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Modeling Nonadiabatic Dynamics at Molecule-Metal Interfaces University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2018 Modeling Nonadiabatic Dynamics At Molecule-Metal Interfaces Wenjie Dou University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Physical Chemistry Commons Recommended Citation Dou, Wenjie, "Modeling Nonadiabatic Dynamics At Molecule-Metal Interfaces" (2018). Publicly Accessible Penn Dissertations. 2699. https://repository.upenn.edu/edissertations/2699 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/2699 For more information, please contact [email protected]. Modeling Nonadiabatic Dynamics At Molecule-Metal Interfaces Abstract The coupled electronic-nuclear dynamics at molecule-metal interfaces are fundamental processes that underlie many distinct areas of science: from electrochemistry, chemisorption, heterogeneous catalysis, quantum dots, all the way to molecular conduction. Simulating these coupled dynamics at molecule- metal interfaces is very challenging, due to the breakdown of the Born-Oppenheimer approximation and the inclusion of a manifold of electrons from the metal. Two methods are presented to investigate these nonadiabatic dynamics: a) In the outer sphere regime (weak electronic coupling between molecule and metal), a surface hopping approach is developed to treat nuclear motion classically with electronic motion captured by hopping between different potential energy surfaces; b) In the inner sphere regime (strong electronic coupling between molecule and metal), electronic dynamics are incorporated into a frictional force (i.e. electronic friction) together with a random force. In addition, a natural combination of these two methods called a broadened classical master equation (BCME) is developed. As benchmarked against numerical exact solutions, the BCME works well in both inner and outer sphere regimes. Finally, a universal form of electronic friction is derived. Such a formula unifies many different forms of electronic friction in the literature and allows the inclusion of electron-electron interactions, and can demonstrate interesting Kondo resonances at low temperature. Degree Type Dissertation Degree Name Doctor of Philosophy (PhD) Graduate Group Chemistry First Advisor Joseph E. Subotnik Keywords chemisorption, electronic friction, interfaces, metal, nonadiabatic dynamics, surface hopping Subject Categories Physical Chemistry This dissertation is available at ScholarlyCommons: https://repository.upenn.edu/edissertations/2699 MODELING NONADIABATIC DYNAMICS AT MOLECULE-METAL INTERFACES Wenjie Dou A DISSERTATION in Chemistry Presented to the Faculties of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2018 Supervisor of Dissertation Joseph E. Subotnik, Professor of Chemistry Graduate Group Chairperson Gary A. Molander, Hirschmann-Makineni Professor of Chemistry Dissertation Committee Andrew M. Rappe, Blanchard Professor of Chemistry Marsha I. Lester, Edmund J. Kahn Distinguished Professor Jessica M. Anna, Professor of Chemistry MODELING NONADIABATIC DYNAMICS AT MOLECULE-METAL INTERFACES c COPYRIGHT 2018 Wenjie Dou This work is licensed under the Creative Commons Attribution NonCommercial-ShareAlike 3.0 License To view a copy of this license, visit ACKNOWLEDGEMENT Graduate school has been very confusing. I would not have gone through graduate school eventually without lots of helps and guidances from many people. Particularly, many thanks to my research advisor Joe Subotnik, who is a great advisor. With great kindness and being very very supportive, he teaches me everything, from writing, communication, presentation all the way to science. I would not have gone that far without he being role model of how to approach science. I would also like to thank Abe Nitzan, who is our close collaborator and effectively my secondary advisor. He is very very patient and has great physical intuition. I will remember his famous saying/question: small (or large parameter) compared to what? Also he got me interested in metal surface during my first year, which becomes the topic of this dissertation. I am very grateful to have such a tremendous pair of advisors in graduate school. I also want to thank our collaborators Prof. Michael Thoss and his student Christian Schinabeck on electron transport properties study. It was a good collaboration and resulted in fruitful outcomes. I would also like to thank my committee members: Prof. Andrew Rappe, Prof. Marsha Lester and Prof. Jessica Anna. Many thanks to them for providing valuable feedback and special thanks to Prof. Rappe for also being helpful during my postdoc searching. I would also like to thank students and postdocs in Subotnik Group that provide friendship