THE EFFECT OF ELECTRONIC SPIN ON THE REACTIVITY OF SPIN - COUPLED TRANSITION METAL COMPLEXES By John Andrew Kouzelos A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Chemistry Doctor of Philosophy 2015 ABSTRACT THE EFFECT OF ELECTRONIC SPIN ON THE REACTIVITY OF SPIN - COUPLED TRANSITION METAL COMPLEXES By John Andrew Kouzelos V ariable temperature X - ray crystal structures for the spin coupled [Fe 2 ( - OH)( - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ] + complex were acquired and studied computationally, where it was found there was observable structural effects attributed to increasing the thermal occupation of high er spin states. These effects were manifest as structural changes in the exchange coupled dimer that were not present in a structural analogue. It was determined through computational studies that these structural changes act to reduce the exchange coupling between the Fe III centers which previous studies have shown could affec t the potential reactivity of this system. Detailed mechanistic studies on the spin coupling have shown this change in coupling is mediated primarily by a change in the ( - OH) bond distance, which may or may not be due to the thermal occupation of higher s pin states or could be due to other external effects. A covalently linked intramolecular donor - acceptor assembly consisting of a ruthenium polypyridyl bound to a Mn II Zn II bearing macrocycle was characterized and the variable temperature time resolved emis sion of this compound was investigated where the presence of a thermally activated quenching process was discovered . This quenching of the emissive excited state of the Ru donor by the macrocyclic acceptor was determined to have a thermal barrier of 80 ± 2 0 cm - 1 and was found to be proceeding via a Dexter energy transfer mechanism. The origin of this barrier was determined to be due to a reorganization process that raised the energy of the acceptor due to the rigid medium in which these compounds were studi ed. This assignment was confirmed through supporting density functional theory calculations. Related to the Mn II Zn II donor - acceptor system , c omputational studies on the exchange coupled Mn II 2 Schiff - base macrocycle that wa s previously studied as the acceptor in a donor - acceptor assembly were performed to provide insight as to the observed increased quenching rate in an analogous Mn II 2 donor - acceptor system compared to Mn II Zn II system. The spin coupled states were investigated via the broken symmetry formalism, and the electronic structure of ligand field excited spin coupled states was also studied. The orbital mechanisms of the exchange interaction were studied and it was determined t hat the linking ligand in the donor - acceptor assembly has minimal impact on the spin coupling of this system, so excited states of the energy donor would have little impact on the thermal occupation spin state in this system. Interestingly, it was also fou nd through the broken symmetry electronic structure investigations that there were substantial thermodynamic differences in the ligand field based excited states of the two systems such that the observed thermal barrier to quenching in the Mn II Zn II system is deduced to be non - existent based on the computational results. In this way there is potential that the spin coupling interaction has affected the dynamics of this system. Copyright by JOHN ANDREW KOUZELOS 2015 v This dissertation is dedicated to my parents and the rest of the Kouzelos family vi ACKNOWLEDGEMENTS I feel the accomplishment of earning my PhD would not have been possible without the contributions and assistance of so many people over the years. Along the way, with this assistance I was able to not only advance chemical research but also advance myself as a person and have fun alo ng the way. All of this help must therefore be mentioned as this accomplishment is almost as much theirs as it is mine. I first want to thank Jim for allowing me to join him in the pursuit of SCIENCE and doing a great job of injecting me with enthusiasm fo r my work. Working for Jim is great because he is one of the sharpest minds (and wits) I have ever had the pleasure of meeting, and it was great having the opportunity to learn from one of the best. Of course my McCusker Group compatriots were the real peo ple I need to thank for putting up for Monica Soler for graciously providing me with a sizeable portion of my dissertation research, Rick for showing me the ropes in the lab and at the Riv, Troy for educating me in the ways of the cryostat, VT emission and pristine glassware, Joel for always being a mellow influence in the lab, Kate for help with ruthenium chemistry and teaching CEM 411, ShenShen for being an inter national man of mystery, Allison for her helpful input and discussions, Dong for being a synthetic god amongst men , Lindsey for always helping out and being the best in the lab, Lisa for the fun times and those wonderful nights of VT emission, Eileen for a lways providing a stark contrast for my disorder and always being around to talk with, Larry for being my partner in crime in the lab and an awesome friend , Jennie for always being so nice cheerful and helpful, Dani for vii more VT nights , sass and proofreadin g this thesis, Monica C arey for your confident opinions, and finally Sara and Jon for taking over my role in the group when I am gone. It also goes without s aying that my family played a large part in allowing me to get this degree as I would not have gotten to where I am today and I would not be who I am today without their love and support. I want to thank Mom and Dad for always pushing me to be the most I a m capable of, Yia - Y ia for teaching me the value of education , Niko for being my best friend , Alexi for always cheering me on , and the extended family for always being interested in my progress . I want to thank my other friends for their support as well. I would like to especially thank the online game night r egulars : Donny, James, Logan, Greg, Tim, and Yu for many great games of Dominion, Carcassone, Skulls, and Cats . It was a great way to keep up with all of you and have fun as well. The rest of the Halo - Frosh need to be thanked for the camping trips that always provided great motivation to get work done (and Donny again for the Fresno boating adventure). Here is to many more adventures! I want to thank my Chemistry/WoW/Lunch friends Shaun and Colin for g iving me a great welcome in Michigan , keeping life in the Chemistry building interesting, and introducing me to Asian Buffett. I want to thank my awesome Chemistry mentors I have had throughout the years including Mrs. Walker, Mr. Cunningham, Professor Cav e, Professor Johnson, and anyone else bold enough to let me loose in the lab. Thanks to you all I have developed and continue to have a fascination with chemistry. viii Thanks again to anyone who has helped me out over the years and who I have not yet acknowled ged; this dissertation would not have been possible without you! ix TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ ........................ xii LIST OF FIGURES ................................ ................................ ................................ ..................... xiv KEY TO ABBREVIATIONS ................................ ................................ ................................ ...... xix Chapter 1: Overview of the Concepts and Modeling of Spin Exchange Coupling and its Effects on Photo i nduced Electron/Energy Transfer Dynamics. ................................ ................................ ... 1 1.1 Introduction ................................ ................................ ................................ .................... 1 1.2 Spin Exchange Coupling ................................ ................................ ................................ 2 1.3 Theoretical Methods for the Modeling of Spin Exchange ................................ ............. 7 1.4 Electron and Energy Transfer ................................ ................................ ...................... 11 1.5 Conservation of Spin in Photophysical Processes ................................ ....................... 14 1.6 Contents of Dissertation ................................ ................................ ............................... 16 APPENDIX ................................ ................................ ................................ ................................ .... 19 REFERENCES ................................ ................................ ................................ .............................. 25 Chapter 2: The Magneto - Structural Effects on the Spin Coupling of a Di - iron Hydroxo Complex as Studied with Variable Temperature X - ray Crystal Diffractometry and Density Functional The ory. ................................ ................................ ................................ ................................ ........... 29 2.1 Introduction ................................ ................................ ................................ .................. 29 2.2 Experimental ................................ ................................ ................................ ................ 33 2.2.1 Synthesis of Complexes ................................ ................................ ............... 33 2.2.2 X - ray Diffraction Crystallographic Studies ................................ .................. 33 2.2.3 Computational Procedure ................................ ................................ .............. 35 2.2.4 Systems Studied ................................ ................................ ............................ 40 2.3 Results and Discussion ................................ ................................ ................................ 42 2.3.1 Crystal Structures ................................ ................................ .......................... 42 2.3.2 C omparison of X - ray Structures to Optimized Geometries .......................... 52 2.3.3 Computational Determination of the Spin - coupling constant as a function of temperature. ................................ ................................ ................................ ........... 59 2.3.4 Calculated J for Optimized Geometries ................................ ........................ 66 2 .3.5 Study of the Molecular Orbital Mechanisms of Spin Exchange in the Fe 2 - OH System ................................ ................................ ................................ ............. 71 2.3.6 Hay - Hoffman Coupling Interaction Studies ................................ ................. 74 2.3.7 Discussion of Hay - Hoffman Results for Optimized Geometries ................. 78 2.3.8 Discussion of Hay - Hoffman Results for X - ray structures ............................ 82 2.3.9 Coupling Contributions Determined via Overlap of Natural Magnetic Orbitals ................................ ................................ ................................ ................................ 85 2.3.10 Alpha Beta Orbital Overlap Analysis of Spin Coupling Mechanisms in Optimized Geometries ................................ ................................ ........................... 92 x 2.3.11 Spin Exchange Contribution Analysis via Alpha Beta Orbital Overlap Integrals in The Broken Symme try Wavefunctions of VT X - ray crystal structures. ................................ ................................ ................................ ............. 100 2.3.12 Magneto Structural Effects Discussion ................................ ..................... 103 2.4 Conclusion ................................ ................................ ................................ ................. 110 APPENDIC ES ................................ ................................ ................................ ............................. 112 Appendix 2.1: Supplementary Figures ................................ ................................ ........... 113 Appendix 2.2: Cartesian Coordinates of Variable Temperature X - ray Structures .......... 115 REFERENCES ................................ ................................ ................................ ............................ 123 Chapter 3: Investigations into t he Energy Acceptor Reactivity of a Mangane se(II) Ligand Field State in a Covalently L inked Donor - Acceptor Assembly ................................ ............................ 128 3.1 Introduction ................................ ................................ ................................ ................ 128 3.2 Experimental ................................ ................................ ................................ .............. 130 3.2.1 Syntheses ................................ ................................ ................................ ..... 130 3.2.2 Physical Measurem ents ................................ ................................ ............... 134 3.2.2.1 Electrochemistry ................................ ................................ .......... 134 3.2.2.2 X - ray Structure Determination ................................ .................... 135 3.2.2.3 Steady State Spectroscopies ................................ ......................... 135 3.2.2.4 Time Resolved Spectroscopies ................................ .................... 136 3.2.2.5 Low Temperature Emission for Complexes 1 and 2 ................... 137 3.2.2.6 Variable Temperature Time Resolved Emission Spectroscopy ... 137 3.2.2.7 Electronic Structure Calculations ................................ ................ 138 3 .3 Results and Discussion ................................ ................................ .............................. 139 3.3.1 Syntheses ................................ ................................ ................................ ..... 139 3.3.2 Mass Spectrometry ................................ ................................ ...................... 146 3.3.3 Electronic Absorption Spectroscopy ................................ ........................... 148 3.3.4 Electrochemistry ................................ ................................ ......................... 149 3.3.5 Photophysical Char 3 ) 2 - bpy) 2 ](ClO 4 ) 2 (PF 6 ) ................................ ................................ ............................... 151 3.3.6 Variable Temperature Emission ................................ ................................ . 153 3.3.7 Transient Absorption Spectroscopy ................................ ............................ 159 3.3.8 Identification of the quenching pathway in Complex 3 .............................. 161 c)] + ................................ .... 163 3.3.10 Computational Results ................................ ................................ .............. 167 3.4 Conclusions ................................ ................................ ................................ ................ 174 APPENDIX ................................ ................................ ................................ ................................ .. 176 REFERENCES ................................ ................................ ................................ ............................ 178 Chapter 4: Electronic Structure Calculations of the [Mn 2 (L)(mcb)] + Exchange Coupled Dimer ................................ ................................ ................................ ................................ ........... 183 4.1 Introduction ................................ ................................ ................................ ................ 183 4.1.1 Background Information ................................ ................................ ............. 183 4.1.2: Unanswered Questions from the MnZn complex ................................ ...... 184 4.1.3 Objectives for Computational Study ................................ ........................... 186 4.2 Experimental ................................ ................................ ................................ .............. 187 xi 4.3 Results and Discussion ................................ ................................ .............................. 190 4.3.1 Geometry Optimization Results ................................ ................................ .. 190 4.3.2 Coupling Constant Determination ................................ .............................. 197 4.3.3 Coupling Pathway Analysis ................................ ................................ ........ 200 4.3. 4 Energetics of the Mn 2 Acceptor System ................................ ..................... 207 4.3.5 Implications for the Conservation of Spin Angular Momentum ................ 214 4.4 Conclusions ................................ ................................ ................................ ................ 216 REFERENCES ................................ ................................ ................................ ............................ 217 Chapter 5: Conclusions and Future Directions ................................ ................................ ............ 221 5.1 Project Goals ................................ ................................ ................................ .............. 221 5.2 Dissertation Results ................................ ................................ ................................ ... 222 5.3 Fut ure Work ................................ ................................ ................................ ............... 224 5.3.1 Current Di - manganese Systems ................................ ................................ .. 224 5.3.2 Aliphatic Bridged Mn 2 /MnZn Systems ................................ ...................... 225 5.3.3 Studying the Energetics of the Fe 2 OH system. ................................ ........... 228 5.4 Concluding Comments ................................ ................................ ............................... 229 REFERENCES ................................ ................................ ................................ ............................ 231 xii LIST OF TABLES Table 2 - 1: X - ray crystal structure parameters for complexes 1 and 2 at all temperatures studied. ................................ ................................ ................................ ................................ 42 Table 2 - 2: Bond distances in Angstroms determined by X - ray crystallography for atoms in the coordination environment of complexes 1 (M=Fe) and 2 (M=Ga) ....................... 44 Table 2 - 3 : Bond angles in degrees determined from X - ray crystallography for atoms in the coordination environment of complex 1 (M=Fe) and 2 (M=Ga) ........................... 45 Table 2 - 4: Selected bond distances (in Angstroms) and angles (in degrees) for atoms in the coordination environm ent of C 2v optimized geometries for all multiplicities, basis sets, and functionals of complex 1 and 2 . ................................ .............................. 53 Table 2 - 5: Comparison of the optimized X - ray geometries with the analogous C 2v optimizations and X - ray structure. ................................ ................................ ......... 54 Table 2 - 6: UB3LYP/6 - 311G(d,p ) values for the determination of J determined at the X - ray c rystal structure geometry excluding the acetone in the crystal lattice. ................ 63 Table 2 - 7: UB3LYP/6 - 311G(d,p) values for the determination of J determined at the X - ray c rystal structure geometries of complex 1 and the Fe @ Ga geometries including the acetone in the crystal lattice. ................................ ................................ ............ 63 Table 2 - 8: Comparison of UBPW91/6 - 311G(d,p) and UB3LYP/6 - 311G(d,p) values for the determination of J at the complex 1 X - ray Crystal struc ture geometries excluding the acetone in the crystal lattice. ................................ ................................ ............ 66 Table 2 - 9: The UB3LYP/6 - 311G(d,p) and UBPW91/6 - 311G(d,p) values for the determination of J at all of the C 2v optimized geometries of complex 1 sans acetone. ................ 67 Table 2 - 10: The UB3LYP/6 - 311G(d,p) and UBPW91/6 - 311G(d,p) values for the determination of J for Fe @ Ga at all of the C 2v optimized geometries of complex 2 sans acetone. ................................ ................................ ................................ ................................ 67 Table 2 - 11: The UB3LYP/6 - 311G(d,p) values for the determination of J at all of the optimized X - ray structure geometries of complex 1 both with and without acetone. ............ 70 Table 2 - 12: The alpha beta overlap integrals determined for all possible permutations of the d - orbital like natural magnetic orbitals for select optimized geometries studied sans acetone. ................................ ................................ ................................ .................. 91 xiii Table 3 - 1: Crystallographic Data for Complexes 1 and 2 ................................ ..................... 135 Table 3 - 2: Com parison of bond distances for X - ray structures of complexes 1 , 2 , and macrocycle core analogues ([M 2 (L)(mcb)] + ) of complexes 4 , and 5 as previously reported. ................................ ................................ ................................ ............... 145 Table 3 - 3: Electrochemical data for complexes 3 , 4 , and [Ru((CF 3 ) 2 - bpy) 2 (mcbEt)](PF 6 ) 2 in CH 2 Cl 2 solution ................................ ................................ ................................ .... 150 Table 3 - 4: Select bond distances for the UB3LYP optimized geometries of complex 1 ...... 168 Table 3 - 5: Table of UB3LY P energy calculation results. Thermodynamic values are corr elated to labels in Figure 3 - 13 ................................ ................................ ........................ 170 Table 4 - 1: Selected bond distances and angles for the optimized geometries of complex 4 compared to the X - ray crystal structure ................................ ............................... 191 Table 4 - 2: Relevant data and the coupling constants determined with the data for the optimized geometries of the ground state spin manifold ................................ ...................... 197 Table 4 - 3: Relevant data and the coupling constants determined for the optimized geometries of the 6 A 1 4 T 1 excited state spin manifol d ................................ ......................... 199 Table 4 - 4: Calculated alpha - beta overlap integral absolute values for the NMOs of complex 4 , as seen in Figure 4 - 4 ................................ ................................ ............................ 204 xiv LIST OF FIGURES Figure 1 - 1: Two S= ½ ions showing an anti - ferromagnetic interaction, where J is the coupling constant ................................ ................................ ................................ .................... 5 Figure 1 - 2: The spin ladder for two S= 5 / 2 spin centers in a bime tallic exchange coupled complex ................................ ................................ ................................ .................... 6 Figure 1 - 3: Spin density plot for the [Fe 2 - - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ] + exchange coupled system. ................................ ................................ ................................ ................... 10 Figure 1 - 4: An adapted diagram showing the electronic transitions associated with photoinduced electro n and energy transfer processes ................................ ............ 13 Figure 1 - 5 : A scheme showing the proposed spin - conserved nature of Ru 3 MLCT quenching by O 2 and the proposed inability of N 2 to quench the e xcited state of [Ru(bpy) 3 ] 2+ due to the inaccessibility of a spin - allowed excited state. ................................ ..... 15 Figure A1 - 1: Color coded diagram of [Fe 2 - - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ] + with blue corresponding to fragment 1, red to fragment 2, and green to fragment 3. ........... 23 Figure 2 - 1: Drawings of [Fe 2 - - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ] + ( 1 ) and [ Ga 2 - - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ] + ( 2 ), excluding the coordinated acetone and ClO 4 cations present i n the X - ray crystal structures. ................................ ................................ .. 30 Figure 2 - 2: The Boltzmann distribution of the spin states for complex 1 as a function of temperature ................................ ................................ ................................ ............ 31 Figure 2 - 3: A Simple diagram explaining the axis system used to assign the orbital labels for orbitals involved with coupling on the Fe III ions and µ - OH ................................ .. 40 Figur e 2 - 4: (Left) X - ray crystal structure of complex 1 at 20 K, with the atom in the coordination environment labeled. (Right) X - ray crystal structure of complex 2 at 20 K, with the atom in the coordination environment labele d ............................... 43 Figure 2 - 5: Plots of releva nt bond distances concerning the µ - OH bridge in the X - ray crystal structures of complexes 1 and 2 as a function of temperature ............................... 47 Figure 2 - 6: Bond distances associated with the metal and HBpz capping ligand in complexes 1 and 2 ................................ ................................ ................................ ....................... 48 xv Figure 2 - 7: M1 - O5 - M2 bond angle in the X - ray crystal structures as a function of temperature for complexes 1 and 2 . ................................ ................................ ........................... 49 Figure 2 - 8: Relevant bond angles involving the HBpz cap from the X - ray structures as a function of temperature. ................................ ................................ ......................... 50 Figure 2 - 9: The UB3LYP/6 - 311G(d,p) determined J values for X - ray crystal structures of complex 1 and Fe @ Ga. ................................ ................................ ........................ 62 Figure 2 - 10: Visualizations of the ten lowest unoccupied beta orbitals from the high spin UB3LYP/6 - 311G(d,p) wavefunction calculated at the UB3LYP/6 - 311G (d,p) high spin optimized geometry. ................................ ................................ ....................... 76 Figure 2 - 11: Visualizations of thet en lowest unoccupied beta orbitals from the high spin UBPW91/6 - 311G(d,p) wavefunction calculated at the UBPW91/6 - 311G(d,p) high spin optimized geometry. ................................ ................................ ....................... 77 Figure 2 - 12: Hay - Hoff man coupling contributions from UB3LYP/6 - 311G(d,p) and UBPW91/6 - 311G(d,p) for geometries optimized with the same functional and the indicated basis set and multiplicity. ................................ ................................ ....................... 78 Figure 2 - 13: Hay - Hoffman coupling contributions from UB3LYP/6 - 311G(d,p) for X - ray structure optimized geometries optimized with the same functional and the indicated multiplicity. ................................ ................................ ............................ 81 Figure 2 - 14: Complex 1 Hay - Hoffman analysis of coupling contributions for the symmetric d orbital interactions in X - r ay structures as a function of temperature using B3LYP (left) and BPW91 (right) wavefunctions. ................................ ............................... 83 Figure 2 - 15: Fe @ Ga Hay - Hoffman analysis coupling contributions for the symmetric d orbital interactions in X - ray structures as a function of temperature using B3LYP (left) and BPW91 (r ight) wavefunctions. ................................ ................................ .............. 84 Figure 2 - 16: Visualizations of the ten NMOs from the broken symmetry singlet UBPW91/6 - 311G(d,p) wavefunction calculated at the UBPW91/6 - 311G(d,p) low spin optimized geometry. ................................ ................................ .............................. 89 Figure 2 - 17: Visualizations of the ten NMOs from t he broken symmetry singlet UB3LYP/6 - 311G(d,p) wavefunction calculated at the UB3LYP/6 - 311G(d,p) low spin optimized geometry. ................................ ................................ .............................. 90 xvi Figure 2 - 18: - pathways calculated from br oken symmetry orbitals generated with BPW91 (A) and B3LYP (B) density functionals. ................................ ................................ ...... 94 Figure 2 - 19: - pathways calculated from broken symmetry orbitals generated with BPW9 1 density functional at the optimized B3LYP geometries. ................................ .................... 95 Figure 2 - 20: - pathways calculated from broken symmetry orbitals generated with B3LYP for the X - ray crystal structures of complex 1 . ................................ ................................ . 102 Figure 2 - 21: Plot of the UB3LYP/6 - 311G(d,p) ca lculated J values for the unaltered X - ray crystal structures of complex 1 , the aforementioned X - ray structures altered such that the O5 - H50 bond distance was fixed at the 20 K value of 0.82707 Å , and the X - ray structures altered such that the O5 - H50 bond distance was fixed at the 296 K value of 0.58853 Å ................................ ................................ ................................ ........ 105 Figure 2 - 22: Relative contributions to the spin coupling determined with UB3LYP/6 - 311G(d,p) in modified complex 1 X - ray crystal structures as determined via the Hay - Hoffman method. The modifications involved holding the O5 - H50 bond distance constant for all temperatures. ................................ ................................ ............................. 106 Figure 2 - 23: Energy diagram of the absolute energy of the Broken Symmetry electronic states of the complex 1 crysta l structures relative to the value at 20 K for structures both including and excluding the acetone. ................................ ................................ ... 108 Figure A2 - 1: Acetate C - O bond distances in the X - ray structures as a function of temperature. Distances for complex 1 are on the left and distances fo r complex 2 are on the right. ................................ ................................ ................................ .............................. 113 Figure A2 - 2: Bond distances for the M - O bond distances for the acetate bridges for complexes 1 and 2 as a function of temperature. ................................ ................................ ...... 113 Figure A2 - 3: The M - O(acetate) - C(acetate) bond angles for complexes 1 and 2 as a fun ction of temperature. ................................ ................................ ................................ ......... 114 Figure A2 - 4: The O(acetate) - M - O5 bond angles for complexes 1 and 2 as a function of temperature. ................................ ................................ ................................ ......... 114 Figure 3 - 1: Chemic al drawings of systems studied. ................................ ............................... 129 Figure 3 - 2: Synthetic scheme of complexes 1 and 3 . ................................ ............................. 139 xvii Figure 3 - 3: Drawings of X - ray crystal structure cations of complex 1 with at oms drawn as thermal ellipsoids ................................ ................................ ................................ . 142 Figure 3 - 4: Comparison of the different crystal structures obtained for complexes 1 and 2 compared to those previously acquired for the acceptor model complexes of 4 ([Mn 2 (L)(mcb)](PF 6 )) and 5 ([Zn 2 (L)(mcb)](PF 6 )) ................................ ............. 143 Figure 3 - 5: Extinction coefficient plots for complexes 1 (green -- -- -- ), 2 (teal - - - ), 3 (Blue line), 4 (black -- - -- - -- ). And 5 (red --- --- --- ). ................................ ............... 147 Figure 3 - 6: Electrochemical data for complex 3 , with potentials plotted relative to the ferrocene/ferrocenium redox couple ................................ ................................ .... 150 Figure 3 - 7: 10 K corrected emission spectra for complexes 3 (blue) and 5 (red). Sample was excited at 475 nm. ................................ ................................ ................................ 152 Figure 3 - 8: Variable temperature time resolved emission data of complexes 3 and 5 ........... 156 Figure 3 - 9: Observed quenching rate (difference between observed rate of complex 3 and observed rate of complex 5 ) plotted a s a function of temperature. ...................... 159 Figure 3 - 10: (left) Transient absorption kinetic trace for complex 1 excited at 475 nm and probed at 370 nm. (right) Transient absorption decay trace of complex 1 excited at 475 nm and probed at 490 nm ................................ ................................ ........................... 159 Figure 3 - 11: Low temperature emission spectra of complex 1 (blue) and complex 2 (red) ..... 163 Figure 3 - 12: Drawing of the three UB3LYP optimized geometries of complex 1 . .................. 168 Figure 3 - 13: A simple energy diagram of th e B3LYP thermochemistry results ...................... 170 Figure 3 - 14: Simple energetic diagram showing relative energies of the Ru 3 MLCT states as determined experimentally and the experimentally derived energies of the emissive + ligand field states ................................ ................................ . 173 Figure A3 - 1: ESI - MS results of complex 3 in dichlorome thane ................................ ............... 177 Figure 4 - 1: Drawings of the systems either referred to or studie d in the course of this chapter ................................ ................................ ................................ .................. 184 Figure 4 - 2: The reported X - ray structure of complex 4 , with the hydrogen atoms omitted for clarity and the atoms displayed as thermal ellipsoids ................................ .......... 187 xviii Figure 4 - 3: The Cartesian axis system used for the assignment of d - orbital nature of the NMOs used to study the coupling pathways of the system ................................ ............. 200 Figure 4 - 4: Plots of the NMOs of complex 4 as determined from the low spin B3LYP/6 - 311G(d, p) wavefunction for the geometry opti mized under the same conditions ................................ ................................ ................................ ............. 203 Figure 4 - 5: A side by side comparison of the NMO surfaces corresponding to the d yz and d x 2 - y 2 II centered orbitals for complex 4 ................................ ....... 206 Figure 4 - 6: An energetic diagram depicting the relative energetic positioning of the ground and excited state spin manifolds relative to the S=0 ground state in complex 4 ........ 210 Figure 4 - 7: A depiction of the calculated thermodynamic quantities for complex 4 (left) and complex 5 (right) ................................ ................................ ................................ .. 212 Figure 5 - 1: Drawings of the previously studied [Mn 2 (L)(mcb)Ru((CF 3 ) 2 - bpy) 2 ] 3+ (A) complex and the propos ed extended linker analogue (B) ................................ ................... 226 xix KEY TO ABBREVIATIONS NMR ................................ ...... Nuclear Magnetic Resonance DFT ................................ ........ Density Functional Theory HOMO ................................ ... Highest Occupied Molecular Orbital LUMO ................................ .... Lowest Unoccupied Molecular Orbital SCF ................................ ........ Self Consistent Field UKS ................................ ........ Unrestricted Kohn Sham GGA ................................ ....... Gen eralized Gradient Approximation B3LYP ................................ ... Becke 3 - parameter hybrid functional with Becke 88 exchange and LYP correlation. UB3LYP ................................ Unrestricted B3LYP BPW91 ................................ ... Density functional with Becke 88 exchange and PW91 correlation. UBPW91 ................................ Unrestricted BPW91 STO ................................ ........ Slater Type Orbital BS ................................ ........... Broken Symmetry SP ................................ ........... Single Point Energy O 2 CCH 3 ................................ .. Acetate HBpz 3 - ................................ .... T rispyrazolylborate CCD ................................ ....... Charge Coupled Device NPA ................................ ........ Natural Population Analysis VT ................................ .......... Variable Temperature EPR ................................ ........ Electron Paramagnetic Resonance LS ................................ ........... Low Spin electronic state HS ................................ .......... High Spin electronic state NMO ................................ ...... Natural Magnetic Orbital ESI - MS ................................ .. Electro - Spray Injection Mass Spectrometry DMSO ................................ .... Di - Methyl Sulfoxide xx UV/Vis ................................ ... Ultraviolet/Visible Absorption Spectroscopy CV ................................ .......... Cyclic Voltammetry THF ................................ ........ Tetrahydrofuran 2 - Me - THF .............................. 2 - Methyl - Tetrahydrofuran CH 2 Cl 2 ................................ .... Dichloromethane DPV ................................ ........ Differential Pulse Voltammetry LT ................................ ........... Low Temperature RT ................................ .......... Room Temperature OPO ................................ ........ Optical Parametric Oscillator CW ................................ ......... Continuous Wave Experiment LC ................................ .......... Liquid Chromatography OA c ................................ ........ Acetate m cb ................................ ......... 4 - methyl - 4' - carboxy - 2, 2' - bipyridine ( CF 3 ) 2 - bpy .............................. 4,4' - bis(trifluoromethyl) - 2, 2' - bipyridine bpy ................................ .......... B ipyridine ( L ) ................................ .......... Symmetric Macrocycle (see Chapter 3 for details ) ( L' ) ................................ .......... Asymmetric Macrocycle (see Chapter 3 for details ) MLCT ................................ .... Metal - to - Ligand Charge Transfer State PF 6 ................................ .......... Hexafluorop ho s phate ClO 4 ................................ ........ Perchlorate 1 Chapter 1: Overview of the Concepts and Modeling of Spin Exchange Coupling and its Effects on Photoinduced Electron/Energy Transfer Dynamics. 1.1 Introduction As chemists, we are introduced early on to the concept of the valence electrons of atoms and their participation in chemical bonding, the most studied form of int eraction between atoms. In much the same way that bonding interactions can be rationalized through the electronic structure of the interacting atoms or molecules, the inverse relationship is also true and the electronic structure must be used to understan d chemical properties and reactivity; this constitutes the general discipline of chemistry. An important property of electrons is their quantum mechanical spin angular momentum, which is a fundamental property, the influence of which permeates into a vari ety of commonly encountered physical and chemical phenomena. A material is said to be diamagnetic if all its electrons are paired, and paramagnetic if there are unpaired electrons present. It is these unpaired electrons, for example, that are responsible f or the colorful absorption features observed for organic radicals. If a system contains multiple paramagnetic centers these are able to interact. This interaction is known as electronic exchange coupling or spin exchange coupling, and it has the potential to cause large perturbations to the electronic structure of a system. Consequently, spin coupled systems might display unique properties, as will be discussed later. A wide range of extremely important chemical reactions occur ubiquitously in our world, a nd many of them involve biological processes where electrons interact with metal centers known to contain transition metal centers or clusters (photosynthesis, respiration, etc.), which due to the open d - orbital manifolds common in transition metal ions us ually contain unpaired electrons with 2 an associated spin angular momentum. It is therefore relevant to investigate any possible effects of unpaired electrons and their interactions on chemical reactivity to better understand the functioning of these biolog ical and other chemical systems of interest that contain paramagnetic centers. 1 This dissertation chronicles our continuing mission to explore the effects of electronic spin, either in exchange coupled systems or in other paramagnetic systems, on the chemi cal dynamics of molecular systems. This is afforded either through the direct study of electron and energy transfer dynamics in the aforementioned systems, or via theoretical studies that are used to gain an understanding of how this electronic spin can af fect chemical reactivity in previously or yet to be studied molecular systems. This chapter will provide a brief theoretical overview of the spin exchange coupling interaction, theoretical methods used to model said interaction, electron and energy transfe r, and the concept of spin conservation in these reactions. Previous work from our group and other groups will also be discussed as it pertains to the understanding of the effects of electronic spin on chemical reactivity. 1.2 Spin Exchange Coupling Spin exchange coupling has been observed to cause a variety of recognized effects on the spectroscopic, magnetic and electronic properties, all in the absence of applied electric or magnetic fields. 2 Often times spin forbidden d - d bands have their intensities g reatly amplified as a consequence of spin coupling. Another change brought about by spin exchange coupling are changes in the bulk magnetic properties of a system. In a hypothetical system where there are two unpaired electrons present in the complete abse nce of coupling, there should only be one observed 3 value for the magnetic moment. If exchange coupling is present in a similar hypothetical system, this single value will transform into a range of values possible for the same number of unpaired electrons. It is in fact this distinction that enables the use of magnetic measurements in the acquisition of parameters used to model this interaction. 3 In any chemical system, in order for spin coupling to occur the unpaired electrons must be localized in differen t parts of the molecule and there must be a thermodynamically favorable pathway to facilitate the interaction leading to spin exchange. 4 While weak intermolecular spin coupling is possible, 5 in most cases electron exchange coupling occurs intramolecularly. The interaction between the two spin bearing centers can occur via direct overlap of the spin centers (direct exchange) or through the mutual interaction with a diamagnetic bridge in what is termed a superexchange mechanism. 4,6,7 The unpaired electrons o n each spin center can interact via exchange coupling in either a ferromagnetic or an antiferromagnetic manner when there is sufficient electronic interaction between the orbitals containing the unpaired electrons. 4 It is also true that both types of intra molecular spin coupling can be ferromagnetic or antiferromagnetic. Both types of coupling are commonly seen in direct exchange coupled systems. In the binuclear metal complexes studied in this dissertation, the superexchange coupling pathway is predominant . Even in a superexchange mechanism, where antiferromagnetic coupling is common, Ferromagnetic interactions can occur, usually when the interacting unpaired electrons are housed in centers that are 90 degrees to each other relative to the diamagnetic bridg e. Since superexchange is usually mediated between p - orbitals on the diamagnetic bridges, this results in the spin centers interacting via orthogonal p orbitals on the diamagnetic ligand and these interactions are typically rather weak. 6 4 An antiferromagn etic interaction occurs commonly in superexchange coupled systems. This spin interaction can be thought of an extension of the more logical direct exchange where in interaction between non - orthogonal orbitals is mediated through the electron hopping betwee n the ligand and the spin centers. 6 The antiferromagnetic stabilization occurs as a result of the interacting unpaired electrons being stabilized by adopting the lowest possible spin state due to the necessity of the spins being antisymmetric to get effici ent hopping between the diamagnetic bridge and the spin centers. The non - orthogonality of the interacting orbitals means that the electrons can be thought to have the opportunity to freely mingle between the two spin centers. As a consequence of the anti - s ymmetry requirement of the Pauli Exclusion Principle, this means the electrons can more effectively delocalize if they have opposite spins on each spin center. This spin exchange interaction can be written as the scalar product of the spin operators of a toms in molecules and solids. Thus, the net spin coupling between two spin bearing centers in a molecule can be represented and quantified quantum mechanically with single - ion spin operators S 1 and S 2 for each of the metal centers in the form of the Heisen berg - Dirac - Van Vleck Spin Hamiltonian as defined in Equation 1. 7,8 H HB = J S 1 S 2 (1) If one makes the assumption that the total spin operator is the sum of the spin operators of each spin center, one can obtain the eigenvalues of the spin exchange operator which have energies given by Equation 2, which describes the energy displacement of an individual spin state S from the spin barycenter of an exchange - coupled binuclear system in terms of the coupling constant J. (2) 5 The exchange interaction removes the degeneracy of the various total spin values possible for the exchange - coupled clusters. The result of this loss of degeneracy is that the spins are ordered into parallel (ferromagnetic) and antiparallel (antiferromagnet ic) configurations to form an energetic spin ladder whose energy separations can be expressed as a function of J , which is shown in figure 1 - 1 for an interacting pair of S= 1 / 2 spin centers. It is possible to use Heisenberg exchange - coupled metal clusters a s a way to vary spin without affecting other gross properties of the system. By changing the temperature of the sample, one controls the access to spin states thermally accessible to the complex, which in turn will change the spin of the cluster. This prop erty makes spin exchange coupling in binuclear metal clusters an ideal tool for varying the quantity of spin. Figure 1 - 1: Two S= ½ ions showing an anti - ferromagnetic interaction, where J is the coupling constant. 6 For all of the exchange coupled dimers studied in this thesis, both transition metal ions are high spin with d 5 occupation, Fe III (OH)Fe III in one case and Mn II 2 in the other. This means that for the ground states of these molecules we have two S= 5 / 2 centers participating in spin exchange. In both cases the spin coupling is antiferromagnetic as determined via variable temperature magnetic susceptibility measure ments. This results in a spin ladder which is portrayed in figure 1 - 2. The energy difference between each spin level depends on the value of the coupling constant, which is unique for each system studied. Figure 1 - 2: The spin ladder for two S= 5 / 2 spin centers in a bimetallic exchange coupled complex. 