6294 10.7047 128 981.9576 4.6382 2.635 10.3943 129 982.8075 4.6238 2.6314 0. 3104 Full frequency results in file: " CrTBut3_freq_UB3LYP_6311gdp_tight_CH2Cl2_3 .log" 231 REFERENCES 232 R E F E R E N C E S (1) Damrauer, N. H.; Cerullo, G.; Yeh, A. T.; Boussie, T. R.; Shank, C. V.; McCusker, J. K. Science (80 - . ). 1997 , 275 (5296), 54. (2) Damrauer, N. H.; McCusker, J. K. J. Phys. Chem. A 1999 , 103 (42), 8440. (3) Juban, E. A.; Smeigh, A. L.; Monat, J. E.; McCusker, J. K. Coord. Chem. Rev. 2006 , 250 (13 - 14), 1783. (4) Zinato, E.; Riccieri, P.; Sheridan, P. S. Inorg. Chem. 1979 , 18 (3), 720. (5) Kirk, A. D. Chem. Rev. 1999 , 99 (6), 1607. (6) Forster, L. S. Chem. Rev. 1990 , 90 (2), 331. (7) Figgis, B. N. Introduction to Ligand Fields , 2nd ed.; John Wiley & Sons: New York, 1966. (8) Tanabe, Y.; Sugano, S. J. Phys. Soc. Japan 1954 , 9 (5), 766. (9) Schrauben, J. N. Electronic Structure and Excited State Dynamics of Chromium(III) Complexes, Michigan State University, 2010. (10) Juban, E. A.; McCusker, J. K. J. Am. Chem. Soc. 2005 , 127 (18), 6 857. (11) Maçôas, E. M. S.; Kananavicius, R.; Myllyperkiö, P.; Pettersson, M.; Kunttu, H. J. Am. Chem. Soc. 2007 , 129 (29), 8934. (12) Maçôas, E. M. S.; Mustalahti, S.; Myllyperkiö, P.; Kunttu, H.; Pettersson, M. J. Phys. Chem. A 2015 , 119 (11), 2727. (1 3) Ando, H.; Iuchi, S.; Sato, H. Chem. Phys. Lett. 2012 , 535 , 177. (14) Schrauben, J. N.; Dillman, K. L.; Beck, W. F.; McCusker, J. K. Chem. Sci. 2010 , 1 (3), 405. (15) Wang, W.; Demidov, A. A.; Ye, X.; Christian, J. F.; Sjodin, T.; Champion, P. M. J. R aman Spectrosc. 2000 , 31 (1 - 2), 99. (16) WaveMetrics, I. Portland 2015 . ( 17) MathWorks. Natick, MA 2015 . (18) Demid ov, A. A.; Champion, P. M. 1997 . (19) Shimanouchi, T.; Linstrom, P. J. Vibrational Frequency Data http://webbook.nist.gov/chemistry/ ( accessed May 10, 2015). 233 (20) National Instruments Inc. The Fundamentals of FFT - Based Signal Analysis and Measurement in LabVIEW and LabWindows / CVI www.ni.com/white - paper/4278/en/. (21) Veen, R. M. Van Der; Cannizzo, A.; Mourik, F. Van. J. Am. Chem. Soc. 2011 , 133 (2), 305. (22) Consani, C.; Prémont - Schwarz, M.; ElNahhas, A.; Bressler, C.; van Mourik, F. ; Cannizzo, A.; Chergui, M. Angew. Chemie Int. Ed. 2009 , 48 (39), 7184. (23) Dexheimer, S. L.; von Feilitzsch, T.; Peteanu, L. A.; Pollard, W. T.; Mathies, R. A.; Shank, C. V. Chem. Phys. Lett. 1992 , 188 (1 - 2), 61. (24) Pollard, W. T.; Fragnito, H. L.; B igot, J. - Y.; Shank, C. V.; Mathies, R. A. Chem. Phys. Lett. 1990 , 168 (3 - 4), 239. (25) Beck, W. F. P r i v a t e C o m m u n i c a t i o n . 2015 . (26) Weiner, A. M. Ultrafast Optics ; Boreman, G., Ed.; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2009. (27) Dolati, F.; Vakili, M.; Ebrahimi, A.; Tayyari, S. F. J. Mol. Struct. 2015 , 1099 , 340. (28) Pinchas, S.; Shamir, J. J. Chem. Soc. Perkin Trans. 2 1975 , No. 10, 1098. (29) Naumov, V. N.; Bespyatov, M. A.; Basova, T. V.; Stabnikov, P. A.; Igumenov, I. K. Thermochim. Acta 2006 , 443 (2), 137. (30 ) Browne, W. R.; McGarvey, J. J. Coord. Chem. Rev. 2007 , 251 (3 - 4), 454. (31) Chönherr, T.; Atanasov, M. A.; Schmidtke, H. - H. Inorganica Chim. Acta 1988 , 141 (1), 27. (32) Christensson, N.; Avlasevich, Y.; Yartsev, A. P.; Müllen, K.; Pascher, T.; Pullerits, T. J. Chem. Phys. 2010 , 132 (17), 174508. (33) Wand, A.; Kallush, S.; Shoshanim, O.; Bismuth, O.; Kosloff, R.; Ruhman, S. Phys. Chem. Chem. Phys. 2010 , 12 (9), 214 9. (34) Mishima, K.; Yamashita, K. J. Chem. Phys. 1998 , 109 (5), 1801. (35) Hiller, E. M.; Cina, J. A. J. Chem. Phys. 1996 , 105 (9), 3419. (36) Bardeen, C. J.; von Feilitzsch, T.; Shank, C. V. J. Phys. Chem. A 1998 , 102 (17), 2759. (37) Yang, Q.; Xu, G .; Liu, X.; Si, J.; Ye, P. Appl. Phys. B 1998 , 66 (5), 589. (38) Islam, M. N.; Mollenauer, L. F.; Stolen, R. H.; Simpson, J. R.; Shang, H. - T. Opt. Lett. 1987 , 12 (8), 625. 234 (39) Kovalenko, S. A.; Dobryakov, A. L.; Ruthmann, J.; Ernsting, N. P. Phys. Rev. A 1999 , 59 (3), 2369. (40) Ruhman, S.; Joly, A. G.; Nelson, K. A. IEEE J. Quantum Electron. 1988 , 24 (2), 460. (41) Takeuchi, S.; Tahara, T. J. Phys. Chem. A 2005 , 109 (45), 10199. (42) Kukura, P.; McCamant, D. W.; Mathies, R. A. Annu. Rev. Phys. Chem. 2007 , 58 , 461. (43) Bardeen, C. J.; Shank, C. V. Chem. Phys. Lett. 1993 , 203 (5 - 6), 535. (44) Liebel, M.; Schnedermann, C.; Kukura, P. Phys. Rev. Lett. 2014 , 112 (19), 1. (45) Brother, F. E.; Palma, S. M.; Sathianandan, K. In Developments in Applied Sp ectroscopy ; Springer US: Boston, MA, 1963; pp 58 64. (46) Suffren, Y.; Rollet, F. - G.; Reber, C. Comments Inorg. Chem. 2011 , 32 (5 - 6), 246. (47) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr. , J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M. ; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayal a, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, Ö.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Cliffor d, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al - Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C .; Pople, J. A. Gauss ian, Inc.: Wallingford, CT 2004 . 235 (48) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratch ian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, Jr., J. A.; Peralta, J. E.; Ogliaro, F.; Be arpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; F arkas, Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gauss ian, Inc.: Wallingford, CT 2009 . (49) Damrauer, N. H.; Boussie, T. R.; Devenney, M.; McCusker, J. K. J. Am. Chem. Soc. 1997 , 119 (35), 8253. 236 4 Magnetic Field Dependence of Intersystem Crossing in Cr(III) Compounds 4.1 Introduction External magnetic fields have been shown to alter the rates and mechanisms of reactions involving electron spins, including triplet - triplet annihilat ion, intersystem crossing (ISC), and electron transfer. 1 3 These magnetic field effects have received interest since the late 1960s, primarily focusing on radical pairs, separate but correlated spi ns in unique orbitals on the molecule; the application of an external field can change the rate of spin evolution and therefore the rate at which these two spins can recombine into a singlet state. 