Active Space Methods in Electronic Structure Theory and Applications to Gas Separations in Metal-Organic Frameworks A DISSERTATION SUBMITTED TO THE FACULTY OF THE UNIVERSITY OF MINNESOTA BY Samuel Joseph Stoneburner IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Laura Gagliardi, advisor June 2019 © Samuel Joseph Stoneburner 2019 ALL RIGHTS RESERVED Acknowledgements My gratitude goes out to my advisor, Laura Gagliardi, for conversations, explanations, pieces of advice and insight, amazing collaborative opportunities, and countless other forms of mentorship and support. I would also like to thank the others who have mentored me within the group, Allison Dzubak, Giovanni Li Manni, and especially Konstantinos (Kostas) Vogiatzis. There have been many collaborators and co-authors, and they all have my appreciation, but in particular I wish to thank WooSeok Jeong, whose tireless quest for understanding is inspiring, and Don Truhlar, who has taught me so much about precision in technical writing. On a more personal note, I want to thank my wife, Jamie, for keeping me grounded and providing necessary perspective on so many parts of life, and my children, Halili, Jocelyn, John, and Zuri, for the sheer joy of watching them grow and learn over these many months. Finally, I give highest thanks to God for everything, and especially for making the universe run on math, without which none of the work in this dissertation would have been possible. i Dedication This dissertation is dedicated to my wife, Jamie, who knew I was a science nerd and married me anyway. ii Table of Contents Table of Contents Acknowledgements .................................................................................................. i Dedication ............................................................................................................... ii Table of Contents ................................................................................................... iii List of Tables ....................................................................................................... viii List of Figures ....................................................................................................... xii List of Abbreviations ......................................................................................... xviii 1 Introduction .......................................................................................................... 1 1.1 Organization of this Dissertation .................................................................. 2 1.2 Theoretical Background and Methods .......................................................... 4 1.2.1 Wave Function Theory .......................................................................... 4 1.2.2 Hartree-Fock .......................................................................................... 6 1.2.3 Density Functional Theory .................................................................. 10 1.2.4 CSFs and CI ......................................................................................... 14 1.2.5 MCSCF ................................................................................................ 17 1.2.6 CASPT2 ............................................................................................... 21 1.2.7 SplitGAS .............................................................................................. 24 1.2.8 MC-PDFT ............................................................................................ 26 1.3 Active Space Selection ............................................................................... 30 1.4 Applications: Gas Separations in Metal-Organic Frameworks .................. 31 List of Papers Featured in this Dissertation .......................................................... 34 iii 2 Systematic Active Space Selection .................................................................... 36 2.1 Systematic Expansion of Active Spaces beyond the CASSCF Limit: A GASSCF/SplitGAS Benchmark Study ......................................................................... 37 2.1.1 Overview .............................................................................................. 38 2.1.2 Introduction .......................................................................................... 38 2.1.3 Computational Methods ....................................................................... 42 2.1.4 Results .................................................................................................. 44 2.1.5 Discussion and Conclusions ................................................................ 69 2.1.6 Additional Information ........................................................................ 72 2.2 Systematic Design of Active Spaces for Multi-Reference Calculations of Singlet–Triplet Gaps of Organic Diradicals, with Benchmarks Against Doubly Electron-Attached Coupled-Cluster Data ..................................................................... 73 2.2.1 Overview .............................................................................................. 74 2.2.2 Introduction .......................................................................................... 74 2.2.3 Computational Details ......................................................................... 79 2.2.4 Results and Discussion ........................................................................ 89 2.2.5 Conclusions ........................................................................................ 101 2.2.6 Additional Information ...................................................................... 103 3 Spin Energetics in MC-PDFT .......................................................................... 104 3.1 MC-PDFT Can Calculate Singlet-Triplet Splittings of Organic Diradicals ..................................................................................................................................... 105 3.1.1 Overview ............................................................................................ 106 iv 3.1.2 Introduction ........................................................................................ 106 3.1.3 Computational Details ....................................................................... 109 3.1.4 Results and Discussion ...................................................................... 113 3.1.5 Conclusions ........................................................................................ 119 3.1.6 Additional Information ...................................................................... 120 3.2 Full Correlation in a Multiconfigurational Study of Bimetallic Clusters: Restricted Active Space Pair-Density Functional Theory Study of [2Fe-2S] Systems ..................................................................................................................................... 121 3.2.1 Overview ............................................................................................ 122 3.2.2 Introduction ........................................................................................ 123 3.2.3 Computational Methods ..................................................................... 127 3.2.4 Results and Discussion ...................................................................... 132 3.2.5 Conclusions ........................................................................................ 142 3.2.6 Additional Information ...................................................................... 144 3.3 Affordable and Accurate Transition Metal Spin-State Energetics via MC- PDFT Using tPBE with High Local Exchange ........................................................... 145 3.3.1 Overview ............................................................................................ 146 3.3.2. Introduction ....................................................................................... 147 3.3.3 Computational Methods ..................................................................... 152 3.3.4 Results and Discussion ...................................................................... 155 3.3.4.1 Ground Spin States ................................................................................. 157 3.3.4.2 Active Space Dependency for FeP ......................................................... 158 v 3.3.4.3 Timing Comparisons ............................................................................... 159 3.3.5 Conclusions ........................................................................................ 161 3.3.6 Additional Information ...................................................................... 162 4 Gas Separations in Metal-Organic Frameworks .............................................. 163 4.1. Origin of the Strong Interaction between Polar Molecules and Copper(II) Paddle-Wheels in Metal Organic Frameworks ........................................................... 164 4.1.1 Overview ............................................................................................ 165 4.1.2 Introduction ........................................................................................ 165 4.1.3 Computational Methods ..................................................................... 170 4.1.4 Results and Discussion ...................................................................... 172 4.1.5 Conclusions .......................................................................................