7 1.3 Theoretical Methods for the Modeling of Spin Exchange Since the energy separations of the individual spin states in a Heisenberg exchange coupled cluster depend on the value of J , it is important to determine the value of said constant in order to understand the intricacies of how thermal population of states in a Heisenberg spin ladder can control spin. Although the constant can be determined experimentally via variable temperature magnetic susceptibility and the Evans NMR methods, 3 it is also beneficial to determine the value of J using theoretical methods, 9,10 as these are a powerful diagnostic tool. These theoretical methods offer not only the advantage of providing information on the electronic structure of these complexes, but by comparing the calculated values of the coupling constant to experi mentally obtained values and determining the theoretically determined values to be accurate, one can then use theory to determine the coupling in synthetically unobtainable molecules, such as the excited states of spin exchanged systems where bulk magneti zation methods are not typically available. Exchange coupled molecules have been modeled for many years, 7b and while there are more thorough methods for theoretically determining the Heisenberg coupling element such as s or spin projection, 11 the easiest and one of the most prominent in the chemical literature is the broken symmetry formalism for density functional theory (DFT), as developed by Noodleman 9 and Yamaguchi, 10 which was chosen for our research. This method is prized for its ease in implementation as well as its accuracy in predicting the coupling of complicated systems when the proper theoretical procedures are used. In the broken symmetry treatment, two individual DFT calculations are carried out on a particular chemical system which exhibits exchange coupling. The first is a high - spin single point energy calculation to determine the energy of the highest possible spi n electronic state, which in the case of our spin coupled systems is a spin - pure electronic configuration described by a single 8 determinant wavefunction. The second is a single point energy calculation of a special low spin electronic state corresponding t o the lowest possible spin state and generated by the broken symmetry formalism. This low spin state, which in the case of our systems in this thesis is a singlet, is often termed the broken symmetry electronic state or the broken symmetry wavefunction. 12 A broken symmetry electronic state is generated by disturbing the symmetry of the electronic spin density across a system consisting of more than one paramagnetic site. This is accomplished by creating an initial guess that has sufficient lack of spin sym metry. In practice, this is achievable by mixing HOMO and LUMO orbital guesses at the onset of the DFT calculation, 13 or in other cases the guess may have to be manually generated. 14 In recent years, new methods to systematically generate guesses with appr opriate broken symmetry across a molecule have been developed. These methods create a broken symmetry guess by either flipping the spin density of one of the spin centers in a spin coupled molecule 15 (such as one of the transition metal centers in the comp ounds studied in this thesis) or by using fragment based guessing 16 which allows for the generation of wavefunction guesses for molecular fragments in isolation of the rest of the fragments in the molecule that can have their individual charge and multipli city relative to the rest of the molecule specified; with fragment based guessing, a broken symmetry guess is generated by specifying at least one fragment to have negative multiplicity. The broken symmetry state is not a true electronic state of the syste m studied but rather is a linear combination of spin states that places heavy emphasis on the actual singlet state. 9b,12 It is for this reason that the spin expectation values for the broken symmetry singlet states are not the ideal value of zero, but are instead spin contaminated with spin expectation values usually in the range of 4.5 to 5. 9 This broken symmetry state, while not being an actual electronic state of the system studied, is used to determine the Heisenberg coupling constant according to Equat ion 3 developed by Yamaguchi and coworkers. 10 (3) In this equation, E U - DFT values are the high - spin ( S=S max ) and broken symmetry ( S=S min ) energies as obtained from the single point energy unrestricted DFT calculations, and are the spin expectation values calculated for the aforementioned states in the single point energy calculations. Once the required values have been found from the two single point calculation s, the Heisenberg coupling constant can be obtained, providing valuable information about the energy levels of the spin states in the Heisenberg coupled system. It is often times possible to perform the actions necessary to generate a guess that should sub sequently generate a broken symmetry electronic state, but the DFT procedure will not converge to the proper low spin electronic wavefunction. It is therefore necessary to identify the properties of an adequate broken symmetry state and be able to distingu ish them from inadequate broken symmetry states. It is fortunate that over a long research career the author has many opportunities to identify the hallmarks of a good broken symmetry state. In an unrestricted electronic structure calculation, the electro ns are modeled as two sets of individually optimized one - electron eigenfunctions of the energy operator where the spin operator is essentially decoupled from the calculation. In a paramagnetic system, there will be more electrons of one spin than the other . By convention the spin with a majority of the electrons is labeled alpha ( ) and the minority spin is labeled beta ( ). Spin density is defined as the difference 10 between alpha and beta electron population at a given point in space. 17 By tracking spin den sity in a broken symmetry calculation, one can make sure the wavefunction is behaving properly. Figure 1 - 3: Spin density plot for the [Fe 2 ( - OH)( - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ] + exchange coupled system. The plot shows alpha density on one Fe III center (left) and beta spin density on the other (right). This is an example of a good broken symmetry state. In a proper broken symmetry state for a bimetallic spin exchange coupled system, there should be unpaired spins located on both spin centers, with an equal and opposite magnitude of spin on each spin center, as can be seen in figure 1 - 3. 18 This results in spin density that is close to but slightly less in magnitude than that present in the high spin electronic state on both metal centers, and m ost importantly the spin densities oppose each other. This means that there is a preponderance of alpha spin density on one of the metal centers, and an equal amount of beta spin density on the other metal center. In improperly converged low spin states, the SCF procedure often falls into the trap of attempting to pair up the occupation of the orbitals such that a portion of the spin density on each spin center is lost. This results in lower than expected values for both the spin density on the metal cente rs and 11 the spin expectation value for the low spin state, as spin contamination depends on the number of open shell orbitals in your low spin state. Once one obtains a proper broken symmetry electronic state, it is possible to theoretically determine coupl ing constants for systems of interest. This will prove to be an integral part of the research presented in this thesis. 1.4 Electron and Energy Transfer Electron and energy transfer processes are an important field of study and justifiably well studied as they are relevant to the understanding of important biological processes 19 and applications to molecular devices with light - induced functionality. 20 Electron transfer is a basic chemical event where an electron is transferred between chemical species. As one can imagine, the simplicity and relevance of this reaction has led to countless studies on the dependence of the rate of electron transfer on various parameters. It has been found that the rate of electron transfer can be described by the semi - classica l Marcus equation, 21a which describes the rate for nonadiabatic electron transfer between a donor and an acceptor at a fixed distance and orientation as shown in Eq. 1.4, where h b is the Boltzman constant, and T is temperature. 0 , which is the free energy driving - and outer - sphere 12 structural changes associated with the electron transfer, and H DA , which is the measure of electronic coupling between donor and acceptor. Photo - induced electron transfer occurs as a consequence of the thermodynamics of the photo - excited donor - acceptor pair and functions most often via a through bond mechanism which h as been extensively studied. 21 The advantage of using photo - excited states in the study of electron transfer processes is that allows the use of a well - studied chromophores with defined kinetic properties, such as ruthenium trisbipyridyl complexes, 22 such that electron transfer into or out of the complex has measurable effects on these already known kinetics, sometimes allowing for the rate of electron transfer to be elucidated. Energy Transfer is generally an electronically excited donor transferring its e xcess energy to an acceptor in its ground state. This process requires energy conservation (thermodynamic viability) and a way for these states to interact. The interaction between donor and acceptor states can occur via a through bond (Dexter) or through space (Förster) mechanism. 23 While these energy donors can be excited in a variety of ways, a common method of exciting energy transfer donors is through photoexcitation. Since this method makes the study of kinetics easier by allowing the use of well char acterized chromophores as either donors or acceptors, 22 photo - induced energy transfer processes will now be discussed as they were targeted for study in this dissertation. The through space mechanism is a dipolar coupling of the donor and acceptor states which can function at large distances with a rate dependence of r - 6 and a dependence on spectral overlap between the donor and acceptor states; 24 electrons are not transferred between the donor and acceptor as can be seen in figure 1 - 4. As Forster transfe r is not present in any of the systems studied in this dissertation, it will not be discussed further. 13 Figure 1 - 4: An adapted diagram showing the electronic transitions associated with photoinduced electron and energy transfer processes. 31 The through - bond Dexter energy transfer mechanism can only operate effectively at shorter distances due to its dependence on orbital overlap between the donor and acceptor states. 25 The transfer is mediated by the simultaneous exchange of electrons between donor and acceptor. Upon formation of the excited donor state, an excited electron is transferred into an unoccupied orbital on the acceptor. An electron from the acceptor HOMO is concomitantly transferred to the hole in the donor, resulting in an excited acceptor s tate and a ground donor state, as seen in figure 1 - 4. 6 While the above explanation depends on the concept of transferring electrons, this is a distinct process that is differentiated from an electron transfer by the identity of the products formed. Due to the similarities inherent to transferring electrons, much of the theory for electron transfer can be 14 related to Dexter energy transfer processes, 26 with the exception being that the two electron nature of Dexter energy transfer means the rates of energy tr ansfer fall off much more precipitously as a function of distance between donor and acceptor. To better understand the dynamics of these electron and energy transfer processes, it is beneficial and common practice to synthesize and study covalently bound d onor - acceptor complexes. 27 These assemblies offer the inherent advantage of not having to contend with diffusion related kinetic phenomena 29 when trying to study their photochemistry and photophysics. It is therefore the case that in the course of the rese arch presented in this dissertation covalently bound donor - acceptor complexes were studied. However, distinguishing between energy transfer and electron transfer processes can still be difficult when both are thermodynamically viable. 26 As electron transfer creates charge - separated products, any charge separated spectral features observed spectroscopically would confirm the presence of an electron transfer process. As Dexter energy transfer has a smaller outer - sphere reorganization energ y, a comparison of kinetic studies in different media can help distinguish between the two processes. 25 1.5 Conservation of Spin in Photophysical Processes One of the primary ways in which we propose spin to effect the reactivity of these systems is through the conservation of spin angular momentum. A good example of this is provided in figure 1 - 5, where the quenching of the excited state of [Ru(bpy) 3 ] 2+ is p ossible for O 2 because there exists an accessible excited state of O 2 (S=0) that both conserves spin and is thermodynamically downhill. The only spin allowed excited state for N 2 (S=1) is not thermodynamically downhill compared to the energy of the reactan ts and thus N 2 is not capable of quenching photo - excited [Ru(bpy) 3 ] 2+ . 15 This concept of a reaction only proceeding if it is both thermodynamically and spin allowed is being proposed as a primary way in which electronic spin affects the reactivity of chemica l systems. The possible total spin angular momentum values for a combination of two atoms or compounds | S| = S 1 and | S | = S 2 will have the following values: | S total | = |S 1 S 2 | , | S total | = |S 1 S 2 S total | = S 1 + S 2 . (5) Since in the course of standard chemi cal reactions, there is no way to convert the spin of an electron, this means that there is no way the total spin of the system can change in the course of the reaction. Therefore, the total spin angular momentum of the reactants remains the same in the pr oducts. This conservation of spin angular momentum has important ramifications in the realm of photo - induced chemical reactivity, because it provides an important qualification for whether or not a reaction will occur. One can now add a new condition to th e standard requirement of a reaction proceeding only if the process is spontaneous. That condition is that the reaction will only proceed if for all the possible total spin angular momentum values of the reactants and products, there is at least one spin v alue for which the reaction is thermodynamically downhill. It is through this mechanism that we propose spin will have an easily determined effect and thus photo - induced energy and electron Figure 1 - 5: A scheme showing the proposed spin - conserved nature of Ru 3 MLCT quenching by O 2 and the proposed inability of N 2 to quench the excited state of [Ru(bpy) 3 ] 2+ due to the inaccessibility of a spin - allowed excited state. 16 transfer reactions should serve as convenient reactions for which the effects of spin on reactivity can be observed. The previously mentioned donor - acceptor example shows the rudimentary relationship between spin and reactivity, but there are too many hidden variables in these systems for a quantitative relationship to be determined. It can be the case that for a system where more detailed thermodynamic information is available, on can see spin having an effect on the reactivity of a system is when it is the case that the presence of different amounts of spin causes a th ermodynamic change in a molecule or changes in the observed reaction of a system. Our group has investigated how changing the amount of spin in a compound affects the observed reactivity in a system. It was via this method that we were able to show the dep endence of a Forster energy transfer process on the conservation of spin angular momentum. 28 Our research group wishes to study a series of systems that can change spin states without changing any other aspect of the molecular structure of the system, whic h could allow for a quantitative relationship between spin and reactivity to be determined. 1.6 Contents of Dissertation To further the goals of establishing the effects of electronic spin on chemical reactivity, a few different studies were performed wh ich are chronicled in this thesis. From these studies, the impact of spin on various aspects of photophysical reactivity is investigated. Chapter 2 details the acquisition and computational study of variable temperature X - ray crystal structures for the spi n coupled [Fe 2 ( - OH)( - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ] + complex to determine if there were observable structural effects as a result of increasing the thermal occupation of high spin 17 states, afforded by the small value for the spin coupling constant (34 cm - 1 ). It was the intention that since the effects of changing the energetics of these systems has been linked to changes in reactivity. Specifically it has been found that decreasing the spin coupling between the spin centers results in an increased rate of quenching f or analogues of this complex are used as energy and electron acceptors. 29 Therefore, density functional theory is used to test if the structural changes had an effect on the electronic structure of these systems. From that conclusion, we should be able to logically extend these results to infer any resulting changes in reactivity that can result from these structural changes. Chapter 3 reports the variable temperature dynamics of a covalently linked intramolecular donor - acceptor assembly consisting of a rut henium polypyridyl covalently bound to a Mn II Zn II bearing macrocycle. This quenching of the emissive excited state of the Ru donor by the macrocyclic acceptor was determined to have a thermal barrier of 80 ± 20 cm - 1 and was found to be proceeding via a Dex ter energy transfer mechanism. This rate behavior of quenching by the excited states on the Mn II ion, is compared to previously studied donor - acceptor complexes. Density functional theory was utilized to support the characterization of the mechanism of ene rgy transfer. Chapter 4 discusses the computational studies on the exchange coupled Mn II 2 Schiff - base macrocycle that was previously studied in our group 30 as the acceptor in a donor - acceptor assembly. Electronic structure calculations were performed to provide insight as to the observed increased quenching rate in Mn 2 compared to the previously mentioned MnZn system. The results of this computational study shows thermodynamic differences in the excited states of a spin coupled molecule when compared to a non - spin coupled analogue that may be due to the exchange coupling interaction. 18 Finally, future research directions involving the results and techniques dis cussed in this thesis applied to other potential systems of interest will be briefly outlined and discussed. 19 APPENDIX 20 Appendix: Procedure for Broken Symmetry Calculations in ORCA and Gaussian 09 This section is to provide detailed examples of how proper broken symmetry states were obtained in the course of the research presented in this dissertation. The [Fe 2 ( - OH)( - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ] + exchange coupled system will be used as an example for the purposes of explaining these methods. General Procedure for ORCA ORCA has two ways to generate broken Symmetry low spin states. One is to use the spin - flip mechanism to force the spins generated in a high spin electronic state on a single atom to be antisymmetric to the rest of the spin in the system if one starts from a high spin state and knows the final multiplicity of the broken symmetry state. The second is the program will attempt to construct a proper broken symmetry state from a known high spin state if input on the nu mber of unpaired electrons on each spin center is provided. For the purposes of the systems studied in this thesis consisting of two S= 5 / 2 metal ions, both methods yielded equivalent results. Spin Flip Method: In a molecule with two interacting spin centers, you first need to determine which spin center should be flipped. For this guess generation, the following input commands were entered, as shown from this input file excerpt, which is annotated to explain th e inputs. See the ORCA manual for more details on other calculation parameters. #Orca Energy Calculation for Broken Symmetry ! UKS B3LYP/G STO - 3G VeryTightSCF Direct Grid4 NoFinalGrid %pal nprocs 4 Use four processors to expedite calculation 21 end %scf MaxIter 2000 Set a high number for SCF cycle limit, as optimizing the wavefunction is difficult. FlipSpin 1 Flips the spin on the second iron atom FinalMs 0 Our broken symmetry state is a singlet end * xyz 1 11 Based our broken symmetry state on a S=5 high spin state. Fe 4.211000 0.298000 4.449000 Fe 1.650000 2.410000 5.180000 It should be noted that the smallest possible basis set is being used here to generate the broken symmetry guess, as it is easier to converge to a good broken symmetry wavefunction with a smaller basis set. After this calculation is complete, the following calculation was run to get the broken symmetry state in the desired basis set. ! UKS B3LYP/G 6 - 311G(d,p) TightSCF Direct Grid4 NoFinalGrid %pal npr ocs 4 end %scf MaxIter 2000 Guess=MORead Base the wavefunction on a previously calculated one MOInp="Fe2_hydroxo_DG_Fe20K.gbw" File name with previous wavefunction guess end * xyz 1 1 Now calculating a singlet wavefunction 22 This results in the desired broken symmetry wavefunction. If a geometry optimization is desired, one should perform the aforementioned single point energy calculation to obtain the full wavefunction and then use this wavefunction as the guess in the geometry optimization . file header for the first file: ! UKS B3LYP/G STO - 3G VeryTightSCF Direct Grid4 NoFinalGrid %pal nprocs 4 end %scf MaxIter 2000 BrokenSym 5,5 The two hig hest spin centers have 5 unpaired electrons each end * xyz 1 11 Fe 4.211000 0.298000 4.449000 Fe 1.650000 2.410000 5.180000 After calculating a proper guess from this file, the second input example would remain unchanged to get the d esired broken symmetry state in the proper basis set. 23 General Procedure for Gaussian 09 To generate a broken symmetry guess, the spin centers need to be designated as their own fragments. One can choose to make each individual ligand its own fragment as well, but it was not necessary for the system in the example. The fragments were chosen as can be seen in figure A1 - 1. Figure A1 - 1: Color coded diagram of [Fe 2 ( - OH)( - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ] + with blue corresponding to fragment 1, red to fragment 2, and green to fragment 3. These fragments and the guess to generate them are integrated into the input for generating the broken symmetry guess in the following manner: %chk=Fe2_hydroxo_jorge_g0 9BS_guess.chk %mem=400MW %nproc=4 # ub3lyp/6 - 311G(d,p) guess=(fragment=3,only) Hydroxo Bridged B3LYP Jorge Optimized g09 BS state BS Guess 1,1 3,6 3, - 6 - 5,1 Charge, Multiplicity for overall molecule and each fragment in order Fe(Fragment=1) 0.00000000 1.75648300 - 0.35022500 Fe(Fragment=2) 0.00000000 - 1.75648300 - 0.35022500 O(Fragment=3) 0.00000000 0.00000000 0.59296700 O(Fragment=3) 1.43159900 1.12553300 - 1.60188500 24 This input specifies that individual guesses for each of the three fragments be run and then just added together to make a guess for the overall molecule. This is why the charge and multiplicity for each fragment is specified. After this guess is generated, it is incorporated into the checkpoint file, which is copied and used to generate a full wavefunction using the following input: %chk=Fe2_hydroxo_jorge_g09BS_BigLS.chk %mem=400MW %nproc=4 # ub3lyp/6 - 311G(d,p) guess=checkpoint scf=(nosymm,maxcycle=500) stable=opt Hydroxo Bridged B3LYP Jorge Optimized g09 B S state BS SP 1,1 Fe(Fragment=1) 0.00000000 1.75648300 - 0.35022500 Fe(Fragment=2) 0.00000000 - 1.75648300 - 0.35022500 O(Fragment=3) 0.00000000 0.00000000 0.59296700 O(Fragment=3) 1.43159900 1.12553300 - 1.60188500 The re sulting wavefunction will provide the proper broken symmetry low spin state. Note that this wavefunction is checked for stability, which is important as it sometimes is the case that the broken symmetry wavefunction is not optimal the first time it is eval uated. 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Manuscript in preparation. 2015. 29 Chapter 2: The Magneto - Structural Effects on the Spin Coupling of a Di - iron Hydroxo Complex as Studied with Variable Temperature X - ray Crystal Diffractometry and Density Functional Theory. 2.1 Introduction Our research group has had a perennial interest in the [Fe 2 ( - OH)( - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ] (ClO 4 ) 1 and Fe 2 ( - O)( - O 2 CCH 3 ) 2 (HBpz 3 ) 2 2 complexes first synthesized and studied by Lippard and coworkers in 1984. These bimetallic complexes are interesting to study for a broad range of reasons including their mimicry of the active centers of non - heme oxygen transport proteins , 3 but our primar y reason for studying complexes of this form is to learn more about the nature of the Heisenberg spin exchange interaction 4 of the unpaired electrons present in both of the Fe III ions contained in the bimetallic complex. Previous studies in our research gr oup have focused on the mechanisms of spin exchange in oxo and hydroxo bridged iron dimer complexes, 5 to deduce how structural changes perturb their electronic structure. It is important to investigate these perturbations, as changes in the magnitude of sp in exchange in these complexes have been shown to affect their reactivity in electron and energy transfer reactions. The effects on protonation of the oxo - bridge were studied to understand the changes in the orbital mechanisms of spin exchange brought on b y the addition of the proton. It was determined that said proton alters the degree of communication between the two metal centers by stabilizing an orbital on the bridging oxygen that comprised a primary coupling pathway in the oxo bridged dimer. This stab ilized orbital reduces the energetic match with the magnetic orbitals on the iron centers, resulting in a reduced ability of the metals to mix with said orbital. This effectively removes one of the key coupling pathways found in the oxo dimer, causing a su bstantial decrease in coupling constant for the hydroxo bridged dimer compared to that for the 30 oxo. Research also found that the structural changes due to the protonation also acted to a roughly equal extent to reduce the coupling between the two iron cent ers even in the absence of the proton itself. This reduction was caused by increased Fe - - OH group which act to reduce the coupling between the Fe III centers. The concept of these magneto - structural effects where conformational c hanges affect the magnetic communication between the spin bearing centers of a molecule has been observed for many years, with the first studies on bridged di - copper bridged compounds by Hatfield and Hodgson. 6 In many reported cases of magneto - structural effects, synthetic modifications were used to create geometric changes in the molecule, which were then studied using bulk magnetic characterization methods. 7 The issue with measuring magneto - structural effects with bulk magnetization studies is that since variations in temperature are used to determine the magnetic properties of the molecules in general, any specific effects of the change in temperature on the structure of the molecule are not considered. Figure 2 - 1 : Drawings of [Fe 2 ( - OH)( - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ] + ( 1 ) and [Ga 2 ( - OH)( - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ] + ( 2 ), excluding the coordinated acetone and ClO 4 cations present in the X - ray crystal structures. 31 However, temperature dependent structural changes that are not necessarily a direct consequence of the spin exchange interaction can stil l result in changes in the communication between the spin centers in question, which can cause magnetic data to indicate that the coupling constant varies as a function of temperature, as has been observed in previous instances. 8 We wished to further probe which changes in structure could be observed when the total electronic spin of a system changes with temperature. Our primary system studied consists of the [Fe 2 ( - OH)( - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ] + spin coupled system as seen in figure 2 - 1. Based on the Heisenberg spin exchange creating a ladder of spin states as seen in Chapter 1 , one can use the published experimental value of the coupling constant to determine the thermal population for each spin state Figure 2 - 2: The Boltzmann distribution of the spin states for complex 1 as a function of temperature. This plot was generated using the previously reported value for J of 34 cm - 1 by Lippard and coworkers. Vertical lines represent the temperatures at which crystal structure data were obtained. 32 in the spin ladder based on the Boltzmann equation, as seen in figure 2 - 2. The best way to probe structural changes as a function of total spin magnitude is to perform variable temperature X - ray crystal diffraction studies on this spin coupled system , providing us with insight as to what structural changes could be correlated with populating the higher spin states in an otherwise unchanged system. Here it is conceivable that by looking at the crystal structure of the molecule while only the low spin s tates on the spin ladder are thermally accessible and comparing it to the crystal structure at higher temperature geometries, one should observe how the molecular geometry changes with respect to the thermal population of the higher spin states on the spin ladder. It was therefore determined that structures would be obtained for a series of temperatures, which are indicated in figure 2 - 2, to sample the different thermal population of spin states and see if there were any observable structural changes. To differentiate any possible effects of crystal lattice expansion as the temperature is increased from the effects caused by the spin coupling interaction in the iron dimer, the gallium analogue as seen in figure 2 - 1 was also synthesized and studied. Further more, this study sought to correlate these structural changes brought about by thermal population of the higher spin states with changes in the electronic structure of the complexes, with the goal of identifying which magnetic coupling pathways were becomi ng more or less active as the temperature was increased by using the molecular orbital analysis methods previously used in the computational study of these compounds. 5,7 33 2.2 Experimental 2.2.1 Synthesis of Complexes [Fe 2 ( - OH)( - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ](ClO 4 )·CO(CH 3 ) 2 ( 1 ) was prepared by Dr. Dong Guo using a synthetic procedure previously reported by our research group. 9 Crystals suitable for X - ray diffraction studies were obtained by ether diffusion into a solution of complex 1 in acetone. [Ga 2 ( - OH)( - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ](ClO 4 )·CO(CH 3 ) 2 ( 2 ) was prepared by Dr. Dong Guo as an adaptation on the synthetic procedure used for complex 1 , substituting Ga(ClO 4 ) 3 for Fe(ClO 4 ) 3 with other slight procedural modifications. Crystals suitable for X - ray diffraction studies were obtained by ether diffusion into a solution of complex 2 in acetone. 2.2.2 X - ray Diffraction Crystallographic Studies The X - ray diffraction crystal diffracti on structure determinations for complexes 1 and 2 were performed by our former research group member Dr. Dong Guo with the assistance of Dr. Richard Staples (Michigan State University), Dr. Vladimir V. Zhurov (University of Toledo), and Prof. A. Alan Pinke rton (University of Toledo). Two different instruments were used for the acquisition of X - ray crystal structures. The same mounted single crystals for complex 1 and complex 2 were used on both instrumental setups to maintain consistency between the two X - r ay crystal diffraction data collection sessions. Diffraction data at 20 K and 50 K were collected on a Rigaku diffractometer equipped with a high - power Mo rotating anode generator (18 kW), R - Axis Rapid curved image plate detector, flat graphite monochrom ator, 0.5 mm collimator, and an open flow helium cryostat for temperature 34 control within 0.3 K of the desired temperatures, which was located at the Instrumentation Center at the University of Toledo. 10 To ensure sufficiently high resolution and redundancy in the at different chi and phi - scan range was taken to avoid significant overlap of reflections in any given image. For each pair of runs, a 2° shift in start angle provided a half - oscillation range overlap for precise scaling and avoided the use of partial reflections. A frame time of 220 s was chosen to maximize the intensity of the Bragg reflections and to avoid saturation of the str ongest reflections. The experiment for single structure at a specific temperature was completed in about a day. The reflections were indexed with HKL2000, 1 1 and the collected data were integrated by using the VIIPP 1 2 data integration program based on the r eflection positions predicted from HKL2000. Data were corrected for absorption. The program SORTAV 1 3 was used for scaling and averaging of reflections into a reduced data set. Diffraction data at 100, 173, 234, and 296 K were collected on a Bruker Apex - II diffractometer, equipped with a Bruker CCD (charge coupled device) based detector, and an Oxford Cryostream low - temperature apparatus located in the Department of Chemistry Crystallographic Facilities at Michigan State University. Data were measured using omega and phi scans of 0.5° per frame for 30 s. The total number of images was based on results from the program COSMO 1 4 where redundancy was expected to be 4.0 and completeness of 100% out to 0.83 Å. Cell parameters were retrieved using APEX II software 1 5 and refined using SAINT on all observed reflections. Data reduction was performed using the SAINT software 1 6 which corrects for Lp. Scaling and absorption corrections were applied using SADABS 1 7 multi - scan technique, supplied by George Sheldrick. 35 Once re duced diffraction data sets were obtained from each of the different crystallographic facilities, the structures were solved by the direct method using the SHELXS - 97 program and refined by least squares method on F 2 , SHELXL - 97, which are incorporated in SH ELXTL - PC V6.10. 18 Anisotropic thermal parameters were refined for all non - hydrogen atoms, with the exception of the proton on the hydroxo bridge (labeled H50). All other hydrogen atoms were localized in their calculation positions and refined by using the riding model. Crystal structure parameters are reported in table 2 - 1. Coordinates of the solved crystal structures are available in Appendix 2.2 of this chapter. 2.2.3 Computational Procedure Unrestricted Density Functional Theory 19 with the Kohn - Sham v ariational implementation 20 was used to determine the electronic structure of the Diiron(III) hydroxo system. Functionals used were the ubiquitous B3LYP 21 as implemented in the Gaussian 09 22 electronic structure package, and the pure GGA BPW91 23 functional . B3LYP offers the advantages of energetic accuracy found for hybrid functionals with regard to calculating the energy differences necessary in the determination of the spin - coupling element in the Heisenberg spin Hamiltonian, based on this and prior resea rch. 4 BPW91 offers the potential benefit of allowing less ligand mixing with the higher energy metal d - orbitals, especially with the low spin electronic states, which allows for better analysis of the mechanisms by which spin coupling can occur. Basis sets employed for relevant computations in this research were used based on prior work in the group, and included 6 - 31G(d) 24 and 6 - 311G(d,p). 25 The 6 - 31G(d) basis set was used only for geometry optimizations for both the low spin and broken - symmetry states, whereas the 6 - 311G(d,p) basis set was also used for the aforementioned geometry optimizations in addition to its use for all the high spin an d broken - 36 symmetry single point energy calculations used for the electronic structure analysis of all geometries studied in this dissertation. Calculations were performed in Gaussian 09 22 and to a lesser extent ORCA. 26,27 It was determined through various comparisons of the electronic wavefunctions generated by these two packages that the resulting low spin and high spin wavefunctions were significantly congruous, having similar compositions as determined by Mulliken population analysis 28 and nearly identi cal energies. The use of Mulliken population analysis is in contrast to previous studies in our group that utilized the Natural Population Analysis of Weinold and coworkers. 29 This decision is a consequence of NPA being unavailable in ORCA and this project initially required the use of ORCA for all the low spin calculations. It was de termined that the Mulliken and n atural population analyses scale accordingly such that comparisons between wavefunctions in either will show similar trending behavior. Therefor e, to maintain a consistent analysis of the electronic structure of these systems, Mulliken population analysis was used for this study. Geometry optimizations were performed on a cornucopia of structural variants of complexes 1 and 2 . These geometries in clude full C 2v symmetrized versions of the di - iron hydroxo cation without the acetone present utilizing different basis sets, functionals and multiplicities, as well as the corresponding gallium analogues. Also optimized was the 296 K crystal structure of complex 1 including the coordinated acetone using a subset of the basis sets and functionals in an attempt to get consistency with the observed X - ray crystal structures in our optimized geometry study. These optimized geometries were also studied without the coordinated acetone molecule to compare between the electronic structures of the di - iron hydroxo with the inclusion or absence of the acetone molecule. The optimization procedures for each of these variants will be discussed below. 37 The geometry opti mizations carried out in full C 2v point - group symmetry were performed as a starting point for comparison with previous studies from our group, as well as to establish the basic behavior of the computational geometric modeling of the di - iron hydroxo system independent of the basis sets and functionals used to study them. These optimizations were performed with tight optimization criteria on the cation without the acetone present, based on the previously reported UB3LYP/6 - 31G(d) S=5 geometry optimization repo rted from our group, which was in turn based on the published X - ray crystal structure of Lippard and coworkers. 1 This structure was used as a starting point since, at the onset of this project we were interested in replicating the previously published resu lts so as to ensure that the proper electronic states were being obtained and studied. Geometries were optimized in both 6 - 31G(d) and 6 - 311G(d,p) basis sets to check the similarity of results between the two basis sets and as a test bed for future w ork on the system described in C hapter 4, where the desire to compute reorganization energies 30 required the optimizations be carried out in the same basis set that was used to calculate the energies of the systems studied. Combined with the different functionals used, this brings the total number of optimized C 2v diiron(III) hydroxo geometries studied to eight. The g allium geometries were also optimized in B3LYP and BPW91 using both basis sets to see if similar geometric differences were observed between the X - ra y structures and the optimized geometries, as well as to see if the bond distances for 6 - 31G(d) were shorter than those observed for 6 - 311G(d,p). The optimized geometries derived from the X - ray crystal structures were studied in an attempt to model the ele ctronic structure of complex 1 on an optimized geometry while accounting for both the coordinating solvent and the asymmetric character of the diiron coordination environment that is observed in the crystal structures. With this in mind, the optimizations were based on the 296 K X - ray structure of complex 1 , as it had the highest degree of asymmetry in the crystal structure as 38 is discussed further on in this chapter and as is seen in t ables 2 - 2 and 2 - 3. By starting with the greatest degree of asymmetry, we can ensure that the asymmetric character of the coordination environment will be preserved in the optimized geometries if it is necessary for the stability of the complex. The Fe 296 K X - ray structure including acetone was imported into Gaussian in the man ner described below for the importing of crystal structures, and an initial optimization was performed in the high - spin state using UB3LYP/6 - 311G(d,p). The resulting structure was a local minimum on the potential energy surface, as there were negative calc ulated frequencies present. Inspection of this initial optimized geometry revealed that the acetone molecule was far out of the plane consisting of the two iron cations and the hydroxo ion. It was suspected that the acetone molecule needed to rotate a bit plane by adjusting the dihedral angle between the Fe2 - O5 vector and the acetone carbonyl vector to zero, thereby swinging the acetone in line with the diiron hydroxo plane. This modified geo metry was then optimized in the high - spin state again using UB3LYP/6 - 311G(d,p) to obtain the final high spin optimized geometry, which was confirmed by performing a frequency calculation on the obtained geometry and observing an absence of negative frequen cies. This high spin geometry was in turn used as a starting point for the low spin optimized geometry in UB3LYP/6 - 311G(d,p) which was successfully obtained with no additional modification necessary, as confirmed by the lack of negative frequencies in a su bsequent frequency calculation. The optimized geometries of the X - ray crystal structures with the acetone excluded were not considered for study, as it is the case that the previously mentioned C 2v optimized geometries are a good approximation of the resul ting geometry and are studied with much more facility than the slightly asymmetric counterparts that could be obtained by performing said optimizations. 39 When studying the electronic structure of the obtained crystal structures the geometries were imported from the .cif files. This was done by isolating a single cationic complex in the unit cell of the .cif file using the Mercury crystallographic software, 31 which was then saved as a .pdb file and subsequently opened in the ChemBioDraw 3D software 32 to save the structure as a Gaussian formatted input file or as Cartesian coordinates suitable for inserting into an ORCA input file. In studies where the O5 - H50 bond distance was manipulated to be a constant value across the temperature series, the X - ray structure Gaussian input files were opened in GaussView, 33 and the O5 - H50 bond was selected and set to the desired value with careful attention given to ensure only the proton position was shifted while extending the bond. The O5 - H50 bond distance was the only parameter altered, which preserves the bond angles and dihedral angles associated with the O5 - H50 bond. Studies on the electronic properties of the cation - acetone hydrogen bound complex were also performed, with the geometries being imported in a simi lar fashion with the exception of the associated acetone molecule not being removed from the crystal structure as was the case for the isolated cation. When assigning the orbital designations and discussing certain aspects of the molecular geometries of c omplexes 1 and 2 , it is useful to designate a Cartesian axis system for the sake of clarity. The Cartesian axis system used throughout this chapter had the z - axis primarily oriented toward the bridging hydroxo group, with the y axis in the same plane as th e trans - pyrazole and the x - axis being perpendicular to the trans - pyrazole, as depicted in figure 2 - 3. 40 2.2.4 Systems Studied The primary focus of this study were the variable temperature X - ray crystal structures solved by Dr. Dong Guo. These structures consisted of the Fe - hydroxo complex at 20, 50, 100, 173, 234, and 296 K, and the corresponding structures of the gallium(III) analogue. The Fe - OH crystal structures had their low and high spin wavefunctions evaluated with UB3LYP/6 - 311G(d,p) whic h allowed for the determination of the spin coupling constant at each crystal structure geometry studied. When considering what changes to expect in these VT X - ray structures as a function of temperature, one can expect that there could be effects on the g eometry that are solely due to the change in temperature. In the case of complex 1 we expect that there could be additional geometric changes due to the thermal population of additional spin states as the temperature changes. To determine if the thermal in duced changes would have an effect on the communication between the Figure 2 - 3: A Simple diagram explaining the axis system used to assign the orbital labels for orbitals involved with coupling on the Fe III ions and µ - OH. The x axis for both the Fe and OH centers is going into and out of the plane of the paper. 41 spin centers on its own, the X - ray structures of the gallium analogue were also studied, with the gallium(III) centers replaced with iron(III), to determine the coupling constants. For the sake of clarity, these theoretical structures will be subsequently referred to as the Fe @ Ga geometries in this work. These Fe @ Ga coupling constants allowed us to discern if any observed changes in coupling constants in complex 1 X - ray structures are u nique to the changing electronic structure in the Heisenberg spin coupled diiron hydroxo complex as a function of temperature. Our previous studies where the coupling constant was determined via theoretical methods reported the values resulting from energy calculations using the UMPW1PW91 functional developed by Barone and coworkers 42 along with a 6 - 311G(d) basis set. This functional was not used in this work as suitable values for coupling constants were obtainable with B3LYP, which is also a hybrid densit y functional and had the benefit of being the function which obtained better geometry optimizations in our earlier work. The high and low spin wavefunctions of C 2v geometries optimized with B3LYP and BPW91 were also studied to check for consistency of re sults between the different functionals and basis sets used, as well as to establish the expected changes in geometry between a low spin state and a high spin state based on the optimized geometries obtained for those states. The optimized geometries deriv ed from the X - ray crystal structures had their high and low spin wavefunctions evaluated only with B3LYP, as it was determined from the results of calculated coupling constants as discussed further on in this chapter suggested this was the best choice. Cou pling constants were determined using the method of Yamaguchi and coworkers, 34 were the spin expectation values as determined by the electronic structure program are used in the determination of the coupling constant as discussed in Chapter 1. This methodo logy offers the advantage of offsetting any destabilization of the low spin broken symmetry state, which is 42 typically spin contaminated, while incurring minimal costs in effort. There exist other methods for determining the coupling constant, 35 but they ar e typically used in cases where more is known about the electronic structure ahead of time and are usually more specific in application. The Yamaguchi formalism used herein is relatively accurate over a broad range of applications and thus is preferred for the studies performed in this dissertation . 