3 This rate dependence on magnetic field arises from the Zeeman splitting of the initial spin states, as can be seen in Figure 4 . 1 . T he Zeeman splitting is given b y: ( 4.1 ) in which is the Bohr magneton (0.4668 cm - 1 T - 1 ) , g is the effective g factor, H is the magnetic field strength (in Tesla , T ), and m s is the spin quantum number. 4 Shown in Figure 4 . 1 are the Zeeman splittings of a singlet and triplet state with an applied magnetic field, in which the Zeeman splitting is a perturbation on the initial energy of the state. The singlet, with m s = 0, shows no dependence on the magnetic field, as would be expected from Equation 4.1. The triplet state, howe ver, is composed of m s = - 1, 0, 1 values. As for the singlet, the energy of the triplet's m s = 0 level shows no field dependence, however, the m s = 1, - 1 states do show a field dependence where the m s = - 1 level is stabilized with increasing field strength while the m s = 1 level is destabilized with increasing field strength. As long as the energy gap between the states involved is small compared to the mechanism mixing them (i.e. spin - orbit coupling or hyperfine 237 coupling), state mixing is allowed . When the Zeeman splitting produces an energy gap larger than the magnitude of this mixing, the states may no longer communicate and the rate of the process is affected. 5 Figure 4 . 1 Schematic of Radical Ion Pair Energy Levels as a Function of Magnetic Field The radical ion pair depicted here involves exchange between a singlet (S) and triplet (T) state, however the T state is split in a magnetic field into individual m s levels by Zeeman splitt ing. The coupling between the states is represented by 2J, and where the splitting is larger than 2J, the states may no longer couple to produce the singlet product. Reprinted with permission from reference 3 . © (1989) American Chemical Society. These radical pairs are primarily systems with low total spin (i.e. singlets, doublets, and triplets) based on organic compounds, but recently transition metal systems have gained traction for their access to higher spin multiplicities. 6 Many of these studies focus on photochemical processes such as quenching , 7 ligand loss , or photoaquation 8 ; however , some have focused on the photophysics between states within a single transition metal compound. 7 9 Ferraudi and c oworkers have studied the rate of emission in a series of Cr(III) polypyridine compounds - 238 tris(2,2'bipyridine)chromium (III) tris(perchlorate ) and tris(1,10 - phenanthroline)chromium (III) tris(perchlorate) - and found a 10% increase in the rate w ith applied fields of 5 T. 8 Aside from this simple decrease in the lifetime of the doublet emissive state, the emission spectra as a function of field showed an intensity shift from 725 nm to 690 nm, indicating the population of a different state. These compounds can be represented by the same d 3 Tanabe - Sugano diagram presented in Chapter 3 (Figure 3.1) for tris(2,4 - penta nediono)chromium(III) , Cr(acac) 3 , wher e the lowest energy states are closely spaced 2 T 1 and 2 E states . The nominal D 3 symmetry of the Cr(III) polypyridyls forces the 2 T 1 excited state to split into E and A 2 states in zero field, and the Zeeman splitting with applied field causes these states to split further. The increase in emission at 690 nm is assigned to intensity stealing from the 2 E excited state after the 2 T 1 state splits in the field. The overall effect of the field then is to increase the coupl ing between the excited and ground states, which causes a decrease in the lifetime (increase in the rate). 8 While Cr(acac) 3 is roughly oc tahedral in symmetry and should not suffer from this same geometric splitting in zero field, it is anticipated that application of large magnetic fields might perturb the ISC dynamics in th is compound . Using very simplistic m odeling, the splitting of the ground and excited states for Cr(acac) 3 with applied fields up to 25 T is shown in Figure 4 . 2 . This model assumes the 4 T 2 and 2 E initial energies are given by their absorption and e mission maxima, respectively, does not account for any splitting in zero field from g eometric considerations, and assumes g = 2 for the g factor. The Zeeman splittings have been calculated according to Equation 4.1, giving a reduction in 239 the 4 T 2 - 2 E energy gap of 46.7 cm - 1 at 25 T. Whether this perturbation is enough to measurably affect the rate of ISC is unknown . Figure 4 . 2 Proposed Zeeman Splitting of Cr( acac) 3 in Fields up to 25 T The ground (black), 4 T 2 (green), and 2 E (blue) states of Cr(acac) 3 and their proposed Zeeman splitting in fields up to 25T. This model assumes g = 2 for all states and the 4 T 2 and 2 E states are located at their absorption and e mission maxima in zero field, respectively. Investigation of this possible effect utilizes ultrafast laser spectroscopy with sub - 50 fs pulses in high (>15 T) magnetic fields in fluid solutions, which is a very new combination in this area of research. For fields of this magnitude, experiments were carried out at the National High Magnetic Field Laboratory (NHMFL) to make use of the specially designed Split Florida - H elix magnet, capable of producing fields up to 25.2 T. The two compounds investigated in this study are Cr(acac) 3 and tris( 2,2,6,6 - tetramethyl - 3,5 - heptanediono)chromium(III), Cr(TMHD) 3 , which have been well characterized in zero field time resolved measurements. As discussed in Chapter 3, following excitation into the 4 T 2 state, Cr(acac) 3 undergoes sub - 100 fs ISC to the 2 E state, where vibrational 240 cooling is proceeds on a 1.1 ps timescale. Following the same 4 T 2 excitation, Cr(TMHD) 3 exhibits a much slower ISC process, occurring in ~1.8 ps followed by vibrational cooling. Any field induc ed modulations to this ISC timescale should be easy to measure. Cr(acac) 3 therefore forms the control for monitoring the behavior of vibrational cooling in the presence of a large magnetic field. It is simplistically assumed that vibrational cooling will be field independent because it involves the oscillation of the electric dipole of the molecule, but not the spin of electrons in the molecule . These experiments seek to confirm that vibrational cooling is a field independent process and that the applica tion of high magnetic fields can modulate the ISC timescale in simple Cr(III) compounds. 