Electronic Structure of Excited States with Configuration Interaction Methods by Alan D. Chien A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Chemistry) in The University of Michigan 2017 Doctoral Committee: Assistant Professor Paul Zimmerman, Chair Professor John Kieffer Professor Roseanne J. Sension Assistant Professor Dominika Kamila Zgid Alan D. Chien [email protected] ORCID iD: 0000-0002-3103-0697 © Alan D. Chien 2017 Dedication To my parents, whose wisdom I benefit from every day. ii Acknowledgements During my time at the University of Michigan, I have encountered many great minds and made many great friends, all of whom have broadened my view of the world. First and foremost, I would like to express my sincere gratitude to my advisor Dr. Paul Zimmerman. Without his continuous support, guidance, and patience, I would not have been able to complete the work contained within this thesis. His hard work and quick mind are truly top notch, and I am forever thankful that he took the time to share his insights and critiques of my work. I would also like to thank my committee members for spending their time guiding yet another graduate student towards graduation, as well as their flexibility and kindness. Of course, my lab mates also played a large role in the completion of my degree, not only offering technical help, but companionship as well. Special mention has to be made of Andy Vitek, a fellow Hoo and a wonderful friend to me for the past four years. From playing ping-pong to climbing down at the Red, spending time with him is always a nice refueling session that I look forward to. Other lab mates include: Mina Jafari, who literally refueled me, providing me with many snacks over the years. Though her habit of forcing me to clean my keyboard was a slight pain in the neck. Josh Kammeraad’s analytical mind continues to astound me to this day. The clarity with which he sees problems is something I will (most likely) always remain envious of, as well as his never-ending cheerfulness and willingness to help. Laura Motta is a whirlwind of energy, whose enthusiasm for her work is infectious. Collaborating with her briefly exposed me to the world of relativistic quantum chemistry, which I may one day dive back into. Cody Aldaz helped me briefly fulfill the childhood dream of learning to skateboard, for which I am forever grateful. Ian Pendleton, Andrew Molina, and Jordan Metz were there from day one, pushing through the chaos that is graduate school with me, and a better crew to run with I could not have asked for. I would also like to thank all of the post-docs for their wide knowledge base that I often made use iii of. Special mention goes to Yu Zhao, Jared Hansen, and Hyungjun Kim, who were good friends as well as sources of technical help. David Braun deserves a mention here as well, being the best System Administrator one could ask for. There are many people outside of lab that I have spent ample time with and who deserve mention. The Crotchball crew from high school, whose friendship I will always treasure. Anthony Yeh and Stephen Cronk, my old college roommates and video game partners. Mitchell Smith, Matthew Wolf, and Tejas Navaratna, old and current roommates who made returning home a joy and not a chore. All of the staff at Planet Rock, whose hard work provides me with endless vertical terrain to scamper up. My numerous climbing buddies: Adam Neitzke, Josh Golec, Audrey Akcasu, Seth Elliot, Jenny Hebert, John Farr, Sin Sar Hsie, Jessie and Blake Tracy, Marissa Linne, Justin Li, and Laura Haskins to name a few, with whom I always enjoyed crushing at the crag or the gym. Special mention goes to Anita Luong, one of the few climbers that I’ve managed to convince to go lead climbing with me. Finally, I would like to acknowledge my family, who have been there since the beginning. My dad, my mother, my brother, and my sister are all wonderfully supportive and inspiring people, whom I love dearly. iv Table of Contents Dedication ................................................................................................................................................ ii Acknowledgements ............................................................................................................................. iii List of Figures ....................................................................................................................................... vii List of Tables ............................................................................................................................................ x List of Equations .................................................................................................................................. xii List of Appendices .............................................................................................................................. xiii Abstract ................................................................................................................................................. xiv Chapter 1: Introduction ...................................................................................................................... 1 1.1 Exploring Excited States with Computational Chemistry ............................................................ 1 1.2 Theoretical Background .......................................................................................................................... 2 1.2.1 Schrödinger’s Equation, Operators, and Wave functions .................................................................. 2 1.2.2 Hartree-Fock, Basis Functions, and Molecular Orbitals ..................................................................... 4 1.2.3 Configuration Interaction (CI) and Matrices in Quantum Chemistry ........................................... 5 1.2.4 CI for Excited States, FCI Approximations, and Spin-Flip Methodology...................................... 7 1.3 Dissertation Outline .................................................................................................................................. 9 1.4 References ................................................................................................................................................. 11 Chapter 2: Structure and Dynamics of the 1(TT) State in a Quinoidal Bithiophene, Characterizing a Promising Intramolecular Singlet Fission Candidate ........................... 13 2.1 Abstract ....................................................................................................................................................... 13 2.2 Introduction .............................................................................................................................................. 14 2.3 Methods ...................................................................................................................................................... 16 2.3.1 Computational Details .................................................................................................................................... 16 2.3.2 Experimental Details ...................................................................................................................................... 18 2.4 Results and Discussion .......................................................................................................................... 18 1 2.4.1 Immediate Evolution of the Bright 1 Bu Exciton ................................................................................. 18 1 2.4.2 Nature and Transformations of the 2 Ag Excited State .................................................................... 22 1 2.4.3 The Possibility of Long-Lived 2 Ag ............................................................................................................ 28 2.5 Conclusion.................................................................................................................................................. 34 2.6 References ................................................................................................................................................. 36 Chapter 3: Recovering Dynamic Correlation in Spin Flip Configuration Interaction through a Difference Dedicated Approach ................................................................................. 41 3.1 Abstract ....................................................................................................................................................... 41 3.2 Introduction .............................................................................................................................................. 42 3.3 Theoretical Background of Proposed Spin-Flip Extensions .................................................... 44 3.3.1 RAS(h,p)-SF ......................................................................................................................................................... 45 3.3.2 DDCI ....................................................................................................................................................................... 46 3.3.3 RAS(S)-SF and RAS(S,2h,2p)-SF ................................................................................................................. 46 3.4 Computational Details ........................................................................................................................... 49 3.5