2.3 Results and Discussion 2.3.1 Crystal Structures The solved crystal structures are pictured in figure 2 - 4. The crystal data for all twelve X - ray crystal structures obtained by Dr. Dong Guo are summarized in table 2 - 1. It is noteworthy that the cell dimensions for both the gallium and iron compounds unit cells did increase with temperature, as would be expected due to the thermal expansion of the material. Table 2 - 1: X - ray crystal structure parameters for complexes 1 and 2 at all temperatures studied. 43 Each crystal structure was analyzed and the major bond distances and angles present within the coordination environment of the Iron and Gallium centers were tabulated to show changes in said environment of the metal centers that could correlate to changes in t he calculated properties of the complexes. The bond distances are reported in table 2 - 2 and the bond distances are reported in table 2 - 3. Figure 2 - 4: (Left) X - ray crystal structure of complex 1 at 20 K, with the atom in the coordination environment labeled. (Right) X - ray crystal structure of complex 2 at 20 K, with the atom in the coordination environment labeled. For both structures, non - hydrogen atoms are di splayed as thermal ellipsoids, and the perchlorate anions are omitted for clarity. These atom labels are consistently used for all complex 1 and 2 crystal structures reported herein, and were determined based on the relative orientation of the bridging acetone molecule in the crystal lattice. 44 Table 2 - 2: Bond distances in Angstroms determined by X - ray crystallography for atoms in the coordination environment of complexes 1 (M=Fe) and 2 (M=Ga). Refer to f igure 2 - 4 for atom labels. 45 Table 2 - 3: Bond angles in degrees determined from X - ray crystallography for atoms in the coordination environment of complex 1 (M=Fe) and 2 (M=Ga). Refer to figure 2 - 4 for atom labels. 46 The bond distances with significant trending differences with respect to temperature in the Iron system are the O5 - H50 bond distance and the Fe1 - O5 bond distance, where O5 is the oxygen and H50 is the proton of the µ - hydroxo group, and the H50 - O100 hydroge n bond distance between the µ - hydroxo proton and the associated co - crystallized acetone molecule present in the crystal lattice, as depicted in figure 2 - 5. Here it can be seen that there is a significant shortening of the O5 - Fe 1 bond distance at the higher temperatures studied. We can also see that the O5 - H50 bond distance shortens at the higher temperature points and there is a complementary lengthening of the H50 - O100 hydrogen bond distance in the iron crystal structures. Both of these changes are absent in the gallium (III) analogue. There is some concern over the validity of bond distances involving hydrogen atoms in X - ray structures, as there are no core electrons that can give a reliable estimate of the location of the proton. It is the case that the reported X - ray determined bond d istances are especially shorter for bonds with hydrogen atoms, as the crystal structure looks for the locations of highest electron density, which for bonds involving a hydrogen will be located between the proton and the nucleus of the atom to which it is bound. However, since we are comparing changes in bond distances to a structural model, we feel that any resulting changes in the X - ray determined O5 - H50 and H50 - O100 bond distances that are not due to the bonds changing in distance in complex 1 relative t o complex 2 would be mirrored in both X - ray structures. Therefore, even though the accuracy of the bond distances for these bonds is not to be innately trusted, it is reasonable to conclude that trends in these bond distances due to differences in electron ic structure are being faithfully reproduced in their X - ray determined values. The Fe - N bond distances showed variations amongst individual bond lengths as a function of temperature. However, if one only considers the list of bond lengths as a function of temperature 47 and does not concern themselves with the identity of each bond distance, there are no significant changes in Fe - N bond distances that are not also present in the Ga - N bond distances found in complex 2, as seen in figure 2 - 6 . The acetate C - O bon d distances also showed temperature dependent behavior (refer to supplemental figure A2 - 1), but a general trending decrease in in the acetate C - O bond distances can still be observed in complex 2 , making this change in bond distance less signi ficant for studying the magneto - structural effects in complex 1 . In fact, apart from the previously mentioned significant changes, the majority of the bond distances that had temperature dependent behavior for the iron exhibited similar changes in the gallium dimer. Examples of this include C - O bond distances along the acetate bridges, as plotte d in supplementary figure A2 - 2. Figure 2 - 5: Plots of relevant bond distances concerning the µ - OH bridge in the X - ray crystal structures of complexes 1 and 2 as a function o f temperature. The line between data points is added for clarity. Note how complex 1 exhibits significant changes in the O5 - H50 bond distance, and that the Fe1 - O5 bond distance gets shorter than Fe2 at higher temperatures exceeding the error of the experim ent, both of which do not occur for complex 2 . Notice also that the H50 - O100 bond distance complements the O5 - H50 bond distance in complexes 1 and 2 . See text for details. 48 Generally speaking, the bond angles showed few cases where there was a significan t change in bond angle value outside the experimental error as one goes from the low to high temperature structures for both complexes. However, but there were more cases of trending differences as a function of temperature in the iron crystal structures t hat seemed to parallel those found in the gallium crystal structures. It was however the case that the actual values in these parallel bond angle trends routinely were significantly different when comparing equivalent values from complexes 1 and 2 . A prominent case of differences in observed bond angle as a function of temperature is the M1 - O5 - M2 bond angle, which for all temperatures is larger for the gallium complex as seen in figure 2 - 7. The values for the Ga1 - O5 - Ga2 angle gradually increase over th e temperature range studied, but there is no significant difference between the value at 20K and the value at 296 K. In the case Figure 2 - 6: Bond distances associated with the metal and Tp capping ligand in c omplexes 1 and 2 . The line between data points is added for clarity. M1 bond distances for both complexes 1 and 2 appear on the left, and M2 bond distances appear on the right. Note how the bond distances appear to swap atom labels for certain temperatures as discussed in the text. 49 of the iron complex, the Fe1 - O5 - Fe2 angle also increases over the temperature range studied, but in this case there is a signif icant difference between the lowest and highest temperature values. Other bond angles which exhibited significant changes in magnitude across the temperature range studied include the O5 - Fe - N( trans ) bond angles, where N is the coordinating nitrogen from th e Tp ligand trans to the µ - hydroxo group. There is a parallel trend in the O5 - Ga - N( trans ) bond angles in complex 2 , albeit the change is not of the same magnitude as depicted in figure 2 - 8. This makes the changes in the O5 - Fe - N( trans ) bond angles unlikely to be a magneto - structural factor in the temperature dependent behavior of complex 1 . Figure 2 - 7: M1 - O5 - M2 bond angle in the X - ray crystal structures as a function of temperature for complexes 1 and 2 . Note the larger change with temperature for complex 1 compared to complex 2 . 50 Significant changes as a function of temperature were also present in the N( cis ) - Fe - N( cis ) bond angles with the nitrogens cis to the µ - hydroxo which give a measure of how well these side groups envelop the metal ions. The temperature dependence of these bond angles is plotted in figure 2 - 6. It can be seen that there are parallel changes in N( cis ) - Ga - N( cis ) bond angles for the gallium analogue, which means this too is not a signific ant magneto - structural effect. The Fe - O - C bond angles with the bridging acetate ligands, and the O - Fe - O5 angles between the acetate oxygens and bridging µ - hydroxo oxygen atom exhibited a degree of temperature dependent behavior, but this was not observably different than that observed for complex 2 , as can be observed in the supplemental figur es A2 - 3 and A2 - 4. Figure 2 - 8: Relevant bond angles involving the Tp cap from the X - ray structures as a function of temperature. On the left, the O5 - M - trans - N bond angle for complexes 1 and 2 reflecting the linearity of the z axis of the metal. On the right is the cis - N - M - cis - N bond angles for complexes 1 and 2 , reflecting how square the two cis - pyrazole rings are to each other. Lines between data points were added for clarity. 51 The O1 - M1 - O3 and O2 - M2 - O4 angles, which are a measure of the perpendicularity of the two acetate bridges have different values, with the labels on the oxygens appearing to be switched between the gallium and iron complexes and the iron c omplexes generally having the larger and therefore less perpendicular angles. The O - C - O angles on the acetate bridges show no significant changes across the temperatures studied and no significant difference between the values for the two different complex es. It is important to note that for many of these trends, most notably the metal Tp nitrogen bond distances and acetate - O - M - O5 bond angles, some of the atoms appear to switch roles in a way as was mentioned above, with atoms assuming bond angles congruous to differently labeled bond angles at different temperatures. These atom labels were meticulously scrutinized and were found to be consistent with the orientation of the hydrogen bound acetone molecule in the X - ray lattice over all temperatures studied fo r both the Ga 2 and Fe 2 structures. As for an explanation for this role swapping, we can only postulate. Since these crystals were not stored at cryogenic temperatures between the collection of each temperature run, it is possible that much of this role swa pping occurred between collection of crystal diffraction data, which implies that at higher temperatures or over time, the ligand environment may fluctuate between two or more stable configurations, which is reflected in the role - swapping observed in the b ond distance and angle data obtained by X - ray crystal structures. For the purposes of isolating which structural changes are potentially a function of the magnetic properties of the Fe - hydroxo system, we can use the gallium structure as a guide to identify changes that are only due to the change in temperature. More specifically, any structural changes in the Fe - hydroxo system that show a corresponding change in the Ga - hydroxo analog must be a consequence on the changes in temperature, and not the unique ma gnetic properties induced by 52 the spin - exchange of the Fe - hydroxo system. This allows us to disregard almost all of the changes in bond angles observed as a function of temperature, with the exception of the Fe - O5 - Fe bond angle which has much more significa nt temperature dependent changes than those observed for the Ga analog. By contrast, most of the bond distances with significant changes in the Fe - hydroxo system are likely correlated with magneto - structural effects in the system. In particular, the temper ature dependent changes in the Fe O5 and O5 - H50 bond distances should be investigated for being caused by the magnetic interaction, since we have already established in previous work by the group the importance of the µ - hydroxo bridge to the exchange i nteraction in this system. Going forward, it is these metrics with changes unique to the Fe - hydroxo system that will be monitored for their possible contributions to changes in the electronic structure of the Fe - hydroxo system. 2.3.2 Comparison of X - ray S tructures to Optimized Geometries A selection of resulting bond distances and angles obtained from the C 2v geometry optimizations without acetone present contrasted with X - ray structure values for the same parameters are tabulated in table 2 - 4. Unlik e in the previous studies on this system, both the low spin broken - symmetry state and the high spin state were optimized and studied utilizing both the pure GGA BPW91 functional, and hybrid B3LYP density functional to ensure that the observed trends were n ot specific to the high spin electronic state. The results of the same bond distances and angles from the B3LYP/6 - 311G(d,p) optimized X - ray structures compared with the B3LYP derived values from C 2v optimized geometries and the values from select X - ray cry stal structures are tabulated in table 2 - 5. 53 Table 2 - 4: Selected bond distances (in Angstroms) and angles (in degrees) for atoms in the coordination environment of C 2v optimized geometries for all multiplicities, basis sets, and functionals of complex 1 and 2 . Note that these geometry optimizations did not inc lude the acetone molecule. See f igure 2 - 4 for atom labels. 54 Table 2 - 5: Comparison of the optimized X - ray geometries with the analogous C 2v optimizations and X - ray structure. Note that M = Fe III . 55 The almost immediate observation that can be made for all structures is that all of the geometry optimizations almost universally over estimate bond distances compared to the X - ray crystal structures. This is not unexpected as the geometry optimizations ar e calculated in the gas phase as free molecules without accounting for the presence of solvent or neighboring molecules. It goes to follow that a gas phase calculation would not account for the crystal packing stabilization energy that leads to compressed molecular structures in the solid state structures obtained by X - ray crystallography. Another general trend that is observable across the series of optimized geometries is that for a geometry optimized with a given basis set and multiplicity, the BPW91 op timized geometry will have longer bond distances compared to those obtained with the B3LYP functional. This is attributable to the larger amount of mixing between the metal d - orbitals and the ligand based orbitals in B3LYP, which is an empirical observatio n in these compounds that will be discussed further in the proceeding discussions on the electronic structure of these complexes. This increased ligand mixing causes stronger interactions between the ligands and metal centers, which results in reduced bond distances as reported in table 2 - 4. When comparing basis sets, the 6 - 31G(d) basis set consistently gives smaller bond distances than 6 - 311G(d,p) for all combinations of functional and electronic state available for study. Finally, just as in the X - ray cry stal structures, the bond distances for gallium optimized in a given basis set and functional are universally less than or equal to those of the analogous iron optimized geometryWhen comparing the bond angles around the metal coordination environments for the optimized geometries and X - ray crystal structures, it can be generally stated that the trends in angles are seemingly less significant than the bond distance changes encountered for the optimized geometries when the basis set and functional were varie d. This likely has to do with the highly symmetric nature of the optimized geometries offering fewe r 56 degrees of freedom than available in the area of bond distances. This in turn would have the effect of constraining the degree of variance that could be ex pected when optimizing the different electronic states of a given functional and basis set combination. It should be noted that BPW91 offered larger variance between the different electronic states in the optimized angles of a given basis set and functiona l. The most significant amount of variation in the optimized geometries as a whole is the value of the M1 - O5 - M2 angle, where the general observable trends include that of the larger basis set having larger optimized angle values across all different funct ionals, systems and electronic states studied, all high spin optimized geometries having smaller angles than their corresponding broken symmetry optimized bond angles, and B3LYP generally having smaller calculated angle values than those with otherwise equ ivalent electronic states and basis sets but calculated with the BPW91 functional. Most of these trends also apply to the O1 - M1 - O3 and O2 - M2 - O4 bond angles, but they are inverted for the other angles mentioned in table 2 - 4. The M1 - O5 - M2 angle was appreciab ly higher for all the optimized geometries of Iron than was observed in the X - ray crystal structures, and the O - M - O5 angles between the acetate oxygens and the bridging oxygen were larger in all of the X - ray structures than what was optimized. These trends and the previously mentioned differences in bond distances suggest that the X - ray structures has a more compressed structure along the Fe - OH - Fe bond vectors, and a pinching of together of the metal ions as evidenced by the smaller M - OH - M bond angle. The a cetate bridges have wider bite angles when referenced to the bridging hydroxo but shorter distances than the optimized geometries, which is consistent with the metals being pinched in by the smaller M - O5 - M bond angle. The acetates were similarly close to p erpendicular in the optimized and X - ray geometries. 57 The effect of these differences will be discussed in relation to the differences calculated electronic structure properties of these molecules in the following sections. When focusing on the optimized cry stal structure geometries it can be generally said that the same general statements made concerning the optimized C 2v geometries also apply to the optimized crystal structures, with a few differences. An easily observable difference between the optimized X - ray structures and the C 2v B3LYP/6 - 311G(d,p) optimized geometries was the shorter M - O5 bond distances, which surprisingly were more consistent with those obtained for the high spin B3LYP/6 - 31G(d) geometries. However, it was also the case that the high spi n B3LYP/6 - 31G(d) geometry had the closest bond distances to our X - ray crystal structures out of the C 2v optimized geometries, so this is a welcome result. The O5 - H50 bond distances were also longer for the optimized X - ray structure geometries than in any o f the other geometries studied, but this is easily explained by the presence of the hydrogen bonding acetone in the course of the geometry optimization which was absent in the C 2v optimized geometries. The fact that this bond distance was longer is also li kely to be correlated to the O100 - H50 bond distance being substantially shorter in the optimized X - ray structure, likely because the hydrogen bond interaction was allowed to stabilize without the external influences of the crystal lattice that may lengthen the hydrogen bond in our actual crystal structures. This implies that the hydrogen bonding interaction is less significant in the X - ray structures than it could be, given that acetone prefers to be closer in an uninhibited environment as in the geometry o ptimization. Apart from the singular differences mentioned before, the most obvious difference between the optimized X - ray geometries and the other geometries studied is that the X - ray and X - ray optimized geometries have asymmetric elements that are symme tric in the C 2v geometry. This is not at all surprising since imposing C 2v symmetry forces many of the selected bond distances and angles to 58 be identical by symmetry. What was surprising was that the most prominent asymmetric feature of the X - ray structure s, which was the difference between Fe1 - O5 and Fe2 - O5 bond distances is sort of the reverse of what occurs in the crystal structures relative to the position of the bridging acetone. In the case of the optimized X - ray structures, the O5 - Fe2 bond distance i s consistently determined to be shorter than the O5 - Fe1 bond distance, even though the reverse is true in our obtained crystal structures. The reason for this is unknown at this time. The same sort of opposite trend is true for the M - O(acetate) bond dista nces, where M1 - O1 and M2 - O4 are shorter in the optimized X - ray structure and the opposite is true in our actual X - ray structures. Again this is also observed for the M - N(cis) bond distances where M1 - N5 and M2 - N7 bond distances are shorter than the M1 - N1 an d M2 - N11 bond distances in the optimized X - ray geometries and longer for the actual X - ray geometries. The odd part about all of these relations is that it seems they are related by a C 2 rotation around the OH bond axis. One can imagine that if the labels w ere rotated by a C 2 symmetry operation, the bond distance trends would be consistent with the X - ray geometries. It is possible that the coordinated acetone molecule may have flipped over to the other side during the optimization process so that the labels were effectively rotated by a C 2 symmetry optimization, but the optimized geometries have no negative frequencies, so it is not known why this would occur. It is nonetheless an interesting observation. The bond angles showed much less variation in the opti mized X - ray geometries when compared with the X - ray crystal structures. It is noteworthy that the optimized X - ray structures have M1 - O5 - M2 bond angles intermediate between the X - ray structures and the C 2v optimized geometries. This could be due to the opti mized X - ray geometries not having the rigid symmetry restrictions that are found in their C 2v brethren, but it does not seem likely considering that the acetone was included in the optimized X - ray structures but not the C 2v structures. It could just be tha t since the 59 C 2v geometries were optimized with tight optimization criteria, the angles were better able to optimize towards their ideal value which were not reached in the X - ray geometry optimizations since they were run with normal optimization criteria. Similar arguments can be made for the O(acetate) - M - O5 bond angles which in the optimized X - ray geometries are intermediate to the C 2v optimized geometries and the X - ray crystal structures. Regardless of these trifling differences between the optimized geom etries and the X - ray crystal structure, it was extremely gratifying to obtain an optimized geometry which bore a great resemblance to our observed crystal structures, as it will serve as an effective bridge between our subsequent studies on the X - ray struc tures and the same studies on the C 2v optimized geometries. 2.3.3 Computational Determination of the Spin - coupling Constant as a Function of T emperature. It is well known that the Heisenberg - Dirac - Van Vleck Spin Hamiltonian is an empirical explanation of the energetic ordering of different spin states in spin coupled systems. 4 The energetic spacing of these different spin states is determined by the spin coupling constant J. Experimentally, this quantity is determined using bulk temperature dependent magne tic susceptibility measurements or using EPR techniques. 43 By performing electronic structure calculations on X - ray structures or optimized geometries, it is also possible to determine the spin - coupling constant using computational chemistry methods. It wa s our intent that by using electronic structure theory to determine coupling constants for our variable temperature X - ray crystal structures, the resulting values would function as a useful guide for determining the amount of communication between the spin centers as a function of temperature. It may seem nonsensical to determine different coupling constants for different temperatures when in theory this is a 60 temperature independent property of the systems studied, but it still is an effective indication of the amount of electronic communication between the spin centers, and thus is a useful tool in determining if the observed structural changes have corresponding consequences on the electronic structure of these complexes. Electronic coupling constants were determined using B3LYP for all temperatures for the Fe 2 - hydroxo system. This required the high spin energy as determined from a single point energy calculation and the corresponding low spin energy as determined from a broken - symmetry single point energy calculation, as well as the two spin expectation values of those two wavefunction as is required in the Yamaguchi method 33 for the determination of the spin coupling constant. To ensure the proper broken symmetry state had been obtained by way of either th e spin - flip methodology of ORCA or the fragment based guess of Gaussian 09, the spin and charge density on the two iron(III) centers was routinely monitored via the Mulliken population analysis. 28 A proper broken symmetry singlet state will have a spin den sity of with an absolute value over 4 on each metal center, with one center having positive alpha spin density and the other center possessing negative beta spin density. Values less than this result in an inadequate singlet state, which can result in an a rtificially stabilized singlet state in the case of BPW91, or an artificially destabilized singlet state in the case of B3LYP. This was encountered when the complex 1 X - ray structures sans acetone were studied with the BPW91 functional, resulting in only t hree of the temperatures studied having adequate spin coupling values when determined with BPW91. The case of the destabilized singlets determined from bad broken symmetry calculations with B3LYP was discussed in C hapter 1. The spin expectation value has also been found to be a suitably good indicator of the quality of a broken symmetry state. It has been observed in the course of this research that a good broken 61 symmetry state has a spin expectation value close to 5. This is a high amount of spin contamin ation considering the theoretical value for a singlet is zero. However this amount of spin contamination is expected due to the large number of unpaired electrons in this molecule. In this way, much like how a good broken - symmetry state will have a high sp in density value on the metal centers, it will also have a large amount of spin contamination. Broken symmetry states with lower than expected spin expectation values were consistently found to also lack the required spin density on the metal centers as wa s previously reported by our group. 4 In addition to calculating the spin coupling constant for the X - ray structures of complex 1 using the Yamaguchi method as previously mentioned, the theoretical coupling constants of the Fe @ Ga structures including and excluding acetone for all temperatures using the B3LYP functional. This was done as an added control, to the analysis of crystal structures of complex 2 , to make sure that any of the temperature dependent changes observed in the gallium crystal structures and inherent in the Iron crystal structures would not greatly influence spin coupling constant and thus the magnetic communication between the spin centers. It should be noted that only the B3LYP functional was employed to determine the coupling constants of the complex 1 X - ray crystal structures when the acetone was included and all of the Fe @ Ga geometries studied. This is due to the complications regarding the instability of the BPW91 broken symmetry state. It was figured that if difficulties were enco untered with the simplest system that was closest to the calculated equilibrium geometry for complex 1 , that there would be more problems when the acetone was added to the system and when the Fe @ Ga geometries were studied, so BPW91 studies were not attem pted for these systems. The relevant results of the calculations on the high and low spin B3LYP wavefunctions and the calculated coupling constants on the acetone free X - ray structures are shown in table 2 - 6, and the 62 results of these calculations includin g the acetone molecule are shown in table 2 - 7. Both results are plotted as a function of temperature in figure 2 - 9. The prominent result present in all of these calculations on the variable temperature X - ray structures for complex 1 is that as the tempera ture increases, the calculated coupling constant decreases for both cases with and without the acetone present as seen in figure 2 - 9. Furthermore, the decrease is non - linear, occurring noticeably above 100 K. It is also easy to see that the calculated coup ling constant for the Fe @ Ga geometries is relatively constant for the studies both including and excluding acetone. This can be taken to mean that the geometric changes occurring in the crystal structure of complex 2 as a function of temperature, which s hould also be inherently present in complex 1 , are not resulting in substantial changes in the communication between the Figure 2 - 9: The UB3LYP/6 - 311G(d,p) determined J values for X - ray crystal structures of complex 1 and Fe @ Ga. Both the acetone - omitted and acetone included structures were analyzed and the pertinent data fo r this analysis is reported in t ables 2 - 6 and 2 - 7. 63 Table 2 - 6 : UB3LYP/6 - 311G(d,p) values for the determination of J determined at the X - ray c rystal structure geometry excluding the acetone in the crystal lattice. The previous result was obtained for a B3LYP optimized C 2v geometry as will be discussed in the text. Table 2 - 7: UB3LYP/6 - 311G(d,p) values for the determination of J determined at the X - ray Crysta l structure geometries of complex 1 and the Fe @ Ga geometries including the acetone in the crystal lattice. Note the roughly 4 cm - 1 increase in coupling constant for the Fe @ Ga and low temperature Fe crystal structure geometries when compared to the anal ogous values with the acetone omitted. spin centers. To phrase it another way, the observed temperature dependent structural changes in complex 2 do not make a significant impact on the calculated coupling constant value. This substantiates the argument that structural changes in the crystal structures of complex 1 can only be attributed to magneto - structural effects if those same changes are absen t in the crystal structures of complex 2 . With this conclusion in hand, it was decided to focus the analysis on the changes in 64 electronic structure solely on the diiron hydroxo crystal structures, as only those structures show meaningful changes in the spi n - related properties of the system as a function of temperature. Furthermore, we can now look to rationalize the changes in the spin coupling as a function of temperature in terms of the significant magneto - structural changes listed in the previous section . An equally important result of this exercise is that the inclusion of the acetone in the electronic structure calculations increases the calculated coupling constant universally for both complex 1 X - ray structures and Fe @ Ga structures. This is likely d ue to the acetone being able to draw some of the H50 electron density away from O5 and towards the O100 when it is included. This has the effect of effectively increasing the O5 - H50 bond distance from the perspective of the electron density when compared t o the same O5 - H50 bond distance without the acetone present in the model. As we have already seen in our previously published results, 7 the interaction of the H50 proton with the O5 oxygen lowers the coupling constant. It is therefore reasonable to deduce that since the presence of the acetone in the model weakens this O5 - H50 interaction by pulling electron density from the bond, it should strengthen the coupling. Indeed the O5 - H50 bond distance is one of the most significant temperature dependent structura l changes in complex 1 that is absent in complex 2 , and we can see that as the bond shortens with temperature, the coupling constant consistently decreases. Therefore, this pseudo - lengthening of the O5 - H50 bond from the presence of acetone in the electroni c structure calculations seems a reasonable explanation for the inclusion of acetone increasing the calculated coupling constants. Since the interaction with acetone makes observable changes in the degree of spin coupling in the X - ray structures, one would think that the results with the included acetone would be the correct ones and should be the ones we focus on in the subsequent studies. Certainly this should be the case when thinking about correlating other results to the calculated coupling constants. However, 65 there are reasons why the omission of acetone in the modeling of certain aspects of complex 1 might not be deleterious. For one, the presence of acetone made it difficult to analyze the broken symmetry wavefunctions as it introduced a good deal of asymmetry to the electronic structure that is not present when the acetone is removed. We also expected the studies on the mechanisms of spin coupling would not be greatly influenced by the absence of the acetone since we are only concerned with d - orbital s on the metals. Initial observation revealed that the calculated coupling constants evaluated in the absence of acetone were closer to the experimental value of 34 cm - 1 reported by Lippard and coworkers. 1 Therefore since the trends in calculated coupling constant are the same with and without the inclusion of acetone, and since it allows the facile study of the electronic structure, many subsequent studies of the electronic structure of these complexes will focus on the acetone excluded X - ray structures. The calculated coupling constant values for the VT X - ray structures using the BPW91 functional suffered problems with the converg ence of the broken s ymmetry state, with half of the temperature values having singlet energies that were excessively low and lo wer than the expected spin density values on the Fe centers. This resulted in large computed values for the spin - coupling constant, with the relevant data summarized in table 2 - 8. What is noteworthy is that even for the correctly determined broken symmetry states having spin density values comparable to those obtained in B3LYP, the calculated spin coupling constants are usually two to three times the magnitude of those determined for B3LYP and the experimental value as determined by Lippard and coworkers. 1 66 The reasons for this could be the propensity of pure density functionals to over stabilize singlet energies, 36 resulting in a larger energy difference and a larger coupling constant. Alternatively, the larger coupling constants could be symptomatic of differences in the modeled electronic structure such as decreased mixing of metal and peripheral ligand electron d ensity that cause a larger amount of spin coupling than the actual electronic structure of the complex or that modeled with the B3LYP density functional. 2.3.4 Calculated J for Optimized Geometries An effective comparison of the geometric differences bet ween the low and high spin optimized C 2v structures for both basis sets in each of the two functionals was obtained, the results of which are discussed previously and summarized in table 2 - 9. It was observed that low spin optimized geometries in both basis sets had higher calculated coupling constants than that calculated for the corresponding high spin optimized geometries. This is consistent with the notion of the bond distances, with M1 - O5 and M2 - O5 in particular, being shorter in the broken symmetry op timized Table 2 - 8: Comparison of UBPW91/6 - 311G(d,p) and UB3LYP/6 - 311G(d,p) values for the determination of J at the complex 1 X - ray crystal structure geometries excluding the acetone in the crystal lattice. The values in red highlight the telltale signs of improper broken symmetry states and the corresponding inflated J values that result. 67 geometries. Fortunately, the problem of convergence in the broken symmetry wavefunctions modeled with BPW91 was not encountered on the analysis of the optimized geometries. lt was also found that the optimized geometries suffered a similar overesti mation of the coupling constant in BPW91. Since the bond distances in the BPW91 optimized geometries are almost universally longer than their counterparts in B3LYP for a given basis set and electronic state, the differences in geometry are not responsible for this large increase in calculated coupling constant. Instead this is likely an intrinsic property of the pure functional to over - stabilize low spin states compared to the hybrid B3LYP density functional. 36 Table 2 - 9: The UB3LYP/6 - 311G(d,p) and UBPW91/6 - 311G(d,p) values for the determination of J at all of the C 2v optimized geometries of complex 1 sans acetone. Compare this to the experimentally determined value of 34 cm - 1 . Table 2 - 10 : The UB3LYP/6 - 311G(d,p) and UBPW91/6 - 311G(d,p) values for the determination of J for Fe @ Ga at all of the C 2v optimized geometries of complex 2 sans acetone. 68 This was confirmed when the B3LYP optimized geometries were then studied with the necessary BPW91 single point energy calculations to determine BPW91 spin coupling constants at the B3LYP geometries. The converse procedure was used to evaluate B3LYP couplin g constants at BPW91 geometries, with the results being very consistent to those obtained with optimized geometries from the same functional as that used for determining the coupling constant. The coupling constants were also calculated on Fe @ Ga optimi zed structures for the range of functionals and basis sets already explored. As these were gallium optimized geometries, there was no high or low spin state to optimize. The values used to determine the coupling constants as well as the coupling constants themselves are listed in table 2 - 10 . When looking at the calculated values, one can see that there is very little variation in the calculated coupling constants within any geometry studied with a particular functional. It is also interesting that for B3LYP , the calculated coupling constants are all within the acceptable range when compared to the previously experimentally determined value by Lippard and coworkers. The calculated coupling constants of the Fe @ Ga structures are almost all higher for a given basis set and functional than either the high or low spin optimized Fe geometries. The exception to this rule is that the BPW91/6 - 31G(d) optimized gallium geometry that does have lower calculated coupling constants than the LS optimized BPW91/6 - 31G(d) Fe c omplex when evaluated with the B3LYP functional. The reason for this is unknown, but since this is a case of the energy calculation being triply off equilibrium as it is Fe substituted for Ga, with a changed functional and a changed basis set compared to h ow the geometry was optimized, one should not read too much into this anomalous result. These C 2v optimized geometries are also helpful in that the variance between high spin and low spin optimized geometries can provide an approximation to the hypothetica l range of geometric 69 distortion for the molecule in an ideal setting void of external forces on the complex. By studying the electronic structure at these two geometries, one can obtain an estimate for determining what constitutes a significant variation i n calculated coupling constants, as such a significant variation would be outside the range of coupling constants possible to be determined using optimized geometries. To figure out this so called uncertainty we followed the suggestion of Ruiz and coworker s that an estimate of the uncertainty of the calculated coupling constant could be determined using this possible range in coupling constant values. 37 As we have already seen for this system, the smallest coupling constant that one can obtain is calculated using values obtained only from the optimized high spin geometry of the system of interest for a given functional and basis set. Since the coupling constant is directly proportional to the difference between the high spin and low spin energies of the syst em, by using values to get the largest energy difference between these high spin and low spin energies one should obtain the largest value for the coupling constant. This is achieved by still using the high spin energy values from the optimized high spin g eometry, but using the now stabilized low spin energy and its accompanying spin expectation value taken from the low spin optimized geometry. It is suggested that by looking at the variance in the two coupling constants calculated in this way, one can get a reasonable estimate of the overall uncertainty associated with the calculated coupling constants, which in this case is on the order of 2 cm - 1 . Spin coupling constants were obtained with UB3LYP/6 - 311G(d,p) for two sets of input geometries derived from t he low spin and high spin X - ray derived optimized geometries as described in the preceding section. The only difference between the two sets is that the acetone molecule was omitted from one of the geometry sets before the electronic structure calculations 70 were performed to determine the coupling constant. These calculated coupling constants and relevant values for the calculation of said coupling constants are reported in table 2 - 11. We see similar albeit slightly elevated values for the coupling constant at both low and high spin geometries calculated in the absence of acetone when compared to the analogous UB3LYP/6 - 311G(d,p) C 2v optimized geometries previously reported. This confirms the suspicion that the C 2v optimized geometries are an appropriate model of the diiron hydro xo system in the absence of the coordinating acetone. The reason for the slight elevation of the calculated coupling constants for this system compared to the C 2v analogous geometry is likely due to the improved orbital overlap afforded by the shorter bond distances in the X - ray based optimized geometries. The calculated coupling constants have their values increased when the acetone is included in the otherwise identical geometry. It is notable and likely coincidental that the calculated coupling constant s for the low and high spin optimized geometries including acetone greatly match the calculated coupling constants of the complex 1 X - ray structures without the acetone at the lowest and highest temperatures studied. The reasons for the inclusion of the a cetone increasing the coupling constant have already been discussed for the case of the X - ray structures and the same Table 2 - 11: The UB3LYP/6 - 311G(d,p) values for the determination of J at all of the optimized X - ray structure geometries of complex 1 both with and without acetone. Compare these to the experimentally determined value of 34 cm - 1 . 71 logic applies in this case as well. What is noteworthy is that the range of calculated coupling constants between the low and high spin op timized geometries does increase when the acetone is included. By surveying the changes in coupling constant values determined over the range of geometry distortions afforded by the plethora of optimized geometries studied, and comparing those results to t he variable temperature X - ray crystal structure values, we are able to show that the calculated coupling constant is a useful tool to study the changes in the communication between spin centers in the Fe - hydroxo system. However, to gain more insight as to what types of communication are changing in the system than what is possible by examining the geometric changes as a function of temperature, a more detailed analysis of the molecular coupling mechanisms is required, as described below. 2.3.5 Study of th e Molecular Orbital Mechanisms of Spin Exchange in the Fe 2 - OH System As was the case in previous studies by our research group, two primary methods were used to elucidate the orbital mechanisms that significantly contribute to the spin coupling within these molecules. The first is the Hay - Hoffman method 7,38 wherein pairs of interacting orbitals, one on each of the two spin centers, are found in both symmetric (same orbital phases) and anti - symmetric combinations. The square of this energy difference is proportional to the relative contribution to the spin coupling provided by the orbitals of that type. This methodology has been used in the past as a way to determine electronic coupling constants and assess other forms of electronic communication. 39 Since spin coupling constants for these systems depend on electronic 72 communication between the spin bearing d - orbitals of the metal ions, this concept was used as a justification for studying the relative contributions to spin coupling by the extension of more strongly interacting d - orbitals should have larger contributions to the spin coupling constant. It has the chief disadvantage that the molecule and its electronic state need to be relatively symmetric such that the orbital nature on each spin center is th e same. This is why only high spin states can be used for these Hay - Hoffman studies as only they have an approximately symmetric electronic state in these systems. While it is convenient that the Fe 2 - hydroxo system does indeed satisfy this requirement for symmetric spin coupled sites, it is still the case that the nature of the interacting orbitals must always be the same for this method. This means that only the contributions between magnetic orbitals of the same type can be assessed. For example, even tho ugh previous results found significant contributions to the spin coupling between the two irons from d z 2 - d z 2 , d z 2 - d xy , and d xy - d z 2 interactions, only the contributions of the d z 2 - d z 2 interaction can be assessed by the Hay - Hoffman method. The flip side of t his method is that while spatial position of orbitals is very sensitive to subtle geometric changes, the energy of those orbitals is relatively unaffected by small geometric changes. This means that for the study of the non - optimized geometries that are pr esent in the X - ray crystal structures, the Hay - Hoffman method could have an advantage in accurately assessing the contributions of these homogenous orbital coupling pathways. The second method for the determination of the spin coupling pathways is the dete rmination of the orbital overlap of Natural Magnetic Orbitals (NMOs) as described by Kahn and coworkers. 7 ,4 0 These natural magnetic orbitals are comprised of occupied molecular orbitals from the broken - symmetry single point energy calculations. Since the s the spin coupling are the highest occupied molecular orbitals where the orbital is predominantly 73 based on the m etal and is of a d - orbital morphology. These orbitals will occur in pairs where the alpha orbital on one metal will have a partner on the other metal that is usually but not necessarily the same numbered beta orbital (meaning both orbitals are ranked the s ame by energetic ordering). The contributions of these spin orbitals to the spin coupling have been found to be proportional to the orbital overlap between these natural magnetic orbital pairs. It is important to note that ideally, molecular orbitals are b y definition orthonormal such that the orbital overlap between two spatial molecular orbitals is by definition zero. However, since our calculations employ unrestricted DFT, the (now spin) molecular orbitals are no longer eigenfunctions of the spin operato r. To put this in more understandable terms, the energy and corresponding spin orbitals of the alpha electrons are solved completely independently of the beta electrons and the total energetics of the system are determined as the sum of the independently s olved alpha and beta electronic systems. This means that there is no requirement for the alpha and beta spin orbitals to be orthogonal to each other, such that if an alpha and beta spin orbital occupy the same space on a molecule, they are likely to have a non - zero value for their overlap. It is this non - zero overlap value that we depend on for the determination of the magnitude of spin coupling contribution between a pair of NMOs. This method has the advantage that the overlaps can be calculated between an y alpha and beta orbital, thus providing for the assessment of the contributions from magnetic orbitals that are not of the same d - orbital character. This allows for the assessment of more potential pathways of magnetic coupling that those studied by the H ay - Hoffman method. The disadvantage of using this method is that the spatial orientation of these natural magnetic orbitals is very sensitive to the small perturbations in geometry that make the X - ray crystal structures less ideal compared to the very idea l C 2v symmetric optimized systems studied herein. Hence the inclusion of the C 2v optimized 74 geometries in conjunction with the X - ray crystal structures for our study on the molecular orbital mechanisms for the spin coupling in the Fe - hydroxo system. 