4.2 Methods The experiments performed in this chapter are TA experiments akin to those described in Chapters 2 and 3, except that the sample is housed within a very lar ge magnet capable of producing fields up to 25 T. Optical windows allow the beams to pass through the magnet to the sample and on to the photodiodes where detection takes place in the standard fashion. Section 4.2.1 details the specifics of the TA experi ment built at the magnet lab, while section 4.2.2 discusses the magnet, the Split - Florida Helix. 4.2.1 Optical Components This data was collected at the National High Magnetic Field Laboratory in Tallahassee, FL with the help of Dr. Stephen McGill and Dr. Michae l Bishop. The laser experimental setup included a Vitara osci llator (Coherent, 80 MHz, 511 mW out at 800 241 nm ) coupled to a Legend Elite Duo (Coherent, 1 kHz, 4.6 W at 800 nm) regenerative amplifier capable of producing 4 W at the output with 35 fs pulses. A portion of the output beam i s routed into an OPerA Solo optical parametric ampifier ( OPA ) to produce visible light output at 520 nm (~300 mW output) . The OPA output power i s attenuated externally with a variable neutral density (ND) filter wheel before passing through a 90° periscope to rotate the polarization from vertical to horizontal. This horizontal polarization is necessary for the prism compressor on the beam line, which uses a one prism configuration . 10 The prism compressor output pass es through a thin wedge ( 1.5 mm fused silica, 2 - 3°) to generate the pump, probe, and reference beams. T he transmitted beam is used as the pump beam, the front surface reflection i s used as the probe beam, and the rear surface reflection i s used as the reference beam. The pump beam was passed over a delay line ( Aerotech, PRO165LM with Ensemble controller ) capable of ~800 ps delays before passing through a wire - grid polarizer , waveplate, and optical chopper (NewFocus, 3501, 217 Hz) just prior to the final turning mirror. A 1 m focal length lens placed after this mirror is used to focus the pump beam onto the sample locat ed inside the bore of the magnet . The probe beam passes through a 1 mm piece of fused silica to balance the chirp caused by the wedge on the pump beam . The probe beam is routed over a distance roughly equal to the pump beam and is passed through a wire grid polarizer and thin waveplate so that the pump and probe beam polarizations are at magic angle. The probe beam is reflected toward the sample at a small angle (vertical offset) from the pump and passes through the center of the same 1 m lens to focus on the sample. The transmitted probe beam is attenuated with a variable ND filter wheel before passing through a monochromator ( Mini - chrom, DMC1 - 242 03) equipped with 300 µm slits (2 nm bandpass) and focused with a lens into the photodiode (Thor Labs, PDA55 ). The reference beam reflection is directed towards the reference photodiode by a single mirror and passes through a variable ND filter wheel before the photodiode (Thor Labs, PDA55 ). This reference detection takes place near the pump delay line in order to minimize the number of open beams near the magnet. The signals a re recorded using lock - in amplification with SRS830 lock - in amplifiers connected to the computer using a GPIB interface. The data a re collected using LabVIEW programs written by Drs. McGill and Bishop , which function in largely the same way as the coheren ce LabVIEW program previously described in Chapter 2. The data sets consist of an average of at least three scans. Sample solut ions were prepared using a home - built UV - Vis instrument coupled to an Ocean Optics USB 2000 spectrometer. Spectra were collec ted after data collection to ensure sample integrity. Typical sample absorptions were 0. 3 - 0. 4 at the pump wavelength in a 1 mm path length cell. The pulse compression was checked each day by alternately routing the prism compressor output to an SHG FROG setup which included a plate of fused silica to compensate for the dispersion of the lens, waveplates, polarizers, and the wedge. FROG trace collection was accomplished using a custom - built LabVIEW program 11 previously described in Chapter 2, and subsequently characterized using the MATLAB FROG code available from Professor Trebino. 12 Typical pulse durations for these experiments were ~ 4 5 fs. 243 4.2.2 Magnet Capabilities and Probe Design The magnet used for these experiments is the Split Florida - Helix, a specially designed split resistive magnet capable of produci ng 25 .2 T fields while accommodating four elliptical viewing/scattering ports in the mid - plane region for optical experiments. Each port is a cone shape with a 45° horizontal spread and an 11.4° vertical spread, allowing for maximum versatility with vario us transmissive and reflective experiments. 13 For the ultrafast experiments described here, the pump and probe beams enter through one port and exit out the po rt on the opposite side; the two side ports are not used. The vacuum plates on the faces of the ports were removed to minimize the dispersion in the experiment. A cross section of the magnet can be seen in Figure 4 . 3 . The vertical channel running through the center of the magnet is called the bore. In this cross sectional view, two of the viewing ports are shown with their apex meeting at the central bo re of the magnet ; this is the sample position inside the magnet . The vertical gold bars , wrapped in shades of orange/brown, above and below these ports represent the five resistive coils generating the magnetic field. In this arrangement, the field is pe rpendicular to the probe beam propagation through the sample. The sample cuvette is lowered into the bore of the magnet, and thus the optical beam path, by a custom - designed probe. This probe, at the most basic level, is a long rod with a special cuvette holder secured to the end capable of holding three sample cuvettes in a vertical arrangement. This allows for a quick vertical adjustment of the probe to change the sample without affecting the pump - probe overlap in the cuvette. Further details about th e probe are given in Appendix A. The data presented here were 244 collected at constant fields, typically with a 0 T data set collected prior to ramping the field and after ramping the field. Figure 4 . 