ABSTRACT Title of dissertation: VISUALIZING QUANTUM REACTIVE SCATTERING DYNAMICS Michael R. Warehime, Doctor of Philosophy, 2015 Dissertation directed by: Professor Millard H. Alexander Department of Chemistry The Born-Oppenheimer approximation, which allows a decoupling of electronic and nuclear motion, underlies the investigation of molecular dynamics. In some cases this decoupling is not possible, so that nuclear motion can induce changes in electronic state. It is then necessary to account for collision-induced transitions between multiple potential energy surfaces. This is an inherently quantum phe- nomena. In this dissertation we present a new way to visualize these non-adiabatic transitions in chemical reactions of open-shell atoms. Toward this end, we have developed new algorithms and developed a MATLAB-based software suite for sim- ulating non-adiabatic reactions. We have also determined new molecular potential energy surfaces and their couplings required to simulate the reactive dynamics. VISUALIZING QUANTUM REACTIVE SCATTERING DYNAMICS by Michael R. Warehime Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2015 Advisory Committee: Professor Millard H. Alexander, Chair/Advisor Professor Christopher Jarzynski Professor Garegin Papoian Professor Paul Dagdigian Professor Dianne P. O'Leary ⃝c Copyright by Michael R. Warehime 2015 To my parents ii Acknowledgments I would like to express my sincere gratitude to my advisor Millard Henry Alexander for providing the opportunity and openness to pursue the research projects contained herein and for his unending support, understanding and guidance, both personally and professionally, as these projects have evolved over the years. I would also like to thank many of my peers at the University of Maryland for their thought- ful conversation, rewarding personal interactions and, at times, for much needed dis- traction. I especially thank Dvir Kafri and Jacek K loswho have been indispensable resources and both possess a seemingly infinite supply of patience. Finally, I thank my family, my parents Brad and Cyndy, and my siblings, Matt, Ness and Nan, who have provided a lifetime of loving support and encouragement. iii Table of Contents List of Abbreviations viii List of Tables ix List of Figures ix 1 Introduction and Overview 1 1.0.1 Published Works ......................... 6 1.0.2 Manuscripts in Progress ..................... 7 2 Nonadiabatic Dynamics of Open-Shell Atom+Diatom Systems 8 2.1 Nonadiabatic Chemistry ......................... 8 2.1.1 Born-Oppenheimer Approximation ............... 9 2.1.2 Beyond the Born-Oppenheimer Approximation ......... 10 2.1.3 Conical Intersections ....................... 11 2.1.4 Spin-Orbit Interactions ...................... 12 2.1.5 Coriolis Coupling ......................... 13 2.1.6 Nonadiabatic Reactive Scattering ................ 13 2.2 Atom+Diatom Reactive Scattering ................... 14 2.3 Collinear Atom-Diatom Reactive Scattering .............. 14 2.3.1 Adiabatic Scattering ....................... 19 2.3.1.1 Potential Energy Surface ................ 19 2.3.1.2 Schr¨odinger'sEquation ................. 20 2.3.1.3 Physical Boundary Conditions ............. 21 2.3.2 Nonadiabatic Scattering ..................... 23 2.3.2.1 Potential Energy Surface ................ 24 2.3.2.2 Schr¨odinger'sEquation ................. 25 2.3.2.3 Physical Boundary Conditions ............. 26 2.4 3D Atom-Diatom Reactive Scattering .................. 27 2.4.1 Adiabatic Scattering ....................... 30 2.4.1.1 Potential Energy Surface ................ 30 iv 2.4.1.2 Schr¨odinger'sEquation ................. 31 2.4.1.3 Physical Boundary Conditions ............. 32 2.5 Conclusion ................................. 35 3 Reactive Atom-Diatom Systems and the Finite Element Method 36 3.1 Overview .................................. 36 3.2 Collinear Bound Systems ......................... 41 3.2.1 Weak Formulation of Schr¨odinger'sEquation .......... 41 3.2.2 Finite-Element Solution ..................... 42 3.2.3 FE Matrix Integrals ....................... 47 3.3 Collinear Adiabatic Scattering ...................... 51 3.3.1 Reactive Scattering Domain ................... 52 3.3.2 Finite Element Solution ..................... 54 3.3.3 Boundary Integrals ........................ 58 3.3.4 Comparison with Earlier FE Implementation .......... 60 3.3.5 MATLAB Code .......................... 66 3.3.6 Test Calculations ......................... 67 3.3.7 Timing, Parallelization and Error ................ 68 3.3.8 Automatic Mesh Generation ................... 73 3.3.9 Probability Density and its Vector Current ........... 74 3.3.10 Discussion ............................. 79 3.4 Collinear Nonadiabatic Scattering .................... 