2.3.6 Hay - Hoffman Coupling Interaction Studies The first step in the Hay - Hoffman analysis is the selection of the symmetric and anti - symmetric interacting orbital pairs from the single point energy calculation on the high - spin state. Fortunately, for this study, this is a relatively trivial task as orbital pairs can either be bonding or anti - bonding in nature and still give satisfactory results about the degree of contribution to the spin coupling. The frontier orbital model would suggest that if a simple atomic orbital basis set was used, the occupied orbitals with d - character would be the ten highest occupied molecular orbitals which would all be alpha in character, with each of the five types of d - orbitals having a symmetric and antisymmetric pairing. With the larger 6 - 311G(d,p) basis set employed for our single point energy calculations, the ten highest occupied molecular orbitals have a large amount of ligand character mixing into our expected d - orbital pairs which makes the identification of the d - orbital cha racter of these molecular orbitals difficult. Fortunately, the antibonding lowest unoccupied beta orbitals possess almost entirely metal d - orbital character. It is thus easy to identify and pair the orbitals together into symmetric and antisymmetric inter acting pairs. Since these are unoccupied orbitals, they have more nodes than would be expected for the interacting spin orbitals, but their energy differences are theoretically equivalent to those one would obtain from the alpha orbitals because the energy difference between symmetric and anti - symmetric d - orbital sets is due to the relative amount of interaction between the mixing orbitals, since the d - orbitals are to a rough estimate isoenergetic. Since the stabilization energy of bonding orbitals arising from an interaction is equivalent to the destabilization energy of the antibonding orbitals arising from the same 75 interaction, the magnitude of the calculated energy differences should be identical for the occupied alpha and unoccupied beta orbitals. Ther efore, it was our general procedure for this study to look at the ten lowest unoccupied beta molecular orbitals and establish the symmetric and antisymmetric pairs as the first order of business for this procedure. While knowing where to find the d - orbita l pairs is not difficult, there is potential for the identification of the symmetric and anti - symmetric pairs to be confounding. Fortunately, this is not the case for the Fe - hydroxo system. In all cases the exact character of the d - orbitals was easily assi gned due to the orbitals conforming to an easily determined coordinate axes system relative to each metal center, as depicted in figure 2 - 4. Examples of these orbital pairs are given in figure s 2 - 10 and 2 - 11 for B3LYP and BPW91 derived orbitals. For both t he B3LYP and BPW91 HS single point energy calculations, orbital pairs were able to be obtained for all of the optimized geometries studied and all twelve of the VT X - ray structures studied. The squared energy differences as derived from the orbital pairs w ere determined as these quantities are proportional to the contributions to spin coupling. These squared energy values are plotted in figure 2 - 12 for the C 2v optimized geometries. 76 Figure 2 - 10: Visualizations of the ten lowest unoccupied beta orbitals from the high spin UB3LYP/6 - 311G(d,p) wavefunction calculated at the UB3LYP/6 - 311G(d,p) high spin optimized geometry. Symmetric and Antisymmetric combinations of the d - orbitals are paired into each table entry. The orbitals are plotted with an iso value of 0.02. 77 Figure 2 - 11 : Visualizations of thet en lowest unoccupied beta orbitals from the high spin UBPW91/6 - 311G(d,p) wavefunction calculated at the UBPW91/6 - 311G(d,p) high spin optimized geometry. Symmetric and Antisymmetric combinations of the d - orbitals are paired into each table entry. The orbitals are plotted with an isovalue of 0.02. 78 2.3.7 Discussion of Hay - Hoffman Results for Optimized Geometries The Hay - Hoffman relative coupling contributions were determined from the high spin state wavefunctions studied with a 6 - 311G(d,p) basis set using either the B3LYP or BPW91 functionals and calculated for select C 2v optimized geometries. Geometries that were optimized with all permutations of high or low spin state as well as 6 - 31G(d) or 6 - 311G (d,p) basis sets were studied; the resulting spin coupling contributions are presented in figures 2 - 12 which will be considered further on in this discussion. Figure 2 - 12: Hay - Hoffman coupling contributions from UB3LYP/6 - 311G(d,p) and UBPW91/6 - 311G(d,p) for geometries optimized with the same functional and the indicated basis set and multiplicity. 79 The first observation that can be made is that for the most part, the relative contributions of a ll of the coupling pathways determined for the spin coupling in the C 2v BPW91/6 - 31G(d) optimized geometry are consistent with those indicated in our previous work. This is highly gratifying as we have independently verified the relative significance of th e symmetric d - orbital interactions on the spin exchange using the Hay - Hoffman method. We know from our calculated coupling constants that the broken symmetry states we obtained in this work are not precisely consistent with those obtained for the same geom etries that we previously studied, as is evidenced by our differing calculated exchange coupling values. The similarity in the calculated Hay - Hoffman coupling contributions both generally and in particular with the ordering of the BPW91/6 - 311G(d,p) High s pin orbitals studied at the BPW91/6 - 31G(d) HS geometry indicates that the calculated high spin electronic wavefunctions are mostly conserved between this work and our former work as the orbitals energy spacing are also similar. When considering the spin c oupling contributions, all combinations of functional and basis set show consistent behavior between low spin and high spin optimized geometries. As a general rule for all B3LYP and BPW91 optimized geometries studied with their corresponding functionals, t he largest contribution was from the d z 2 orbitals. The next significant pathway as determined with B3LYP wavefunctions was the d x 2 - y 2 orbital interactions, followed by a lesser contribution from the d xz orbitals. The contributions from d x 2 - y 2 and d xz as d etermined by BPW91 were roughly equivalent. It was then the case that for both functionals the least contributions came from d yz and d xy in descending order. The only time the magnitude of any of these pathways coupling contributions changed relative to ot her pathways for different geometries was for the d x 2 - y 2 and d xz orbital pairs as determined from BPW91, where d xz was less significant at high spin geometries, and more significant at low spin geometries when compared with d x 2 - y 2 . 80 When looking for trend s in terms of the values of the coupling contributions, we can compare the contributions between l ow spin and high spin geometries, between basis sets used to optimize the geometry and the functional used to study the wavefunction. When comparing the low s pin and high spin optimized geometries, the only significant are increases in contributions from d xz and slight increases in contributions from d z 2 and d yz . The d x 2 - y 2 and d xy orbital contributions remain essentially unchanged between the high spin and low spin optimized geometries. When looking at changes in basis set used for optimizing, it is universally true that coupling contributions are overall larger when a smaller basi s set is used for optimizing the structure. This is likely due to the longer bond lengths in the larger basis sets. Finally , when comparing the functionals used to study the geometries, B3LYP gave larger contributions from d z 2 , d x 2 - y 2 , and d xz compared to those obtained with BPW91. Contributions had similar trends but not identical values for geometries studied in the opposite functional from that in which they were optimized. The optimized X - ray structures were also investigated to determine the d - orbital pathway contributions to the spin coupling using the Hay - Hoffman method. These optimized crystal structure geometries are intermediate between the X - ray structures and the previously discussed C 2v optimized geometries. Therefore by obtaining the d - orbital coupling contributions at these geometries, we can be sure there is consistency between results for the C 2v optimized geometries and the subsequently discussed X - ray structure results. The coupling contributions from the d - orbital coupling pathways were d etermined for both the low spin and high spin B3LYP/6 - 311G(d,p) optimized geometries. To test as to whether or not the presence of acetone has an effect on the calculated coupling mechanisms, the coupling contributions were determined with the acetone incl uded and omitted from the input geometries. The results of these calculations are presented in figure 2 - 13. 81 When comparing the calculated coupling contributions for the optimized X - ray geometries sans acetone with those obtained for the C 2v B3LYP/6 - 311G(d,p) optimized geometries (see figure 2 - 14), one can see that the only significant changes in coupling contribution come from the d xz and d x 2 - y 2 orbital contributions. Specifically the d xz has increased contributions compared to the analogous symmetric geometry whereas the d x 2 - y 2 has decreased coupling contribution. The magnitude of the other coupling contributions remains approximately static. It is not evident as to why the relative contributions of these two orbitals shift, but since the X - ray optimized geometries are closer to the actual X - ray structures, we should expect a similar shift to occur there as well. It is suspected that if analogous studies were performed with the BPW91 functional, one would see a similar increase in the contribution of d xz relative to that for d x 2 - y 2 . The changes in the contributions between low spin and high spin geometries in these optimized X - ray geometries are comparable to those that were observed in the B3LYP/6 - 311G(d,p) C 2v optimized geometries. What is also noteworthy when inspecting the r esults of the optimized X - ray geometries is that while the actual values of the contributions varied slightly between when the acetone molecule Figure 2 - 13: Hay - Hoffman coupling contributions from UB3LYP/6 - 311G(d,p) for X - ray structure optimized geometries optimized with the same functiona l and the indicated multiplicity. 82 was included or excluded, the relative ordering of the contributions was consistent between the two sets of data . Furthermore, the same trends between LS and HS optimized geometries were observed with and without the acetone present. This suggests that the presence of the acetone molecule, while important when performing the geometry optimization, is not essential t o the evaluation of the mechanisms of spin coupling. We are cataloging these changes in d z 2 , d xz , and d x 2 - y 2 as consequences of the inherent changes in electronic structure between low spin and high spin states in the optimized geometries in the absence of other factors present in the X - ray crystal structure. Since the span of geometric changes in the optimized geometries of a given functional and basis set are small compared to the geometric changes present in the variable temperature X - ray crystal structu res, there is the possibility that more pathways are being affected than those merely indicated by the differences in the optimized geometries. Since the d xz and d x 2 - y 2 pathways showed changes between the C 2v and X - ray structure optimized geometries, we ca n expect the actual values of these contributions to be even more different for the X - ray structures. 2.3.8 Discussion of Hay - Hoffman Results for X - ray structures As was the case for the optimized geometries, the energy differences for the symmetric and anti - symmetric d - orbital pairs as obtained from the ten lowest unoccupied beta orbitals were calculated from both the B3LYP and BPW91 high spin wavefunctions for all of the variable temperature X - ray crystal structures. To simplify the analysis, these wave functions were determined with acetone excluded. The squares of these energy differences are reported in figure 2 - 14. 83 One can see that at low temperatures, the coupling contributions for the X - ray structures are similar to those for the optimized geometri es discussed earlier. The B3LYP low temperature X - ray values are very close to those obtained for the optimized X - ray structure geometry. The BPW91 X - ray structure values show a similar increase in the contributions of d xz relative to d x 2 - y 2 compared to th e C 2v optimized geometries that was present in the B3LYP optimized X - ray structure geometries. What is immediately noteworthy for the contributions determined via both BPW91 and B3LYP is that there are significant changes are occurring for the d z 2 - d z 2 and d xz - d xz orbital interactions as the temperature increases, with the d z 2 interaction experiencing a larger magnitude change in coupling contribution. All of the other orbital pairings show little change across the temperatures studied. To confirm the variable effect of these two coupling pathways on the amount of overall coupling between the spin centers, plots of the calculated coupling constant in B3LYP versus the squares of the energy differences have been produced. It is evi dent in these plots that changes in the d z 2 - Figure 2 - 14: Complex 1 Hay - Hoffman analysis of coupling contributions for the symmetric d orbital interactions in X - Ray structures as a function of temperature using B3LYP (left) and BPW91 (right) wavefunctions. Contributions are expressed in units of (cm - 1 ) 2 . 84 d z 2 and d xz - d xz orbital interactions appear proportional to changes in the coupling constant, while the magnitude of the other interactions remains static with regards to the coupling constant. We have already established that the spin coupling constant is a good gauge f or the total interaction between the unpaired spins in these systems, so we can conclude from these results that changes in temperature are affecting the magnitude of the spin coupling contributions that arise from the d z 2 - d z 2 and d xz - d xz spin orbital inte ractions. As the coupling constant decreases when the temperature increases, this means that the contribution of these pathways decreases as a function of temperature. As for the asymmetric spin coupling pathways previously mentioned, Information is unava ilable from the Hay - Hoffman method so the subsequent NMO analysis will need to be relied on to gain information on these pathways. Figure 2 - 15 : Fe @ Ga Hay - Hoffman analysis coupling contributions for the symmetric d orbital interactions in X - ray st ructures as a function of temperature using B3LYP (left) and BPW91 (right) wavefunctions. Contributions are expressed in units of (cm - 1 ) 2 . 85 Since the coupling constant does not change appreciably across the temperature ranges studied for the Fe @ Ga structures, a similar Hay - Hoffman investigation of coupling pathway contributions would not be expected to yield interesting results. It is however worth noting that the contributions of all the possible symmetric pathways in the couplings between the iron centers at the gallium X - ray geometries stay relatively unchanged over the whole temperature range as depicted in figure 2 - 15. This is consistent with the finding that the coupling constant for the iron hydroxo molecule studied at the gallium X - ray geomet ries does not appreciably change over the temperature range studied. In summary, the Hay - Hoffman method for determining the contributions to spin exchange coupling in the variable temperature X - ray crystal structures give consistent results between B3LYP a nd BPW91 functionals. Both functionals show evidence of temperature changes primarily affecting the magnitude of the d z 2 - d z 2 and d xz - d xz spin orbital interaction contributions to the Heisenberg spin exchange, with d z 2 - d z 2 having the largest variance as a f unction of temperature. It shows an inverse relationship between the contributions of these orbital mechanisms for spin exchange and temperature, which is an interesting result as it implies that changes in the Boltzmann population of available spin states act to reduce the efficacy of the primary spin coupling pathways present in the molecule. 2.3.9 Coupling Contributions Determined via Overlap of Natural Magnetic Orbitals The Hay - Hoffman method was a relatively facile way to study the contributions to sp in coupling. However, the necessity of identifying the asymmetric coupling pathways where different types of 86 interacting d - orbitals on each metal center cause meaningful contributions to the spin coupling necessitated the use of the NMO analysis. For the N MO analysis, instead of relying on the single determinant high spin wavefunctions, one must create the approximate singlet broken symmetry wavefunctions to obtain NMOs. Indeed the identification of the NMOs which are the ten broken symmetry orbitals that have the most d - metal character localized on a single metal center can be an entirely subjective undertaking. What is desired is to find an alpha orbital which is predominantly a metal d - orbital in character on one of the metal centers, and to find a corre sponding beta orbital which has the same metal d - orbital character on the opposite metal center. What is subjective is that there can be several broken symmetry orbitals that have similar d - orbital character, and one needs to select orbitals that have a hi gh percentage of metal d - character and do not have excessive ligand character. The orbitals will by necessity have some ligand character, as it is this ligand character that allows the overlap in these complexes which exhibit a super - exchange interaction. However, too much ligand character will result in erroneously high overlap values, which could lead to false interpretations of the importance of certain spin coupling pathways. If given a choice, the orbitals should have ligand character which is located on ligands between the two metal centers, as this is more likely to be relevant as a spin exchange pathway. The task therefore is to select the orbitals which have the most d - orbital character and also have the correct ligand character, which is certainly highly relevant previous example was available from work within our research group. The previously selected orbitals in BPW91 as determined from an optimized geometry were readily reproduced in this work , which provided a valuable starting point for the subsequent study of all the other systems discussed herein. Typical BPW91 broken symmetry orbitals are shown in figure 87 2 - 16 (see pg. 88) . One will note that these orbitals have extremely high metal charact er and that it is very easy to pick out the d - orbital type based on the Cartesian axes described previously. These BPW91 orbitals in turn were used as a starting point for the subsequent identification of natural magnetic orbitals in B3LYP broken symmetry wavefunctions, examples of which are shown in figure 2 - 17 (see pg. 89) . It was the case that for almost all the optimized geometries studied, the orbitals looked very similar to those depicted in figure 2 - 16 when studied with the BPW91 functional. The o rbital numbering was also surprisingly consistent for the optimized geometries studied with the BPW91 functional given that geometric changes can have the effect of reordering the orbital energies. When comparing to the orbital assignments and morphologie s of the BPW91 broken symmetry orbitals to those obtained with B3LYP broken symmetry single point energy calculations, there are some key differences that can be observed. The most notable difference is that the orbital numbers are completely different. In most cases the primarily metal based orbitals as determined with B3LYP are significantly lower in energy than their BPW91 counterparts. When a comparison between the morphologies of the BPW91 and B3LYP NMOs is considered, it becomes more obvious why this might be the case. The B3LYP orbitals, while selected by their similarity in appearance to the BPW91 orbitals, have significantly more ligand character mixed in with the metal orbitals. Furthermore this ligand character is often located on the Tp capping l igands, which delocalizes the interacting spins away from each other. This is a reasonable conjecture as to why B3LYP calculates lower values for the coupling constant than what is calculated for BPW91. More peripheral ligand character is mixed into the NM Os for hybrid density functionals than for pure density functionals, which causes the B3LYP orbitals to be lower in energy than the BPW91 orbitals. This is likely the cause for lower numbered orbitals being the ones with the required d - 88 orbital character fo r B3LYP. It is also the case that this increased amount of ligand involvement in the selected B3LYP metal d - orbitals will provide different values for the alpha beta orbital overlaps than those obtained with BPW91. It should be noted that since the B3LYP e nergies provide better calculated coupling constants, it is not unreasonable that their wavefunctions and in particular the properties that depend on their orbitals should also be closer to representing the true nature of the spin coupling interaction. Once NMOs have been selected for a given system, to ascertain the degree of communication between the orbitals bearing the spin one depends on the anti - symmetric spin distribution of the broken symmetry state so that the analysis of spin coupling contribu tions can be performed via the evaluation of the alpha beta overlap integrals. This only works because the alpha and beta orbitals are not in fact orthogonal to each other in spin unrestricted calculations and the broken symmetry state conveniently places all of the spin electrons on one iron center in alpha orbitals, and it places all the spin electrons for its partner in beta orbitals. This allows for the evaluation of overlap integrals between the NMOs of the two metal centers. The Multi w fn analysis pack age 41 was used in these studies to evaluate the overlap between the alpha and beta orbitals obtained in our broken s ymmetry wavefunctions. 89 Figure 2 - 16: Visualizations of the ten NMOs from the broken symmetry singlet UBPW91/6 - 311G(d,p) wavefunctio n calculated at the UBPW91/6 - 311G(d,p) low spin optimized geometry. The orbitals are plotted with an isovalue of 0.02. 90 Figure 2 - 17: Visualizations of the ten NMOs from the broken symmetry singlet UB3LYP/6 - 311G(d,p) wavefunction calculated at the UB3LYP/6 - 311G(d,p) low spin optimized geometry. The orbitals are plotted with an isovalue of 0.02. 91 Table 2 - 12: The alpha beta overlap integrals determined for all possible permutations of the d - orbital like natural magnetic orbitals for select optimized geometries studied sans acetone. The overlap integrals are listed in descending order as determined with B3LYP for both the symmetric d - orbital interactions and the asymmetric d - orbital interactions. 92 2.3.10 Alpha Beta Orbital Overlap Analysis of Spin Coupling Mechanisms in Optimized Geometries To start, the overlaps were determined for the same system we previously studied and obtained orbital overlap integrals on to verify that the MultiWavef n program was producing reliable re sults. A comparison between the previously reported orbital overlap values for the natural magnetic orbitals obtained with a BPW91/6 - 31G(d) high spin optimized C 2v geometry and our new alpha beta overlap values calculated from the same optimized geometry u sing MultiWavefxn reveals similar overlap values that are nonetheless different from those previously reported. This difference is not alarming however, as we are obtaining our broken symmetry electronic state using the new fragment - based guessing in Gauss ian 09 versus a manual manipulation of the guess as was obtained in Gaussian 98 for our previous studies. If the method for generating the broken symmetry electronic state is different, there should be no expectation that the resulting broken symmetry wave function should be exactly the same. Based on our differing calculated values for the spin coupling constant for the exact same geometry and functional, it seems that we are working with a different broken symmetry wavefunction. If the broken symmetry wave functions are different, so should the orbital overlaps that are determined from those broken symmetry wavefunctions be different. While there are observable differences from our previous values, the BPW91 alpha beta orbital overlaps for the natural magne tic orbitals do show similar relative contributions to the spin coupling for all the C 2v optimized geometries studied, which provides us with a good baseline when evaluating the orbital overlaps of the different optimized geometries and comparing these val ues to overlap values obtained with the B3LYP functional. The alpha beta overlaps for BPW91 93 and B3LYP natural magnetic orbitals for the optimized geometries studied are reported in table 2 - 12. As was previously reported in work from our research group, th e primary spin coupling pathways as determined using this method are Fe1(d z 2 - OH(p || ):Fe2(d z 2 ), Fe1(d x 2 - y 2 ):bis - - acetato:Fe2(d x 2 - y 2 ), Fe1(d xz - OH(p x ): Fe2(d xz ), Fe1(d yz - yz ), Fe1(d yz - z 2 ), and Fe1(d z 2 - yz ). These are reflected in the high alpha beta overlap values derived for the BPW91 broken symmetry wavefunction. The results for the overlap integrals evaluated for the high spin 6 - 31G(d) optimized geometry show good consistency with the previously report ed overlap integral values. It is important to note that it was by evaluating all of the possible 25 permutations of overlap integrals between the natural magnetic orbitals and determining which ones were significant that the assignments of the relevant c oupling pathways in our previous work were made. This is the reason all 25 orbital permutations ar e represented in t able 2 - 12 (see pg. 90) . The cutoff for what is reported as significant seems arbitrary at best, given that there are a few more overlap inte gral values with nearly the same magnitude that were not mentioned as significant in our previous results. However, one can also see in table 2 - 12 that we are getting agreement in the overlap values of the important coupling pathways. While it is debatable to classify what is truly significant, for the sake of consistency and the ease of presentation, we will confine our discussion to the same set of significant pathways that was previously determined since their overlap values are similar for all of the op timized geometries studied. When looking for trends between the different C 2v optimized geometries in both functionals, it is helpful to plot the overlap values in bar graph form, as depicted in figure 2 - 18. 94 From these plots, a few general trends can be observed. The first is that generally speaking, the overlaps in the significant pathways are larger for the broken symmetry optimized geometry than Figure 2 - 18: - coupling pathways calculated from broken symmetry orbitals generated with BPW91 (A) and B3LYP (B) density functionals. Our previously reported result is also included for comparis on. See text for details. 95 for the high spin optimized geome try of a given basis set and functional. This is logical since the broken symmetry optimized geometry will depend on these spin exchange interactions to properly model the low spin state. This means that these exchange interactions should be emphasized mor e in the broken symmetry ground state than in the high spin state, which results in increased overlap values due to these interactions being stabilized in the broken symmetry state. It is also the case that for the geometries optimized with the 6 - 31G(d) ba sis set the overlap values are typically larger than those obtained for geometries optimized with the 6 - 311G(d,p) basis set. This is a simple consequence of the optimized bond distances being shorter for the 6 - 31G(d) basis set, which results in the increas ed overlap values based on increased spatial overlap when the interacting orbitals that are having their overlaps computed are closer together. Figure 2 - 19: - coupling pathways ca lculated from broken symmetry orbitals generated with BPW91 density functional at the optimized B3LYP geometries. Our previously reported result is also included for comparison. Compare to figure 2 - 18: see text for details. When generally comparing the results of the B3LYP and BPW91 natural magnetic orbital overlaps, the effects of the increased ligand character in the NMOs is on clear display. To study these 96 differences without the possible influence of similar but nonethele ss different geometries, the alpha beta orbital overlap values were compared for the B3LYP optimized geometries using both the B3LYP and BPW91 broken symmetry wavefunctions. The plot of BPW91 overlaps at the B3LYP geometry is found in figure 2 - 19, and they can be compared to the second plot in figure 2 - 18 for the B3LYP overlaps at B3LYP geometry. It can be clearly seen that the B3LYP broken symmetry wavefunction has significantly higher calculated alpha beta overlap integral values for the d z 2 natural magne tic orbitals. This is no doubt due to the high amount of bridging ligand character in these orbitals, even those generated with the BPW91 pure density functional. The other alpha beta orbital overlaps between the natural magnetic orbitals with the same d - o rbital assignments was overall consistent for the BPW91 and B3LYP functionals, with the values in some cases being slightly lower than those determined with BPW91. The trends for differences in geometry are similar for overlaps evaluated from broken symmet ry wavefunctions determined with both functionals. The similar trends in the results of the B3LYP and BPW91 orbital overlaps between high and low spin optimized geometries is encouraging since it suggests that B3LYP orbital overlap integrals have the pote ntial to provide meaningful insight on the changes in the spin exchange pathways in the variable temperature X - ray crystal structures. This is important because as has been mentioned previously, the BPW91 broken - symmetry electronic state suffered convergen ce issues for the X - ray crystal structures. This was not the case for the B3LYP broken symmetry wavefunctions, making the B3LYP derived natural magnetic orbitals an ideal target for the study of the contributing orbital pathways to spin exchange in the X - r ay crystal structures. As a further test of the NMO analysis before studying the X - ray structures, the alpha beta overlap integrals were evaluated from the broken symmetry B3LYP/6 - 311G(d,p) wavefunction evaluated 97 on the o ptimized X - ray structure geometries both with and without acetone included. The results of this analysis for all 25 possible orbital interactions are tabulated in the supplementary information. The symmetric overlap values obtained for the optimized X - ray geometries with the acetone omitted should have been similar to those obtained for the B3LYP/6 - 311G(d,p) optimized C 2v geometries that were previously discussed, as both these geometries were optimized with the same functional and basis set. However, the presence of the acetone in the X - ra y optimized geometry had some observable effects on the calculated overlap values, even when the acetone was removed before the orbitals were generated. The X - ray optimized geometry symmetric pathway overlap values had some key similarities with their C 2v counterparts along with some key differences. The calculated overlap values of the d z 2 - d z 2 , and d xy - d xy of the optimized X - ray geometries were similar to those obtained for their C 2v optimized counterparts. Smaller overlap values were observed for the d xz - d xz compared to the C 2v values while there were larger values observed for d yz - d yz and especially for d x 2 - y 2 - d x 2 - y 2 . Besides these differences, the observed trends between low spin and high spin geometries were consistent with those reported for the C 2v geometries as was discussed previously. When comparing these changes relative to the C 2v geometry with the changes in coupling contributions calculated via the Hay - Hoffman method, we can see that most of the changes are consistent between the two. The d z 2 and d xy contributions are unchanged in both, and there are increases in the contributions from d yz and even more increases in the d x 2 - y 2 contributions. However, while the contributions from d xz increase substantially for the Hay - Hoffman method, they decr ease substantially for the NMO contributions. The reason for this is not understood, but since there is a high degree of ligand character on the other side of the molecule for the d xz broken symmetry 98 orbitals, we can postulate that this was enhanced in the asymmetric optimized geometry and let to a cancellation of the overlap between the two metals as the phases were opposite for the wavefunctions on each side of the molecule. Therefore, since the wavefunctions appear less influenced by small geometric chan ges for the Hay - Hoffman method, we will follow those results as more telling of the situation than those obtained for the NMO method. The number of significant asymmetric coupling pathways in the X - ray optimized geometries was substantially increased in th e optimized X - ray geometries with the acetone removed (after optimization) for the generation of the orbitals when compared to the C 2v optimized counterparts. This was to be expected because the presence of the acetone in the X - ray structure optimization f orced a degree of asymmetry on the structure. This asymmetry causes the d - orbitals of each metal center to not line up exactly, which has the effect of increasing the communication between d - orbitals of different symmetry. Since the overall value of the co upling constant is not substantially altered, one can presume that the electronic communication responsible for the spin coupling is now divided amongst the higher number of pathways, making each overlap integral value less significant to the overall coupl ing than it was for the equivalent C 2v optimized geometry. It is interesting to note that the identity of the orbitals in these asymmetric pathways is consistent, with the d yz and d z 2 orbitals showing significant asymmetric coupling contributions being joi ned by contributions involving the d xz and d x 2 - y 2 orbitals. When the acetone is kept in place for the calculations that generate the broken symmetry orbitals used for the NMO orbital overlap analysis, we observe a few changes in the values for the overlap integrals. With the exception of the d xz - d xz orbital overlap, we see increases roughly between 60% and 100% for the remaining symmetric overlap integrals with the d x 2 - y 2 - d x 2 - y 2 showing the largest increase. The d xz - d xz overlap showed an increase by over an order of magnitude. These increased 99 overlaps apart from d xz - d xz are all able to be explained with the earlier explanation of the acetone drawing the electron density away from the O5 hydroxo bridge allowing for increased energetic overlap with the metal d orbitals. However, it is also the case that the overlaps can be increased because the acetone molecule polarizes the electron density on the bridging ligands. This results in the portions of the NMOs with ligand character being localized on the one side o f the molecule resulting in increased overlap as the alpha and beta orbitals are more concentrated in the same space. The d xz - d xz overlap increase with the inclusion of acetone is more puzzling since it appears that it is now ascribing too much contributi ons to the spin coupling whereas the omission of acetone resulted in too small a contribution. It has been observed in all our C 2v optimized geometries that the d xz orbital overlaps are sensitive to geometric changes, but this hypersensitivity to the aceto ne presence may be due to the acetone lining up approximately with the node of the d xz - hydroxo molecular orbital while being not in the nodal plane, which could have the effect of skewing these orbitals when it is present allowing for the huge increase in observed overlap. The number of significant asymmetric overlap pathways is reduced with the inclusion of acetone, with the previously mentioned d z 2 - d xy and d xy - d z 2 pathways no longer being of the same magnitude as they were in the C 2v optimized geometries. Significant asymmetric pathways involved the d x 2 - y 2 and d z 2 orbitals, as well as single pathways involving the d xz and d xy in combination with the aforementioned orbitals. It is not known why the number of pathways decreases, but it may be due to the electronic wavefunction being able to adopt their equilibrium conformations when the acetone is included since these geometries were optimized with the acetone present. Conclusions that we can draw from studying these optimized X - ray str uctures with the NMO method are that most of the symmetric coupling pathways show similar trends between the 100 wavefunctions calculated with and without acetone present. The asymmetric pathways show changed behavior between the two systems, and the NMO analy sis on these optimized geometries all showed inconsistent results with regards to d xz - d xz coupling contributions when compared to the Hay - Hoffman results. This inconsistency combined with the extreme variability of the NMO method means that going forward w ith the actual X - ray structures, we will be focusing on the Hay - Hoffman results with less emphasis on the NMO analysis going forward. 2.3.11 Spin Exchange Contribution Analysis via Alpha Beta Orbital Overlap Integrals in The Broken Symmetry Wavefunctions of VT X - ray crystal structures. It was decided through the course of these studies that the coordinating acetone molecule was not necessary for the accurate modeling of the spin exchange pathways, and this was supported by Hay - Hoffman results being consist ent between the inclusion and exclusion of acetone. It also made the systems easier to study, as the NMOs had more consistent morphologies when the acetone was omitted. Even without the acetone, the asymmetry of the X - ray structures was problematic for the implementation of the NMO method to study these structures. While the BPW91 orbitals showed consistency between the C 2v optimized geometries and the X - ray structures having a similar appearance and energies, there were some differences. Where the optimize d C 2v geometries offered the natural magnetic orbitals in the same numbered alpha beta pairs, the lack of similar symmetric constraints in the X - ray crystal structures led to some of the alpha and beta natural magnetic orbital pairs having different orbita l numbers, as was observed in the optimized X - ray structures when acetone was present. What happened more frequently was that the orbitals were 101 less symmetrically distributed on the ligands, with alpha and beta at times having disparate amounts of ligand c haracter, or having ligand character on only one side of the molecule as was seen in the optimized X - ray crystal structures. It also meant that the asymmetric mixing pathways could and did have different values for the overlap integrals between the two pos sible sets of alpha beta overlaps. Regardless, since only half of the structures for complex 1 were able to converge to a broken symmetry state, the results were less than conclusive. The issues previously discussed for studies with BPW91 were exacerbated with the B3LYP broken symmetry orbitals. It seemed in general that the d - orbital shapes for the B3LYP derived natural magnetic orbitals suffered from the geometric distortions compared to the equilibrium geometries encountered in the previous section. This resulted in apparently smaller d - orbitals when compared to those obtained for the optimized geometries, which led to smaller overlap values for certain d - orbital coupling pathways than were found for the optimized geometries, as can be seen in the data fo r figure 2 - 20. The resulting overlap integrals from these less well defined natural magnetic orbitals obtained for the X - ray crystal structures, particularly in the case of B3LYP where there were already concerns with the proper orbital spatial distribut ions for the broken - symmetry wavefunctions determined for the optimized geometries, had a high degree of variance as seen in figure 2 - 20. 102 In particular, the B3LYP NMO alpha beta overlaps show such high variance for all of the coupling pathways studied that any information on the change in contribution to spin coupling as a function of temperature is essentially lost in the noise . This was a disappointing result, as the B3LYP broken symmetry wavefunction had a much better success rate in obtaining the correct broken symmetry states, not to mention that the energetics of the B3LYP determined spin coupling constants are much closer to the experimentally reported value. However, the irregularity of the natural magnetic orbitals obtained with B3LYP essentially doomed these alpha beta orbital overlap results to be unreliable. Unfortunately, the limited BPW91 results also showed a fair d egree of variance, which was makes drawing conclusions from their differences as a function of temperature difficult if not impossible. This means that for the purposes of looking at coupling pathways in the X - ray crystal Figure 2 - 20: - coupling pathways calculated from broken symmetry orbitals generated with B3LYP for the X - ray crystal structures of complex 1 . Note the inconsistency of contributions, especially at 173 K. 103 structures, the Hay - Hoffman method will be relied upon to provide us with conclusions concerning how the contributions to spin coupling are changing with temperature. 2.3.12 Magneto - Structural Effects Discussion So far, we have observed the changing nature of the coordination environment of the spin - exchanged iron centers in complex 1 , particularly changes associated with the µ - hydroxo bridging ligand, in the variable temperature X - ray crystal structures. We have also seen that the changes as a whole have resulted in systematic changes to the contributions to spin exchange coupling from the individual d - orbitals on each iron center. However, we wanted to pinpoint which changes were having these effects. It was already suspected that the variable bond distances associated with the H50 µ - hydr oxo proton were primarily responsible for these variable contributions, so a few tests were devised to determine if this was the case. The main test that was proposed was to set the O5 H50 bond distance at a constant value without changing any other str uctural parameter of the X - ray structures for complex 1 and to see if similar changes in the spin exchange coupling were observed. To this end, the O5 H50 bond distance was shifted to the same 0.827 Å value (observed for the iron structure at 20K) for al l of the higher temperatures. A similar procedure was used to modify the crystal structures such that the O5 - H50 bond distance was held constant at its 296 K value of 0.58853 Å. For these modified geometries, the acetone was omitted. It is worth mentioning again that the O5 - H50 bond distance is shorter in the X - ray structures than the optimized geometries and it is likely the case that the optimized geometries are much closer to the actual bond distances, since the geometry optimizations tracks the nuclear position of the 104 proton and the X - ray structure only tracks the electron density, which for protons is situated close to the atom to which it is bound. One might think that it is just the increased thermal motion of the acetone that causes the average elect ron density position associated with H50 to get closer to O5 in complex 1 as the temperature increases. However, this phenomenon should have also been observed in the crystal structures for complex 2 , and the fact that it is not leads us to believe that ev en though the bond distances determined via the X - ray structures are not accurate, this trend is likely based in what is really happening in the X - ray structures as the temperature increases. When the Hay - Hoffman contributions for the optimized geometries are compared to those for the crystal structure, one can see that they are similar (refer to figure 2 - 13 and 2 - 14). It is based on this assessment and the fact that we should still expect this trend of bond shortening to occur in complex 1 based on a lack of similar results in complex 2 , that we feel it is valid to investigate how changes in the X - ray structure bond length will affect the orbital mechanisms of spin coupling, as we should expect similar trends to occur, albeit with more muted responses to bond distance changes as the O5 - H50 bond is being studied at geometries distorted from their equilibrium value by using the distances from the X - ray structures. For the study on the O5 - H50 bond distance dependence , the coupling constants were theoretically evaluated via the Yamaguchi method using the B3LYP functional in the manner described previously. These modified geometry results contrasted with those obtained for the actual crystal structures of complex 1 , all of which are presented in figure 2 - 21. It is evident from these results that when the O5 H50 bond distance is held constant, the degree of spin interaction becomes almost static. While it appears that the two highest temperature points have increased coupling in these modified geometries which c an be correlated to the decreasing Fe 1 - O5 bond distance at these temperatures, the degree of change is within the estimated 2 cm - 1 uncertainty described earlier. It 105 can therefore be stated that the only significant change in the electronic structure and thus the spin coupling constants brought about by the changing temperature is a shift in this single bond distance. To determine if the relative mechanistic contribut ions to the spin coupling were also held static with a fixed O5 H50 bond distance, the Hay - Hoffman spin exchange orbital contributions were evaluated for these modified crystal structures. The NMO alpha beta overlap method was not used, due to it being t oo variable for use in studying the X - ray crystal structures as was demonstrated previously. The results of the Hay - Hoffman spin exchange contribution analysis on the 20 K and 296 K O5 - H50 bond altered X - ray structures are shown in figure 2 - 22. Figure 2 - 21: Plot of the UB3LYP/6 - 311G(d,p) calculated J values for the unaltered X - ray crystal structures of complex 1 , the aforementioned X - ray structures altered such that the O5 - H50 bond distance was fixed at the 20 K value of 0.82707 A, and the X - ray structures altered such that the O5 - H50 bond distance was fixed at the 296 K value of 0. 58853 Å. All of these calculated values used geometries that did not include the acetone molecule. 