3 Th e 25 Tesla Split Florida - Helix Magnet While the entire inner workings of the magnet are shown here, only a few components will be highlighted. The central, vertical tube is the bore of the magnet where the probe was loaded and the cuvette height adjusted so that it was centered on the opening of the ports. The cones tapering toward the central tube from the right and left are the viewing ports which were used to pass the beams through the sample. See text for details. Figure reproduced with permission from reference 14 . © National High Magnetic Field Laboratory. 245 4.3 NHMFL Stud ies 4.3.1 D ynamics of Cr(acac) 3 in Acetonitrile and D ichloromethane in High Fields Previous studies on Cr(acac) 3 confirming that the vibrational cooling timescale i s 1.1 ps were performed in acetonitrile (MeCN), so the initial magnet studies reproduced these conditions . 15 Sinc e t he experiments were restricted to one color, the pump pulse was tuned to 525 nm, producing a vibrationally hot 4 T 2 state, while the probe was tuned to 521 nm, corresponding to the 2 E absorption maximum. The data , collected over an ~3 ps window and at f ields of 0, 5, 15, and 25 T , are shown below in Figure 4 . 4 . The inset, wh ich shows an expanded view of the change in absorbance with field, shows Figure 4 . 4 T he Dynamics of Cr(acac) 3 in MeCN in Fields From 0 T to 25 T Shown in the large plot are the full scale dynamics of the solvent window and Cr(acac) 3 dynamics ; the inset focuses on the signals from Cr(acac) 3 . The amplitude of the signals are small, but all of the data fit well to a 1.1 ps decay as expected for vibrational cooling on the 2 E surface. that the kinetics are identical in fields up to 15 T. The 25 T trace, however, does not appear to have the same amplitude, despite the fit of the data being the same. 246 Because of the minimal amplitude change in the signal, the exponential fit results in a large error; however, if the fit is fixed at 1.1 ps, the residuals are reasonable, as shown in Figure 4 . 5 . Figure 4 . 5 Cr(acac) 3 in MeCN with 1.1 ps Fit Shown here is the data collected at 15 T (525 nm pump, 530 nm probe) with a fixed 1.1 ps exponential decay. The residuals, shown at the top of the figure, show a good agreement for this fit, despite the lack of significant amplitude change. This agrees with the zero field vibrational cooling timescale for Cr(acac) 3 . A closer examination of the nonresonant solvent response around time zero reveals there are some changes with field to the shape and amplitude of these peaks. A comparison to the data collected on pure MeCN at the same magnetic fields reveals these same changes. The trace at 0 T is just slightly different than the traces at 5 and 15 T, while the trace at 25 T shows the most marked difference of the grouping. This can be seen in Figure 4 . 6 , below , in which the largest difference in the 25 T trace occurs on the positive side of the differential signal. This is in agreement with the solvent signals observed in the presence of Cr(acac) 3 , where the 25 T solvent response had 247 less amplitude in the positive spike than at other fields. Unfortunately, the cause of this field dependence for the solvent response is not known at this time; it is possible tha t the probe becomes less stable at higher fields and the transient absorption experiment is sensitive enough to register this small change in the sample position at high fields. Figure 4 . 6 Acetonitrile Cross Correlation Signals from 0 to 25 T The MeCN signal shows little variation with field up to 15 T but shows a dramatic difference in the signal at 25 T. This is consistent with the data collected on Cr(acac) 3 solutions and suggests an i ntrinsic field dependence on the solvent signal. The data collected in dichloromethane (DCM) look largely the same as the data in MeCN. The oscillations in the data are from the impulsive stimulated Raman scattering in DCM; an FF T of the raw solvent trace ( Appendix B , Figure 4.B1 ) cleanly returns a 280 cm - 1 frequency component which matches the literature value of 281.5 cm - 1 very well. 16 While t he data have better agreement between all of the fields in this case, the fits are subject to the same errors from a lack of significant amplitude change in the system. As with the MeCN data, t hese traces may also be fit with a fixed 1.1 ps exponential decay to give quite reasonable residuals (Appendix B, Figure 4.B2 ). Closer 248 examination of the dynamics occurring aroun d time zero reveals that the data show close agreement until 25 T. This shifting at full field is consistent with the data on pure DCM (Appendix B, Figure 4.B3 ) and reproduces the shifting observed for MeCN in a 25 T field . Figure 4 . 7 The Dynamics of Cr(acac) 3 in DCM in Fields From 0 to 25 T The traces at different fields have better amplitude matching between different magnetic fields than those seen in MeCN. The oscillations in the data are from DCM and match the ground state - CCl 2 scissor mode. For both of these data sets, the ISC process was not visible in the recovered kinetics. Given the results from 35 fs pump pulses in C hapter 3, this observation is not surprising. And , loosely assuming the ISC perturbation works in the same fashion as the Cr(III) polypyridyls, the ISC would be faster in applied fields because of the increased coupling between the initial and final states . Despite the small amplitude changes observed in these data sets, they uniformly show a 1.1 ps decay which corresponds to the vibrational cooling timescale in zero field, indicating that vibrational cooling is indeed independent of field. 249 4.3.2 Dynamics of Cr(TMHD) 3 in D ichloromethane in High Fields The data for Cr(TMHD) 3 w as collected over a larger time delay window in order to resolve the ~1.8 ps ISC process previously observed in this compound. 