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Dissertation Spin Multiplets: Theory and Application DISSERTATION SPIN MULTIPLETS: THEORY AND APPLICATION Submitted by Jacob M. Nite Department of Chemistry In partial fulfillment of the requirements For the Degree of Doctor of Philosophy Colorado State University Fort Collins, Colorado Spring 2018 Doctoral Committee: Advisor: Anthony K. Rappé Matthew Shores Yian Shi Siu Au Lee Copyright by Jacob Matthew Nite 2018 All Rights Reserved ABSTRACT SPIN MULTIPLETS: THEORY AND APPLICATION Transition metal complexes have seen an increased use as photocatalysts for organic reactions in recent literature, mostly involving the Ru(II)(bpy)3 family of catalysts. Due to the rarity of ruthenium in the Earth’s crust, alternative catalysts using Earth abundant materials are desirable. Recent literature has shown that chromium based catalysts show great promise as a replacement for ruthenium for some reactions. The mechanisms of these first-row transition metal complexes are significantly more complex than those of the second and third row. The excited state complexities of first- row transition metal complexes are challenges for both experimental and theoretical research. The complexities of the excited states require theoretical methods beyond the standard single reference methods commonly used in the literature. Through the use of recent multi-reference post Hartree Fock (HF) methods as well as a new multi-reference density functional theory (DFT), insights into the character of chromium-based photocatalysts were examined. A new multi-determinant DFT method named few-determinant density functional theory (FD-DFT) was described. FD-DFT incorporates multiple DFT determinants using a finite difference approach to calculate the exchanges between multiple determinants for open shell multiplets. The method is implemented in a generalized bond valence (GVB) wave function, and can be converged through an SCF procedure. The system was benchmarked using oxygen atom and diatomic oxygen as well as atomic systems ii with more open shell orbitals. The benchmarking shows stability across many different functional choices, and gives good excitation energies with and without SCF convergence. The Cr(III)(AcAc)3 system has been long studied for its unique excited state properties that defy the standard cascade model for excited state relaxation. The tris(1,3-propanedionato)chromium(iii) (Cr(III)(PDO)3) complex was studied as an analog to the Cr(III)(AcAc)3 system to understand the excited state pathway between the initial 4 2 excited T2g state and the long lived Eg state. Using the FD-DFT method as well as the multi-reference spectroscopy oriented configuration interaction (SORCI) method, the initial excited state energies were studied compared to previous perturbation theory 2 (PT) approaches. Both SORCI and FD-DFT calculate reasonable Eg excitation energies, an improvement over earlier results. The SORCI method was also used to 4 map the potential energy curve between the initial T2g excited state and its fully relaxed distorted structure. The pathway agrees with previous experimental and theoretical studies showing that a transitionless path exists between the quartet and doublet states, 4 2 but spin-orbit coupling calculations suggest that a direct path between the T2g and Eg 2 is possible rather than needing a internal conversion step to the lowest Eg state. Chromium-based photocatalysts have been recently studied in the literature as having a competitive mechanism between the reaction substrate and O2 whereby the O2 quenches the excited catalyst. Using the combined Cr(III)(PDO)3 • O2 system, the likely states by which this quenching event occurs were studied with FD-DFT as well as recent multi-reference PT approaches. Comparing the excited state calculated using the multi-reference based methods to standards DFT calculations shows the inability of iii single-determinant methods to correctly produce the proper excited state character even when obtaining somewhat reasonable energies. The excited state responsible for the quenching of the excited complex is identified using spin density plots of the CASSCF calculations. The search for suitable first-row transition metals requires a search across possible ligands and metal centers. Using the success of chromium-based catalysts, isoelectronic vanadium catalysts were studied to identify any potential differences between the complexes as well as identify the utility of vanadium-based catalysts. Using a variety of methods, including TDDFT-based absorption spectra, vibrational component plots of the excited state distortions, and SORCI potential energy curves (PEC), the differences between the chromium and vanadium catalysts were examined. It was found that vanadium catalysts absorptions are shifted significantly from chromium complexes and the vanadium excited states disperse the unpaired electron over the complex instead of localizing it on the metal center. The distortions in the chromium- based catalysts have a greater amount of asymmetric vibrational character compared to vanadium, which shows mostly symmetric behavior. Lastly, the SORCI PECs show that, unlike chromium, the doublet curves do not intersect the quartet curves, making a transition to a long lived doublet state a significantly slower process. The results highlight significant differences between the complexes even with ligand structure is controlled. iv ACKNOWLEDGEMENTS Graduate school has been a journey that has shaped me as a scientist in ways that could have not been foreseen at the start. While the work I have accomplished has been mine, my achievements have been built upon the people who have supported me in my endeavors. I want thank Anthony Rappé, my advisor, for the tremendous guidance he has provided me during my graduate work. The most important lesson he has taught me is that the cutting edge of science is not always the most complicated problems, but instead it is in determining the relative sizes of each piece within any problem and what you can do to understand which has largest impact. He also has shown me that your ego can only make your science worse, so there isn’t a point to having one. I want to thank my committee, Matthew Shores, Yian Shi, and Siu Au Lee. They have been indispensable in their encouragement for me to finish my PhD. They have taught me to look beyond my expertise and see how it fits into the rest of the science community. I would like to the chemistry faculty, specifically Melissa Reynolds and Nancy Levinger. They have always been students biggest supporters, and have not hesitated to put students before politics. They have been there to help me navigate graduate school even when my personal life was hectic. I want to acknowledge my family, especially my parents for always encouraging me to stick with my PhD program and finish. They always believed that I could finish my degree even when life gets busy. v I want to thank my wife’s family, especially Stacy Dutton. She has been a great source of encouragement for my work, and has been one of my biggest cheerleaders as a scientist and a father. She is always willing to drop everything to come help when she is needed. I want to thank my friends for the rest and relaxation you provided. Graduate school is a long journey. Everyone in it needs to pace themselves and take a break once in a while. I want to thank my children, Augustine and Elisabeth. Daddy is eternally grateful that you slept at night long enough for him to finish this dissertation. Most of all, I want to thank my lovely wife, Collette, for helping me be the best scientist, husband, and father I can be. When I was down, you helped me; when I was frustrated, you encouraged me; when I was joyful, you laughed with me; when I was worried, you consoled me; when I was exploring new adventures; you supported me. I owe everything to you, including my science, and I cannot fully express my gratitude for you being in my life. vi DEDICATION To my wife, Collette, for believing in me. vii TABLE OF CONTENTS ABSTRACT ...................................................................................................................... ii ACKNOWLEDGEMENTS ................................................................................................. v DEDICATION ................................................................................................................. vii LIST OF TABLES ............................................................................................................. x LIST OF FIGURES .......................................................................................................... xi CHAPTER 1: INTRODUCTION ........................................................................................ 1 BACKGROUND: ........................................................................................................... 1 SPECIFIC AIMS OF THIS RESEARCH: .................................................................... 13 REFERENCES ............................................................................................................... 15 CHAPTER 2: FEW-DETERMINANT DENSITY FUNCTIONAL THEORY (FD-DFT), SPIN MULTIPLETS AS PROOF OF CONCEPT ............................................................ 18 INTRODUCTION: ....................................................................................................... 18 THEORY: .................................................................................................................... 19 FD-DFT THEORY: .................................................................................................
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