106 Again, it is easily seen that the coupling pathway contributions are generally lower at the 296 K bond distance compared to the 20 K bond distance. What is clearly demonstrated however is that there is no apparent change in the orbital contributions to th e spin exchange when all other structural parameters are allowed to change with temperature but the O5 - H50 bond distance is held constant. This is strong confirmation of the singular importance of the O5 - H50 bond distance to the spin interaction in this sy stem. It is possible that the O - H bond shortening observed in the µ - hydroxo bridge is correlated with a concomitant destabilization of the hydrogen bonding interaction between H50 and O100 that is observed in the lower temperature crystal structures. While this change is not observed in the VT X - ray structures of complex 2 , it could be merely attributed to the differences in the Lewis acidity of gallium compared to iron. It may be the case that the weaker Lewis acid would make it possible for the O - H bond d istance in the iron complex to be shorter than that in the gallium since it would Figure 2 - 22: Relative contributions to the spin coupling determined with UB3LYP/6 - 311G(d,p) in modified complex 1 X - ray crystal structures as determined via the Hay - Hoffman method. The modifications involved holding the O5 - H50 bond distance constant for all tempe ratures. On the left, the O5 - H50 bond distance is set at the 20 K value of 0.82707 Å . On the right, the O5 - H50 bond distance is set at the 296 K value of 0.58853 Å . These contributions are expressed in units of (cm - 1 ) 2 . See text for more details. 107 accept less electron density from the hydroxo bridge. This could mean that while the O - H bond distance and subsequent hydrogen bonding nature with acetone could vary for comp lex 1 , it would be unable to do so in complex 2 . This was one of the main justifications used to study the crystal structures with acetone included. It is possible that if the hydrogen bonding was the driving influence for the longer O - H bond distance at l ow temperatures, there would be a visible difference in the trending behavior of the changes in absolute energy values as a function of temperature since the hydrogen bonding behavior would stabilize the absolute energies of the crystal structures. A simil ar change in coupling constant behavior seemed less likely, as the acetone provided no communication pathway for the spin interaction. A comparison of the changes in absolute electronic energy as a function of temperature and the calculated coupling consta nt for the VT X - ray structures of complex 1 with and without the associated acetone molecule are shown in graphical form in figure 2 - 23. As was already discussed, the trends in the calculated coupling constant as a function of temperature are very similar for complex 1 with and without the acetone, even though the values are slightly offset as seen in figure 2 - 7. When the changes in absolut e energy of the wavefunctions used to determine said coupling constants as a function of temperature are inspected for the crystal structures with and without acetone, one can notice that there is a deviation of the energies of the two systems. Even though we are looking at the changes in the absolute energy value, we should not expect identical changes in the two systems as energy does not scale linearly with the number of atoms in the system, so the energy differences are not guaranteed to be identical in the absence of the interaction between the acetone and complex 1 . Th is seems to be the case as seen in figure 2 - 23. 108 We can see that the difference in absolute energy varies significantly more at the 100 through 234 K temperatures than it does at the other temperature points. However, the differences between the two systems do not seem to correlate with the changes in th e hydrogen bonding distance, so it cannot be concluded that variation in the hydrogen bonding nature of the acetone is affecting our observed structural and electronic differences as a function of temperature in complex 1 . Given that the crystal structures of both complexes 1 and 2 have an acetone molecule in the same relative position to the µ - hydroxo bridge, and there are no changes in the bond distance in complex 2 , it seems that this change in bond distance has to be due to the unique electronic propert ies of the iron Figure 2 - 23: Energy diagram of the absolute energy of the broken symmetry electronic states of the complex 1 crystal structures relative to the energy value at 20 K for structures both including and excluding the acetone. The difference between with and without the acetone is always positive yet variable, indicating that there is a non - negligible interaction between the acetone and the ene rgetics of the system independent of the differing electron count of the two systems. 109 centers present in complex 1 and that suggests that the spin coupling is responsible for this behavior without conclusively proving that it is the cause of this dynamic behavior. This leads us to the situation of having to decide whether th e differences in O5 - H50 bond distance are causing the observed perturbations in the mechanisms of the spin exchange coupling or if the opposite is true and temperature induced changes in the spin states of the spin coupling mechanisms are manifesting thems elves in this shifting bond distance. Since the contributions from d z 2 and d xz are the ones that change the most as a function of temperature, one would have thought that the coupling constant and orbital mechanisms of spin exchange would have been disturbed as a function of temperature even with the O - H bond distance being held con stant, as there are still significant changes in the Fe - O5 bond distance as a function of temperature. While we can see a slight increase in the calculated coupling constants for the two highest temperature values that correlates nicel y with the shortening of the Fe1 - O5 bond distances, we cannot be sure if this is a real difference in the calculated coupling constant because it fits within the determined error of the calculated coupling constant as was dis cussed previously. Since the Fe1 - O5 bond distance is much more difficult to alter in the crystal structure since the Fe 1 is bonded to many more parts of the molecule, an analogous study of holding the Fe 1 - O5 bond distant at a constant value was not attempted. It is almost certain that the Fe 1 - O5 bond shorte ning has an effect on the spin coupling, as the shorter Ga - O5 bond distances in complex 2 are what is presumed to be at least partially responsible for the increased calculated coupling constant values for the Fe @ Ga structures. However, we cannot determi ne if this bond shortening has a significant effect on the electronic structure of complex 1 at this time based on the uncertainty of our evaluation methods for the coupling constant. 110 Since the changes in the Fe 1 - O5 bond distance are not greatly influenci ng the coupling constant and orbital mechanism contributions to the spin exchange, one can draw the shocking conclusion that these observed changes in the orbital coupling mechanisms and their contribution to the spin exchange coupling as a function of tem perature is likely due to the changing O5 - H50 bond distance. The change in this bond distance is certainly unique to complex 1 , but it is not known at this time if the spin exchange is responsible for this behavior or if it is merely due to the presence of iron and the spin exchange is just a circumstantial side effect of the irons being present. 2.4 Conclusion We have obtained detailed variable temperature X - ray crystal structures of complex 1 and complex 2 . Through comparative analysis of the crystal structures, it was determined that the significant changes in the structures unique to complex 1 involved the shortening of the Fe 1 - O5 and O5 - H50 bonds with increasing temperature . The coupling constant was cal culated for a plethora of optimized geometries and the VT X - ray structures and it was found that the calculated coupling constant for the complex 1 X - ray structures decreases significantly at higher temperatures wile coupling constants determined for Fe @ Ga geometries do not change. These coupling constants were compared and found to be consistent with values obtained for the optimized geometries. The coupling pathways were analyzed via the Hay - Hoffman and NMO methods for the optimized geometries to gain a n understanding of how geometric changes effect the coupling pathways. This same analysis was then performed on the X - ray structures, with the results indicating that the significant geometric changes in the complex 1 X - ray structures correlated with a red uction in the d z 2 and d xz related coupling pathways. A series of calculations on crystal structures with modified O5 - H50 bond distances showed that the change in coupling behavior for complex one is primarily 111 correlated with the O5 - H50 bond distance change . However, we cannot determine if it is the changes in the electronic structure of complex 1 due to the thermal population of higher spin states that cause the changes in this bond distance, or if it is a thermal effect of the weakened hydrogen bond betwee n H50 - O100 at higher temperatures that results in these geometric changes. Therefore, we cannot confidently say from this set of studies if populating the higher spin states of complex 1 has an effect on its geometry, but it can be reported that a correlat ion exists. 112 APPENDICES 113 Appendix 2.1: Supplementary Figures Figure A2 - 2: Bond distances for the M - O bond distances for the acetate bridges for complexes 1 and 2 as a fun ction of temperature. Figure A2 - 1: Acetate C - O bond distances in the X - ray structures as a function of temperature. Distances for complex 1 are on the left and distances for complex 2 are on the right. Note that in both complexes the bond distance shows a general decreasing trend. 114 Figure A2 - 4: The O(acetate) - M - O5 bond angles for complexes 1 and 2 as a function of temperature. Figure A2 - 3: The M - O(acetate) - C(acetate) bond angles for complexes 1 and 2 as a function of temperature. 115 Appendix 2.2 : Cartesian Coordinates of Variable Temperature X - ray Structures Notes: These input geometries were taken from the X - ray crystal structure results. The perchlorate anion is omitted but the coordinated acetone is included. The .cif files will be mad e available at a later time. Fe 20 K: Fe 4.211000 0.298000 4.449000 Fe 1.650000 2.410000 5.180000 N 3.629000 - 1.320000 3.252000 N 4.555000 - 1.979000 2.492000 N 5.924000 - 0.869000 4.907000 N 6 .566000 - 1.544000 3.910000 N 5.399000 0.916000 2.825000 N 6.039000 - 0.003000 2.044000 N - 0.238000 1.857000 4.380000 N - 1.154000 2.834000 4.108000 N 0.506000 3.674000 6.449000 N - 0.549000 4.370000 5.934000 N 1.583000 4.008000 3.826000 N 0.429000 4.714000 3.652000 O 1.535000 0.890000 6.492000 O 3.268000 - 0.472000 6.051000 O 3.282000 3.125000 6.100000 O 4.981000 1.751000 5.590000 O 2.669000 1.348000 3.913000 H 2.437000 1.311000 3.120000 C 2.213000 - 0.165000 6.683000 C 1.749000 - 1.115000 7.752000 H 0.898000 - 0.937000 8.022000 H 1.807000 - 1.993000 7 .443000 H 2.286000 - 1.048000 8.471000 C 4.495000 2.767000 6.168000 C 5.429000 3.603000 6.996000 H 5.934000 4.170000 6.406000 H 6.050000 3.022000 7.460000 H 4.923000 4.154000 7.602000 C 2 .472000 - 1.985000 3.119000 H 1.696000 - 1.710000 3.570000 C 2.637000 - 3.085000 2.272000 H 1.993000 - 3.731000 2.036000 C 3.973000 - 3.045000 1.904000 H 4.478000 - 3.606000 1.357000 C 6.666000 - 1.018 000 6.015000 H 6.381000 - 0.624000 6.824000 C 7.792000 - 1.798000 5.743000 H 8.483000 - 2.029000 6.341000 C 7.690000 - 2.107000 4.392000 H 8.260000 - 2.597000 3.831000 C 5.770000 2.129000 2.387000 H 5.446000 2.922000 2.838000 C 6.650000 2.002000 1.310000 H 7.067000 2.685000 0.853000 C 6.795000 0.635000 1.125000 H 7.304000 0.120000 0.516000 C - 0.845000 0.684000 4.132000 H - 0.385000 - 0.142000 4.270000 C - 2.157000 0.900000 3.702000 H - 2.800000 0.273000 3.463000 C - 2.311000 2.279000 3.703000 H - 3.041000 2.846000 3.489000 C 0.504000 3.894000 7.774000 H 1.177000 3.496000 8 .325000 C - 0.562000 4.726000 8.124000 H - 0.791000 5.019000 8.987000 C - 1.207000 5.003000 6.927000 H - 1.974000 5.525000 6.735000 C 2.496000 4.544000 3.005000 H 3.380000 4.202000 3.033000 C 1 .940000 5.605000 2.287000 H 2.358000 6.145000 1.680000 C 0.627000 5.675000 2.728000 H - 0.082000 6.254000 2.491000 H 6.629000 - 2.091000 1.809000 H - 1.684000 4.923000 4.143000 B 6.014000 - 1.494000 2.458000 B - 0.848000 4.313000 4.422000 O 2.052000 1.109000 1.222000 C 1.234000 1.547000 0.426000 C 1.173000 1.035000 - 0.985000 H 1.697000 0.245000 - 1.101000 H 0.279000 0.859000 - 1.254000 H 1.490000 1.706000 - 1.565000 C 0.255000 2.624000 0.791000 H 0.352000 2.902000 1.702000 H - 0.646000 2.334000 0.622000 H 0.409000 3.370000 0.211000 Fe 50 K: Fe 9.965000 0 .303000 4.453000 O 9.041000 3.138000 6.096000 B 11.771000 - 1.490000 2.467000 H 12.376000 - 2.082000 1.816000 N 9.385000 - 1.316000 3.257000 C 7.966000 - 0.155000 6.683000 Fe 7.408000 2.422000 5.181 000 O 10.731000 1.755000 5.597000 B 4.908000 4.320000 4.422000 H 4.080000 4.923000 4.151000 N 10.312000 - 1.976000 2.498000 C 7.494000 - 1.104000 7.748000 H 6.667000 - 0.925000 8.042000 H 7.534000 - 1.966000 7.457000 H 8.019000 - 1.105000 8.419000 O 7.297000 0.902000 6.494000 N 11.677000 - 0.866000 4.914000 C 10.251000 2.776000 6.167000 O 9.017000 - 0.468000 6.050000 N 12.319000 - 1.541000 3.918000 C 11.189000 3.610000 6.990000 H 10.680000 4.157000 7.597000 H 11.812000 3.046000 7.437000 H 11.695000 4.173000 6.430000 116 O 8.426000 1.356000 3.914000 H 8.189000 1.316000 3 .115000 N 11.156000 0.922000 2.832000 C 8.229000 - 1.983000 3.122000 H 7.458000 - 1.706000 3.572000 N 11.797000 0.000000 2.052000 C 8.395000 - 3.080000 2.277000 H 7.758000 - 3.724000 2.040000 N 5 .521000 1.865000 4.382000 C 9.732000 - 3.041000 1.909000 H 10.238000 - 3.593000 1.370000 N 4.602000 2.840000 4.111000 C 12.416000 - 1.018000 6.022000 H 12.132000 - 0.620000 6.821000 N 6.261000 3.683000 6.448000 C 13.541000 - 1.800000 5.751000 H 14.224000 - 2.022000 6.341000 N 5.207000 4.380000 5.933000 C 13.442000 - 2.106000 4.403000 H 14.009000 - 2.607000 3.825000 N 7.339000 4.020000 3.828000 C 11.524000 2.132000 2.391000 H 11.197000 2.929000 2.833000 N 6.182000 4.723000 3.651000 C 12.403000 2.004000 1.316000 H 12.825000 2.672000 0.842000 C 12.550000 0.640000 1 .134000 H 13.059000 0.123000 0.529000 C 4.917000 0.691000 4.136000 H 5.377000 - 0.143000 4.270000 C 3.605000 0.905000 3.708000 H 2.966000 0.284000 3.471000 C 3.447000 2.278000 3.708000 H 2 .714000 2.837000 3.485000 C 6.257000 3.904000 7.770000 H 6.918000 3.509000 8.327000 C 5.190000 4.734000 8.121000 H 4.952000 5.020000 8.971000 C 4.547000 5.010000 6.924000 H 3.778000 5.533 000 6.726000 C 8.252000 4.564000 3.014000 H 9.134000 4.221000 3.038000 C 7.694000 5.623000 2.296000 H 8.109000 6.160000 1.686000 C 6.380000 5.687000 2.733000 H 5.669000 6.257000 2.496000 O 7.813000 1.119000 1.224000 C 6.996000 1.556000 0.428000 C 6.017000 2.626000 0.792000 H 5.124000 2.364000 0.606000 H 6.112000 2.895000 1.683000 H 6.174000 3.368000 0.247000 C 6.939000 1.042000 - 0.981000 H 7.248000 1.710000 - 1.563000 H 6.056000 0.855000 - 1.238000 H 7.460000 0.251000 - 1.101000 Fe 100 K: Fe 4.122000 10.376000 12.146000 B 5.930000 8.586000 10.161000 H 6.547000 7.979000 9.525000 O 3.169000 9.607000 13.740000 N 3.542000 8.756000 10.950000 C 2.121000 9.923000 14.374000 Fe 1.566000 12.500000 12.871000 B - 0.936000 14.391000 12.107000 H - 1.776000 15.004000 11.82 4000 O 1.458000 10.984000 14.185000 N 4.470000 8.097000 10.190000 C 1.647000 8.976000 15.437000 H 0.885000 9.202000 15.770000 H 2.126000 8.966000 16.128000 H 1.549000 8.171000 15.101000 O 4.884000 11.829000 13.293000 N 5.832000 9.209000 12.609000 C 4.408000 12.852000 13.854000 O 3.201000 13.218000 13.782000 N 6.475000 8.533000 11.615000 C 5.348000 13.690000 14.673000 H 4.804000 14.208000 15.306000 H 5.810000 14.254000 14.121000 H 5.971000 13.100000 15.160000 O 2.583000 11.432000 11.608000 H 2.346000 11.398000 10.832000 N 5.315000 10.997000 10.527000 C 2.389000 8.088000 10 .811000 H 1.626000 8.342000 11.219000 N 5.956000 10.075000 9.748000 C 2.559000 6.996000 9.968000 H 1.933000 6.323000 9.713000 N - 0.322000 11.939000 12.073000 C 3.891000 7.036000 9.603000 H 4 .391000 6.485000 9.065000 N - 1.242000 12.911000 11.801000 C 6.569000 9.052000 13.719000 H 6.277000 9.462000 14.519000 N 0.416000 13.761000 14.137000 C 7.691000 8.271000 13.449000 H 8.367000 8.042000 14.056000 N - 0.639000 14.455000 13.620000 C 7.597000 7.966000 12.103000 H 8.183000 7.468000 11.546000 N 1.495000 14.097000 11.516000 C 5.677000 12.205000 10.081000 H 5.357000 12.991000 10.483000 N 0.337000 14.796000 11.336000 C 6.554000 12.076000 9.008000 H 6.995000 12.742000 8.575000 C 6.707000 10.715000 8.828000 H 7.201000 10.205000 8.206000 C - 0.923000 10.766000 11 .831000 H - 0.464000 9.901000 11.952000 C - 2.234000 10.974000 11.403000 H - 2.871000 10.356000 11.174000 C - 2.395000 12.347000 11.400000 H - 3.166000 12.909000 11.179000 C 0.409000 13.981000 15.458000 H 1 .066000 13.596000 16.042000 C - 0.657000 14.808000 15.805000 H - 0.855000 15.098000 16.688000 C - 1.299000 15.083000 14.612000 H - 2.074000 15.634000 14.428000 C 2.405000 14.647000 10.708000 H 3.284000 14.293 000 10.716000 C 1.847000 15.703000 9.992000 H 2.265000 16.241000 9.396000 C 0.536000 15.760000 10.424000 H - 0.184000 16.327000 10.209000 O 1.974000 11.198000 8.913000 C 1.163000 11.637000 8.111000 C 0.181000 12.696000 8.476000 H - 0.737000 12.441000 8.239000 H 0.207000 12.941000 9.333000 H 0.246000 13.386000 7.913000 C 1.110000 11.120000 6.707000 H 0.231000 10.912000 6.448000 117 H 1.655000 10.306000 6.605000 H 1.375000 11.726000 6.145000 Fe 173 K: Fe 4.198000 9.801000 4.489000 O 4.949000 8.347000 5.639000 B 6.018000 11.583000 2.511000 H 6.674000 12.180000 1.863000 N 5.395000 9.175000 2.874000 C 4.483000 7.311000 6.178000 Fe 1.644000 7.669000 5.203000 O 3.281000 6.940000 6.099000 B - 0.867000 5.798000 4.424000 H - 1.705000 5.217000 4.132000 N 6.046000 10.096000 2.097000 C 5.426000 6.468000 6.981000 H 4.887000 5.918000 7.634000 H 6.058000 7.018000 7.433000 H 5.945000 5.949000 6.411000 O 3.232000 10.573000 6.074000 N 5.908000 10.970000 4.958000 C 2.195000 10.243000 6.709000 O 1.547000 9.176000 6.525000 N 6.557000 11.639000 3.964000 C 1.714000 11.179000 7.777000 H 1.074000 10.901000 8.222000 H 1.559000 11.998000 7 .421000 H 2.277000 11.538000 8.194000 O 2.663000 8.742000 3.945000 H 2.445000 8.779000 3.199000 N 3.628000 11.421000 3.285000 C 5.745000 7.969000 2.418000 H 5.426000 7.193000 2.838000 N 4 .560000 12.073000 2.527000 C 6.619000 8.097000 1.345000 H 7.050000 7.426000 0.904000 N 1.568000 6.075000 3.845000 C 6.783000 9.449000 1.173000 H 7.293000 9.986000 0.552000 N 0.405000 5.391 000 3.655000 C 6.634000 11.133000 6.069000 H 6.306000 10.776000 6.883000 N 0.484000 6.408000 6.462000 C 7.753000 11.915000 5.800000 H 8.457000 12.156000 6.390000 N - 0.571000 5.724000 5.937000 C 7.668000 12.211000 4.462000 H 8.257000 12.695000 3.919000 N - 0.239000 8.244000 4.407000 C 2.482000 12.094000 3.138000 H 1.721000 11.847000 3.488000 N - 1.163000 7.278000 4.126000 C 2.657000 13.182000 2.294000 H 2.046000 13.831000 2.010000 C 3.987000 13.135000 1.936000 H 4.481000 13.698000 1.398000 C 2.477000 5.509000 3.045000 H 3.329000 5.811000 3.086000 C 1.912000 4.462000 2 .333000 H 2.345000 3.906000 1.784000 C 0.604000 4.421000 2.747000 H - 0.114000 3.851000 2.505000 C 0.472000 6.185000 7.781000 H 1.139000 6.537000 8.336000 C - 0.598000 5.358000 8.115000 H - 0 .841000 5.100000 8.958000 C - 1.236000 5.094000 6.923000 H - 2.021000 4.562000 6.720000 C - 0.836000 9.420000 4.170000 H - 0.378000 10.224000 4.296000 C - 2.142000 9.214000 3.742000 H - 2.801000 9.834000 3.528000 C - 2.309000 7.853000 3.728000 H - 3.072000 7.300000 3.516000 O 2.065000 8.961000 1.240000 C 1.269000 8.519000 0.435000 C 1.250000 9.029000 - 0.977000 H 0.342000 9.157000 - 1.266000 H 1.490000 8.394000 - 1.507000 H 1.797000 9.893000 - 1.090000 C 0.268000 7.487000 0.781000 H - 0.642000 7.870000 0.427000 H 0.346000 7.201000 1.670000 H 0.206000 6.828000 0 .124000 Fe 234 K: Fe 1.451000 19.903000 3.226000 B - 0.438000 21.649000 5.171000 H - 1.057000 22.248000 5.831000 O 0.754000 18.425000 2.071000 N 0.241000 19.254000 4.833000 C 1.214000 17.349000 1.61 9000 Fe 4.032000 17.775000 2.585000 B 6.590000 16.043000 3.477000 H 7.416000 15.469000 3.694000 O 2.405000 16.964000 1.733000 N - 0.448000 20.163000 5.583000 C 0.262000 16.454000 0.871000 H 0.747000 15.725000 0.421000 H - 0.374000 16.935000 0.374000 H - 0.338000 16.045000 1.496000 O 2.442000 20.672000 1.652000 N - 0.261000 21.044000 2.726000 C 3.455000 20.303000 1.008000 O 4.073000 19.225000 1.204000 N - 0.938000 21.709000 3.705000 C 3.941000 21.197000 - 0.095000 H 3.297000 21.823000 - 0.467000 H 4.482000 20.816000 - 0.608000 H 4.516000 21.762000 0.577000 O 2.982000 18.868000 3 .802000 H 3.277000 18.934000 4.441000 N 1.972000 21.530000 4.444000 C - 0.057000 18.049000 5.323000 H 0.296000 17.285000 4.874000 N 1.013000 22.159000 5.188000 C - 0.934000 18.165000 6.385000 H - 1 .274000 17.493000 6.950000 N 4.136000 16.216000 3.987000 C - 1.155000 19.513000 6.523000 H - 1.722000 19.926000 7.051000 N 5.321000 15.597000 4.233000 C - 0.958000 21.219000 1.600000 H - 0.726000 20.844 000 0.832000 N 5.260000 16.522000 1.390000 C - 2.074000 21.996000 1.838000 H - 2.686000 22.221000 1.103000 N 6.326000 15.890000 1.962000 C - 2.031000 22.279000 3.179000 H - 2.601000 22.707000 3.708000 N 5.869000 18.446000 3.383000 C 3.098000 22.221000 4.622000 118 H 3.833000 21.964000 4.195000 N 6.818000 17.530000 3.726000 C 2.882000 23.294000 5.471000 H 3.480000 23.963000 5.815000 C 1.559000 23.219000 5.800000 H 1.084000 23.687000 6.228000 C 3.228000 15.601000 4.745000 H 2.308000 15.816000 4.799000 C 3.815000 14.595000 5.485000 H 3.436000 14.124000 6.108000 C 5.124000 14.622000 5 .127000 H 5.761000 14.139000 5.345000 C 5.315000 16.238000 0.089000 H 4.700000 16.639000 - 0.502000 C 6.409000 15.433000 - 0.192000 H 6.774000 15.165000 - 1.060000 C 7.025000 15.247000 1.024000 H 7 .837000 14.650000 1.256000 C 6.393000 19.649000 3.612000 H 5.914000 20.367000 3.386000 C 7.681000 19.500000 4.103000 H 7.987000 20.011000 4.394000 C 7.910000 18.179000 4.171000 H 8.651000 17.577000 4.441000 C 4.329000 18.455000 7.233000 O 3.942000 19.077000 6.347000 C 3.563000 18.191000 8.246000 H 2.647000 18.352000 8.006000 H 3.804000 18.753000 8.986000 H 3.670000 17.269000 8.497000 C 5.632000 17.901000 7.367000 H 6.090000 17.954000 6.526000 H 5.563000 16.983000 7.637000 H 6.121000 18.394000 8.031000 Fe 296 K: Fe 1.443000 19.952000 3.242000 O 0.762000 18 .469000 2.088000 B - 0.467000 21.692000 5.169000 H - 1.098000 22.310000 5.806000 C 1.220000 17.385000 1.649000 N 0.229000 19.298000 4.846000 Fe 4.032000 17.825000 2.620000 O 2.409000 17.005000 1.774 000 B 6.597000 16.126000 3.538000 H 7.444000 15.582000 3.845000 C 0.274000 16.484000 0.910000 H - 0.329000 16.892000 0.361000 H - 0.249000 16.226000 1.412000 H 0.746000 15.764000 0.471000 N - 0.473000 20.201000 5.589000 O 2.444000 20.723000 1.677000 C 3.455000 20.346000 1.035000 N - 0.267000 21.089000 2.729000 O 4.066000 19.269000 1.227000 C 3.952000 21.240000 - 0.067000 H 4.432000 20.716000 - 0.712000 H 4.535000 21.909000 0.301000 H 3.206000 21.669000 - 0.494000 N - 0.956000 21.747000 3.702000 C - 0.052000 18.095000 5.342000 H 0.286000 17.312000 4.923000 N 1.948000 21.580000 4 .470000 O 2.972000 18.920000 3.827000 H 3.179000 18.952000 4.377000 C - 0.933000 18.209000 6.407000 H - 1.261000 17.552000 6.892000 N 0.979000 22.203000 5.206000 N 4.139000 16.270000 4.028000 C - 1 .171000 19.555000 6.532000 H - 1.681000 20.004000 7.148000 N 5.329000 15.672000 4.288000 C - 0.944000 21.271000 1.597000 H - 0.650000 20.906000 0.822000 N 5.277000 16.577000 1.438000 C - 2.060000 22.049000 1.820000 H - 2.680000 22.173000 1.174000 N 6.344000 15.961000 2.028000 C - 2.039000 22.323000 3.163000 H - 2.642000 22.720000 3.772000 N 5.855000 18.521000 3.423000 C 3.071000 22.272000 4.667000 H 3.830000 22.066000 4.192000 C 2.843000 23.336000 5.516000 H 3.353000 24.052000 5.769000 N 6.811000 17.615000 3.779000 C 1.520000 23.261000 5.833000 H 1.017000 23.770000 6 .382000 C 3.238000 15.639000 4.770000 H 2.428000 15.915000 4.714000 C 3.825000 14.639000 5.513000 H 3.432000 14.127000 6.197000 C 5.131000 14.684000 5.177000 H 5.793000 14.119000 5.428000 C 5 .342000 16.288000 0.145000 H 4.719000 16.637000 - 0.444000 C 6.442000 15.489000 - 0.118000 H 6.763000 15.164000 - 0.860000 C 7.052000 15.319000 1.096000 H 7.835000 14.833000 1.371000 C 6.354000 19.737 000 3.651000 H 5.897000 20.452000 3.456000 C 7.645000 19.602000 4.151000 H 8.075000 20.080000 4.565000 C 7.890000 18.284000 4.230000 H 8.699000 17.723000 4.518000 O 3.999000 19.112000 6.357000 C 4.300000 18.460000 7.261000 C 5.658000 18.058000 7.516000 H 6.243000 18.494000 6.892000 H 5.734000 17.108000 7.416000 H 5.902000 18.306000 8.411000 C 3.314000 17.927000 8.083000 H 2.455000 18.250000 7.804000 H 3.476000 18.193000 8.991000 H 3.332000 16.970000 8.023000 Ga 20 K: Ga 4.181000 0.309000 10.946000 B 5.940000 - 1.466000 12.895000 H 6.545000 - 2.081000 13.533000 O 4.961000 1.7 34000 9.807000 N 5.339000 0.940000 12.522000 C 4.485000 2.747000 9.228000 Ga 1.659000 2.421000 10.199000 B - 0.794000 4.312000 10.884000 H - 1.632000 4.938000 11.137000 O 3.287000 3.125000 9.300000 N 5.972000 0.023000 13.311000 C 5.425000 3.564000 8.401000 H 6.063000 2.977000 7.955000 H 4.932000 4.067000 7.780000 H 5.923000 4.139000 8.951000 119 O 3.262000 - 0.454000 9.355000 N 5.833000 - 0.826000 10.449000 C 2.236000 - 0.117000 8.697000 O 1.552000 0.931000 8.884000 N 6.480000 - 1.505000 11.439000 C 1.810000 - 1.031000 7.588000 H 0.914000 - 0.856000 7 .305000 H 2.348000 - 0.940000 6.896000 H 1.932000 - 1.921000 7.821000 O 2.661000 1.359000 11.428000 H 2.425000 1.338000 12.155000 N 3.572000 - 1.276000 12.084000 C 5.736000 2.153000 12.925000 H 5 .422000 2.923000 12.494000 N 4.479000 - 1.942000 12.855000 C 6.629000 2.033000 13.993000 H 7.066000 2.739000 14.443000 N 1.618000 3.999000 11.502000 C 6.754000 0.668000 14.204000 H 7.266000 0.152 000 14.804000 N 0.472000 4.714000 11.668000 C 6.555000 - 0.983000 9.331000 H 6.264000 - 0.596000 8.529000 N 0.589000 3.607000 8.896000 C 7.677000 - 1.774000 9.589000 H 8.327000 - 2.025000 8.983000 N - 0.458000 4.336000 9.379000 C 7.593000 - 2.082000 10.938000 H 8.141000 - 2.573000 11.482000 N - 0.188000 1.864000 10.958000 C 2.410000 - 1.933000 12.186000 H 1.666000 - 1.639000 11.700000 H 0.135000 0.880000 16.590000 N - 1.111000 2.838000 11.214000 C 2.553000 - 3.037000 13.030000 H 1.923000 - 3.673000 13.235000 C 3.880000 - 3.008000 13.426000 H 4.376000 - 3.589000 13.962000 C 2.533000 4.522000 12 .327000 H 3.405000 4.165000 12.317000 C 1.983000 5.587000 13.043000 H 2.403000 6.116000 13.660000 C 0.673000 5.672000 12.595000 H - 0.015000 6.262000 12.838000 C 0.611000 3.788000 7.569000 H 1 .252000 3.381000 7.035000 C - 0.432000 4.632000 7.182000 H - 0.622000 4.896000 6.313000 C - 1.091000 4.951000 8.359000 H - 1.850000 5.490000 8.523000 C - 0.794000 0.688000 11.193000 H - 0.346000 - 0.138000 11.082000 H 1.402000 1.689000 16.944000 C - 2.115000 0.904000 11.602000 H - 2.780000 0.250000 11.810000 C - 2.274000 2.280000 11.599000 H - 3.011000 2.803000 11.790000 H 0.367000 2.931000 13.667000 H 0.310000 3.397000 15.184000 O 2.010000 1.124000 14.152000 C 1.179000 1.558000 14.936000 C 1.072000 1.017000 16.335000 H 1.563000 0.188000 16.459000 C 0.226000 2.657000 14 .571000 H - 0.665000 2.359000 14.662000 Ga 50 K: Ga 4.197000 0.312000 10.963000 O 4.974000 1.739000 9.824000 B 5.956000 - 1.465000 12.907000 H 6.563000 - 2.077000 13.544000 N 5.355000 0.941000 12.53900 0 C 4.500000 2.753000 9.249000 Ga 1.675000 2.427000 10.221000 O 3.304000 3.133000 9.325000 B - 0.780000 4.314000 10.907000 H - 1.615000 4.932000 11.161000 N 5.990000 0.023000 13.326000 C 5.440000 3.570000 8.423000 H 4.950000 4.085000 7.814000 H 6.066000 2.987000 7.958000 H 5.940000 4.131000 8.973000 O 3.274000 - 0.448000 9.372000 N 5.847000 - 0.823000 10.463000 C 2.250000 - 0.109000 8.716000 O 1.569000 0.939000 8.903000 N 6.495000 - 1.503000 11.451000 C 1.818000 - 1.025000 7.610000 H 0.957000 - 0.833000 7.294000 H 2.380000 - 0.980000 6.952000 H 1.919000 - 1.897000 7 .848000 O 2.678000 1.363000 11.447000 H 2.445000 1.344000 12.172000 N 3.589000 - 1.275000 12.098000 C 5.750000 2.153000 12.947000 H 5.431000 2.923000 12.521000 N 4.496000 - 1.942000 12.870000 C 6 .641000 2.031000 14.015000 H 7.079000 2.732000 14.464000 N 1.634000 4.003000 11.525000 C 6.770000 0.666000 14.222000 H 7.288000 0.144000 14.815000 N 0.485000 4.717000 11.692000 C 6.567000 - 0.980000 9.344000 H 6.278000 - 0.585000 8.542000 N 0.605000 3.614000 8.918000 C 7.688000 - 1.773000 9.600000 H 8.338000 - 2.021000 8.990000 N - 0.445000 4.340000 9.402000 C 7.605000 - 2.080000 10.948000 H 8.153000 - 2.576000 11.480000 N - 0.171000 1.866000 10.978000 C 2.427000 - 1.932000 12.201000 H 1.681000 - 1.643000 11.717000 N - 1.096000 2.840000 11.234000 C 2.571000 - 3.037000 13 .045000 H 1.941000 - 3.676000 13.248000 C 3.897000 - 3.007000 13.440000 H 4.391000 - 3.580000 13.972000 C 2.548000 4.531000 12.346000 H 3.418000 4.181000 12.332000 C 1.997000 5.595000 13.062000 H 2 .424000 6.136000 13.678000 C 0.687000 5.677000 12.617000 H - 0.005000 6.268000 12.861000 C 0.627000 3.797000 7.592000 H 1.269000 3.381000 7.061000 C - 0.418000 4.640000 7.206000 H - 0.612000 4.898 000 6.350000 C - 1.078000 4.955000 8.382000 H - 1.830000 5.481000 8.552000 C - 0.775000 0.691000 11.210000 H - 0.331000 - 0.132000 11.089000 C - 2.096000 0.905000 11.618000 H - 2.758000 0.248000 11.826000 C - 2.257000 2.278000 11.617000 H - 2.993000 2.806000 11.800000 120 O 2.030000 1.128000 14.173000 C 1.200000 1.561000 14.959000 C 0.247000 2.656000 14.595000 H - 0.632000 2.372000 14.701000 H 0.380000 2.937000 13.689000 H 0.330000 3.403000 15.208000 C 1.098000 1.020000 16.357000 H 1.582000 0.182000 16.474000 H 0.165000 0.889000 16.610000 H 1.422000 1.703000 16.971000 Ga 100 K: Ga - 4.222000 9. 725000 - 3.302000 B - 5.988000 11.503000 - 5.240000 H - 6.583000 12.127000 - 5.876000 O - 3.293000 10.483000 - 1.714000 N - 3.617000 11.313000 - 4.437000 C - 2.274000 10.139000 - 1.057000 Ga - 1.703000 7.605000 - 2.565000 B 0.756000 5.728000 - 3.257000 H 1.613000 5.106000 - 3.521000 O - 1.603000 9.090000 - 1.245000 N - 4.526000 11.981000 - 5.209000 C - 1.837000 11.052000 0.047000 H - 1.011000 10.888000 0.394000 H - 1.906000 11.906000 - 0.200000 H - 2.343000 11.043000 0.724000 O - 4.994000 8.296000 - 2.163000 N - 5.872000 10.860000 - 2.797000 C - 4.526000 7.280000 - 1.599000 O - 3.335000 6.897000 - 1 .678000 N - 6.522000 11.542000 - 3.784000 C - 5.464000 6.459000 - 0.778000 H - 4.950000 5.923000 - 0.180000 H - 5.947000 5.899000 - 1.259000 H - 6.086000 7.013000 - 0.326000 O - 2.706000 8.673000 - 3.787000 H - 2 .464000 8.730000 - 4.471000 N - 5.382000 9.097000 - 4.877000 C - 2.459000 11.974000 - 4.545000 H - 1.709000 11.657000 - 4.120000 N - 6.021000 10.017000 - 5.663000 C - 2.606000 13.077000 - 5.384000 H - 1.973000 13.735 000 - 5.610000 N 0.143000 8.172000 - 3.319000 C - 3.928000 13.046000 - 5.777000 H - 4.430000 13.601000 - 6.312000 N 1.070000 7.200000 - 3.577000 C - 6.586000 11.020000 - 1.681000 H - 6.290000 10.651000 - 0.873000 N - 0.630000 6.415000 - 1.265000 C - 7.702000 11.815000 - 1.935000 H - 8.355000 12.043000 - 1.347000 N 0.421000 5.694000 - 1.752000 C - 7.625000 12.119000 - 3.271000 H - 8.163000 12.587000 - 3.795000 N - 1.659000 6.030000 - 3.872000 C - 5.772000 7.886000 - 5.294000 H - 5.459000 7.138000 - 4.875000 N - 0.508000 5.321000 - 4.043000 C - 6.657000 8.010000 - 6.362000 H - 7.092000 7.336000 - 6.806000 C - 6.791000 9.373000 - 6 .562000 H - 7.310000 9.922000 - 7.185000 C 0.746000 9.346000 - 3.547000 H 0.303000 10.155000 - 3.430000 C 2.064000 9.134000 - 3.950000 H 2.741000 9.786000 - 4.146000 C 2.228000 7.770000 - 3.957000 H 2 .957000 7.228000 - 4.170000 C - 0.650000 6.228000 0.058000 H - 1.286000 6.616000 0.571000 C 0.394000 5.390000 0.439000 H 0.592000 5.146000 1.298000 C 1.051000 5.081000 - 0.730000 H 1.801000 4.580000 - 0.910000 C - 2.569000 5.492000 - 4.687000 H - 3.440000 5.847000 - 4.658000 C - 2.015000 4.433000 - 5.400000 H - 2.464000 3.889000 - 6.011000 C - 0.708000 4.360000 - 4.965000 H - 0.015000 3.763000 - 5.211000 O - 2.061000 8.902000 - 6.521000 C - 1.238000 8.468000 - 7.310000 C - 0.277000 7.388000 - 6.947000 H 0.581000 7.615000 - 7.083000 H - 0.430000 7.126000 - 6.008000 H - 0.291000 6.690000 - 7 .569000 C - 1.147000 9.004000 - 8.709000 H - 0.246000 9.175000 - 8.932000 H - 1.661000 9.846000 - 8.855000 H - 1.447000 8.336000 - 9.327000 Ga 173 K: Ga 7.282000 9.765000 3.320000 O 6.518000 8.332000 2.1820 00 N 6.121000 9.132000 4.894000 C 6.973000 7.306000 1.632000 B 5.506000 11.537000 5.252000 H 4.909000 12.140000 5.892000 Ga 9.796000 7.638000 2.593000 O 8.161000 6.923000 1.719000 N 5.473000 10.051000 5.673000 B 12.262000 5.777000 3.297000 H 13.095000 5.166000 3.569000 C 6.032000 6.479000 0.831000 H 6.528000 5.990000 0.248000 H 5.434000 7.040000 0.344000 H 5.444000 5.888000 1.308000 C 9.231000 10.169000 1.079000 O 8.220000 10.521000 1.740000 N 5.635000 10.901000 2.811000 O 9.888000 9.115000 1.265000 C 9.666000 11.072000 - 0.025000 H 9.063000 11.539000 - 0 .387000 H 10.318000 10.752000 - 0.495000 H 9.856000 11.807000 0.279000 N 4.979000 11.578000 3.793000 N 7.879000 11.356000 4.459000 O 8.795000 8.712000 3.809000 H 8.988000 8.727000 4.471000 C 5 .741000 7.929000 5.320000 H 6.067000 7.183000 4.915000 N 6.967000 12.017000 5.229000 C 4.860000 8.051000 6.385000 H 4.440000 7.387000 6.837000 N 9.845000 6.066000 3.902000 C 4.715000 9.399000 6.575000 H 4.203000 9.885000 7.150000 N 11.003000 5.368000 4.083000 C 4.928000 11.066000 1.692000 H 5.244000 10.687000 0.873000 N 10.877000 6.450000 1.299000 C 3.819000 11.856000 1.938000 121 H 3.209000 12.102000 1.331000 N 11.926000 5.733000 1.788000 C 3.882000 12.154000 3.275000 H 3.354000 12.660000 3.785000 N 11.639000 8.217000 3.343000 C 9.031000 12.016000 4 .576000 H 9.775000 11.701000 4.132000 C 8.877000 13.114000 5.414000 H 9.460000 13.746000 5.643000 N 12.569000 7.250000 3.607000 C 7.560000 13.078000 5.802000 H 7.071000 13.637000 6.324000 C 8 .939000 5.514000 4.705000 H 8.042000 5.859000 4.694000 C 9.498000 4.460000 5.418000 H 9.063000 3.927000 6.033000 C 10.798000 4.404000 4.998000 H 11.529000 3.810000 5.245000 C 10.861000 6.249 000 - 0.019000 H 10.198000 6.655000 - 0.528000 C 11.904000 5.420000 - 0.391000 H 12.104000 5.180000 - 1.211000 C 12.557000 5.120000 0.776000 H 13.334000 4.638000 0.947000 C 12.233000 9.391000 3.564000 H 11.757000 10.187000 3.434000 C 13.549000 9.183000 3.972000 H 14.175000 9.807000 4.185000 C 13.723000 7.829000 3.984000 H 14.468000 7.288000 4.203000 O 9.438000 8.921000 6.551000 C 10.239000 8.484000 7.348000 C 11.211000 7.435000 6.997000 H 12.134000 7.741000 7.338000 H 11.215000 7.234000 6.100000 H 11.247000 6.730000 7.571000 C 10.292000 9.010000 8.754000 H 9.748000 9.865000 8 .961000 H 11.256000 9.091000 9.029000 H 10.023000 8.273000 9.385000 Ga 234 K: Ga 4.173000 9.817000 4.487000 B 6.006000 11.566000 2.589000 H 6.585000 12.147000 1.955000 O 4.894000 8.362000 5.630000 N 5.344000 9.174000 2.916000 C 4.440000 7.302000 6.108000 Ga 1.638000 7.694000 5.150000 B - 0.863000 5.930000 4.352000 H - 1.677000 5.386000 4.029000 O 3.262000 6.916000 5.995000 N 6.025000 10.078000 2.160000 C 5.384000 6.437000 6.876000 H 4.859000 5.815000 7.410000 H 6.008000 7.002000 7.348000 H 5.873000 5.895000 6.412000 O 3.212000 10.572000 6 .056000 N 5.823000 10.926000 5.026000 C 2.217000 10.187000 6.719000 O 1.581000 9.127000 6.526000 N 6.500000 11.605000 4.058000 C 1.786000 11.064000 7.855000 H 2.467000 11.650000 8.299000 H 1 .178000 10.664000 8.362000 H 1.450000 11.590000 7.285000 O 2.670000 8.777000 3.963000 H 2.395000 8.881000 3.338000 N 3.617000 11.421000 3.342000 C 5.673000 7.971000 2.459000 H 5.279000 7.197 000 2.855000 N 4.552000 12.061000 2.582000 C 6.553000 8.084000 1.400000 H 6.957000 7.493000 0.952000 N 1.568000 6.156000 3.805000 C 6.753000 9.427000 1.240000 H 7.321000 9.893000 0.675000 N 0.386000 5.503000 3.576000 C 6.497000 11.098000 6.160000 H 6.176000 10.746000 6.998000 N 0.511000 6.497000 6.398000 C 7.612000 11.883000 5.932000 H 8.202000 12.113000 6.552000 N - 0.555000 5.828000 5.867000 C 7.582000 12.176000 4.607000 H 8.124000 12.612000 4.168000 N - 0.168000 8.343000 4.406000 C 2.482000 12.099000 3.201000 H 1.753000 11.825000 3.568000 N - 1.120000 7.416000 4 .090000 C 2.672000 13.184000 2.358000 H 2.136000 13.883000 2.122000 C 3.980000 13.127000 1.990000 H 4.467000 13.650000 1.441000 C 2.466000 5.560000 3.033000 H 3.259000 5.847000 2.989000 C 1 .890000 4.542000 2.298000 H 2.293000 3.998000 1.700000 C 0.587000 4.537000 2.676000 H - 0.086000 3.986000 2.510000 C 0.505000 6.254000 7.704000 H 1.122000 6.642000 8.237000 C - 0.566000 5.431000 8.030000 H - 0.837000 5.139000 8.848000 C - 1.213000 5.202000 6.845000 H - 1.961000 4.660000 6.627000 C - 0.717000 9.544000 4.195000 H - 0.266000 10.243000 4.352000 C - 2.019000 9.370000 3.742000 H - 2.479000 10.068000 3.432000 C - 2.238000 8.046000 3.678000 H - 2.955000 7.435000 3.479000 C 1.261000 8.403000 0.491000 O 1.794000 8.986000 1.334000 C 0.037000 7.712000 0 .532000 H - 0.265000 7.650000 1.441000 H 0.154000 6.831000 0.172000 H - 0.616000 8.187000 0.011000 C 1.740000 8.382000 - 0.724000 H 2.226000 9.193000 - 0.891000 H 1.017000 8.308000 - 1.351000 H 2 .327000 7.630000 - 0.822000 Ga 296 K: Ga 1.486000 19.940000 3.328000 O 0.789000 18.477000 2.182000 N 0.306000 19.291000 4.895000 C 1.238000 17.406000 1.726000 B - 0.382000 21.680000 5.202000 H - 0.951000 22.266000 5.829000 Ga 4.034000 17.822000 2.693000 O 2.420000 17.025000 1.853000 C 0.304000 16.530000 0.988000 H - 0.374000 17.066000 0.570000 122 H - 0.107000 15.914000 1.600000 H 0.786000 16.041000 0.317000 B 6.549000 16.107000 3.536000 H 7.368000 15.537000 3.853000 N - 0.392000 20.193000 5.632000 O 2.463000 20.696000 1.768000 N - 0.162000 21.038000 2.770000 C 3.451000 20.302000 1 .104000 O 4.079000 19.244000 1.301000 C 3.896000 21.175000 - 0.030000 H 4.231000 21.867000 0.550000 H 3.216000 21.806000 - 0.409000 H 4.501000 20.737000 - 0.503000 N - 0.856000 21.713000 3.727000 N 2 .019000 21.546000 4.487000 C 0.001000 18.085000 5.370000 H 0.382000 17.324000 4.908000 O 2.987000 18.904000 3.867000 H 3.237000 19.023000 4.485000 C - 0.883000 18.205000 6.426000 H - 1.276000 17.552000 6.914000 N 1.070000 22.180000 5.231000 C - 1.112000 19.536000 6.558000 H - 1.689000 20.013000 7.108000 N 4.111000 16.284000 4.045000 N 5.297000 15.665000 4.295000 C - 0.816000 21.217000 1.634000 H - 0.546000 20.887000 0.878000 C - 1.927000 22.006000 1.831000 H - 2.512000 22.305000 1.164000 N 5.185000 16.627000 1.468000 C - 1.922000 22.293000 3.155000 H - 2.443000 22.686000 3 .595000 N 6.253000 15.981000 2.016000 N 5.820000 18.507000 3.447000 C 3.146000 22.229000 4.645000 H 3.920000 21.970000 4.205000 N 6.783000 17.601000 3.780000 C 2.933000 23.313000 5.494000 H 3 .475000 24.019000 5.744000 C 1.627000 23.240000 5.830000 H 1.187000 23.709000 6.317000 C 3.210000 15.666000 4.795000 H 2.287000 15.843000 4.714000 C 3.792000 14.662000 5.535000 H 3.349000 14.022 000 6.097000 C 5.092000 14.692000 5.192000 H 5.791000 14.088000 5.415000 C 5.211000 16.364000 0.164000 H 4.579000 16.713000 - 0.363000 C 6.290000 15.556000 - 0.143000 H 6.636000 15.214000 - 1.037000 C 6.926000 15.346000 1.045000 H 7.700000 14.831000 1.232000 C 6.337000 19.724000 3.650000 H 5.783000 20.447000 3.353000 C 7.628000 19.592000 4.128000 H 7.959000 20.277000 4.463000 C 7.879000 18.272000 4.197000 H 8.650000 17.673000 4.356000 O 3.982000 19.098000 6.457000 C 4.357000 18.450000 7.326000 C 3.507000 18.006000 8.233000 H 2.633000 18.357000 8.051000 H 3.791000 18.290000 9 .105000 H 3.479000 17.046000 8.203000 C 5.709000 17.994000 7.499000 H 6.261000 18.359000 6.801000 H 5.732000 17.036000 7.455000 H 6.039000 18.284000 8.352000 123 REFERENCES 124 REFERENCES 1 Armstrong, W. 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E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brother s, 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.; Go mperts, 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.; Orti z, J. V.; Cioslowski, J.; Fox, D. J. Gaussian, Inc., Wallingford CT, 2009. 23 (a) Becke, A. D. Phys. Rev. A 1988 , 38 , 3098 3100. (b) J. P. Perdew and Y. Wang, Phys. Rev. B, 45 (1992) 13244 - 49. (c) J. P. Perdew, K. Burke, and Y. Wang, Phys. Rev. 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As the optimized geometries were studied later in the project, they were studied exclusively with G09. 28 Mulliken, R. S. J. Chem. Phys. 1955 , 23 , 1833. 29 ( a) A. E. Reed and F. Weinhold, J. Chem. Phys. 1983 , 78 , 4066 ( b) A. E. Reed, R. B. Weinstock, and F. Weinhold, J. Chem. Phys. 1985 , 83 , 735 ( c) NBO 4.0, E. D. Glendening, J. K. Badenhoop, A. E. Reed, J. E. Carpenter, and F. Weinhold, 1996 Theoretical Chemistry Institute, University of Wisconsin, Madison. 30 Reorgani zation energy is the energy needed for an initial electronic state to change to the geometry of a product state, without the molecule actually transitioning to the product state. For more details refer to Chapter 3 of this dissertation and read: Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985 , 811 , 265 322. 31 Mercury v3.5.1 X - ray structure visualization program. 2015. 32 ChemBioDraw 3D software v13.0. Multi - purpose visualization program. 2015. 33 a) GaussView, Version 5.0.9 , Dennington, R.; Keith, T.; Millam, J. Semichem Inc. , Shawnee Mission, KS, 2009. b) Version 4.0 was also used. 34 Yamanaka, S.; Kawakami, T.; Nagao, H.; and Yamaguchi, K. Chem. Phys. Lett. 1994 , 231 , 25 - 33. 127 35 (a) Ginsberg, A. P. J. Am. Chem. Soc. 1980 , 102 , 111 117. (b)Noodleman, L. J. Chem. Phys. 1981, 74, 5737. (c) Mouesca, J. - M. In Metallo - proteins: Methods and Protocols ; 2014; pp. 269 296. (d) Neese, F. Coord. Chem. Rev. 2009 , 253 , 526 563. 36 Swart, M. J. Chem. Theory Comput. 2008 , 4 , 2057 2066. 37 R uiz, E.; Alemany, P.; Alvarez, S.; Cano, J. Inorg. Chem. 1997 , 36 , 3683 3688. 38 Hay, P. J.; Thibeault, J. C.; Hoffmann, R. J. Am. Chem. Soc. 1975 , 97 , 4884 4899. 39 Pheasant, S.; Kouzelos, J. A.; Van Ryswyk, H.; Cave, R. J. Mol. Simul. 2006 , 32 , 677 693. 40 (a) Girerd, J. - J.; Charlot, M. - F.; Kahn, O. Mol. Phys. 1977 , 34 , 1063 1076. (b) Girerd, J. J.; Journaux, Y.; Kahn, O. Chem. Phys. Lett. 1981 , 82 , 534 538. 41 Lu, T.; Chen, F. Multiwfn: A Multifunctional Wavefunction Analyzer, J. Comp. Chem . 2012, 33 , 580 - 592 42 C. Adamo and V. Barone, J. Chem. Phys. 108, 664. (1998). 43 Drago, R. Physical Methods for Chemists ; 2nd ed.; Surfside Scientific Publishers: Gainsville, FL, 1992. 128 Chapter 3: Investigations into the Energy Acceptor Reactivity of a Manganese(II) Ligand Field State in a Covalently Linked Donor - Acceptor Assembly 3.1 Introduction To better understand the dynamics of electron and energy transfer, it is common to synthesize and study covalently bound donor - accep tor complexes. 1 These donor - acceptor systems offer the inherent advantage of not having to contend with diffusion related kinetic phenomena 2a when studying their photochemistry and photophysics. In spite of this benefit, studying the exact mechanism at wor k in these donor - acceptor complexes can still be challenging, as it is difficult to distinguish between electron transfer and energy transfer processes. 3 Our group has previously explored how to differentiate between different types of electron and energ y transfer in a well characterized series of covalently linked donor - acceptor complexes such that the mechanism of the electron and/or energy transfer can be easily determined. 2 Of particular interest were studies from our group on a series of donor - accept or systems, consisting of a ruthenium polypyridyl complex covalently appended di - manganese Schiff base macrocycle, 4 which includes the [Mn 2 (L)(mcb)Ru((CF 3 ) 2 - bpy) 2 ] 3+ ( 4 ) complex as seen in figure 3 - 1, where (L) is a Schiff base macrocycle, (mcb) is 4 - carbo xy, - - methyl - - bipyridine, and (CF 3 ) 2 - - bistrifluoromethyl - - bipyridine. The ruthenium polypyridyl moiety is used as an extremely well characterized chromophore which exhibits emission from a triplet metal - to - ligand charge transfer state ( 3 MLCT). 5 As ruthenium polypyridyls are known to participate as photo - induced electron or energy donors or acceptors, 6 the 3 MLCT emission allows the ruthenium polypyridyl to function as a kinetic handle by which the rates of energy or electron transfer can be measured. The energetics of the ligands also allow for the directed localization of the 3 MLCT either closer or in the ca se of complex 4 farther from the binuclear macrocycle. 1a The Mn II macrocycle was chosen for its 129 extremely small ligand field absorptions to limit the possible mechanism of energy transfer (by eliminating the Förster mechanism) 7,8 while still allowing for t he study of possible reactivity with a transition metal dimer. In our previous work, we observed the quenching of the 3 MLCT in these previously studied systems and it was determined that this quenching was caused by a Dexter energy transfer mechanism. 4,9 In this work, the Schiff base macrocycle present in complex 4 has been replaced by an analogue with a single manganese which will enable the probing of the possible interaction of the 3 MLCT with a single transition metal ion. This results in the design of complex 3 , which is drawn in figure 3 - 1. If quenching due to a single Mn II is present in complex 3 , this will profoundly enhance our understanding of the temperature dependence of the energy transfer rate in complex 4 , where the Heisenberg spin exchange c oupled macrocyclic core opens up a host of electronic states responsible for the observed quenching of the Ru 3 MLCT. Figure 3 - 1: Chemical drawings of systems studied. 130 3.2 Experimental GENERAL: Commercially available reagents were procured and used as received unless otherwise indicated. Solvents were acquired from Fisher Scientific, Sigma - Aldrich, Acros, or Alfa packaged under an inert gas, in which case they were used as received. The ligands H(mcb), 10 (CF 3 ) 2 - bpy, 11 as well as the complexes Ru((CF 3 ) 2 - bpy) 2 Cl 2 , 12 and the macrocycle precursor 13 were prepared using literature methods. The syntheses of [Mn(L)Mn(mcb)Ru((CF 3 ) 2 - bpy) 2 ]( PF 6 ) 3 ( 4 ), [Zn(L)Zn(mcb)Ru((CF 3 ) 2 - bpy) 2 ](PF 6 ) 3 ( 5 ), were previously reported. 4 Na(mcb) was obtained by addition of NaOH (aq) to an aqueous solution of H(mcb) as previously reported. 4 Na(OAc) was purified by hot recrystallization from hot glacial acetic acid and dried under vacuum. Mn(SO 4 )·4H 2 O was obtained from recrystallization of the commercially available monohydrate from hot water with subsequent evaporation under a stream of nitr ogen. The resulting transparent pink metastable crystals were confirmed to be the tetrahydrate with the aid of elemental analysis. Elemental Analyses were performed by the analytical facilities at Michigan State University or by Midwest Microlab. ESI - MS w ere acquired either by Prof. Gavin Reid (currently at University of Melbourne) or by the Michigan State University Mass Spectrometry facility. 1 H NMR spectra were obtained at the MSU Chemistry NMR facilities on either 300 MHz or 500 MHz Varian/Agilent spec trometers. 3.2.1 Syntheses 4 ) 2 : This complex was prepared using an adapted synthetic procedure previously reported by Okawa and coworkers for an analogous compound. 13 131 in a relatively small amount of methanol (2 0 mL) under nitrogen, and a methanol solution of Pb(ClO 4 ) 2 ·3H 2 O (1.012 g in 15 mL of MeOH) was added slowly into the aforementioned stirring suspension under nitrogen and allowed to stir for an hour. To this, a solution of 1 equivalent (0.258 g / 0.283 mL in 10 mL of MeOH) of N,N - bisaminoethyl - N - was added slowly, and the mixture was then heated using an oil bath to reflux under nitrogen and allowed to stir for an hour. During this time the suspended solid mostly dissolved. Afterwards the solution was allowed to cool and any remaini ng solids were removed via vacuum filtration and the filtrate was evaporated to dryness under nitrogen flow to yield a yellow powder, which is the desired product in 94% yield. 