17 The probe, at 524 nm, is tuned to the 2 E absorption maximum and should be well positioned to observe the formation of the 2 E state. Indeed, this increase in absorption is seen in all fields from 0 T to 25 T; however, these dynamics appear uniform at all fields ( Figure 4 . 8 ). The amplitude change observed in these data sets is enough to obtain reasonable, unrestricted fits for all fields. The recovered time constants agree with the previously observed 1.8 ps component within error (Appendix B, Figure 4.B4 ) . Figure 4 . 8 Dynamics of Cr(TMHD) 3 in DCM at Fields From 0 to 25 T The rise in the change in absorbance is associated with the transfer of population to the 2 E from the 4 T 2 excited state. The kinetic fits of all traces agree within error to the 1.8 ps ISC timescale observed in zero field. 250 The solvent response also appears more uniform for all fields, in contrast to the dynamics observed for Cr(acac) 3 . The shape of the solvent response appears as a negative spike rather than a derivative signal as a result of the increased step size in the experiment. Scans us ing smaller step sizes show the derivative solvent signal around time zero as expected (not shown) . The agreement of the fits for this data set to that collected in zero field indicates that the 25 T field was not enough to perturb the ISC dynamics in Cr(TMHD) 3 . Simplistically, the Zeeman splitting in this system may be viewed in the same way as was illustrated in Figure 4 . 2 for Cr(acac) 3 , despite the slight shifting in absorbance and emission maxima for this compound. 17 T he Zeeman splitting would reduce the 2 E - 4 T 2 energy gap by ~45 cm - 1 , while causing a separation between the ms levels of 70 cm - 1 at full field. Given th at the thermal energy in the system ( k B T ) is 207 cm - 1 , it is not surprising that the Zeeman splitting did not have a large effect on the system. It should be stressed, however, that the proposed Zeeman splitting is based on a number of simplistic assumpti ons about geometry and the g factor that may not be accurate for this system , especially the splittings in the excited states . The Cr(TMHD) 3 data set was only collected once due and so the results need to be verified with subsequent data sets; however, the initial results indicate that the applied magnetic fields are not successfully modulating the ISC dynamics observed in this system. It may also be argued that since the 1.8 ps component was previously assig ned to both ISC and vibrational cooling processes, that the vibrational cooling timescale outweighs the ISC process in this time constant. As vibrational cooling has 251 been shown to be independent of field in Cr(acac) 3 , this would explain the field independ ence of the kinetics observed in Cr(TMHD) 3 . 4.4 Concluding Comments The experiments performed at the magnet lab had an interesting set of limitations which made for less than ideal experimental conditions. The largest factor in the stability of these data s ets resulted from ongoing maintenance in the building, manifesting as instability in the room temperature and thus , the laser output. Unfortunately, these circumstances could not be prevented and efforts were made to obtain t he best laser stability poss ible under such conditions. Another factor affecting the quality of the data was the use of a wedge to form the probe and reference beam s . The reflection off the wedge typically produced a probe pulse with a power of 0.056 µ J for a pump pulse of 3 µ J. V alues for experiments performed in our research lab at Michigan State University typically utilize pump powers of 5 µ J and probe powers at 1/10 th of the pump power, or 0.5 µ J. These lower pump powers result in less excited state population and the extreme ly low probe powers could be responsible for the minimal excited state signals observed. Changing the slit settings on the monochromator to a wider setting did not significantly increase the signals observed. The primary advantage of the wedge is that an y double pulses produce will not trace the same vector as the primary beam direction (i.e. the back reflection used as the reference), which is not the case with traditional beam splitters. It is possible that better signals could have been achieved throu gh the use of anti - reflection coated beam splitters instead of the wedge. 252 Another key dif ference in the experimental set - up is the use of one lens to focus both the pump and the probe on the sample. Not only did the 1 m focal length produce a wider bea m waist at the focal point, it is unlikely that the beam size of the pump and probe beams are significantly different. The lens position was optimized by observing the excited state signal at positive time as a function of lens position, but it is difficu lt to en s ure that the tightest focus at the sample was achieved. The long focal length was necessary due to the breadth of the magnet, as well as safety concerns for the field strength immediately outside of the magnet. While every effort was made to use non - magnetic optical mounts and bases, all optics were kept at least two feet from the surface of the magnet as a precaution. With these restraints in mind, a 1 m focal length lens gave the tightest focus for these parameters. Coupled to the issue of beam spot sizes and focal planes is the changing of the probe rod position each time the set of samples was changed. Th e improved probe adjustment set - up greatly reduced variations in sample position between cuvettes in the same holder, but when the entire probe rod was removed and replaced, it was not guaranteed to maintain the same position as before. The "best probe alignment" ensured that the probe was centered within the bore when viewed from below the magnet an d that the back reflection off the cuvette was not following the incoming pump beam (i.e. the cuvette was slightly canted in the bore). Care was taken to aim this back reflection to the same location each time the sample was changed to ensure the canting remained uniform between cuvettes. Given these issues and the results from the data sets collected, it h as been successfully shown that vibrational cooling is a field independent process. The 253 v ibrational cooling timescales for Cr(acac) 3 in both MeCN an d DCM agree well with data collected in zero field, and are consistent for multiple data