and helps (though this list is not exhaustive): Brian Landry, Kousik Samanta, Andrew Petit, Amber Jain, Ethan Alguire, Greg Medders, Xinle Liu, Qi Ou, Wenjun Ouyang, Nicole Bellonzi, Gaohan Miao, Zuxin Jin, Theta Chen, Alec Coffman, Tao Li, Hung-Hsuan Teh. All members of Rappe Group and Nitzan group during my time as well as all my friends in graduate school also have my appreciation. Finally very sincere thanks to my family, who have been caring me so much but also give me freedom to work on my goal. iii ABSTRACT MODELING NONADIABATIC DYNAMICS AT MOLECULE-METAL INTERFACES Wenjie Dou Joseph E. Subotnik The coupled electronic-nuclear dynamics at molecule-metal interfaces are fundamental pro- cesses that underlie many distinct areas of science: from electrochemistry, chemisorption, heterogeneous catalysis, quantum dots, all the way to molecular conduction. Simulating these coupled dynamics at molecule-metal interfaces is very challenging, due to the break- down of the Born-Oppenheimer approximation and the inclusion of a manifold of electrons from the metal. Two methods are presented to investigate these nonadiabatic dynamics: a) In the outer sphere regime (weak electronic coupling between molecule and metal), a surface hopping approach is developed to treat nuclear motion classically with electronic motion captured by hopping between different potential energy surfaces; b) In the inner sphere regime (strong electronic coupling between molecule and metal), electronic dynam- ics are incorporated into a frictional force (i.e. electronic friction) together with a random force. In addition, a natural combination of these two methods called a broadened classical master equation (BCME) is developed. As benchmarked against numerical exact solutions, the BCME works well in both inner and outer sphere regimes. Finally, a universal form of electronic friction is derived. Such a formula unifies many different forms of electronic friction in the literature and allows the inclusion of electron-electron interactions, and can demonstrate interesting Kondo resonances at low temperature. iv TABLE OF CONTENTS ACKNOWLEDGEMENT . ii ABSTRACT . iii LIST OF ILLUSTRATIONS . xvii CHAPTER 1 : Introduction . 1 1.1 The Born-Oppenheimer approximation . 1 1.2 Nonadiabatic dynamics: Tully's fewest switch surface hopping . 3 1.3 Nonadiabatic dynamics at molecule-metal interfaces . 5 1.4 Theory . 8 1.5 Overview of this dissertation . 12 CHAPTER 2 : Surface Hopping with A Manifold of Electronic States II: Application to the Many-Body Anderson-Holstein Model . 14 2.1 Introduction . 14 2.2 Theory . 16 2.3 Results and Discussion . 26 2.4 Conclusions . 35 2.5 Appendix . 37 CHAPTER 3 : Surface hopping with a manifold of electronic states, III: transients, broadening and the Marcus picture . 40 3.1 Introduction . 40 3.2 Transient dynamics . 42 3.3 ET rate for the AH model . 47 3.4 Broadening by the Marcus rate . 52 v 3.5 Steady state current . 53 3.6 Conclusions . 58 CHAPTER 4 : Frictional effects near a metal surface . 61 4.1 Introduction . 61 4.2 Electronic friction . 63 4.3 Results . 69 4.4 Conclusions . 77 4.5 Appendix . 78 CHAPTER 5 : A broadened classical master equation approach for nonadiabatic dy- namics at metal surfaces: beyond the weak molecule-metal coupling limit . 83 5.1 Introduction . 83 5.2 Theory . 86 5.3 Modified surface hopping procedure . 91 5.4 Results . 93 5.5 Conclusions . 97 5.6 Appendix . 101 CHAPTER 6 : A broadened classical master equation approach for treating electron- nuclear coupling in non-equilibrium transport . 109 6.1 Introduction . 109 6.2 Broadened classical master equation (BCME) . 111 6.3 QME and bQME . 117 6.4 Hierarchical Quantum Master Equation (HQME) . 119 6.5 Results . 122 6.6 Conclusions . 127 6.7 Appendix . 128 vi CHAPTER 7 : A generalized surface hopping algorithm to model non-adiabatic dy- namics near metal surfaces: The case of multiple electronic orbitals 130 7.1 Introduction . 130 7.2 Equation of motion . 132 7.3 Surface hopping algorithms . 135 7.4 Results and Discussion . 144 7.5 Conclusions . 148 7.6 Appendix . 148 CHAPTER 8 : Born-Oppenheimer Dynamics, Electronic Friction, and the Inclusion of Electron-Electron Interactions . 154 8.1 Introduction . 154 8.2 Theory . 157 8.3 Anderson-Holstein model . 160 8.4 Conclusions . 162 CHAPTER 9 : Universality of electronic friction I: the equivalence of von Oppen's nonequilibrium Green's function approach and the Head-Gordon{ Tully model at equilibrium . 165 9.1 Introduction . 165 9.2 Non-Equilibrium Green's Function . 169 9.3 A model with system-bath separation . 174 9.4 Discussion . 178 9.5 Conclusions . 179 CHAPTER 10 : The universality of electronic friction II: Equivalence of the quantum-
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