1 H - NMR ( d 6 - 3.25 (m, 2H), 3.89 (m broad, 6H), 4.18 (t, 2H), 7.42 (dd, 4H), 8.58 (d, 4H). Elemental Analysis found (calculated) 4 ) 2 ·2H 2 O: %C: 31.59 (31.98) %H: 3.465 (3.54) %N: 7.345 (7.46) ESI - MS: ( m/z ) = 802.1 (M - ClO 4 ) UV/Vis peaks in MeOH: 215, 252, 378 nm. )Zn](ClO 4 ) 2 : This complex was prepared in a nitrogen glovebox by suspending 0.200 g equivalent (0.049 g) of Mn(SO 4 )·4H 2 O in 10 mL of MeOH dropwise to the stirring suspension. After two hours of stirring the suspension was filtered through a celite pad to remove the yellow - stained white PbSO 4 precipitate, resulting in a filtrate that is evaporated under nitrogen to dryness. This yellow powder was then dissolved in 40 mL of dichloromethane under nitrogen and the insoluble portions were removed via vacuum filtration under nitrogen and discarded. The desired product was crashed out of solution under nitrogen by addition of approximately 60 mL of diethyl ether to the afor ementioned filtrate, and the precipitate was separated via vacuum filtration under nitrogen and dried in a vacuum desiccator to yield the desired product in 54% yield. Note: The unbridged complex is especially susceptible to complexation with any residual carboxylates 132 present in the mass spectrometer, and since formate and acetate salts are typically used as standards in of ESI - MS, the desired complex is likely to pick up any of these spare carboxylates present. This was the case for our ESI - MS results, whi ch mirrored those obtained for the complex with an acetate bridge due to the acetate present in the mass spectrometer. ESI - MS (m/z) = 609.1 (M+OAc - 2ClO 4 ) UV/Vis peaks in MeOH: 215, 252, 370 nm. 4 ) 2 : This complex was synthesized in an analogou s fashion as the 4 ) 2 complex, substituting an equivalent of Zn(SO 4 )·7H 2 O for the Mn(SO 4 )·4H 2 O in the added methanol solution. Yield 42%. 1 H - NMR (MeOH - d 4 2.99 (t, 4H) 4.03 (s, broad, 8H), 7.49 (d, 4H), 8.52 (s, 2H), 8.64 (s, 2H). UV/Vis peaks in MeOH: 214, 252, 372 nm. 4 ) ( 1 ): This compound was prepared by slow addition of a methanol solution (15mL) o f Na(OAc) (1 eq., 0.0094 g) to a concentrated stirring solution of 0.0862 g of 4 ) 2 in 25 mL of methanol under nitrogen. Gradual formation of a yellow precipitate was observed, which after stirring for 3 hours was separated via vacuum filtrati on to yield the reported product as a yellow microcrystalline powder in 64% yield. Single crystals suitable for crystallography were obtained via ether diffusion into a solution of the compound in methanol with a few drops of acetonitrile under nitrogen. E SI - MS: m/z 609.1 (M - ClO 4 ). Elemental Analysis found (calculated) 4 ) · 0.2 NaClO 4 : %C: 43.78 (44.13), %H: (4.39), %N: 9.88 (9.53). UV/Vis peaks in MeOH: 215, 252, 374 nm. 4 ) ( 2 ): This compound was prepared in an analogous fashion to the 4 4 ) 2 for the 4 ) 2 in the procedure above. Yield 44%. Single crystals suitable for crystallography were obtained from slow evaporation of a sol ution of the compound in methanol. ESI - MS m/z: 133 620.1 (M - ClO 4 ), Elemental Analysis found (calculated) 4 ) · 0.2 NaClO 4 : %C: 43.41 (43.51), %H: 4.38 (4.33), %N: 9.21 (9.40). 1 H - NMR (MeOH - d 4 (s, 3H), 2.30 (s, 6H), 2.51 (s, 3 H), 3.03 (t, 4H), 3.54 (s, broad, 2H), 3.76 (s, broad, 2H), 4.22 (s, broad, 4H), 7.38 (dd, 4H), 8.50 (d, 4H). UV/Vis Peaks in MeOH: 215, 252, 375 nm. [Ru((CF 3 ) 2 - bpy) 2 (mcb)](PF 6 ): The synthesis of this intermediate complex was developed and performed by pre vious group member Dr. Monica Soler via a modification of previous literature methods. 14,15 0.4311 g (1.0 eq.) Ru((CF 3 ) 2 - bpy) 2 Cl 2 , 0.1149 g (mcb)H (1.15 eq.), and 0.1031 g (3.0 eq.) NaHCO 3 were dissolved in a mixture of 15 mL of water and 10 mL methanol under nitrogen. The solution was allowed to reflux under nitrogen for 2 to 3 hours in the dark, after which 20 eq. of NaPF 6 dissolved in water were added to the hot solution and impure cryst als of the product were obtained by allowing the reaction mixture to cool overnight in the refrigerator. Solid precipitate was isolated via vacuum filtration and the solid was dissolved in acetonitrile, filtered through celite and the filtrate purified via an alumina column. The column was initially loaded with acetonitrile, and after impurities had run through the column, methanol was added to the eluent until a 1:1 mixture of acetonitrile to methanol was eluting through the column, after which the fractio ns containing the desired product were collected, identified via NMR, and subsequently used in the following reaction without further characterization. 1 H - NMR (MeCN - d 3 (s, 3H), 7.24 (d, 2H), 7.48 (d, 1H), 7.60 (d, 1H), 7.68 (t, 4H), 7.80 (dd, 1H), 8.05 (m broad, 4H), 8.59 (s, H) 8.96 (s, 2H) 9.04 (s, 2H). 3 ) 2 - bpy) 2 ](ClO 4 ) 2 (PF 6 ) ( 3 ): The synthesis of this complex was developed and performed by Dr. Monica Soler and is roughly analogous to that of 4 ), with th e substitution of [Ru((CF 3 ) 2 - bpy) 2 (mcb)](PF 6 ) for sodium acetate. 15 0.1093 g of [Ru((CF 3 ) 2 - bpy) 2 (mcb)](PF 6 ) was dissolved under nitrogen in 15 mL of 134 distilled and degassed acetonitrile. After the solid was completely dissolved, 0.0783 g (1 eq.) of 4 ) 2 was added to the stirring solution and the mixture was allowed to stir under nitrogen for 2 days. Addition of an equivalent volume of ether resulted in the formation of a yellow/brown precipitate, which was separated via vacuum filtration , and the resulting solid was recrystallized from 1:1 acetonitrile and ether and subsequently from 1:1 dichloromethane and ether to obtain the pure product. Yield: 7%. Sample was characterized for use in the subsequent experiments. ESI - MS m/z: 1649, 1695, 1741. Elemental Analysis found (calculated) for 3 ) 2 - bpy) 2 ](ClO 4 ) 2 (PF 6 ) · 1.5 Et 2 O · CH 3 CN: %C: 42.19 (42.57) , %H: 3.48 (3.52) , %N: 8.38 (8.63) . 3.2.2 Physical Measurements 3.2.2.1 Electrochemistry Cyclic voltammetry (CV) and differen tial pulse voltammetry (DPV) measurements were performed in an argon - filled glovebox using a CH Instruments electrochemical analyzer. Compounds were dissolved in dried and degassed CH 2 Cl 2 , with the addition of a 0.1 M NBu 4 PF 6 as a supporting electrolyte. CH 2 Cl 2 offers similar solvent properties to the 3:2 solvent mixture that was used to produce the optical glass for the emission experiments, without the restrictively small solvent window present in the 2 - Me - THF. The experimen tal setup used the standard 3 - electrode configuration, with a platinum working electrode, graphite counter electrode, and Ag/AgCl as the reference electrode. Ferrocene was added as an internal standard. Potentials are reported as E 1/2 values in accordance to the DPV peaks. 16 135 3.2.2.2 X - Ray Structure Determination Quality crystals of complexes 1 and 2 were selected and mounted on a 'Bruker APEX - II CCD' diffractometer. The crystals were kept at 173(2) K during data collection. Using Olex2, 17 the structure was solved with the olex2.solve structure solution program 18 using Charge Flipping and refined with the XL refinement package using Least Squares minimization. 19 Structural parameters of the solved structures are reported in table 3 - 1. Table 3 - 1: Crystallographic Data for Complexes 1 and 2 . 3.2.2.3 Steady State Spectroscopies UV/Visible electronic absorption spectroscopy was obtained in lidded quartz cuvettes with samples dissolved in spectro - grade dichloromethane or methanol on a Varian Cary 50 or Perkin Elmer Lambda 1050 spectrometer. Absorption and room temperature emission samples were 136 prepared in an Ar - filled glovebox by dissolving the sample in dried and distilled CH 2 Cl 2 with an absorbance of 0.1 to 0.2 at the excitation wavelength of 475 nm and placed in sealed 1 cm path - length quartz cuvettes. Room temperature emission spectra were collected on either a Hamamatsu Quantaurus fluorimeter or a Horiba Jobin - Yvon Fluorolog 3 fluorimeter. Emission Spectra on the Fluorolog 3 were corrected for instrumental response by using a NIST standard of spectra irradiance (Optronic Laboratories, Inc., OL220M Tungsten quartz lamp). The Quantaurus - QY instrument is capable of determining ab solute quantum yields in addition to LT and RT emission spectra without the need for correction as described by Tobita and coworkers. 20 Low temperature steady state emission was obtained on samples prepared in the same Ar - filled drybox by dissolving the s amples in a 3:2 mixture of dichloromethane to 2 - Me - THF for the purposes of optical glass formation necessary for low temperature emission measurements with an absorbance between 0.1 and 0.2 for samples run on the Fluorolog 3 or an absorbance of 0.4 to 0.6 for the Hamamatsu Quantaurus - QY samples and for were placed in sealed quartz test tubes with a round cross section. Steady state emission spectra were collected on both instruments but while using the liquid nitrogen accessory on the Quantaurus or using th e Janis SVT - 100 optical cryostat equipped with two LakeShore resistive heaters and temperature controllers in conjunction with the Fluorolog 3 fluorimeter. 3.2.2.4 Time Resolved Spectroscopies Room temperature time - resolved absorption and emission spectro scopy measurements were obtained using the same sample preparation as room temperature steady state emission, with the exception of the transient absorption samples having an optical absorbance between 0.4 and 0.7 at the excitation wavelength of 475 nm. Ti me resolved absorption and emission spectroscopy were obtained using an updated Nd:YAG laser system which has been previously described, 21 upgraded 137 with the addition of an OPOTEK VIBRANT 355 LD tunable pulsed laser system incorporating both a flashlamp pul sed Nd:YAG laser harmonically producing a 355 nm laser pulse and an optical parametric oscillator (OPO) to allow the production of a visible light laser pulse of nominally 5 ns duration which was used to excite the samples. Excitation energies at the sampl e were in the range of 0.5 - 2 mJ/pulse, and all data were checked for linearity with regards to the excitation source power. Samples intensity was verified before and after by UV/Vis spectroscopy to verify sample integrity through the course of photophysi cal measurements. All data manipulations were carried out using the Origin software package. 3.2.2.5 Low Temperature Emission for Complexes 1 and 2 Microcrystalline powder samples of complexes 1 and 2 were loaded into quartz EPR tubes to a height of about 1 cm and placed inside a Janis SCVT - 100 optical cryostat, which was cooled to a temperature of 5 K with liquid helium. The samples were excited with a 405 nm laser from PICOQUANT (LDH - D - C - 405M, CW - 80MHz) operated in CW mode. The resulting emission spectrum was measured on a liquid nitrogen cooled CCD array. The spectra of both compounds were obtained under similar instrumental settings so that comparisons of the two spectra would be possible. 3.2.2.6 Variable Temperature Time Resolved Emission Spectroscopy Samples were prepared in the same manner as the aforementioned LT steady state emission samples, and placed in round quartz test tubes and sealed with rubber septa before removal from the drybox. Samples were inserted into a Janis SVT - 100 optical cryostat charged with liquid helium and equipped with two LakeShore resistive heaters and temperature controllers. The samples were slowly cooled down to 10 K, and allowed to reach a final stable temperature where 138 the average of the top and bottom temperature readi ngs on the controllers averaged to within 0.5 K of the desired temperature. These temperatures were held for 10 minutes before data was acquired at each temperature point. Time resolved kinetic traces for the compounds excited at 475 nm were obtained on th e Nd:YAG laser system with probing the emission at 670 nm and 700 nm. To obtain a full temperature profile, kinetic traces were obtained in 5K increments stepping between 10 K and 100 K and an additional trace at 110 K was obtained. Observations have led u s to determine that the glass to fluid transition for the solvent mixture used in these experiments occurs near 120 K, so additional points beyond 110 K will not be considered for modeling the temperature dependent behavior this study, as the nature of the ruthenium emission lifetime changes due to decay processes that are available in fluid solution that are inaccessible in a rigid glass medium, causing discontinuity in the kinetic behavior of these complexes. 22 3.2.2.7 Electronic Structure Calculations Electronic structure calculations reported in this work were determined using unrestricted density + ( 1 ) cation. The Becke 3 - parameter hybrid density functional based on the correlation functional of Lee, Yang, and P arr (B3LYP) 23 as implemented in the Gaussian 09 software package 24 was employed for these electronic structure calculations. The 6 - 311G(d,p) Pople - type basis set 25 was used as it provided the necessary energetic resolution for the energetic studies perform ed in this research. Optimized geometries were obtained starting with the previously mentioned X - ray crystallographic structure, which was then optimized for the sextet ground state. The optimized geometry was then further optimized for the quartet state, which was subsequently optimized for the doublet state. Each optimized geometry was checked via frequency calculations for a lack of negative frequencies, signifying that the geometry had reached 139 a potential energy minimum. Single point energy calculations were used to determine the energies of the relevant spin states at their non - equilibrium geometries. 3.3 Results and Discussion 3.3.1 Syntheses Figure 3 - 2: Synthetic scheme of complexes 1 and 3 . Our previous work determined that a Dexter energy transfer mechanism was responsible for the quenching of the Ru((CF 3 ) 2 - bpy) 2 (mcb) - based 3 MLCT in the [Mn(L)Mn(mcb)Ru((CF 3 ) 2 - bpy) 2 ](PF 6 ) 3 ( 4 ) relative to the rate of decay for the di - zinc model complex. 4 However, we were unable to determine the exact nature of the energy transfer pathway present in the Mn 2 macrocycle. To elucidate the cause, we attempted to make a mixed - metal equivalent to these two structures that would allow us to gauge the effect of tr ansition metals on the energy transfer mechanism without the complications of the antiferromagnetic spin coupling observed in the Mn 2 - macrocycle studied 140 previously. However, due to the symmetric nature of the macrocycle, initial attempts at a completely an alogous structure were unable to afford pure complexes due to metal scrambling between the coordination sites in the macrocycles, affording a mixture of Zn 2 - , Mn 2 - , and MnZn - macrocyclic acceptors. To prevent this, an asymmetric version of the macrocycle, w hich implements a lead(II) template intermediate based on work by Okawa and coworkers 13 was used to ensure that each macrocycle had a site specific to each metal, so that pure MnZn - macrocycles could be isolated. The synthetic procedure for the synthesis of complexes 1 and 3 is summarized in figure 3 - 2. The asymmetric macrocycle starts with the synthesis and isolation of diformyldimethylsalen by the condensation of ethylenediamine and 2,6 - diformyl - p - cresol in ethanol, which is deprotonated and metalated by t he addition of a stoichiometric amount of zinc acetate in methanol solution to a suspension of diformyldimethylsalen. The completion of the macrocycle is achieved by templating the condensation of the diformyldimethylsalen and N,N - bis(2 - aminoethyl) - N - methy lamine with lead(II) 13 - macrocycle is isolated, the templating lead is extracted via the addition of Mn(SO 4 )·4H 2 O to precipitate out the lead as PbSO 4 from a methanol solution less hydrated forms of MnSO 4 are insoluable - macrocycle is obtained, a carboxylate bridge can be installed to complete the desired complexes, either from sodium acetate to obtain the [ + ( 1 + ( 2 ) model complexes, or from [Ru((CF 3 ) 2 - bpy) 2 (mcb)](PF 6 ) to obtain the desired mixed - metal macrocycle appended ruthenium complex. + ( 1 + ( 2 ) wer e obtained as described above. These structures are shown in figure 3 - 3 and figure 3 - 4 respectively. Complex 1 141 crystalizes in the monoclinic space group with a C2/c space group. Each unit cell has two distinct macrocyclic cations arranged with the acetate bridges parallel and the macrocycles facing each other and two perchlorate anions. While each macrocycle is distinct, the structures are very similar for each one. Upon initial inspection, the two cations are observed to be roughly mirror images of each ot her, with the plane going between the two metal ions and the acetate bridge. The manganese(II) ion in a six coordinate site and a zinc(II) ion in a 5 - coordinate site, bridged by both phenolic oxygens from the Schiff base macrocycle and the acetate bridge. The remainder of the Mn(II) six - coordinate site consists of the three triamine nitrogens, two of them imine - based and the third aliphatic central nitrogen, coordinated in a facial manner. The zinc(II) five - coordinate site is rounded out by the ethylenediamine - based imine nitrogens of the macrocycle. The configuration of the macrocycles in these structures is dissimilar to that reported for the Pb(II)Zn precursor, 13 in w hich the two macrocycles are bridged by two co - crystallized water molecules and the macrocycle is sort of pleated to make a roughly flat plane instead of an outwardly folding sheet as seen in complex 1 . This is likely due to the Pb(II) ion having a poor fi t in the 6 - coordinate site, causing the folding of the macrocycle. 142 Figure 3 - 3 : Drawings of X - ray crystal structure cations of complex 1 with atoms drawn as thermal ellipsoids. The orientation of both structural variants relative to each other is portrayed on the left, with a detailed figure of each variant depicted in the center and right portions. Note the top macrocycle for complex 1 is structure A and the bottom macrocycle i s structure B. Anions, solvent molecules, and hydrogens omitted for clarity. 143 Figure 3 - 4: Comparison of the different crystal structures obtained for complexes 1 and 2 compared to those previously acquired for the acceptor model complexes of 4 ([Mn 2 (L)(mcb)](PF 6 )) and 5 ([Zn 2 (L)(mcb)](PF 6 )). The same atom labeling scheme is observed throughout. The B structural variant is displayed for complex 1 (see figure 3 - 3). The N5 - M1 bonds are not depicted for the analogues of 4 and 5 as they are long enough to not be modeled as a bond by the crystallographic software. Atoms are portrayed as thermal ellipsoids. Anions, solvent molecules, and hydrogens omitted for clarity. 144 Examination of the 6 - coordinate Mn(II) sites in fo und in the X - ray structure for [Mn 2 (L)(mcb)](PF 6 ) (where (L) is a symmetric Schiff base macrocycle derived from the condensation of 2,6 - diformyl - p - cresol and the triamine) as previously reported shows an analogous coordination environment for the Mn(II) io n in the six - coordinate site of complex 1 . It is worth noting that in the complex 1 macrocycle, the aliphatic nitrogen is coordinated, albeit at a longer distance than the imine nitrogens, with the bond distance (average 2.471 Å) being a closer match for t he shorter of the two aliphatic nitrogen manganese bonds in the symmetric Mn 2 analogue (2.438 and 2.613 Å). This is significant as the symmetric Mn 2 analogue was asymmetric with one of the aliphatic nitrogens coordinating at a significantly longer distan ce. The complex 1 structure suggests that the asymmetry in the aliphatic nitrogen coordination in the Mn 2 macrocycle was caused by the sterics of the symmetric macrocycle, which are less pressing with our asymmetric macrocycle variant. Complex 2 crystalize s in the triclinic system with a P - 1 space group. The unit cell consists of a + macrocyclic cation, and a single perchlorate anion. The cation is very similar to that in complex 1 , consisting of the asymmetric Schiff base macrocycle ( (II) ions, and the bridging acetate. Inspection of the 6 - coordinate Zn(II) site in complex 2 reveals that it is very similar to one of the Zn coordination sites in the [Zn 2 (L)(mcb)] + as seen in figure 3 - 4, with the aliphatic nitrogen from the triamine having a bond distance (2.463 Å) resembling the shorter of the two zinc aliphatic nitrogen bonds in the symmetric Zn 2 macrocycle (2.317 and 2.813 Å). Figure 3 - 4 shows that the structure determined for complex 2 is a very close match for crystal structure determined for complex 1 . Comparisons of the Mn(II) ion and Zn(II) ion in the six - coordinate site of complexes 1 and 2 , as well as the five - coordinate site in both 145 complexes show that the complexes are analogous, which makes complex 2 an excellent structural model of complex 1 , as seen in the coordination site bond distances summarized in table 3 - 2. Table 3 - 2: Comparison of bond distances for X ray structures of complexes 1 , 2 , and macrocycle core analogues ([M 2 (L)(mcb)] + ) of complexes 4 , and 5 as previously reported. 4 To synthesize complex 3 , instead of sodium acetate, [Ru((CF 3 ) 2 - bpy) 2 (mcb)](PF 6 ) is substituted as the bridging carboxylate group in an analogous procedure using acetonitrile as the solvent. [Ru((CF 3 ) 2 - bpy) 2 (mcb)](PF 6 ) is synthesized from Ru((CF 3 ) 2 - bpy) 2 Cl 2 and (mcb)H while refluxing in water and methanol in the dark to drive off the chloride ions without the formation of photoactive side products. The desired product is crashed out of solution with the addition of exces s NaPF 6 . Purified [Ru((CF 3 ) 2 - bpy) 2 (mcb)](PF 6 ) is then introduced as a bridging ligand to 2+ by stirring the two together for a couple of days, and then precipitating out the product with addition of ether. We have been unable to grow X - ray qualit y crystals of complex 3 , but since it and complex 1 are derived from the same starting material, one can be confident that complex 1 is a suitable model for the independent behavior of the macrocycle in complex 3 . 146 3.3.2: Mass Spectrometry For this pro ject, we relied heavily on Electrospray Injection Mass Spectrometry (ESI - MS) as a primary characterization technique for our complexes. This was due to the lack of reliable 1 H - NMR data for our complexes containing Mn II , our inability to get crystal struc tures of complex 3 , as well as the advantages offered by ESI - MS in determining the presence of impurities in our samples consisting of other possible metals in the coordination sites of our mixed metal macrocycles in complexes 1 and 3 which would have been detrimental to our study because they would have had different photophysical behavior than the molecules we wished to study. For made as a side product in the synt impurities in the sample for complex 3 that would not have the same quenching behavior as the intended molecule, which would cause inaccuracies in the kinetic fitting that could affect the outcome of ou r study. Fortunately, ESI - MS has the ability to pick up on these otherwise undetectable impurities in our systems. So in our characterization of complexes 1 and 3 , we checked for the presence of these other compounds to make sure there were no impurities t hat could affect the outcome of our study. The ESI - MS results for complexes 1 and 2 were relatively straightforward, with the expected singly charged cationic peaks being observed for the two model systems. Unbridged bi - metallic precursors were often observed to be bridged by residual free acetate or formate ions used as a buffer in the LC injection systems attached to the ESI - MS instruments, which owes to the high affinity of these bimetallic precursors for carboxylate ions. Measurements for complex 3 on the other hand were much more complicated, as the synthetic procedure for this comp lex yields the triply charged cation in addition to three anions, in a 2:1 ratio 147 of ClO 4 - to PF 6 - . When dissolved to make the liquid ESI - MS sample in MeCN, these anions can freely interchange such that when a single anion is removed in the ESI - MS instrumen t to get a single cation signals, there is the possibility that each ion can have (ClO 4 ) 2 , (ClO 4 )(PF 6 ), or (PF 6 ) 2 as associated anions in the singly charged cations. If there is a 2:1 ratio of ClO 4 - to PF 6 - as is expected from the synthetic procedure, then the relative intensity of the [M - 2(PF 6 )] signal should be roughly half of the intensity of the other two anion combinations for the singly charged cationic signals. This is observed in the ESI - MS results in the appendix figure A3 - 1 indicating that all thr ee signals can be ascribed to complex 3 . Figure 3 - 5 : Extinction coefficient plots for complexes 1 (green -- -- -- ), 2 (teal - - - ), 3 (Blue line), 4 (black -- - -- - -- ). And 5 (red --- --- --- ). 3.3.3 Electronic Absorption Spectroscopy The UV/Vis spectra of all five complexes of interest are presented in figure 3 - 5. Complexes 1 and 2 have an absorption spectra that is fairly representative of other macrocyclic Schiff base ligands 148 similar in structure, with two absorptions correlating to - cresol regions of the macrocycle at ~220 nm (observed in methanol, but not pictured since extinction coefficients were obtained in dichloromethane) and 255 nm. These peaks are observed in previous work on similar Schiff base ch romophores 26,27 and are associated with the phenol - portions of the macrocycle as they are present in all the compounds studied. The third peak of both spectra occurs base macrocycle. This absorption has a fair degree of variability since it is corresponding to an area of + complex has the third absorption at 381 nm while the cor responding absorption occurs at 377nm + . This absorbtion feature is slightly higher in energy than the corresponding absorptions in the symmetric macrocycle, which is representative of the lower charge density associated with the azometh ine nitrogens having fewer bound carbons in the asymmetric macrocycle than in the symmetric one. The fact that the energy of the N - in complex 1 than in complex 2 is contrary to the intuition of Zn(II) being a better Lewis acid than Mn(II), which was seen for the symmetric macrocycle where the N - 2 (L)(mcb)] + was higher in energy. No explanation for this behavior is available at this time. When appended to the Ru((CF 3 ) 2 - bpy) 2 (mcb) moiety, the resulting spectral featur es due to the asymmetric macrocycle do not appreciably change, with the N - nm in the mixed metal ruthenium complex versus 376 nm in the acetate bridged model complex. Compare this to the absorption maximum at 388 nm for c omplex 4 and 391 nm for complex 5 , which show similar behavior to their mcb bridged analogues as previously reported. The phenolic - chromophore. The addition of the Ru((CF 3 ) 2 - bpy) 2 (mcb) also brings along the Ruthenium 149 polypyridyl - based electronic absorption features that are found commonly found in this class of compounds. Specifically, there is a new sharp absorption feature in the UV region at 297 nm that correspond s to the bpy - - polypyridyl fragment. These transitions are unperturbed between the mixed metal complex and our previously reported Zn 2 and Mn 2 analogous compounds. 4 Also present with the addition of the ruthenium polypyrid yl fragment are absorption features occurring between 400 and 500 nm that correspond to the electronic transitions from the ruthenium ground state to the 1 MLCT that are a defining characteristic of ruthenium polypyridyl complexes. There is also a sloping s houlder of uniform profile that extends beyond 550 nm present in the three ruthenium appended compounds of interest that is typically ascribed to the 3 MLCT spin forbidden optical transition. It is fitting that the MLCT absorption features almost perfectly mirror those of the previously reported Mn 2 (L)(mcb) analogue as we were pursuing a model that would behave as electronically similar to the Mn 2 complex with respect to the Ru - chromophore as possible without having two transition metal ions in the macrocycl e and by the electronic absorption spectroscopy it appears we have hit the mark. 3.3.4 Electrochemistry The electrochemical properties of complex 3 were examined using cyclic voltammetry and differential pulse voltammetry, the results of which are plotte d in figure 3 - 6. In complex 3 there is one readily observable irreversible oxidation at 0.69 V that correlates to the Mn II to Mn III oxidation. 150 This feature is in a similar range as that reported for the second Mn oxidation in a Mn 2 macrocycle as seen in complex 4 , as well as other similar Mn 2 macrocycles reported previously. 4,26 A Ru II /Ru III oxidation feature was not observable using our setup with platinum working electrode as described, however an analogous experiment utilizing a glassy carbon working electrode indicated a pseudo - reversible oxidation feature near 1.16 V, 28 which is assigned as a Ru II /Ru III oxidation feature by Table 3 - 3: Electrochemical data for complexes 3 , 4 , and [Ru((CF 3 ) 2 - bpy) 2 (mcbEt)](PF 6 ) 2 in CH 2 Cl 2 solution. a [Ru((CF 3 ) 2 - bpy) 2 (mcbEt)](PF 6 ) 2 data are presented as electrochemical data were unobtainable for complex 5 . Figure 3 - 6: Electrochemical data for complex 3 , with potentials plotted relative to the ferrocene/ferrocenium redox couple. 151 merit of its reasonable match with the Ruthenium oxidation potential in complex 4 as was previously reported. Two reversible reductions and one pseudo - reversible reduction were also observed for complex 3 , at potentia ls of - 1.23 V, - 1.47 V and - 1.92 V, corresponding to the three incremental bpy reductions in this system. While these are in the neighborhood of what was previously reported for complex 4 , as summarized in table 3 - 3, they are not exactly the same. These di fferences could be attributed to the difference in counter ions between complex 4 , which has only PF 6 anions, and complex 3 which has two perchlorate anions and a single PF 6 anion, but we are not certain at this time. 3.3.5 Photophysical Characterization 3 ) 2 - bpy) 2 ](ClO 4 ) 2 (PF 6 ). The presence of the ruthenium polypyridyl chromophore on the main complexes of interest ( 3 and 5 ) allows us to tap into several decades of experience when interpreting their photophysical properties. 5,29 The centerpiece of this work is the variable temperature kinetic profile of complex 3 , especially when compared to the variable temperature kinetic profile of the structural analog, complex 5 . To adequately gauge which wavelengths to probe, the steady state em ission spectra of both complexes were obtained at 10K while exciting the sample at 475 nm which for most ruthenium polypyridyl complexes is on the red edge of the 1 MLCT absorption. However, due to the electronic withdrawing effects of the trifluoromethyl g roups on the (CF 3 ) 2 - bpy ligands, the charge transfer bands are lower in energy, placing our excitation wavelength right in the middle of the 1 MLCT absorption band for both complexes. However, exciting the sample at the edge of the MLCT absorption at 500 nm had no effect on the emission profile, so 475 nm was chosen for consistency with previous results. 152 Figure 3 - 7: 10 K corrected emission spectra for complexes 3 (blue) and 5 (red). Sample was excited at 475 nm. Figure 3 - 7 shows the LT emission spectra for complexes 3 and 5 , which show a strong vibronic progression as can be expected for emission spectra obtained in rigid media. Noteworthy is the shift in emission maximum from 604nm for complex 5 , to 608 nm for co mplex 3 . Since the emissive state for this feature is localized on the (CF 3 ) 2 - bpy ligands, this implies that the ground state of the ruthenium is slightly higher in energy in this complex than for the di - zinc, which is consistent with the apparent 1 MLCT ab sorption features being slightly higher in energy for complex 5 than for complex 3 . This points to the slight differences between the emission spectra of these two complexes being related to the differences in the Lewis basicity of the two different macroc ycles, which effects the ruthenium center via the aromatic linkage provided by the (mcb) bridging ligand. A single - mode spectral fitting analysis of Claude and Meyer 30 was used to determine the value of E 00 of the low temperature emission spectra. The E 00 value of the 3 MLCT 153 was determined to be 16,550 cm - 1 for complex 5 , which will be used in the proceeding analysis of the photophysics of complex 3 . It is based on these spectra that the probe wavelengths for our time resolved emission studies were selected . On first inspection one would believe that the optimal probe wavelength would be near 610 nm for both these complexes. However, at low temperatures residual emission from both macrocyclic impurities and stabilizers from the 2 - Me - THF make probing at these shorter wavelengths impractical. We therefore picked two wavelengths that were well red of these features in 670 and 700 nm. These wavelengths are not near the emission maximum at low temperatures, but they are guaranteed to have stable emission throughou t the temperature range studied as 670 nm corresponds roughly to the room temperature emission maximum of these compounds, in agreement with the room temperature emission spectra previously reported. 4 3.3.6 Variable Temperature Emission Initially, we wis hed to probe the effects of having available ligand field excitations as a potential energy acceptor on the ground state recovery of an emissive energy donor. It was suspected that the transition metal could quench the energy donor, since this was found to be true for complex 4 , which contains a pair of spin coupled transition metal ions. However, we needed to test this hypothesis on a donor - acceptor complex analogous to complex 4 , but containing a transition metal ion without any of the complicating factor s that could be folded into the Heisenberg spin - exchanged system present in complex 4. It was for this purpose that complex 3 was created. As was the case in our previous studies, to discern the effects on the dynamics of the ruthenium polypyridyl donor, b aseline studies containing no transition metal based dynamics on the complex 154 5 structural model were also necessary. We therefore proceeded to collect variable temperature time resolved emission spectra on both complexes 3 and 5 to better understand the dy namics in these model systems before attempting to determine the cause of the dynamics in complex 4 . Kinetic Traces for each individual emission experiment, as well as background traces where the laser beam was blocked in front of the sample in an attempt to correct for scatter were obtained from the digital oscilloscope and saved as ASCII text files. These text files were then imported into the Origin data analysis software and plots of the corrected signal versus time were generated. The kinetic lifetime of the emissive state is determined by fitting the corrected kinetic data to an exponential decay function of the form: (1) Since the time resolved emission features are presumed to be due to the 3 MLCT emissive state of the Ru chrom ophore present in complexes 3 and 5 , it makes sense that there should only be one kinetic process occurring and the data should follow a mono - exponential decay model. In the case of the kinetic traces from complex 5 , a single exponential decay model was adequate for the kinetic traces at all temperatures studied. The rates of decay were determined while probing at 670 and 700 nm, and the average of those two is reported as the observed rate of decay, with the range o f values serving as the uncertainty. For complex 3 , kinetic traces were collected while probing at 670 and 700 nm, but at the lowest temperatures studied the data could not be properly fit to a monoexponential decay. These deviations from the mono - exponen tial model are consistent with the presence of a second short time component to the decay signal. To account for this fact, the kinetic traces for complex 3 were fit with a bi - exponential model, of the form: 155 (2) These bi - e xponential fits revealed that an unexpected shorter lifetime kinetic process was present in addition to the longer lifetime component, assigned to the ruthenium emission lifetime due to the similarity in observed lifetime compared to the Zn 2 analogue. Thes e two distinct decay processes were significant at low temperatures only, necessitating a bi - exponential fit of the decay traces for temperatures up through 35 K. Starting at 40 K, the magnitude of the second component to the decay was small enough to not make a significant difference between the long time component from a bi - exponential fit, or a mono - exponential fit of the decay trace. A mono - exponential model was used to fit the data starting at 40 K for the rest of the experimental temperature profile. The presence of the second exponential decay component of the observed decay traces is most likely due to an emissive impurity of additional unbound mixed metal macrocycle which results from the excess of macrocycle used in the preparation of complex 3 . W hile the impurity amount is too small to detect via elemental analysis, it could be present in high enough amounts that at the lowest temperatures the organic based emission would have an extremely high quantum yield and a long enough lifetime to be detect ed in our experiment, while at higher temperatures, the decay of the macrocycle impurity would be too fast to be detected on a nanosecond timescale. The emission of this impurity is expected to peak near between 500 and 520 nm and is visible in the low tem perature steady state emission spectra seen in figure 3 - 7, where the emission peak is much larger at 10 K for complex 3 than it is for complex 5 , explaining why it affected the data for complex 3 but not 5 . It is also much higher in intensity at 10 K than it is at 77 K, which is consistent with our hypothesis of a trace organic impurity affecting the kinetics of complex 3 . 156 Figure 3 - 8: Variable temperature time resolved emission data of complexes 3 and 5 . Red points correspond to the observed rate of decay for complex 5 . Blue points correspond to the observed rate of the decay (for the longer lived decay process when kinetic traces were fitted with a bi - exponential decay) of complex 3 . It is possible to fi t the data to an Arrhenius (complex 5 ) and a double Arrhenius (complex 3 ) equation, which are shown in black. The rates of emission decay determined from exponential fits were plotted as a function of temperature for both complex 3 and 5 , as is shown in figure 3 - 8. When observing figure 3 - 8, one can make a few general observations of how the plotted rates of decay change with temperature. Most easily observed is the fact that both the mixed metal complex and the di - zinc model both have temperature depend ent behavior. The rate decay of the mixed metal complex 3 seems to increase faster than that for the Zn 2 bearing complex 5 . For the latter, this behavior can be easily explained as a thermal population of an addition electronic state in the multiplex of st ates commonly described as the 3 MLCT as described in previously reported works by Crosby and 157 coworkers. 31 The energy barrier (E a ) for this thermally activated decay pathway can be determined by fitting the kinetic trace to an Arrhenius model of the form: (3) This activation barrier is determined to be 60 ± 5 cm - 1 higher in energy than the populated states in the 3 MLCT at 10 K. This barrier is consistent with previously reported in heteroleptic ruthenium polypyridyl complexes. 31 Th e pre - exponential factor (A) for this Arrhenius fit also provides useful information, as it can be thought of as the intrinsic rate of decay for the thermally activated state at the limit of no thermal barrier. For complex 5 , the pre - exponential factor from the Arrhenius fit is 4.8 ± 3 x10 5 s - 1 , which gives an indication of the innate rate of decay for the additional pathway in the 3 MLCT that is thermally accessible. When a simple Arrhenius model was used to fit the temperature rate profile of complex 3 , a similar result for the activation barrier is obtained, along with a larger pre - exponential factor determined by the fit. This indicates that at least one additional process is occurring in complex 3 and being folded into the kinetics of the ruthenium 3 MLCT seen in complex 5 . This is the case because the intrinsic rate of decay afforded by accessing an additional level of the 3 MLCT (the pre - exponential term) should be the same for both complex 3 and complex 5 since they both have the same ruthenium poly pyridyl fragment. The difference in pre - exponential factors indicates that there is an additional thermally activated process occurring in the mixed metal complex. However, since they exhibit the same decay rates at the lowest temperatures, this process m ust also be thermally activated. To capture the dynamics of a second thermally activated pathway, a double Arrhenius fit was required with the following form: 158 (4) Initial attempts to allow the fitting software dete rmine the parameters was fruitless. However, since we had a very good idea of the similarity of any ruthenium related thermal rate dependence between the two complexes, double Arrhenius fits were obtained where the first temperature dependent component had fixed values determined by the single Arrhenius fit of the di - zinc rate versus temperature data. Using this approach, we were able to determine that there is a second thermally activated decay pathway in the mixed metal complex. The activation barrier det ermined by this fit had errors on the order of 50% of the energy barrier value, so another way to determine the thermal barrier was needed. An alternative way to obtain the value of this thermally activated decay process is to subtract the observed rates for complex 5 from the observed rates for complex 3 . Figure 3 - 9 shows the results of this treatment, which shows a clearly thermally activated process that only grows in at higher temperatures. A fit of this data to the single Arrhenius equation yields a v alue of 84 ± 5 cm - 1 for the activation barrier. Considering the values and variance in the thermal barriers obtained for the double Arrhenius fits described earlier, an activation barrier of 80 ± 20 cm - 1 higher than the populated states at 10 K is what we can confidently report from this fitting analysis. Furthermore, inspection of the pre - exponential factor for the quenching rate (A = 1.4 ± 2 x10 5 s - 1 ) yields that the intrinsic rate of this decay pathway is slower than the rate of decay afforded by the additional pathway in the 3 MLCT, which explains why a single Arrhenius fit yielded an activation barrier that was very close to the ruthenium temperatur e dependent behavior. 159 Figure 3 - 9: Observed quenching rate (difference between observed rate of complex 3 and observed rate of complex 5 ) plotted as a function of temperature. A fit to the Arrhenius equation is shown in black corresponding to an activation energy of 84 ± 5 cm - 1 . 3.3.7 Transient Absorption Spectroscopy Figure 3 - 10: (left) Transient absorption kinetic trace for complex 1 excited at 475 nm and probed at 370 nm. (right) Transient absorption decay trace of complex 1 excited at 475 nm and probed at 490 nm. The red lines are plotted fits to a single exponential decay, which had the same kinetic lifetime within the error of the experiment. See text for details. 160 The transient absorption spectra were obtained for both complex 3 and complex 5 to assign the observed quenching in complex 3 as being caused by either electron transfer or energy transfer. Room temperature time resolved emission studies showed complex 3 having an emission lifetime of 440 ± 30 ns in the solvent mixture used for the variable temperature measurements while exciting at 475 nm. Therefore, the lifetimes of different spectral features observed via transient abs orption spectroscopy should have a similar lifetime if there are no electron transfer photoproducts. The electrochemical measurements indicate that at room temperature the reductive quenching of the 3 MLCT of the Ru chromophore is thermodynamically viable. The transient absorption spectra of complex 5 were previously reported 4 and the emissive excited state has two main transient features that were assigned with the aid of spectroelectrochemistry. 32 There is an absorption feature centered near 350 nm associa ted with the reduced bipyridine radical, and there is a bleach centered near 470 nm that corresponds to the loss of the MLCT absorption in the complex. For reductive quenching, the MLCT bleach should disappear with the same lifetime as the emission but the absorption from bpy - will persist as the negative charge will be stranded on the ligand as the Ru III will have already been reduced by the Mn II . This means the transient absorption lifetime for the bpy - radical should be longer than the observed emission lifetime. Transient absorption lifetimes were measured at 370 nm and 490 nm with the resulting kinetic traces shown in figure 3 - 7. The observed lifetimes of these transient absorption features were 390 ± 40 ns at 370 nm and 360 ± 40 ns at 490 nm. The trans ient absorption data were noisy as the experimental setup had weak probe white light intensity at the time of these experiments. This in turn gives a larger than desired uncertainty on the fits of the transient absorption data. These lifetimes are not stat istically different from the observed emission lifetime of complex 3 , which indicates that there is no sustained intramolecular electron transfer processes occurring at room 161 temperature in complex 3 . Time resolved transient absorption measurements were als o performed on complex 5 as a standard for the experiment. At the same probe wavelengths, the transient absorptions had lifetimes of 660 ± 70 ns at 370 nm and 650 ± 70 ns at 490 nm. These are not statistically different from the observed room temperature l ifetime of 730 ± 30 ns. 3.3.8 Identification of the quenching pathway in Complex 3 If one inspects the body of data on complex 3 and its various models up to this point one can deduce the following: There is the standard temperature dependent excited sta te decay for both complexes 3 and 5 and there is an additional thermally activated quenching mechanism present with an energy of 80 ± 20 cm - 1 above the ground state at 10 K. Low temperature emission studies on complex 1 show there is a low energy emissive state whose presence is attributable to the Mn II ion since the state is not seen in complex 2 , as will be discussed below. Since the only substantial difference between the Zn II and Mn II ions is the presence of excited ligand field states, one can conclude that the emissive state seen in the LT emission is the lowest energy excited ligand field state for the Mn II ion. If these ligand field states of the Mn II ion are lower in energy than the emission maximum observed for the ruthenium chromophores, which is suggested by the LT emission spectra for complex 1 as seen in figure 3 - 8, then any sort of quenching could be thermodynamically allowed. The fact that there is a thermal activation to the process implies that there is a mechanism that makes the quenching energetically uphill (by 80 cm - 1 ). Based on the room temperature transient absorption measurements, we know there is no sustained electron transfer quenching processes. The Rehm - Weller equation 33 applied to the electroc hemical data suggests that reductive quenching of the 3 MLCT emission is thermodynamically viable, with 162 - 0.96 eV. However, in optical glasses the large outer sphere reorganization energy associated with the solvent has to be added to the driving forc e for the electron transfer. 34 Most electron transfer processes have outer sphere reorganization energies in the range of 1 - 2 eV. 35 A large reorganization energy that is suddenly added to the driving force for electron transfer means that the formation of an optical glass should result in a discontinuity in the rate of emission decay of complex 3 that is drastically different from that observed for complex 5 , which is not what we observe in this case. This suggests that any electron transfer process, which includes rapid subsequent back electron transfer to the Mn center, is very unlikely to occur as the outer sphere reorganization energy is more than enough to can cel out the driving force for electron transfer in rigid media. Since there is not any significant absorption of the ligand field states of Mn II in the macrocycle of complex 1 , we can assume the same is true for complex 3 , which rules out the possibility of a Forster electron transfer mechanism as there is no donor - acceptor spectral overlap. 