sets. The lack of any ISC signatures in these kinetic traces precludes any modulation of the ISC timescale for Cr(acac) 3 . I nitial e xperimental observations for Cr(TM HD) 3 indicate that the application of fields up to 25 T does not result in a measurable difference in the time constant for ISC. This should be verified in f uture experiments , which would also benefit from moving to a two color experimental set - up. This would allow the pump to be tuned to the ground state absorption maximum, while the probe could be tuned to the 2 E maximum. These conditions should increase the signal - to - noise of the data set and hopefully provide larger amplitude changes in the observed signals. I t may also be possible to expand these experiments variable temperature data sets, along with changing the applied field. The magnet is capable of variable temperature measurements, but a new probe designed to work with a cryostat will be nee ded. Th e reduction in temperature would reduce the thermal energy in the system, potentially magnifying the effect of the Zeeman splitting on the ISC kinetics. 254 APPENDI CES 255 Appendix A : Probe Design The results presented in this chapter are the product of two trips to the NHMFL - one in July of 2014 and one in January of 2015 - both of which proved to be a useful learning experience for all parties involved. The trip in July helped to resolve many unexpected data collection issues, as this was the second time transient absorption experiments had been performed in the Split Florida - Helix. The data collection programs were refined, the delay line programming improved, and the cuvette holder went under a redesign. This first iteration of a probe for transient absorption experiments consisted of a cage - like apparatus being attached to the top of the magnet to hold the probe in place during experiments. This holder, depicted in Figure 4.A1 B, consisted of four arms, spaced around a circle 90° apart with two vertically spaced tension screws in each arm. The top screws were used to tilt the probe rod ( Figure 4.A1 , A) as necessary to ensure it was centered in the bore of the magnet, while the bottom screws were optimized initially for centering in the bore and then not significantly ad justed when the probe was reins erted into the magnet. The cuvette holder at the end of the probe ( Figure 4.A1 , B and C), pinches the sides of the cuvette in a narrow track and is mounted to the bottom of the probe rod with a set screw. While this design allowed for optimal use of the cuvette face, it required the probe rod to be removed from the magnet each time a new sample was necessary. When removing the probe from the magnet, only two of the top tension scre ws and two of the bottom tension screws of the probe holder were loosened. It was hoped that by not adjusting two of the screws, a probe position close to the previous position 256 Figure 4 . A 1 Initial Probe Design Panel A dis plays the entire probe rod, where the thicker spacers near the top help secure the rod in the probe holder above the magnet. Panels B and C detail the cuvette holder design, where narrow tracks help hold the sides of the cuvette and ensure it stays uprigh t in the probe. Panel D shows the tension screw apparatus used to align the probe inside the bore of the magnet; the bottom screws aligned the bottom of the rod, while the top screws tilted the top of the rod. might be obtained. However , in practice, the cuvette was most likely in a different position. The aluminum spacers seen at the top of the rod were prone to deformation, and required successively more adjustments of the tension screws to obtain a reasonable alignment in the bore as the experiments progressed throughout the week. To circumvent some of these issues, a new probe was designed which would allow for three cuvettes to be loaded vertically at one time and for the probe position to 257 be largely maintained between sample changes. The new probe design can be seen in Figure 4.A2 , below , where the probe rod now contains an outer "s leeve" to allow the inner rod to move up and down without adjusting the tilt of the rod overall. The probe holder was changed from the cage - like apparatus to two plates with x - y axis adjustments on them. These plates were sandwiched on the top and bottom of the optical table above the magnet to achieve the same fixed position and adjustment settings as the cage - like apparatus in the previous version. The x - y plate below the optical table ( Figure 4.A2 C) fits snuggly around the probe rod and is optimized for probe centering in the bore; for all successive sample changes, this position is not adjusted. The top x - y plate is adjusted as necessary after the samples were changed, though this was hardly necessary. The opening of th e x - y plate is fairly snug ar ound the probe rod, but the tension clamp at the top of the probe rod locks the probe arm in its vertical position. The rang e of motion allowed by this set - up is really quite minimal and greatly reduced alterations in the probe position when changing the cuvettes. To move to a different cuvette, the top tension clamp was loosened and the inner rod was adjusted and reclamped. As before, the cuvette was canted slightly to ensure the back reflection of the pump did not trace the original beam path. The a bility to switch samples by a simple vertical adjustment of the probe was a phenomenal improvement over the initial probe design and greatly reduced the time required to get a new sample in place for the experiment. The experiments detailed in this chapte r were collected with this new, three sample probe. 258 Figure 4 . A 2 Improved Probe Design Panels A,B,C detail t he x,y micrometer adjustment design for precise probe rod alignments. The new probe rod, seen in panels D and F, allows for the inner rod to be adjusted while the outer rod maintains the alignment within the bore. Panel E displays the new three cuvette design, so that three samples may be monitored with a single probe alignment. 