82 3.4.1 FE Solution ............................ 83 3.4.2 Basis Choice for Coupled Potential Surfaces .......... 87 3.4.2.1 Quasi-Diabatic Bases .................. 87 3.4.2.2 Electronically Adiabatic Basis ............. 91 3.4.3 Time-Independent, Hydrodynamic Interpretation ....... 92 3.4.4 F+HCl!FH+Cl Reaction .................... 95 3.4.4.1 Potential Energy Surface ................ 96 3.4.4.2 Results: Scattering Dynamics ............. 96 3.4.5 F+H2 ! HF+H (Reactions with Mixed Boundary Conditions) ......... 106 3.4.5.1 Potential Energy Surface ................ 108 3.4.5.2 Two-State Scattering with Mixed Boundary Condi- tions ........................... 108 3.4.6 Discussion ............................. 110 3.5 Ultracold Nonadiabatic Reactions: Li+CaH .............. 117 3.5.1 Introduction ............................ 117 3.5.2 ab initio Potential Surfaces ................... 119 3.5.3 Results and Discussion ...................... 122 v 4 Representation of Reactive Potential Surfaces 125 4.1 Overview ................................. 125 4.2 A(2P)+BC ................................. 126 4.2.1 Kramers States .......................... 128 4.2.2 Collinear Geometry ........................ 130 4.2.3 Comparison with Previous Work ................ 131 4.2.4 Scattering Calculations ...................... 132 4.2.4.1 Two Possible Diabatic Bases ............. 132 4.2.4.2 S Matrix ........................ 134 4.2.4.3 Adiabatic Basis ..................... 135 4.2.4.4 Kramers Basis ..................... 136 4.2.4.5 ja Basis ......................... 138 4.2.5 Mixed Halogen X+HY!XH+Y Reaction ............ 139 4.2.6 Reaction of Halogen Atom with H2 ............... 139 3 4.3 A( P)+B2 ................................. 140 4.3.1 Spin-Orbit Hamiltonian ..................... 143 4.3.2 Cartesian Coordinates ...................... 145 4.3.3 Kramers Basis ........................... 147 3 1 + 4.4 O( P )+H2( Σg ) .............................. 150 4.4.1 Ab initio Calculations ...................... 154 4.4.2 3P Potential Surfaces ....................... 156 4.4.3 Discussion ............................. 159 4.4.4 Conclusion ............................. 164 5 A Comparison of ab initio and Density Functional Potential Energy Surfaces 166 5.1 Overview .................................. 166 5.2 Potential Energy Surfaces ........................ 168 5.3 Bound States ............................... 173 5.4 Adiabatic Bender States ......................... 181 5.5 Scattering Calculations .......................... 182 5.6 Discussion ................................. 187 5.7 Conclusions ................................ 192 6 Conclusions and Future Directions 194 6.1 Conclusions ................................ 194 6.1.1 Reaction Dynamics ........................ 194 6.1.2 Potential Surfaces ......................... 196 6.2 Future Directions ............................. 198 6.2.1 Three-Dimensional Scattering Software ............. 198 6.2.2 Photodissociation Spectrum ................... 199 6.2.3 The Roaming Mechanism .................... 200 3 1 6.2.4 O( P; D)+H2 ........................... 201 6.2.5 Modeling Dispersion Forces with DFT Potentials ....... 202 vi A Statistical Learning and Potential Energy Surfaces 203 A.1 Introduction ................................ 203 A.2 Neural Networks ............................. 205 A.2.1 Single Hidden-Layer Feed-Forward Network .......... 208 A.3 Identifying Ideal Neural Network Architectures for PES Fitting ...................... 209 A.3.1 Network Depth and Connectivity 1D .............. 211 A.3.2 Fitting the Collinear H3 PES with PIP Input Layer ...... 212 A.3.3 Neural Networks and Multibody Expansions .......... 216 A.4 Discussion and Conclusions ....................... 218 Bibliography 228 vii List of Abbreviations BO Born-Oppenheimer PES Potential Energy Surface FE(M) Finite Element (Method) DFT Density Functional Theory JCP Journal of Chemical Physics MSJ Mass-Scaled Jacobi SO Spin-Orbit BVP Boundary Value Problem LHS Left Hand Side FD Finite Difference MEP Minimum Energy Path CRESU Cin´etiquede R´eactionen Eclement´ Supersonique Uniforme, (reaction kinetics in uniform supersonic flow) SA-CASSCF State-Averaged Complete Active Space Configurational Self- Consistent Field ic-MRCISD Multi-Reference Configuration Interaction Calculations in- cluding explicitly Single and Double excitations RHF Restricted Hartree-Fock CCSD(T) Coupled Cluster Method with inclusion of Single, Double, and (perturbatively) Triple Excitations UHFBR Post-Hartree-Fock scheme with corrections for dispersion in- teractions XDM eXchange-hole Dipole Moment RCCSD(T) Restricted CCSD(T) CEPA Coupled Electron PAir method CC Close-Coupling