5 This leaves us with Dexter energy transfer as the only viable mechanism by which the 3 MLCT can be quenched in complex 3 . However, it is not enough to know that the pr esence of Mn II is causing a thermally activated energy transfer quenching pathway. We carried out LT steady state emission studies on complex 1 in the hopes of learning more about the identity of the ligand field states that could be quenching the emission from the 3 MLCT in complex 3 . 163 Emission at 5 K was collected for complex 1 and is shown in figure 3 - 8. The primary feature observed in this compound is a broad emission band centered near 500 nm that is due to the ligand - based emission of the macrocycle. This macrocycle - based emission is observed in the 4 ( 2 ) c omplex as well, which confirms the assignment of this feature, as there can be no metal - involved charge transfer states deriving from the d 10 Zn II ion. Of more interest however are the two shoulders present in the complex 1 sample that are absent from the complex 2 sample as seen in figure 3 - 11. Figure 3 - 11: Low temperature emission spectra of complex 1 (blue) and complex 2 (red). These shoulders derive from the Mn II ions, which is possible as emission from Mn II has been reported in the past for crystalline systems. 36 Ligand field emission for Mn II is typically reported 164 from the 4 A 1 state. However, the observed emission is too low in energy, with values well below the 20,000 to 25,000 cm - 1 range that is usually reported. The first shoulder is relatively sharp and has a maximum at 683 nm, while the second shoulder peak is slightly broader and less intense, centered at 725 nm. Since these emission features have to come from lower energy ligand field transitions than those re ported for 4 A 1 emission, our emission shoulders can be assigned as being derived from quartet ligand field states; either a symmetry split 4 T ligand field state, or an extreme case of vibronic progression for the emission of a single 4 T ligand field state. The coordination environment of the Mn II center is low in symmetry, owing to both the fac - N 3 O 3 coordination environment and the identities of the ligands to which the coordinating atoms are attached. The structure obtained via X - ray crystal diffraction confirms this coordination asymmetry, resulting in the Mn II center possessing at most C S symmetry . This low symmetry coordination environment cannot support the three - fold degeneracy of the 4 T 1 ligand field state, resulting in it splitting into theoretically three states, of which only two are readily observed in the emission shoulders reported herein . The shoulders are only derived from the equivalent of a single octahedral 4 T 1 ligand field state since there is no evidence of additional peaks observed outside the window reported. Splitting of the emissive 4 T 1 states has been reported in the past for l ow symmetry Mn II systems, 37 although the published splitting is of a higher magnitude. Since the 683 nm feature is sharper and more intense, the potential energy surfaces between this feature and the ground state are better nested, so the total energy diff erence between the emissive states is better estimated by the higher - energy emission shoulder. There is another case in which the lower energy shoulder is an observed emission from a separate frozen geometric configuration that is in the microcrystalline compound, in addition to the sharper emission line described above. If one presumes that in the microcrystalline lattice there were two 165 configurations present, which is entirely feasible given the two morphologies observed in the X - ray crystal structure of complex 1 , and imagines that one of these is at the absolute equilibrium geometry for the 6 A 1 ground state while the other is distorted slightly towards the 4 T equilibrium geometry on the reaction coordinate of the complex. In this case any emission from the exactly frozen 4 T would be sharp as it does not need to change geometry during the relaxation back to the ground state, while any emission from the slightly distorted geometry would be lower in energy as the 4 T state would be lower and the 6 A 1 state wo uld be higher in energy at this distorted geometry and therefore the energy difference between the two states would be lower. Also, the slight geometric difference between the two states would broaden out the emission peak as is observed in the LT emission spectra. Therefore the actual energy of the emitting ligand field excited state is significantly lower in energy than the 3 MLCT excited state energy as determined by the single mode spectral fitting analysis because the high - energy emission line from the 5 K emission on complex 1 represents an upper limit to the energy of the quartet ligand field state. As a result, the observed thermal barrier to quenching of the 3 MLCT seen in the VT Time resolved emission studies must be due to a reorganization of the Mn II ion which in the frozen medium that the sample is dissolved in manifests itself as a driving force barrier as there are no geometric degrees of freedom that can serve to reorganize the acceptor geometry in a rigid medium. Based on this assignment of th e quenching state to the 4 T 1 ligand field excited state of the Mn II ions, we can then use the information from the Arrhenius fits to determine the reorganization energy associated with this excitation since all kinetics associated with the ruthenium reorga nization are tied into the Zn 2 molecule, which is already accounted for when we subtract the Zn 2 kinetics from the mixed metal kinetics. To estimate the reorganization energy, we will depend 166 on the standard Marcus equation for electron transfer rates, 38 un der the assumption that rates for energy transfer processes are proportional to the same variables as a Dexter energy transfer is the same as two simultaneous electron transfer events: 39 This equation has similarities to the Arrhenius equation and if one assumes the components of the equation are interchangeable, one can solve for an expression that gives the activation barrier in terms of Marcus equation variables as seen below: (6) Some rearrangement of equation 2 and solving the resulting quadratic equation gives two possible values for the reorganization energy as shown in equations 7 and 8, which are determined by whether or not the magnitude of the thermodynamic driving force of the reaction is larger or smaller than the reorganization energy: (7) (8) In this case, the thermodynamic driving force for this energy transfer reaction is essentially fixed since the entropic effects are negligible for this system, resulting in two possible values for the reorganization energy. In determining which of the two values is correct, we must rely on previously reported reorganization energies for transition metal ligand field excitations. Our fitting of the variable temperature kinetic data is used in addition to the energy values from the low temperature emission results on both complex 1 and complex 5 to determine the reorganization 167 energy of the mixed metal core for the promotion of the Mn II into an excited ligand field state. Depending on which value is used from the low temperature emission of complex 1 , one obtains a reorganization energy of either 0.16 ± 0.02 eV or 0.36 ± 0.02 eV when an emission energy of 14,640 cm - 1 is used or 0.24 ± 0.02 eV or 0.48 ± 0.05 eV when an emission energy of 13,790 cm - 1 is used. Recent work in our group has found a value for the reorganization energy associated with Fe II spin - crossover of ~1.0 eV. 40 Since that transition requires the removal of two e g * electrons and the pairing of a two sets of electrons, while our suspected 6 A 1g to 4 T 1 transition only requires the removal of a single e g * electron and a single electron pairing in the t 2g orbital set, one can assume that the reorganization energy of the Mn II ligand field in our complex should be close in energy to ~0.5 eV. Based on this reasoning, of the two values determined from the parameters from the Arrhenius fit, it makes sense to as sume the reorganization energy is near the average of the two values, or in the range of 0.43 ± 0.10 eV. However, the sharp peaks of the LT emission of complex 1 indicate relatively similar geometries between the quartet and the sextet as measured. This sh ould result in smaller reorganization energy value unless there are other factors involved. To give ourselves a better idea of what is happening in this system, electronic structure calculations were performed on the ligand field states of interest and the ir results are discussed below. 3.3.10 Computational Results For the theoretical determination of reorganization energies, Optimized geometries for the lowest energy sextet, quartet, and doublet electronic state were obtained starting from the X - ray crys tal structure using unrestricted B3LYP density functional theory. The resulting optimized geometries reveal geometric distortions in both the quartet and doublet state relative to the sextet ground state of the complex, which are evident when viewing the g eometries in figure 3 - 9. 168 Figure 3 - 12: Drawing of the three UB3LYP optimized geometries of complex 1 . The top view is from the side and the bottom view is from the top looking down. The indicated non - bonding distance in the 4 T 1 geometry is highlighted as this correlates to a bond in the other two structures. The dashed lines are shown to emphasize the geometric changes as a function of the multiplicity. Table 3 - 4: Select bond distances for the UB3LYP optimized geometries of complex 1 . 169 These distortions take the form of a pinching together of the two cresol ring moieties of the macrocycle and a slight canting of the ring planes relative to each other, both of which are more pronounced in the doublet relative to the quartet. The Mn - ligand bond distances on average also shorten as the multiplicity drops, as would be expected from ligand field theory. These bond distances are summarized in table 3 - 4.This is consistent with what would be expected from ligand field theory, as lower multiplicities have less antibonding character in the metal ligand bonds. The energies of the lowest lying quartet and doublet state were evaluated at their optimized equilibrium geometries, an d at the optimized ground state (sextet) geometry, in addition to the evaluation of the sextet energy at all three optimized geometries. The results from these calculations are summarized in table 3 - 5. From these results, a qualitative picture of the relat ive ordering of the potential energies of these states can be assembled, and it is pictured in figure 3 - 13. The first noteworthy result from these calculations is that for all geometries studied, the sextet electronic state is the lowest in energy. This m eans that the magnitude of the reorganization energy is smaller than that of the free - energy difference between the sextet ground state and the quartet and doublet excited states. The second result of note in these calculations is the determination of the reorganization energy values by evaluating the energy of the sextet electronic state at the equilibrium geometry of the quartet and the doublet and subtracting the energy of the ground state sextet at its equilibrium geometry. These values are noteworthy b ecause the reorganization energy for the doublet is more than twice that for the quartet, agreeing with our assessment of greater geometric distortions in the doublet. Since the reorganization energy is smaller than the free energy difference any emission from the max at wavelengths correlating with an energy lower than that of the 170 Table 3 - 5: Table of UB3LYP energy calculation results. Thermodynamic values are correlated to labels in figure 3 - 13. Figure 3 - 13: A simple energy diagram of the B3LYP thermochemistry results. Energy difference labels match values listed in table 3 - 5. Each color and corresponding italic term state corresponds to the electronic state calculated for a particular geometry designated by the column in which the state is placed. 171 free energy diffe rence assuming the emission is from a thermalized quartet state into a non - thermalized ground state. However, emission into a non - equilibrium ground state would result in a relatively broad emission feature, which is not what is observed in this case. In order to have the relatively sharp emission features that are observed, the geometry must not change much between the emissive and ground states. Since the low temperature emission is occurring in the rigid medium of a micro - crystalline lattice, one could make the assumption that the emissive state is frozen at the ground state geometry. If this is the case, then the emission energy would include the additional energy of the destabilized quartet state in addition to the free - energy difference, as has been r eported previously for emissive compounds in rigid media. 34 Since the conformation of the molecule would be stationary in this case, the observed emission peaks would be relatively sharp in appearance. Based on the agreement of the observed emission peak s harpness to that expected for a frozen geometry, it is more likely that the observed emission peaks in complex 1 include both the free energy change and the destabilization energy of the quartet relative to the sextet. Indeed the match between the energy o f the higher energy LT emission peak for complex 1 and the calculated energy difference between the sextet and quartet states with the geometries frozen at the ground state sextet geometry is uncanny. This means that if we use the emission values for the free - energy difference when fitting the VT data, as was previously discussed, there is the potential for this energy value to already include the being unable to reorganize, which then leads to the issue of what is causing the observed thermal barrier. The variable temperature emission measurements are taken in a rigid glass, so ostensibly the core is in a similar locked ground state geometry. Sinc 172 lattice, there could be a different outer - sphere reorganization energy for the two experiments or the differences in the reorganization of the carboxylate bridges that could make up the obser ved difference in reorganization energy. If that is the case however, then the additional reorganization energy is likely the smaller of the two possible values that were determined earlier. If one uses the LT emission energy as a value for free - energy, on e could take the smaller solved value of the reorganization energy (0.16 ± 0.02 eV) as an additional reorganization process not accounted for in the destabilized LT emission. If one then adds the destabilization energy to the additional solved reorganizati on energy, this result of 0.59 eV is still plausible as a value for the reorganization energy for this process in a locked ground state geometry. There is of course the alternate scenario to be considered in the case of a rigid geometry. While the sharp em ission peaks for the LT emission of complex 1 indicate that the geometry is frozen at 5 K in a microcrystalline lattice, there is no guarantee that this is the case in the optical glass medium that the VT time resolved emission measurements are collected i n. Especially since the excited states involved require a net qualitative shrinking of the molecule, it is possible that the excited states could be accessible in their relaxed states. If that is the case, if we use the non - frozen free energy difference de rived from calculations in our equations to determine the reorganization energy, one obtains 0.53 ± 0.02 eV and 0.84 ± 0.05 eV as the possible values of the reorganization energy. The smallest of these two values is the reasonable estimate of the reorganiz ation energy as was discussed earlier, and is close to the value for the 0.49 eV reorganization energy value as was determined by the calculations. While the two scenarios discussed above operate on different assumptions and there is an inherent question as to the accuracy of using the Marcus equation to solve for additional reorganization processes, it is comforting that the two different assumptions on how the macrocyclic core could 173 behave in the VT emission spectroscopy of complex 3 still give similar v alues for the reorganization energy as the origin of the observed thermal barrier to quenching by the quartet state of the manganese in the mixed metal macrocycle found in complex 3 . As it is the case that the energetics of all the involved electronic stat es that observed experimentally are such that energy transfer should be spontaneous, as is depicted in the summary diagram seen in figure 3 - 14, this reorganization energy barrier seems a most logical explanation for the kinetics seen in complex 3 . Figur e 3 - 14: Simple energetic diagram showing relative energies of the Ru 3 MLCT states as determined experimentally and the experimentally derived energies of the emissive + ligand field states. The computationally derived value of the quartet a nd typical literature value for the 4 A 1 listed for reference. 174 It is tempting to think that perhaps the doublet could also quench the emission in a similar fashion as that which was determined for the quartet. If one plugs in the calculated reorganization energy from the lowest energy doublet state as was determined with DFT and uses the energy determined from DFT when calculating the energetic difference for the energy transfer process, one can plug the values and determine a hypothetical th ermal barrier for quenching by the doublet state. When all the values are substituted and the math evaluated, the doublet state would have a thermal barrier to quenching of approx. 1340 cm - 1 , which would have virtually no influence in the variable temperat ure quenching rate in the optical glass temperature range studied in this report. This means that while it is not spin allowed for the doublet to quench the 3 MLCT of the energy donor, it would also not be thermodynamically allowed. This study initially set out to show a spin dependence on the quenching of the 3 MLCT. However, since the high reorganization energy of the doublet state would not allow for it to participate in quenching, such a conclusion cannot be made based on this study. 3.4 Conclusion s We h ave observed the temperature dependent quenching behavior of a ruthenium polypyridyl 3 MLCT excited state by a manganese (II) containing Schiff - base macrocycle in covalently linked intramolecular donor - acceptor assemblies. This quenching process was compare d to an equivalent structural model and determined to have a thermal barrier of 80 ± 20 cm - 1 . It was determined that this quenching process is due to a Dexter energy transfer from the Ru - based 3 MLCT into the 4 T 1 ligand field state of the Mn II in the macroc ycle. Since the energy of the acceptor states in the Mn II is lower than the 3 MLCT, this thermal barrier is found to be due to a reorganization process in the mixed - metal macrocycle as both theory and experiment show that the energy difference between 175 the l owest sextet and quartet states is below the energy of the 3 MLCT in the ruthenium donor. For a variety of scenarios considered, this reorganization process was determined using a simplification of the Marcus equation into the Arrhenius equation and solving for reorganization energy. In all the cases considered above, the reorganization energy for this quenching process is determined to be on the order of 0.5 0.6 eV. While we were unable to find conclusive evidence of a spin conservation requirement in Dex ter energy transfer, this study has enabled us to gain a great deal of knowledge concerning the quenching of a Ru 3 MLCT by the ligand field excited states of a transition metal center, which will prove invaluable when considering the variable temperature q uenching behavior of complex 4 . Furthermore, this is to our knowledge the first instance of simple ligand field transitions acting as energy transfer acceptors exclusively via a Dexter energy transfer mechanism, even though it has been observed for Forster energy transfer processes. 2b - e We hope to utilize the detailed understanding of how the Mn II ion quenches the Ru chromophore in the 3 ) 2 - bpy) 2 ] 3+ complex to better interpret future studies on the [Mn 2 (L)(mcb)Ru((CF 3 ) 2 - bpy) 2 ] 3+ complex. 176 A PPENDIX 177 Appendix: Supplemental Figures Figure A3 - 1: ESI - MS results of complex 3 in dichloromethane. 178 REFERENCES 179 REFERENCES 1 (a) Balzani, V.; Bergamini, G.; Marchioni, F.; Ceroni, P. Coord. Chem. Rev. 2006 , 250 , 1254 1266. (b) Sun, S. - S.; Lees, A. J. Coord. Chem. Rev. 2002 , 230 , 171 192. (c) Ward, M. D.; Barigelletti, F. Coord. Chem. Rev. 2001 , 216 - 217 , 127 154. (d) Barbieri, A.; Ventura, B.; Ziessel, R. Coord. Chem. Rev. 2012 , 256 , 1732 1741. 2 (a) Weldon, B. T.; Wheeler, D. 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Chem. 2014 , 53 , 15 17. 183 Chapter 4: Electronic Structure Calculations of the [Mn 2 (L)(mcb)] + Exchange Coupled Dimer 4.1 Introduction 4.1.1 Background Information Previous research in our group has explored how to differentiate between electron transfer and different types of energy transfer in a well characterized series of covalently linked donor - acceptor complexes such that the mechanism of the electron and/or energy transfer can be easily determined. 1,2 Of particular interest were studies on a series of donor - acceptor systems consisting of a ruthenium polypyridyl complex covalently appended to a di - manganese Schiff - base macrocycle, 1 which includes the [Mn 2 (L)(mcb)Ru((CF 3 ) 2 - bpy) 2 ] 3+ ( 1 ) complex as seen in figure 4 - 1, where (L) is a Schiff base macrocycle, (mcb) is 4 - carboxy, - - methyl - - bipyridine, and (CF 3 ) 2 - - bistrifluoromethyl - - bipyridine. The rutheniu m polypyridyl moiety is used as an extremely well characterized chromophore which exhibits emission from a triplet metal - to - ligand charge transfer state ( 3 MLCT). 3 This emission allows the ruthenium polypyridyl to function as a kinetic handle by which the r ates of energy or electron transfer can be measured. 4 The energetics of the ligands also allow for the directed localization of the 3 MLCT either closer or in the case of complex 4 farther from the binuclear macrocycle. 1,4 The Mn II macrocycle was chosen for its extremely small ligand field absorptions to prevent the possibility of Forster energy transfer 6 while still allowing for the study of possible Dexter energy transfer or electron transfer reactivity with a transition metal dim er complex. In our previous work, we observed the quenching of the 3 MLCT in these previously studied systems and it was determined that this quenching was caused by a Dexter energy transfer mechanism. 3 184 In the previous chapter, the Schiff base macrocycle f rom complex 1 was replaced by an analogue 3 ) 2 - bpy) 2 ](ClO 4 ) 2 (PF 6 ) ( 3 ) and it was found that the 3 MLCT was quenched via a similar Dexter energy transfer mechanism by a excited liga nd field state of the Mn II ion. The rate of this quenching was relatively small for the range of temperatures studied. However, in the case of the complex 1 , preliminary results indicate the rate of quenching of the 3 MLCT by the macrocycle is much larger. 4 Figure 4 - 1 : Drawings of the systems either referred to or studied in the course of this chapter. Complexes 1 - 3 and 5 were studied previously, the results of which are referred to in this work. Complex 4 was the primary molecule studied via computation in this work. 4 .1 .2 Unanswered Questions from the MnZn C omplex From our studies on complex 3 which were supplemented with studies on complex 5 , when the Mn II ion in its ground 6 A 1 state participates in quenching, it is excited to its lowest energy excited state, which is the 4 T 1 state. If one now considers this occurring for a single Mn II ion in the Mn 2 macrocycle, the 4 T 1 state on the excited metal center can still interact with t he five unpaired spins on the other Mn II center in the binuclear cluster. It was not known initially what the nature of this spin coupling would be, as it was possible for it to be ferromagnetic or anti - ferromagnetic, large 185 or small in magnitude. Dependin g on the magnitude and nature of the spin coupling in the excited state, it was possible that the energetics of the quenching ligand field transition could have been substantially changed. It was therefore necessary to study both the ground state 6 A 1 + 6 A 1 spin between the 4 T 1 and the 6 A 1 states in the Mn 2 dimer. While our previous results were able to ascertain the mechanism of the quenching in Mn 2 dimer, there remained many questions on this system that needed to be answered. We have obtained preliminary data on the LT emission lifetime of the complex 1 at low temperatures and have determined that the emission lifetime at 10 K is less than 30 ns and on the orde r of tens of nanoseconds. This is similar to the observed room temperature emission lifetime of 1.5 ns which was also previously reported. While our data are extremely limited, and there is a lack of data on the intermediate temperature points such that we cannot tell if there is a discontinuity in the quenching rate as a function of temperature at the glass - to - fluid transition of the optical glass solvent mixture, it appears that the temperature is not having much of an effect on the emission lifetime of t he complex. It is hoped that by developing a more detailed understanding of the electronic structure of the Mn 2 acceptor, we will be able to determine the cause of the faster quenching from the Ru polypyridyl moiety where the Heisenberg spin exchange coupl ed macrocyclic core opens up a host of spin allowed electronic excited states responsible for the observed quenching of the Ru complex. 186 4. 1. 3 Objectives for Computational Study One of the key assumptions we are forced to make when relying exclusively on experimental data is that all of the energetics associated with the ligand field transition that was determined to be causing the quenching in MnZn are unchanged in the Mn 2 system. While the macrocycles are similar, there are structural differences that could cause this assumption to be incorrect. Specifically, the analysis of these systems depends on having a good estimate of the energy difference between the excited and ground ligand field states and the reorganization energy associated with populating the excited state. We were able to obtain experimental estimates of these values on the MnZn system, with the help of electronic structure theory. We wish to corroborate the strength of the MnZn model at estimating the ligand field state energy difference s and reorganization energy values for the Mn 2 system. If it is found from theory that these estimations are not accurate, we then wish to use the theoretically determined values to better understand the thermodynamics of this system, while referring to th e similar calculations in the MnZn structure to ensure the determined values are reasonable. The energy difference between the 6 A 1 and 4 T 1 ligand field states and the reorganization energy were computationally determined in C hapter 3. The resulting reorg anization energy had good agreement with the experimental determination of the reorganization energy for the ligand field excitation of the mixed metal dimer. The experimental value for the ligand field energy difference (derived from LT emission) was als o able to be explained using values derived from theory. These results provided confidence in the ability of computational studies to estimate the reorganization energy in the Mn 2 system. It was also desirable to obtain an estimate for the energetics of th e analogous transitions in the Mn 2 complex and ensure they are not significantly altered compared to the transition for the mixed metal dimer as was previously mentioned. We also want to 187 understand the electronic structure of the Mn 2 acceptor as hopefully by understanding how the spin states are altered between the ground and excited state of the energy acceptor, we can gain insight as to why the reaction proceeds so much faster in the Mn 2 than it does in the MnZn molecule. 4. 2 Experimental All computational work reported herein was performed using the Gaussian 09 7 electronic structure package. Geometry optimizations were started from the previously reported X - ray crystal structure 1 for the [Mn 2 (L)(mcb)] + ( 4 ) , which is depicted i n figure 4 - 2 and whose Cartesian coordinates were imported in a manner similar to that described in Chapter 2. Figure 4 - 2 : The reported X - ray structure of complex 4 , with the hydrogen atoms omitted for clarity and the atoms displayed as thermal ellipsoids. The atom labels from this structure were used consistently in reporting the results of our computational studies. 188 Geometries of the so called ground state spin coupled manifold (where each Mn II ion has S= 5 / 2 ) of complex 4 were optimized using the B3LYP 8 and BPW91 9 density functionals along with a 6 - 311G(d,p) basis set. 10 These functionals wer e again chosen as they were in C hapter 2 for the verification of functional independent behavior in these systems. The 6 - 311G(d,p) basis set was exclusively used as this is the required level of theory for energetic accuracy and so the optimizations were performed at the same level to assure the molecules were optimized to the proper potential energy surfaces. Also studied was an excited state spin coupling of the Mn 2 sy stem where one of the two Mn II centers has been excited to the lowest energy quartet state. The high spin (S=4) and low spin (S=1) geometries were optimized in B3LYP for this quartet excited spin coupled system as well. It was procedurally efficient to fir st optimize the high spin state for B3LYP since it was expected this would be the closest match for the X - ray structure. Then the low spin optimization for B3LYP was performed starting at the high spin optimized geometry. Finally, the BPW91 geometries were optimized using the corresponding B3LYP optimized geometry as a starting point. A similar approach was taken for the quartet excited state spin manifold optimizations, where the quartet excited high spin state (S=4) optimization was performed first starti ng from the B3LYP high spin optimized geometry for the ground state spin manifold (S=5). After this geometry was obtained, the quartet excited low spin state (S=1) was optimized from its corresponding high spin optimized geometry. The electronic structure of low spin states (S=0 and S=1) and where appropriate high spin states (S=4) was modeled with broken symmetry wavefunctions, 11 which were generated with the fragment based gue ss methodology as described in the appendix of C hapter 1. Guesses for these brok en symmetry electronic states were generated before optimizations were performed, and as 189 recommended form C hapter 1, the spin density on the metal centers was tracked for all broken symmetry wavefunctions to ensure a proper low spin state was obtained. For each optimized geometry, a high spin and low spin energy calculation was performed as is necessary for the determination of the electronic coupling constants via the Broken Symmetry method as implemented by Yamaguchi and coworkers. 12 To investigate the possibility of a functional dependence on the calculation of the coupling constants, these energy calculations were performed in both BPW91 and B3LYP for the low spin and high spin optimized [Mn 2 (L)(mcb)] + molecules optimized in B3LYP and BPW91. This mean s that a total of four optimized geometries resulted in the need for sixteen energy calculations. All optimized geometries were checked for convergence to a global minimum by performing a frequency calculation on the resulting geometry and confirming a lac k of negative frequencies. In addition to the geometry optimizations on the full [Mn 2 (L)(mcb)] + complex, a geometry optimization on the high spin state using B3LYP/6 - 311G(d,p) was performed on a simplified version of the complex based on the full optimized geometry where the mcb was replaced with a carboxypyridine bridge to see if the mcb was impart ing asymmetry to the macrocyclic core. The optimized simple geometry and the optimized excited state coupling manifolds were studied only with B3LYP/6 - 311G(d,p) as this was determined to be the best energetic match to experiment for the sake of modeling t he spin exchange mechanism before these other calculations were attempted. Again, these optimized geometries required two energy calculations to be performed to determine the spin coupling constants. For the determination of the ligand field energy differe nces between the sextet and the quartet spin manifolds, the difference in calculated B3LYP/6 - 311G(d,p) energies from the already available 190 optimized S=4 ground state of the excited manifold and the optimized singlet ground state of the basal spin manifold was determined. This was subsequently corrected by using information available from the calculations mentioned above and described in subsequent sections to yield the energy difference between the lowest energy excited state of the quartet excited state sp in manifold and the ground state of the molecule. The calculation of the reorganization energy associated with this process was determined by performing an additional electronic structure calculation of the ground S=0 state of the Mn 2 system had its energy evaluated at the optimized quartet excited S=4 geometry. This was done with B3LYP since again it had the best energetic accuracy of the functionals used in this study. 4. 3 Results and Discussion 4.3.1 Geometry Optimization Results The optimized geometrie s of the X - ray crystal structures were obtained for both the S=0 and S=5 states of the ground state spin coupling manifold with both BPW91 and B3LYP density functionals, the results of which are summarized for select bond distances and compared to the X - ra y structure values in table 4 - 1. As was found previously in C hapters 2 and 3, the theoretically determined bond distances were in all cases longer than those found in the X - ray crystal structure, with the exception of the Mn1 - N5 and Mn2 - O3 bond distances. These longer bonds are a common occurrence when comparing geometries determined via X - ray diffraction with geometries obtained via electronic structure calculations. It is not directly known why the Mn1 - N5 bond and Mn2 - O3 distances are longer in the X - ra y structures, but since in all the optimizations so far mentioned these bond distances are shortened, it is presumed that these 191 bonds are lengthened in the crystal structure due to intermolecular forces present in the crystal lattice that are not present a nd accounted for in our computational modeling of the system. It is possible that these forces are related to a pressing or torqueing down of the bipyridine ligand which is pivoting around O4 and sterically interacting with the methyl group on N5, causing the observed lengthening of the two bond distances. When comparing the high and low spin geometries obtained with B3LYP, it is generally observable that the metal oxygen bond distances associated with bridging the two metal centers together are slightly shorter in the low spin geometries than they are in th e high spin geometries. It is also the case that the metal nitrogen bonds associated with the diethylenetriamine portion of the macrocycle are either slightly longer or unchanged between the high spin and low spin optimized geometries. While the trends in the Mn - O bond distances were consistent between B3LYP and BPW91, the behavior of the Mn - N bond distances was not consistent with the B3LYP Table 4 - 1: Selected bond distances and angles for the optimized geometries of complex 4 compared to the X - ray crystal structure. 192 optimized geometries. Since all of these geometries were confirmed to converge to global minima via a lack of negativ e frequencies, these geometries should be rather accurate. Therefore, it is unclear why the behavior of these bonds is less uniform when transitioning between high and low spin states. When generally comparing the performance of the different functionals in matching the X - ray crystal structure, it was surprising to observe that for a majority of the bonds investigated, the both functionals obtained bond distances within the experimental error of the X - ray structure. Furthermore, it appears that there is no systematic outperformance of one functional over the other, with B3LYP being closer to experiment for some values, and BPW91 being closer to experiment for other values. It is significant that when low spin and high spin bond distances are averaged, there were more B3LYP calculated Mn - O bond distances that were closer to the X - ray structure values than there were BPW91 calculated Mn - O bond distances closer to the X - ray structure values. Since it is the Mn - O bonds that are responsible for the spin coupling interaction between the two metal centers, it can be said that B3LYP is ever so slightly better than BPW91 for the purposes of modeling the geometries of these systems. Angles involving the bridging oxygens and the Mn atoms were also tracked for changes ac ross the geometries studied. In general the Mn1 - O - Mn2 bond angles were larger in the optimized geometries than they were in the X - ray structure, and the O1 - Mn - O2 bond angles were smaller in the optimized geometries than in the X - ray structures. As for the differences between functionals, BPW91 usually had the larger deviations from X - ray structure angles, with the B3LYP values being intermediate to the X - ray structures and the BPW91 bond angles. The optimized geometries showed bond angles near 90 degrees fo r O1 - Mn1 - O4 and O2 - Mn2 - O3, which are smaller than the bond angles for O1 - Mn2 - O3 and O2 - Mn1 - O4, which had values near 99 and 97 degrees 193 respectively. These sets of bond angles show similarity via a rotation of the molecule around a pseudo - C 2 rotation axis c entered between the oxygens of the bridging phenoxy groups and bisecting the carboxylate bridge. The differences in the values of the O1 - Mn2 - O3 and O2 - Mn1 - O4 angles are likely due to the asymmetry imposed by the bipyridine bridge as has been discussed earl ier. These values contrast with the X - ray structure where Mn1 shows large variance between the 90 degree O1 - Mn1 - O4 and 100 degree O2 - Mn1 - O4 angles, but the corresponding O2 - Mn2 - O3 and O1 - Mn2 - O3 angles are the same within the error of experiment with a valu e near 93 degrees. It appears that the optimized geometries prioritize the interaction of O1 with Mn1 and O2 with Mn2, which is reflected by the more square angles even though the bond distances are not that different from the Mn1 - O2 and Mn2 - O1 bond distan ces. When comparing bond angles from the low spin and high spin optimized geometries, for both B3LYP and BPW91 the Mn1 - O - Mn2 bond angles were larger for the high spin state, and the O1 - Mn1 - O4, O2 - Mn1 - O4, O1 - Mn2 - O3, and O2 - Mn2 - O3 bond angles were smaller in the high spin state. The O1 - Mn - O2 bond angles did not really change much between high and low spin states. It is assumed that these bond angle changes between low and high spin state must destabilize the spin interaction between the Mn 2+ ions as the low s pin state is the ground state of these molecules. Besides bond angles, other useful structural parameters were able to help determine morphological changes in the molecules. The easy to identify parameters were the Mn1···Mn2 intermetallic distance and the O1···O2 interatomic distances in the optimized geometries. The intermetallic bond distance is helpful because it gives an easy way to track the overall change in the shape of the Mn1 - O1 - Mn2 - O2 core, while the O1···O2 interatomic distance gives a superb ha ndle for how folded the macrocycle is since the only way the distance between the two oxygens can change is by folding the phenoxide portions of the macrocycle closer together. 194 In the optimized ground state spin coupling manifold geometries, we can see th e intermetallic bond distances are longer in B3LYP than for the X - ray structures, and even longer in BPW91. This is consistent with the closing of the O1 - Mn - O2 bond angles that causes the core to elongate along the Mn1···Mn2 axis. The O1···O2 interatomic d istance shows the opposite trend, with the macrocycle getting more folded as one goes from the X - ray structure to B3LYP to BPW91 optimized geometries. Since there seems to be a correlation between the two interatomic distances changing, it may be the case that the folding together of the macrocycle portions forces the other angles to change as has been discussed, but it is not certain since both distances increase slightly when comparing low spin and high spin optimized geometries. The optimized geometries of the quartet excited spin manifold had several key differences when compared to the X - ray structures and the optimized ground state spin manifold optimized geometries. When these structures were optimized, it is important to note that Mn2 was the Mn cent er which was designated to be in the lowest quartet excited state, so we would expect to see larger distortions in the bond distances associated with Mn2 when compared to those for Mn1. This notion is certainly consistent with what we observe for the Mn - N bonds in these optimized geometries. As for the deviations in the Mn - O bond distances, when averaged the deviations for Mn - O bond distances were larger for Mn2 than for Mn1. However, it is noteworthy that the Mn1 - O2 bond distance is much longer than the X - ray structure while the Mn2 - O2 is shorter than the X - ray structure. This may have been due to the contraction of the Mn2 - O bond distances as all of the Mn2 - O bond distances were shorter than the X - ray structure and optimized ground state spin manifold geom etries. In fact, with the exception of the Mn2 - N2 bond distance, all of the bond distances associated with the Mn2 ion were shortened compared to the X - ray structure and optimized geometries of the 195 ground state spin manifold. This behavior is consistent wi th what one would expect from ligand field theory as the lowest energy quartet state involves a pairing of an electron from the e g * orbital into a t 2g orbital, which results in less occupation of the antibonding e g orbital set and a subsequent shortening o f bond distances. As for why the Mn2 - N2 bond distance is lengthened, the best hypothesis available at this time is that is a steric consequence of the other bond distances being shortened. The differences between high and low spin optimized geometries in the quartet exited spin manifold were extremely small, with no bond distances changing more than 0.002 Å. These changes were not really consistent between high and low spin states either, so there is really not much that can be inferred by comparing the bo nd distances of these high and low spin optimized geometries. Inspection of the bond angles in the quartet excited spin coupling manifold revealed some interesting changes relative to the ground state spin coupled manifold geometries optimized with B3LYP. For one, the Mn1 - O - Mn2 bond angles were more obtuse than their equivalents in the ground state manifold, which could be due to the shifting of the Mn - O(phenoxy) bond distances discussed above. As for the O1 - Mn - O2 bonds, there is a decrease in the value of the O1 - Mn1 - O2 bond angle and an increase in the O1 - Mn2 - O2 bond angle relative to the ground state spin manifold optimized B3LYP geometries. These changes can be interpreted as an increase in the interaction of the bridging oxygens as a consequence of the s hortening bond distances, which opens up the O1 - Mn2 - O2 bond. The average bond angles for O(phenoxy) - M - O(carboxy) also decrease towards 90 degrees in the quartet excited spin coupling manifold geometry relative to their values in the ground state spin manif old B3LYP optimized geometries. Again, this is likely due to the Mn - 196 O(carboxy) bond distances getting shorter for both Mn atoms and thus the angles getting more square due to this increased interaction. There were few significant changes in the bond angle s that were tracked when comparing the low and high spin optimized geometries in the quartet excited spin manifold, with no change being larger than 0.2 degrees. The Mn1 - O2 - Mn2 bond angle was larger for the spin optimized geometry but the Mn1 - O1 - Mn2 bond a ngle was unchanged between the low spin and high spin geometries. The only other angle variations are slight changes with the O(phenoxy) - Mn - O(carboxy) oxygen angles, but they do not appear to be systematic, with O1 - Mn1 - O4 and O1 - Mn2 - O3 appearing to decreas e and O2 - Mn2 - O3 increasing between low spin and high spin optimized geometries. Indeed, the overall shape of the complex appears to be conserved between the low spin and high spin optimized quartet excited spin manifold geometries as the Mn1···Mn2 and O1·· ·O2 interatomic distances are seemingly unchanged between the high spin and low spin forms. When comparing the interatomic distances for O1···O2 and Mn1···Mn2 between the quartet excited spin coupled manifold geometries and the ground state spin coupled m anifold optimized geometries for B3LYP, one can see that there are significant deviations between the two sets of geometries. Specifically, the Mn1 - O1 - Mn2 - O2 core is actually less elongated than in the ground state spin coupled manifold, while the macrocyc le is more folded as seen in the reduced O1···O2 interatomic distance in the quartet excited spin manifold optimized geometries. The reason for this likely resides in the shorter Mn - O bond distances which have the overall effect of contracting the core rel ative to the ground state spin manifold geometries. 197 4.3.2 Coupling Constant Determination Coupling constants were determined using the Yamaguchi method 12 which utilized the electronic energy and spin expectation values derived from the low spin and high spin calculated wavefunction at each geometry studied. In this way, the coupling constants for the ground state spin coupled manifold at the X - ray crystal structure geometry and all of the optimized geometries were obtained using both B3LYP and BPW91 wavefunctions, with the relevant computationally derived parameters and the resulting coupling constants recorded in table 4 - 2. For both functionals at all geometries, the Yamaguchi method in concert with the appropriate high spin and broken symmetry low spin wavefunctions correctly predicted the weakly antiferromagnetic coupling present in the di - manganese macrocyclic core, as was previously determined via VT magnetic susceptibility measurements to be approximately 6 cm - 1 . 1,13 Furthermore, this method of calculating coupling constants was extremely accurate even though the energy differences between high and low spin states h ave extremely small values. This also resulted in excellent consistency, as the coupling constants were within 2 cm - 1 for B3LYP at all Table 4 - 2: Relevant data and t he coupling constants determined with the data for the optimized geometries of the ground state spin manifold. This data was obtained from low and high spin wavefunctions studied with UBPW91 and UB3LYP functionals in conjunction with a 6 - 311G(d,p) basis se t. 198 geometries and within 3 cm - 1 for the BPW91 determined values. When comparing the B3LYP and BPW91 coupling constants, the BPW91 values are substantially larger than the B 3LYP values as was observed in C hapter 2 for the Fe 2 complexes. This propensity to overestimate antiferromagnetic coupling constants again is likely due to the qualities of the pure GGA functional to over - st abilize singlet states 14 and the increased metallic character of the orbitals responsible for spin coupling. Theoretically determined coupling constants on Mn 2 systems have been reported in the past, and it been observed that hybrid functionals such as B3L YP give adequate estimates of the coupling constant. 