Density Functional Theory: Toward Better Understanding of Complex Systems in Chemistry and Physics A Dissertation SUBMITTED TO THE FACULTY OF UNIVERSITY OF MINNESOTA BY Sije Luo IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Advisor: Professor Donald G. Truhlar June 2014 © Sijie Luo 2014 Acknowledgements I want to particularly thank Professor Donald G. Truhlar, whose continuous supports and encouragements made all the work presented here possible. One of the wisest and most aspiring human beings I have ever met, Don is a true mentor in both work and life. I also want to thank Professor Laura Gagliardi for her helps in class, my fellowship applications, and collaborative research projects. I am grateful for all the other faculty members in my preliminary and thesis committee – Professor Sanford Lipsky, Professor Ilja Siepmann, and Professor Matteo Cococcioni. I find it lucky to be surrounded by a body of brilliant researchers. My special thank you goes to my closet collaborators in various projects – Yan Zhao, Roberto Peverati, Xuefei Xu, Ke Yang, Boris Averkiev, Haoyu Yu, Shaohong Li, Wenjing Zhang, and Giovanni Li Manni. I owe an unimaginable amount to my parents, without whose support I would not have travelled so far. Finally, I feel more than blessed to have Chulan Qing, my fiancée, in my life for the past seven years. Her supports helped me through difficulties that would otherwise be insurmountable, and her love made every bit of my effort worthwhile. i Dedication This dissertation is dedicated to Chulan Qing, for whom I try to be a better self. ii Abstract Density functional theory (DFT) has become the workhorse of computational chemistry and physics in the past two decades. The continuous developments of high- quality exchange-correlation functionals (xcFs) have enabled chemists and physicists to study complex as well as large systems with high accuracy at low-to-moderate computational expense. Although a wide range of normal systems have been well understood by DFT, there are still complex ones presenting particular challenges where most commonly used xcFs have failed due to the complex nature of the system, lack of or difficulty to obtain reliable reference data, or the practical limitations of the Kohn-Sham DFT (KS-DFT) formulation. This thesis presents studies with various exchange-correlation functionals on a wide selection of complex systems in chemistry and solid-state physics, including large organic molecules, adsorption on metallic surfaces, transition states, as well as transition metal atoms, ions, and compounds, to (i) draw conclusions upon recommendations of xcFs for important practical applications; (ii) understand the root of errors to help design better xcFs or propose new theoretical schemes of DFT; (iii) explore the utility of noncollinear spin orbitals in KS-DFT for better description of multi-reference systems. iii Table of Contents List of Tables .................................................................................................................... vii List of Figures .................................................................................................................... ix Chapter 1. Introduction ....................................................................................................... 1 1.1 Density Functional Theory (DFT) ............................................................................ 1 1.1.1 Kohn-Sham Density Functional Theory (KS-DFT) .......................................... 1 1.1.2 Exchange-correlation Functionals ..................................................................... 3 1.2 Multi-Reference Systems .......................................................................................... 6 1.3 Noncollinear Density Functional Theory (NC-DFT) ............................................... 7 1.4 Organization of the Thesis ........................................................................................ 9 References for Chapter 1 .............................................................................................. 10 Chapter 2. Density Functional Theory for Isomerization Reactions of Large Organic Molecules .......................................................................................................................... 12 2.1 Introduction ............................................................................................................. 12 3.2 Methods................................................................................................................... 13 3.3 Reference Values .................................................................................................... 16 3.4 Testing Density Functionals ................................................................................... 17 3.5 Concluding Remarks ............................................................................................... 21 References for Chapter 2 .............................................................................................. 22 Chapter 3. Density Functional Theory for Solid State Physics: CO Adsorption Energies, Site Preferences, and Surface Formation Energies of Transition Metals ......................... 36 3.1 Introduction ............................................................................................................. 36 3.2 Computational Details ............................................................................................ 39 3.3 Results and Discussions .......................................................................................... 40 References for Chapter 3 .............................................................................................. 44 Chapter 4. Density Functional Theory for Open-Shell Systems I: The 3d-Series Transition Metal Atoms and Their Cations ...................................................................... 51 4.1 Introduction ............................................................................................................. 51 4.2 Computational Details and Experimental Data....................................................... 53 4.3 Density Functionals Tested ..................................................................................... 55 4.4 Theory and Methods ............................................................................................... 59 iv 4.4.1 Stability Optimization ...................................................................................... 59 4.4.2 Treatment of Open-Shell States ....................................................................... 61 4.4.3 Orbital Analysis ............................................................................................... 65 4.5 Results ..................................................................................................................... 67 4.5.1 Orbital Bias: s and d Orbitals ........................................................................... 67 4.5.2 Spin States and Ionization Potentials ............................................................... 70 4.5.3 Broader Comparisons....................................................................................... 73 4.6 Summary and Conclusions ..................................................................................... 77 References for Chapter 4 .............................................................................................. 80 Chapter 5. Density Functional Theory for Open-Shell Systems II: The 4d-Series Transition Metal Atoms and Their Cations .................................................................... 106 5.1 Introduction ........................................................................................................... 106 5.2 Experimental Data ................................................................................................ 109 5.3 Density Functionals .............................................................................................. 110 5.4 Theory and Computational Details ....................................................................... 113 5.4.1 Theory ............................................................................................................ 113 5.4.2 Computational Details ................................................................................... 116 5.5 Results AND Discussion....................................................................................... 118 5.5.1 5s and 4d subshell occupations ...................................................................... 118 5.5.2. Group 1 cases ................................................................................................ 121 5.5.3. Group 2 cases ................................................................................................ 123 5.5.4. Group 3 cases ................................................................................................ 126 5.5.5 Group 4 cases ................................................................................................. 128 5.6. Overall performance ............................................................................................ 129 5.7. Conclusions .......................................................................................................... 133 Appendix ..................................................................................................................... 134 References for Chapter 5 ...........................................................................................