259 Appendix B: Exponential Fits for Cr(acac) 3 and Cr(TMHD) 3 Figure 4 . B1 FFT of the Oscillatory Component in the DCM Signal The oscillatory feature observed in the DCM signal was processed in IGOR to give the FFT of the signal as described in chapter 2. The 280 cm - 1 agrees well with t he expected 282 cm - 1 - CCl 2 scissoring mode for DCM. Figure 4 . B2 Cr(acac) 3 in DCM with 1.1 ps Fit Typical data for Cr(acac) 3 in DCM is shown here for 15 T (518.5 nm pump, 514 nm probe) with a fixed exponential fit of 1.1 ps, corresponding to the vibr ational cooling observed in zero field. The residuals of this fit, seen at the top of the figure, reflect the validity of this fit. 260 Figure 4 . B3 Dichloromethane Solvent Response in Fields from 0 T to 25 T The solvent response of dichloromethane in fields of 0, 5, 15, and 25 T. Signals exhibit more amplitude modulation in the negative peak than that observed with MeCN, but overall the traces are largely the same at fields up to 25 T where larger deviations in the positive peak are observed. Figure 4 . B4 Cr(TMHD) 3 Exponential Fit The data collected for Cr(TMHD) 3 exhibited enough amplitude change to be individually fit. The data shown here for 16 T agrees well with the data collected at other fields and exhibits a 1.7 ps rise, which agrees well with the expected ~1.8 ps ISC process in zero field. 261 REFERENCES 262 R E F E R E N C E S (1) Cohen, A. E. J. Phys. Chem. A 2009 , 113 (41), 11084. (2) Aich, S.; Basu, S. Chem. Phys. Lett. 1997 , 281 (4 - 6), 247. (3) Steiner, U. E.; Ulrich, T. Chem. Rev. 1989 , 89 (1), 51. (4) Drago, R. S. Physical Methods For Chemists , 2nd ed.; Surfside Scientific Publishers: Gainsville, FL, 1992. (5) Ferraudi, G. Pur e Appl. Chem. 1998 , 70 (4), 10335. (6) Mori, Y.; Hoshino, M.; Hayashi, H. Mol. Phys. 2002 , 100 (8), 1089. (7) Ferraudi, G.; Arguello, G. A. J. Phys. Chem. 1988 , 92 (7), 1846. (8) Ferraudi, G.; Arguello, G. A.; Frink, M. E. J. Phys. Chem. 1987 , 91 (1) , 64. (9) Ronco, S.; Perkovic, M.; Ferraudi, G.; Cozzi, M. Chem. Phys. 1992 , 162 (1), 95. (10) Aktürk, S.; Gu, X.; Kimmel, M.; Trebino, R. Opt. Express 2006 , 14 (21), 10101. (11) Bishop, M. M. Tallahassee , FL, 2014 . (12) Wong, T. C.; Trebino , R. Atlanta , GA, 2013 . (13) IEEE Trans. Appl. Supercond. 2012 , 22 (3), 4301604. (14) Laboratory, N. H. M. F. 25 Tesla, 32 mm Split Helix Magnet (Cell 5) https://nationalmaglab.org/user - facilities/dc - field/instruments - dcfield/resistive - magnets/split - magnet - cell - 5 (accessed Feb 9, 2014). (15) Juban, E. A.; McCusker, J. K. J. Am. Chem. Soc. 2005 , 127 (18), 6857. (16) Shimanouchi, T.; Linstrom, P. J. Vibra tional Frequency Data http://webbook.nist.gov/chemistry/ (accessed May 10, 2015). (17) Schrauben, J. N.; Dillman, K. L.; Beck, W. F.; McCusker, J. K. Chem. Sci. 2010 , 1 (3), 405. 263 (18) Schrauben, J. N. Electronic Structure and Excited State Dynamics of Chromium(III) Complexes, Michigan State University, 2010. 264 5 Outlook and Future Work A significant portion of the work carried out for th e studies presented in this dissertation was invested in the experimental aspects presented in C hapter 2: acquiring a new 35 fs laser system, implementing pulse compression techniques to maintain the 35 fs pulse duration at the sample, successfully characterizing pulses at the sample, and re working the existing 120 fs pulse laser system to achieve 13 ns delays. These efforts have resulted in the lab's ability to perform transient absorpt ion experiments with ultrashort pulses , not only for vibrational coherence measurements presented in this document, but also for anisotropy experiments on Ru(II) polypyridyls and o ther transition metal compounds. The 120 fs laser system can successful ly c haracterize ground state recovery dynamics between 1 - 10 ns , a time span that was previously immeasurable in this lab . Preliminary investigations of the solvent dependence on ground state recovery in tris(2,4 - pentanediono)chromium(III) , Cr(acac) 3 , (Chapte r 3, Appendix B ) indicate that this could be a rich new area of study for transition metal complexes that few research labs have the ability to explore. The data collection and work up programs have also benefitted from the experience and information gai ned over the course of this work. New programs/attribut es include: the automatic adjustment to the appropriate wait time based on the step size during data collection, the collection of both X (data) and Y (phase) channels from the lock - in amplifier, a pr ogram to rephase the data should the phasing change over the course of an experiment, the use of two lock - in amplifiers to simultaneously collect the reference photodiode signal and the differential signal at every time delay , frequency resolved optical ga ting experiments and data workup, linear 265 predictive single value decomposition data processing, and time - dependent fast Fourier transforms ( TD FFT ) . The availability of these programs greatly enhances the capabilities of this lab. The ability to reliabl y collect vibrational coherence data opens the door to studies on other substituted Cr(acac) 3 - type compounds. Many derivatives have been previously synthesized by Dr. Joel Schrauben over the course of his PhD work in this group and are available for study . 1 A summary of these molecules is presented in Figure 5 . 1 , where both the R and R' positions are available for substitution. Transient Figure 5 . 1 Cr(acac) 3 Derivatives Available for Future Coherence Studies Synthesized and initially characterized on the 120 fs laser system, these compounds are available for future studies and represent a variety of substituents. absorption experiments utilizing 120 fs pulses revealed that substitution at the - R position is largely ineffective for altering the intersystem cr ossing (ISC) and potentially, the ground state recovery timescales in these compounds. 1 In light of the vibrational 266 motions observed in Cr(acac) 3 in C hapter 3, it may prove interesting to investigate these compounds utilizing 35 fs pulses in conjunction with computational studies to see if the key vibrations are significantly affected by the substituent. The scissoring motions at 235 and 255 cm - 1 ( see Chapter 3) may be li mited by the steric bulk introduced in this R position , potentially altering the other modes observed during ISC if they are strongly coupled to the s e vibration s . The ground state recovery timescales of these compounds may now be quantified utilizing the 13 ns delay line, which could bring to light some differences for this series of compounds. As for substituents in the - R' positions, the 120 fs data show some variation from Cr(acac) 3 dynamics, but not all of the substituents exhibit as pronounced of an effect as tris( 2,2,6,6 - tetramethyl - 3,5 - heptanediono)chromium(III) ( Cr(TMHD) 3 , R'= t - butyl). 