15,22 This was the case in our B3LYP calculated coupling constants as the calculated constants were extremely close to the experimental value at all geometries; even the simplified Mn 2 optimized geometry . As the simplified molecule showed no discernable difference in coupling value, it was determined that further analysis for this system was unnecessary. When comparing the low spin and high spin optimized geometries for both functionals studied, we again see the trend of the low spin optimized geometries having slightly larger coupling constants when evaluated with the same functional. This is again hypothesized to be due to the shorter bond distances between the Mn II and bridging oxygen atoms in the macr ocyclic core in the low spin optimized geometries. The deviation between high and low spin optimized geometry values was higher for coupling constants evaluated with the BPW91 functional, but this was exaggerated for geometries optimized in BPW91 in coupli ng constants calculated in both functionals suggesting that this is due to the larger variance in the bond distances for the BPW91 functional optimized geometries. Quartet excited spin manifold calculated coupling constants were evaluated on the appropriat e B3LYP optimized high and low spin states with values derived from the B3LYP energy calculations and are reported in table 4 - 3. 199 The resulting coupling constants were about half as large and ferromagnetic, with the high energy state being lower in energy than the low spin state. The calculated coupling constant was smaller for the low spin optimized geometry, which is consistent wit h the notion of this state being ferromagnetic, as the appropriately coupled ground state should be lowest in energy. The explanation for why the coupling is ferromagnetic in nature is has much to do with the changed nature of the spin unpaired electrons in the transition metal centers. Specifically, now that there is an entirely empty d - orbital in one of the Mn II centers which is in its lowest energy quartet state ( 4 T 1 state) there is an enhanced spin coupling pathway where electrons can freely go from one metal to the other without flipping spin. This results in an enhanced ferromagnetic coupling between the metal centers, yielding an overall ferromagnetic interaction. 15,16 There is literature precedence for this type of excited quartet manifold ferromagnetic coupling which was reported by Gamelin and coworkers. 15 They too did broken symmetry calculations to determine the coupling of a Mn II Mn II spin coupled excited sta te. Their results were similar to ours, with the excited state being weakly ferromagnetically coupled. This is encouraging as it validated our methodology used to obtain information on these excited states. Table 4 - 3: Relevant data and the coupling constants determined for the optimized geometries of the 6 A 1 4 T 1 excited state sp in manifold. These data were obtained from low and high spin UB3LYP/6 - 311G(d,p) wavefunctions. 200 4.3.3 Coupling Pathway Analysis As was previousl y done for the Fe 2 (OH) systems discussed in C hapter 2, it was thought to be beneficial to look at the molecular orbital mechanisms of spin exchange 17 as they could provide possible insight both into the electronic structure of the Mn 2 acceptor complex in i ts ground and excited state, as well as possibly provide insight as to which coupling mechanisms could interact via the mcb bridge with the ruthenium portion of the donor - acceptor complex. However, there were some unique challenges in the interpretation of the coupling pathways in these systems that were not present in the Fe 2 (OH) dimers previously analyzed with these techniques. The first challenge was the identification of a suitable Cartesian axis system that could be used to identify the type of d - orbitals on each of the metal centers. Remarkably, this was difficult since the coordination sites of the Mn II ions were only vaguely similar by a pseudo - C 2 rotation, as the presence of the mcb bridge makes the molecule asymmetric overall. Since the strongest interaction between the Mn centers is mediated by the presence of the phenoxide bridging units of the macrocycle, it is not illogical for the axes to be aligned with them, as was the case of the axes of Figure 4 - 3: The Cartesian axis system used for the assignment of d - orbital nature of the NMOs used to study the coupling pathw ays of the system. The y - axis on each Mn 2+ ion is oriented perpendicular to the plane of the paper along the metal - carboxylate oxygen bonds. 201 the Fe centers lining up with the hydr oxo brid ge in the systems discussed in C hapter 2. 1 8 With this idea in mind, the axes were established as shown in f igure 4 - 3. The problems with this axis systems were encountered because the morphologies of the d - orbitals were not extremely clear cut when using this system to assign d - orbital labels. While the axis system we have portrayed here is acceptable for the B3LYP NMO morphologies, it has deficiencies in that the d - orbitals appeared in certain cases distorted such that there was not a rigid adheren ce to the axes. This is most notable for the d xy and d x 2 - y 2 orbitals, which look nearly superimposable, even though ideally they would be more easily differentiated. This means that the establishment of the axes is much more open to interpretation, with th e axes ultimately being decided by the idea that they should be oriented toward the phenoxide bridges and the identification of a few easily distinguishable orbitals such as the d z 2 orbital. However, this axis system did not match well to the symmetric Ha y - Hoffman 17 ,18 type orbitals that we were also interested in studying in C hapter 2 . Since it was suspected that the axes would not be symmetric between the two metal centers based on the asymmetry in the molecule, the Hay - Hoffman method was not likely to p rovide easily interpretable results in any case, so it was decided that the NMO analysis 1 7a ,19 would be the focus when studying this system. Since we saw better and more consistent results in optimized geometries for the Fe 2 (OH) system from C hapter 2 when compared to results from the X - ray structures, it was these that we focused on for this study. The established axis system was then used to make Natural Magnetic Orbital assignments for the broken symmetry orbitals that were obtained with B3LYP on the B3LY P low and high spin optimized geometries. These NMOs are plotted in figure 4 - 4. It was fortunate that we were able to obtain good looking NMOs with a high degree of metal character using B3LYP broken symmetry orbitals on these optimized geometries contain ing the 202 full mcb ligand, as it made the determination of the orbitals easier than it otherwise would have been. What was noteworthy about these NMOs was that most of the orbitals had little interaction with the mcb bridging ligand apart from the coordinati ng carboxylate oxygen that was coordinating to the metal of interest. The only NMOs with significant mcb character were those for the d yz orbitals, which had electron density on most of the mcb bridge. The implications of this are that any coupling pathway s that depend on the d yz NMOs could be directly influenced by a 3 MLCT located on the mcb ligand in the full donor - acceptor complex. The alpha - beta overlap values were calculated with the MultiWfn program 20 for the low and high spin optimized geometries of the quartet excited spin manifold using the NMOs generated with the B3LYP density functional. The resulting overlap values are presented in table 4 - 4. These overlaps were analyzed to determine the greatest contributing pathways to the coupling the Mn 2 mac rocycle. As would be expected, there were many significant contributions to the spin coupling from the so called local symmetry asymmetric orbital pathways, where a d - orbital on one Mn II center interacted with a different type of d - orbital on the other Mn II center, since the coordinate axis system was not symmetric between the two metal centers. However, what was unexpected was the quantity of large overlaps compared to those found in the Fe 2 OH system in C hapter 2. In this system there are many more significantly overlapping pathways for spin coupling, which is likely due to the unsquare nature of the angles in the Mn1 - O1 - Mn2 - O2 macrocyclic core. Even the so called symmetric coupling pathways were large as a result o f this distorted nature of the core. 203 Figure 4 - 4: Plots of the NMOs of complex 4 as determined from the low spin B3LYP/6 - 311G(d,p) wavefunction for the geometry optimized under the same conditions. These surfaces are plotted with a 0.04 isovalue from a top down perspective with the majority of the bridging mcb ligand and associated surfaces clipped for clarity. The assigned d - character of each NMO is provided in the top row of the table . 204 Table 4 - 4: Calculated alpha - beta overlap integral absolute values for the NMOs of complex 4 , as seen in figure 4 - 4. All 25 possible overlaps between NMOs are enumerated, with the resulting overlap values ranked in descending order for the symmetric and asymmetric coupling pathways. When comparing the overlap values between the high and low spin optimized geometries, there are not any drastic differences observed between the high and low spin states, which is consistent with the small devi ation we observed for the bond distances between these optimized geometries. There are many pathways that increase when the geometry goes from the low to high spin state, 205 and there are just as many pathways with significant overlaps that decrease over the same change in geometry. It is possible to think of the former pathways as ferromagnetically coupled because they are enhanced as the geometry goes from low to high spin and the latter pathways are antiferromagnetic because their overlaps decrease between the low and high spin states. This could mean that there is a virtual tug - o - war between ferromagnetic and antiferromagnetic coupling pathways in the macrocyclic core. It is significant that the overlaps of the antiferromagnetic pathways have higher average values than the ferromagnetic pathways, which suggests that the molecule is overall antiferromagnetic in the ground state because these interactions slightly win out over the ferromagnetic pathways. It was of interest in this study to look for coupling pathways that involved electron density on the mcb bridging ligand, as this ligand is thought to be excitable in the donor - acceptor complex. The only NMOs that had significant mcb ligand character were those associated with the d yz metal based orbitals, as can be seen in from figure 4 - 4 and also seen in figure 4 - 5. It was thus found that only in the symmetric coupling pathway of d yz - d yz was the mcb ligand able to possibly influence the spin coupling of the system. This makes se nse, as the overlap depends on similar ligand character between the NMOs, so only the d yz symmetric pathway had the same ligand character for both metals, as was seen in figures 4 - 4 and 4 - 5. This means that while an MLCT state located on the bridging mcb l igand could have considerable influence, it would not necessarily greatly interfere in the ground state coupling pathways of the macrocycle acceptor, especially since the electron density responsible for the large overlap value of the d yz - d yz spin coupli ng pathway is located mostly on the mcb, and it is possible that it does not actually participate in the spin coupling of the metal centers to the degree suggested by the orbital overlap value. The fact that spin coupling value on our simplified geometry w as 206 identical to that obtained for the equivalent optimized geometry of complex 4 suggests that any transient electronic changes to the mcb would have a minimal effect since the calculated coupling constant does not change despite the modification of the br idging carboxylate ligand. Figure 4 - 5: A side by side comparison of the NMO surfaces corresponding to the d yz and d x 2 - y 2 4 . The d yz orbitals possess the only significant electron density on the mcb ligand, with the NMOs containing the next highest amount corresponding to d x 2 - y 2 . These two surfaces are plotted to show that only the d yz NMOs would have significant overlap mediated throu gh the mcb ligand. Surfaces are plotted with an isovalue of 0.04. An analysis of the coupling pathways in the quartet excited spin manifold was attempted to understand what changes caused a ferromagnetic excited state. However, the broken symmetry orbit als for triplet state that corresponds to the low spin state of this excited spin system did not yield satisfactory NMOs that could be used for the orbital overlap analysis of the coupling pathways. It was noteworthy however, that the unpaired alpha orbita ls that did not have equivalent occupied beta orbitals corresponded to d xy located on Mn2 and d x 2 - y 2 on Mn1. The overlap of this 207 pathway would by definition be zero since they are both alpha orbitals, and while this is a significant coupling pathway in the ground state, since it has a lower overlap at the low spin geometry, it seems that it may be a ferromagnetic pathway for the NMO analysis. It may be the case that since these electrons no longer have anti - symmetric spins, that they can still interact in a spin coupling interaction in the absence of orbital overlap and in that case, it makes sense that this would be a ferromagnetic interaction. However, as there were no appropriate metal rich orbitals with the exception of the two aforementioned orbitals, a ny additional analysis of coupling pathways in the quartet excited spin manifold is not available at this time. 4. 3 .4 Energetics of the Mn 2 Acceptor System As was previously mentioned in C hapter 3, DFT can be used to understand the energetics of the ligand field excitation of the Mn II to the 4 T 1 state that is responsible of the Ru 3 MLCT in complex 3 . It seems logical that any excited state in the Mn 2 complex that is analogous to the 6 A 1 to 4 T 1 transitio n in the MnZn should also be responsible for the quenching observed in complex 1 , as there are states that are derived from 6 A 1 to 4 T 1 transitions present in the spin coupled dimer. Therefore, the first step was to determine equivalent ligand field excitat ion energy in complex 4 and compare to the value calculated for complex 5 . The first challenge was to determine what comprised the analogous ligand field excitation in the Mn 2 spin coupled system. At the onset it is assumed that quenching will only provid e energy to excite on of the Mn II centers, but not both, as there is insufficient energy in the 3 MLCT for a double excitation event, allowing us to focus on a single excitation. When a single Mn II ion is promoted to its lowest energy ligand field excited state, the resulting 4 T 1 state on one metal center can still 208 interact with the five unpaired spins on the other Mn II ion in the binuclear cluster. It was not known initially what the nature of this spin coupling would be, as it was possible for it to be f erromagnetic or anti - ferromagnetic but determining this allows the identification of the lowest energy excited state derived from the excitation to a quartet ligand field state. Based on the previously discussed results on the X - ray structure and the optim ized geometries, it was determined that this lowest energy excited state corresponds to the high spin S=4 state of the excited spin manifold. If we take the difference between the calculated electronic energy of that S=4 state at its equilibrium geometry a nd the calculated S=0 optimized low spin state that is the ground state of the molecule we can determine the equivalent ligand field energy differences for the sextet to quartet transition in the Mn 2 system. This value was determined to be 1.23 eV. It sho uld be noted that at this level of significance, the difference in energy between the broken 0.002eV), but this difference is 19 cm - 1 , which is significant as the ground state spin coupling constant for this system is on average 6.8 cm - 1 . This correction is necessary because the spin contamination of the calculated low spin states inadvertently increases the energy of the low spin state by mixing in higher multiplicity spin state character into the low spin state, which increases the calculated energy in anti - ferromagnetic coupled systems. This spin contamination is accounted for in the Yamaguchi method 12 used to determine the calculated coupling constants. The calculated high spin states on the other hand have almost no spin contamination, as at least in the ground state spin manifold the high spin state can be described as a single determinant wave function with all the spins parallel. So, to adjust the cal culated low spin energy to be closer to the true value, the energy of the high spin state at its optimized geometry was used as a set point, and 15 J was subtracted from that energy as it is the case that the total energy between low and high spin states 209 f or two S= 5 / 2 centers is 15 J . The J value used for this determination was the average of that obtained at the low and high spin optimized geometries. The resulting energy was 19 cm - 1 lower than the energy of the optimized broken symmetry state. Using the e nergy expression for spin coupled states described in C hapter 1 (equation 1.2) and the average ground and excited state B3LYP coupling constants from optimized geometries, one can then use the previously determined values to plot out the all of the energet ic states for these spin manifolds. The resulting plot is portrayed in figure 4 - 6. Using similar concepts one can also determine what the energy difference between the spin barycenters in the absence of the spin coupling interaction would be. By using the equation for the energy of spin coupled states and the calculated ground state and excited state J values that were discussed in the previous section, one can determine that the energy difference between the barycenters would be 9850 cm - 1 . This means that the energy difference between the lowest energy states of the ground and excited state spin manifolds is actually larger by ~55 cm - 1 than the ligand field transition would be in the absence of spin coupling as the large stabilization of the ground state b y the spin exchange interaction (59.7 cm - 1 ) and the smaller stabilization of the S=4 state of the quartet excited spin manifold (6.6 cm - 1 ) have the net effect of making the ligand field state higher in energy for the spin coupled complexes that the transit ion would be for their hypothetical spin barycenters. This means that the lowest energy state associated with the sextet to quartet transition in one of the Mn II ions in the Mn 2 (~9900 cm - 1 ) is significantly lower in energy than the 4 T 1 state relative to the 6 A 1 ground sta te of the MnZn macrocycle (~11,1 00 cm - 1 ). To be specific, this makes energy difference between the excited ligand field state and the ground state about 1, 2 00 cm - 1 lower in 210 Figure 4 - 6: An energetic diagram depicting the relative energetic positioning of the ground and excited state spin manifolds relative to the S=0 ground state in complex 4 . The solid double ended arrow indicates the calculated energy difference between the optimized ground states of the 6 A 1 6 A 1 and 6 A 1 4 T 1 spin manifolds. The dashed single ended arrows depict the eight spin allowed energetic transitions between the 6 A 1 6 A 1 and 6 A 1 4 T 1 spin manifolds that are presumed to be responsible of the quenching of the 3 MLCT in complex 1 . See text for details. 211 energy than the analogous quantity in the MnZn. Given that we have an approximately 80 cm - 1 thermal barrier to quenching in the mixed metal system, this lower ing of the ligand field excited state should potentially remove the thermal barrier to this quenching pathway in the Mn 2 donor acceptor assembly. However, as was discussed in C hapter 3, the thermalized ligand field excited states of the MnZn were already lower in energy than the emissive 3 MLCT of the Ru polypyridyl chromophore. The cause of the thermal barrier was determined to be due to a reorganization energy associated with the quenching process, 21 composed of the reorganization energy theoretically determined for the sextet to quartet ligand field transition and an additional reorganization term that was found from fitting the quenching rate as a function of temperature. It is reasonable to assume that this additional reorganization is constant between the MnZn and Mn 2 systems, as the two systems are geometrically similar and the nature of the excited states is involved in energy transfer are analogous. Therefore, by comparing the sums of the reorganization energy and thermalized energy differences between the analogous sextet to quartet ligand field transitions, we should be able to see if the thermal barrier to quenching is in fact removed in the Mn 2 donor - acceptor assembly. The reorga nization energy of the Mn 2 acceptor for the transition to the quartet ligand field excited state was calculated by obtaining the energy of the antiferromagnetic ground state at its optimized geometry using broken symmetry DFT wavefunctions and obtaining th e energy of the same electronic state at the optimized geometry of the quartet excited spin manifold high spin state. The difference between these energies corresponds to the reorganization energy, which was found to be on the order of 0.60 eV. This value was of a similar magnitude to the reorganization energy of the sextet to quartet ligand field transition in the mixed metal macrocycle of 0.49 eV. It is however 212 larger than that calculated for the equivalent transition in the mixed metal dimer. These and the proceeding results compared to the analogous results for complex 5 are plotted in figure 4 - 7. While the spin contamination of the broken symmetry states causes the exact energy of the low spin states to be offset from the actual singlet state, these broken symmetry states still represent the best approximation of the singlet wavefunction we have available wi thout resorting to multi - reference methods. 11 This means that for our purposes, the optimized geometries obtained with the Figure 4 - 7: A depiction of the calculated thermodynamic quantities for complex 4 (left) and complex 5 (right). The two positions on the x axis depict the optimized geometries of the indicated states (ground on left, ligand field excited on right) while green states show relative energies of the ground state (S=0) wavefunctions at the indicated geometry and red sta tes are the excited state wavefunction (S=4) evaluated at the indicated geometry. FC indicates the Franck - Condon excitation energy and DE indicates the energy difference between the FC energy and the thermalized energy of the excited state. 213 broken symmetry wavefunctions were assumed to be equal to the actual singlet geometries for the sake of evaluating reorganization ene rgies. It should also be noted that the systems used to determine the reorganization energies in the Mn 2 and MnZn systems were not perfectly analogous; in that the Mn 2 system was modeled with complex 4 which has a mcb ligand while the mixed metal system wa s modeled using complex 5 , with only an acetate bridging ligand. However, it does not seem likely that these differences would contribute greatly to the changes in the reorganization energy of the Mn II centers upon ligand field excitation, so for the sake of simplicity, we will assume the difference is negligible. The calculated sum of the energy difference and reorganization energy associated with a single 6 A 1 to 4 T 1 transition in the Mn 2 macrocycle was determined to be 1.83 eV. This value is less than th e analogous value of 1.87 eV for the MnZn system by approximately 300 cm - 1 . This puts the overall energy of the quenching state lower in energy than 3 MLCT in the Mn 2 complex even after accounting for the reorganization energy requirements, which contrasts with the quenching being thermally activated with an 80 ± 20 cm - 1 barrier for the mixed metal. This means that the quenching of the 3 MLCT is spontaneous at all temperatures. While it cannot be said that these calculations represent what is actually happen ing in this donor - acceptor system without further experimental results with which to compare, it seems likely given the insensitivity of the quenching rate to temperature that was observed in our preliminary results that there is no thermal barrier to quen ching and that there are insufficient data at this time to suggest otherwise. This lowered energy difference associated with a single 6 A 1 to 4 T 1 transition in the Mn 2 macrocycle is likely caused by an effective increase in the ligand field strength of the Mn 2 macrocycle compared to that for the MnZn macrocycle. This ligand field increase can either be caused by the presence of spin exchange in the Mn 2 increasing the ligand field felt by the Mn II ions contained 214 within compared to that felt by the Mn II center in the MnZn acceptor complex, or it can be caused by other structural differences between the two systems affecting the ligand field strength felt by the contained Mn II ions. The only way the presence of spin exchange can conclusively be determined to be the sole cause of the ligand field increase is to rule out the aforementioned latter possibility. Unfortunately, there is a large number of structural differences between com plexes 4 and 5 , some of which were necessary for the synthetic implementation of a MnZn acceptor complex as was discussed in Chapter 3.The ligand field strength of the two different macrocycles is suspected to be different as the Schiff base absorption pea k in the symmetric macrocycle bearing systems is visibly lower in energy than the equivalent absorption present in the systems with the asymmetric macrocycle. Additionally, the bridging carboxylate bridge is different between complex 4 and 5 such that it i s possible this too is contributing to differences in the ligand field strength between the two macrocycles. This means that additional studies will be necessary to determine if the structural differences in the macrocycles are causing differences in the l igand field experienced by the Mn II ions before we can conclude if the spin exchange interaction itself is responsible for the reduced 6 A 1 to 4 T 1 energy difference. 4. 3.5 Implications for the Conservation of Spin Angular Momentum At the onset of this work, we wished to use the information gained in C hapter 3 on the quenching dynamics of the 3 MLCT by the 4 T 1 excited ligand field state in the MnZn macrocycle in concert with new information on the Mn 2 macrocycle obtained via theory to determine a plausibl e reason for the vastly increased 3 MLCT quenching in the Mn 2 appended donor - acceptor complex. Based 215 on the results here described, we cannot say that a new type of quenching is now accessible, since the computational results suggest the quenching is still related to the 6 A 1 to 4 T 1 ligand field transition in the Mn II centers. The fact that there is no longer a thermal barrier cannot alone account for the increased rate of quenching. Based on the pre - exponential term from the Arrhenius fit for the rate of qu enching from the MnZn compared to the Zn 2 donor - acceptor complexes, if there was only one quenching pathway that facilitated the decay of the 3 MLCT, it would conceivably only have a rate of 1. 4 ± 2 x10 5 s - 1 since the pre - exponential term is a good approximation of the rate of quenching if there was no thermal barrier. What has changed when the Mn II is exchange - coupled is the quantity of spin allowed quenching pathways. This is because the ground and excited state spin manifolds together allow for a total of eight spin allowed pathways as depicted in figure 4 - 6. Furthermore, since the excited state is ferromagnetic and the ground state is antiferromagnetic, this means that as one increases the temperature and thermally accesses more pathways, the energy difference associated with these pathways decreases, which means these pathways are always thermodynamically favorable. Since at 10 K half of the ground state spin manifold is already accessible, there are alre ady many spin allowed pathways at the lowest temperature studied. Another point worth considering is whether or not thermal population of all the states is even necessary for all of them to contribute to the quenching of the 3 MLCT. The fact that the rate of quenching appears insensitive to temperature suggests that the opposite is true, and that the quenching pathways are accessible at all temperatures via coupling to the rest of the spin allowed pathways. This means that there are at least eight spin allo wed pathways via which quenching can occur at all temperatures for the Mn 2 system as opposed to a single spin allowed pathway that is thermally activated in the MnZn system. It is this change in the number of spin allowed states and 216 the removal of the ther mal barrier that makes the quenching of the Mn 2 system able to be described as still deriving from an excitation of a manganese ion to the 4 T 1 from its ground state. 4. 4 Conclusion s We wanted to investigate how spin affects chemical reactivity using these covalently bound donor - acceptor complexes. The interaction of the different spins in the Heisenberg spin coupled dimer creates many spin allowed pathways where there was only one in the absence of the Heisenberg spin exchange. By performing electronic str ucture calculations, we have confirmed the antiferromagnetic nature of the ground state spin manifold and have determined that the lowest ligand field excited state spin manifold is ferromagnetic. We have also been able to use the results of these electron ic structure calculations to deduce the absence of a thermal barrier to the quenching of the Ru 3 MLCT excited state in the Mn 2 donor - acceptor complex which is in contrast to what was encountered in the MnZn system. It is the interaction of spins that opene d up the multiple pathways and may have lowered the energy of the analogous ligand field excited state, so we can conclude spin has an effect on the reactivity of these systems. 217 REFERENCES 218 REFERENCES 1 Soler, M.; McCusker, J. K. J. Am. Chem. 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Theory Comput. 2006 , 2 , 981 989. 221 Chapter 5: Conclusions and Future Directions 5.1 Project Goals The goal of this project was to demonstrate cases where the effects of populating different available spin states in molecules were manifested by changes in the reactivity of those molecules. In the course of the research presented in this dissertation , th is was tested in two main ways. The first portion of this dissertation investigated whether thermal population of higher spin states in a spin - coupled cluster resulted in changes to the crystal structure that were independent of other effects associated with the temperature change. These results in conjunction with already performed studies would have provided information on the reactivity of this system since there already exists a large body of prior work on magneto - structural correlations such that if there were measurable structural changes in a spin coupled molecule, it has already been established that this would result in the potential to change the reactivity of the system. 1,2 After these temperature dependent changes due to different spin states were identified, a detailed analysis using density functional theory was performed to identify changes in the calculated spin coupling constant and the molecular orbital contributions to the spin exchange associated with these structural changes. 3 - 7 This s tudy was then concluded with an investigation to determine whether these conformational changes were correlated to changes in the spin state population. The second part of this research focused on whether there was a spin angular momentum conservation req uirement in a Dexter energy transfer donor - acceptor complex. 8 ,9 It was thought that by examining the rates of energy transfer to both a spin coupled bimetallic acceptor and its 222 single transition metal analogue, one could show a requirement of spin conservation by determining the energetics of spin allowed and spin forbidden energy transfer pathways. 5.2 Dissertation Results In the first section of the dissertation , we were able to show significant changes in the crystal structures of [Fe 2 ( - OH)( - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ](ClO 4 ) with an increase in temperature that were independent of temperature induced changes in the non - coupled [Ga 2 ( - OH)( - O 2 CCH 3 ) 2 (HBpz 3 ) 2 ](ClO 4 ) structural analogue. These changes unique to the spin coupled complex involved two main distortions in the bond distances: a slight shortening in one of the Fe - µOH bond distances and a substantial shortening of the O - H bond distance on the µOH. These changes were found to cause substantial changes in the calculated coupling constant and the m echanisms of spin coupling. This allows a correlation between the changes caused by population of higher spin states and the energetics of the various spin states in this system. However a direct relationship between the populations of the higher spin stat es in the spin coupled dimer and these geometric changes was unable to be established. In the second section of this dissertation , we were able to observe the temperature dependent quenching behavior of a ruthenium polypyridyl 3 MLCT excited state 10 by a ma nganese (II) containing Schiff - base macrocycle in covalently linked intramolecular donor - acceptor assemblies. This quenching process was found to be due to a Dexter energy transfer 9 from the Ru - based 3 MLCT into the 4 T 1 ligand field state of the Mn II in the macrocycle and was found to have a thermal barrier of 80 ± 20 cm - 1 based on comparisons to an equivalent structural model. Since the energy of the acceptor states in the Mn II as measured by experiment and theoretical calculations on a model 223 of the energy acceptor was found to be lower than the 3 MLCT energy donor. By using theory it was determined that while the energy of the doublet state was in the same range as the donor 3 MLCT state, the reorganization energy was too great to allow participation of the d oublet state in the quenching at for temperatures studied, leading to the conclusion that the only confirmed effect the different possible spin states were having on quenching activity was due to their different reorganization energies. 11 In the final sec tion of the dissertation , we were able to use density functional theory and the analytical methods used in the study of the previous systems to thoroughly analyze the thermodynamics of the Mn 2 acceptor. This included gaining detailed knowledge of the energ etics of the different spin states present in the 6 A 1 + 6 A 1 ground state spin manifold, the energetics of the spin manifold that correlates to a single ligand field excitation that was found to quench the energy donor in the mixed metal system (the 6 A 1 + 4 T 1 excited spin manifold), and most importantly, the energies of the spin levels of both spin manifolds relative to each other. The major conclusion of these studies is that 6 A 1 + 4 T 1 excited spin manifold is substantially lower in energy that the 4 T 1 state in the mixed metal system. The energy difference is reduced such that there is no thermal barrier to the quenching of the Ru donor by this excited spin manifold. This, coupled to the fact that there are eight spin allowed quenching pathways in the M n 2 system compared to the single spin allowed pathway in the mixed metal system is what is proposed to result in the observed increase in the quenching rate in the few preliminary experimental results on this system. In this manner, evidence was found of m ore spin affecting reactivity in energy transfer by Heisenberg spin coupling allowing for more spin allowed pathways and potentially lowering the energy of the excited ligand field states. 224 5.3 Future Work 5.3.1 Current Di - manganese Systems As we were una ble to get a full variable temperature time resolved emission profile for the Mn 2 donor - acceptor system, the most pressing future work to be done on this system should be the acquisition of the VT time resolved emission profile analogous to those obtained for the di - zinc model and mixed metal donor acceptor complex. Our estimates on the quenching rate in the di - manganese are based on only a couple of low temperature emission lifetime measurements in the optical glass solvent mixture and the room temperature lifetime measured in dichloromethane. While these values show low variability (room temperature lifetime is only about an order of magnitude higher than the low temperature values), it is important to get the full temperature profile before concluding tha t there is no significant temperature dependence on the quenching rate of this system. As was previously mentioned, the energetics of the doublet excited state spin manifold were not considered in this work due to the difficulty of these studies and time c onstraints. As the entire manifolds consists of an S=2 and S=3 state, there is the potential to obtain optimized geometries of the entire spin manifold. If one were to estimate the nature of the coupling in this spin manifold, one should be inclined to thi nk that any changes between the ground state and quartet excited spin manifolds would be roughly repeated between the quartet and doublet excited spin manifolds. This leads us to predict a larger ferromagnetic coupling in this doublet spin manifold. Based on this - manganese ligand field excited spin manifold and based on comparisons to the mixed - metal acceptor, where the energetics of the doublet state was studied, we can make a few loose predictions on the thermodynamic s of these doublet exited spin manifold states. One would expect the energy difference of the ground state of the doublet excited spin 225 manifold and the S=0 ground state of the di - manganese to be in a range of 1.5 eV to 1.7 eV as well as a reorganization en ergy in the range of 1.2 to 1.4 eV. While these predicted values would result in a thermal barrier that could not be crossed in the low temperature studies, one cannot be certain until the DFT calculations are actually performed. Therefore, it would be ben eficial if a similar energetic study for the doublet excited spin manifold were performed in the future for the di - manganese acceptor. 5.3.2 Aliphatic Bridged Mn 2 /MnZn Systems It was determined in our previous work that the activation barrier to accessing the 3 MLCT located on the mcb bridge of the di - manganese system is sufficiently high such that the quenching pathway of the 3 MLCT of the Ru donor is only mediated by the bonding interaction between the donor and acceptor portions of the donor - acceptor assembly. This is in contrast to the possibility that the observed quenching is a multi - step energy transfer process between the 3 MLCT located on the ((CF 3 ) 2 - bpy) ligands, followed by an inter - ligand energy or electron transfer to the mcb, and followed by a subsequent energy transfer into the di - manganese acceptor. However, when these molecules were initially designed, it was with a mind to study the rate of the different thermal population of the spin states on electron transfer, as electron transfer processes involving spin - coupled systems are much more prevalent in biological systems. It is thought that the reorganization energy for electron transfer is such that the Dexter energy transfer process outcompetes the electron transfer for all of the solution and glass phase temperatures studied previously. 226 To perhaps coax the system into performing a desired electron transfer quench ing of the ruthenium donor, it is postulated that extending the mcb linker by the addition of a methylene group between the carboxylate and the bipyridine ring , as pictured in figure 5 - 1, could promote electron transfer compared to the previous sytem with the mcb linker which is known to not undergo electron transfer . The addition of an aliphatic linker to the mcb ligand would lessen the bonding interaction between the donor and acceptor states as the carboxylate would no longer be coupled into the aromatic group in addition to the weakening the bonding interaction between the donor and acceptor states could reduce the rate of energy transfer in such a donor - acceptor s ystem. This would be beneficial for two reasons; in the first place, if this promoted electron transfer quenching in the donor acceptor system, and second, if there was still no electron transfer quenching, it is likely that the Dexter energy transfer rate would be reduced such that it would be much easier to study on the nanosecond timescale, perhaps providing us with more detail on the rate of energy transfer quenching as a function of temperature. Figure 5 - 1: Drawings of the previous ly studied [Mn 2 (L)(mcb)Ru((CF 3 ) 2 - bpy) 2 ] 3+ (A) complex and the proposed extended linker analogue (B). 227 This extended mcb linked system would also provide the advantage that the thermal population of the spin states in the di - manganese spin coupled dimer would remain unchanged. This was concluded by performing preliminary calculations on the high spin optimized di - manganese cluster with the mcb replaced with an acetate to approximate the aliphatic linker for the determination of the coupling cons tant as wa s previously done in C hapter 4. The resulting coupling constant derived from B3LYP is almost identical to that found for the analogous mcb bridged structure, with the acetate bridged dimer having a calculated coupling constant of 6.7 cm - 1 compared to 6.6 cm - 1 for the mcb bridged complex. The significance of this result is that one would know that the temperature controlled changes in spin would be consistent between the already studied system and the analogous systems with the extended mcb linker. This fa ct may allow for interesting comparisons between the two systems especially if it is found that the extended linker still quenches via a Dexter energy transfer mechanism. The syn thesis of this modified bridging ligand has already been worked out by another esteemed group member, 12 such that it would be a trivial matter to adapt this ligand for use in our already established synthetic procedures to making all of these complexes. It is likely that the di - zinc analogue would not be necessary to synthesize as t he difference in ground state recovery between the existent di - zinc complex and one with the methylene extended bridge is likely to be negligible. The existing procedures for the mixed metal and di - manganese donor - acceptor complexes could be followed with the substitution of this new extended bridge for the mcb with minimal modification, as the solubility of the starting materials and intermediates incorporating this modification should be similar to our preexisting versions. Therefore the syn thesis and var iable temperature emission studies of these two modified donor - acceptor complexes would seem to be 228 a facile extension of this work to elucidate the effects of varying population of spin states on the reactivity of donor - acceptor complexes. 5.3.3 Studying the E nergetics of the Fe 2 OH system. Previous and ongoing work in our group is dedicated to the determination of spin effects on the electron and energy transfer dynamics in covalently linked donor acceptor complexes where our extensively studied Fe 2 µ - OH and the analogous Fe 2 µ - O spin coupled dimers are integrated as energy and electron acceptors in a similar manner to the di - manganese acceptor from the donor - acceptor complexes reported in this dissertation . 1,13 To correctly interpret the results of these s tudies it would be beneficial to know the energetics of both the reduced di - iron core as if it had played the role of an electron acceptor and the quartet excited di - iron core as if it had acted as an energy acceptor in a donor - acceptor complex. Preliminar y investigations of these states employed the optimized high spin X - ray structures for the Fe 2 OH molecule reported in C hapter 2 and us ed methods similar to those in C hapter 4 to optimize the high spin excited quartet state (S=4) and the high spin reduced versions of the Fe 2 OH complex. (S=9/2) From these optimized geometries one is able to obtain an estimate for the energy difference between the ground and excited state spin manifolds of 0.30 eV, which is substantially less than the equivalent energy diffe rence in the di - manganese system. An inner sphere reorganization energy of 0.38 eV was calculated for the reduction of the di - iron hydroxo complex, which is a useful quantity to have available when interpreting results from electron transfer donor - acceptor systems. Coupling constants were also obtained employing the standard broken symmetry wavefunctions for the low spin states. These were determined to be - 3 cm - 1 for the excited quartet 229 spin manifold, and - 189 cm - 1 for the reduced spin exchange manifold. T he small ferromagnetic coupling value obtained for the quartet excited spin manifold remarkably mirrors the results obtained for the analogous di - manganese state. The calculated coupling constant for the reduced spin manifold of the di - iron is ferromagneti c and much larger than for its native unreduced value. It is not surprising that the magnitude of the coupling should increase as the mixed valent nature of the reduced core opens up a double exchange mechanism resulting in large coupling constants. It is noteworthy too that the coupling is ferromagnetic in the reduced state, as this would have the effect of causing the relative population of high spin states to substantially increase upon photo - induced electron transfer into this system, especially if the electron transfer photoproducts are long lived. One can therefore imagine an intriguing experiment to test for electron transfer in a donor - acceptor system the system by comparing the magnetic moment of the sample in the dark and under illumination. 5.4 C oncluding Comments The methods described herein and some of their derivations have broad applicability to any system where estimates of thermodynamic quantities of spin coupled or other transition metal complexes are desired. Therefore it would be trivial to extend these kinds of electronic structure investigations and obtain other similarly useful results pertinent for donor - acceptor complexes with other spin - coupled acceptors. Indeed the author hopes that this dissertation will provide a strong foundation on which to build the use of these electronic structure methods in our research group. Using experiment and theory, we have been able to answer questions that neither technique could confidently answer in isolation, which has furthered our understanding o n the subtle ways spin 230 effects chemical reactivity. In effect, what we have accomplished over the course of this dissertation is to reaffirm the validity of using density functional theory to provide insight into actual experimental results, which is in th used to advance the knowledge of the chemical sciences. 231 REFERENCES 232 REFERENCES 1 Weldon, B. T.; Wheeler, D. E.; Kirby, J. P.; McCusker, J. K. Inorg. Chem. 2001 , 40 , 6802 6812. 2 Crawford, V. H.; Richardson, H. W.; Wasson, J. R.; Hodgson, D. J.; Hatfield, W. E. Inorg. Chem. 1976 , 15 , 9 12. 3. (a) Becke, A.D. J. Chem. Phys. 1993 , 98 , 5648 - 5652. (b) Lee, C. ; Yang , W. ; Parr, R .G . Phys. Rev. B 1988 , 37, 785 - 789 . (c ) Stephens, P.J.; Devlin, F.J. ; Chabalowski, C.F. ; Frisch, M.J. J. Phys. Chem. 1994 , 98 , 11623 - 11627. 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