1 A common theme among thi s series though, is the presence of two features: one in the blue that decays and one in the red that grows in as a function of time. The particular dynamics for each system are different, and some have disparate timescales for the decay and rise feature s (i.e. 700 fs and 7 ps) which bear further investigation. 1 The protocols in place for setting the polarization of the pump and probe beams when the initial data on these m olecules were collected is now suspect after polarization experiments performed over the course of this thesis. It is possible that the fast decay dynamics observed in bluer wavelengths for these compounds are the result of residual solvent signals or ani sotropy in the data. Those processes would account for the ten - fold difference in decay and rise times for these data sets. With the cur rent optimized experimental set - ups, these systems would benefit from a re - characterization to verify that these short decay times are not the result of artifacts in the data. If these disparate 267 time scales are in fact real, further investigation into the vibrational modes active in these systems could be enlightening. Aside from a wealth of additional compounds that w ould benefit from vibrational coherence experiments, the data presented in this dissertation may benefit from a more thorough analysis using the TD FFT program described in C hapter 2, A ppendix H. This program was used to investigate data sets on a few occ asions with no concrete results, but an improvement in the window function could increase the utility of this program. Kraszewski and coworkers have detailed the impact of the window function on the results of these kinds of analyses and have successfully shown that a smoothed rectangular function gives more accurate results without artificially weighting parts of the data within the window. 2 Successful use of this program would give a pseudo - two dimensional view of the data to view the transfer of vibrational energy with time. The primary advantage of this analysis is that it requires no extra steps during data collection and can monitor the exchange of vibrational energy between the low frequency modes observed in the experiment. An alternative approach would be to collect transient 2D IR (t - 2DIR) data to resolve which vibrational modes are active and coupling as a funct ion of time. Dr. Kevin Kubarych has succinctly summarized the benefits of two types of transient 2DIR experiments , which yield different information about the system. "[T riggered - exchange 2DIR ] provides vibrational mode correlation in optically triggered processes by mapping reactant vibrations to product vibrations, thus avoiding ambiguities as sociated with one - dimensional transient absorption methods . [Transient - 2DIR] extends to transient spec ies the structural ly sensitive information inher ent to 2DIR, such as normal - mode 268 coupling and vibrational energy transfer rates with a temporal dynamic range spanning multiple time scales ." 3 While these experiments directly probe the relationship between vibrational modes, the y are currently used in the mid - IR to observe modes between 1,700 and 2100 cm - 1 , typically. 3 6 If IR sources between 100 - 600 cm - 1 were available for this experiment, a direct measurement of the TD FFT 2D "spectra" would be possible. Another experimental technique, 2D electronic spectroscop y (2DES), while not directly probing IR transitions, may be able to resolve these vibrations at low frequencies. In a recent paper by Greg Scholes and coworkers , 2DES is applied to methylene blue and the population dynamics are removed from the resulting 2D spectra to give the coherent oscillations in the data, which is then Fourier transformed to give the frequencies . 7 By coupling thi s data with traditional pump probe spectra collected with a broad - band white light probe, they are able to observe the frequencies of the Franck Condon active vibrations in this molecule and associate them with the geometry change observed in the excited s tate of methylene blue. By inspecting the amplitudes of the observed frequencies, they were able to refine the important displacement coordinates for the ground and excited state surfaces. The works of Scholes, Ando, Tahara, and others highlight the imp ortance of computational modeling to interpret the results of observed vibrational coherences and surface crossings. 7 9 Geometry optimizations have been performed by these authors using both density functional theory and complete active space self - consistent field (CAS - SCF) methods . The primary advantage of CAS - SCF is the ability to model the wavepacket d ynamics. In light of this, a collaboration with Dr. Ben Levine at M ichigan 269 S tate U niversity seeks to model these dynamics for further insights into the vibrations and the connection between geometric changes and photophysical processes in these Cr(III) compounds. 270 REFERENCE S 271 R E F E R E N C E S (1) Schrauben, J. N. Electronic Structure and Excited State Dynamics of Chromium(III) Complexes, Michigan State University, 2010. (2) Biomed. Opt. Express 2014 , 5 (9), 3023. (3) Baiz, C. R.; Nee, M. J.; McCanne, R.; Kubarych, K. J. Opt. Lett. 2008 , 33 (21), 2533. (4) Nee, M. J.; McCanne, R.; Kubarych, K. J.; Joffre, M. Opt. Lett. 2007 , 32 (6), 713. (5) Delor, M.; Sazanovich, I. V.; Towrie, M.; Weinstein, J. A. Acc. Chem. Res. 2015 , 48 (4), 1131. (6) Hunt, N. T. Dalt. Trans. 2014 , 43 (47), 17578. (7) Dean, J. C.; Rafiq, S.; Oblinsky, D. G.; Cassette, E.; Jumper, C. C.; Scholes, G. D. J. Phys. Chem. A 2015 , 9098. (8) Ando, H.; Iuchi, S.; Sato, H. Chem. Phys. Lett. 2012 , 535 , 177. (9) Hua, L.; Iwamura, M.; Takeuchi, S.; Tahara, T. Phys. Chem. Chem. Phys. 2015 , 17 (3), 2067.