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Orbital Surface Hopping from Orbital Quantum-Classical Liouville Equation for Nonadiabatic Dynamics of Many-electron Systems

Yong-Tao Ma, Rui-Hao Bi, Wenjie Dou

Abstract

Accurate simulation the many-electronic nonadiabatic dynamics process at metal surfaces remains as a significant task. In this work, we present an orbital surface hopping (OSH) algorithm rigorously derived from the orbital quantum classical Liouville equation (o-QCLE) to deal with nonadiabatic dynamics for many-electron systems. This OSH algorithm closely connects with the popular Independent Electron Surface Hopping (IESH) method, which has shown remarkable success in addressing these nonadiabatic phenomena, except that electrons hop between orbitals. We compare OSH with IESH approach and benchmark these two algorithms against the surface hopping method with a full Configuration Interaction (FCI) wavefunction. Our approach shows strong agreement with IESH and FCI-SH results for molecular orbital populations and kinetic energy relaxation and in high efficiency, demonstrating the ability of the new OSH method in capturing key aspects of many-electronic nonadiabatic dynamics.

Orbital Surface Hopping from Orbital Quantum-Classical Liouville Equation for Nonadiabatic Dynamics of Many-electron Systems

Abstract

Accurate simulation the many-electronic nonadiabatic dynamics process at metal surfaces remains as a significant task. In this work, we present an orbital surface hopping (OSH) algorithm rigorously derived from the orbital quantum classical Liouville equation (o-QCLE) to deal with nonadiabatic dynamics for many-electron systems. This OSH algorithm closely connects with the popular Independent Electron Surface Hopping (IESH) method, which has shown remarkable success in addressing these nonadiabatic phenomena, except that electrons hop between orbitals. We compare OSH with IESH approach and benchmark these two algorithms against the surface hopping method with a full Configuration Interaction (FCI) wavefunction. Our approach shows strong agreement with IESH and FCI-SH results for molecular orbital populations and kinetic energy relaxation and in high efficiency, demonstrating the ability of the new OSH method in capturing key aspects of many-electronic nonadiabatic dynamics.
Paper Structure (12 sections, 37 equations, 5 figures, 1 table)

This paper contains 12 sections, 37 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theory and Methodology
  3. The Orbital Quantum Classical Liouville Equation
  4. Orbital surface hopping method (OSH)
  5. IESH method
  6. Full Configuration Interaction Surface Hopping
  7. Results and discussions
  8. Equilibrium system simulation
  9. Vibrational relaxation simulation
  10. Conclusion
  11. Derivation of Orbital Liouville-von Neumann Equation (Eq. \ref{['eqn:single_body_lvn']})
  12. Derivation of the fist order derivative coupling (DC) of different states.

Figures (5)

  • Figure 1: Impurity hole population dynamics as a function of time for OSH, IESH and FCI-SH. The inset shows the short-time behavior of the same dynamics. $n_\text{b} = 10$. $N_\text{traj}=128$ for FCI-SH.
  • Figure 2: Convergence of the population dynamics over $n_\text{b}$. The left and right panels show results for IESH and OSH, respectively. Line colors correspond to the number of bath metal orbitals, as indicated in the top color palette. The inset in the right panel compares IESH and OSH when $n_\text{b} = 100$.
  • Figure 3: Comparison of OSH, IESH, and FCI-FSSH in modeling the relaxation of NO ($\nu = 16$) at Au (111) surface. (a) Impurity hole population dynamics over time. (b) Kinetic energy evolution over time. $n_\text{b} = 10$. $N_\text{traj}=512$ for FCI-FSSH.
  • Figure 4: Convergence of final vibrational state $\nu$ over $n_\text{b}$. The left and right panels show results for IESH and OSH, respectively. Line colors correspond to the number of bath metal orbitals, as indicated in the top color palette. The inset in the right panel compares IESH and OSH when $n_\text{b} = 150$.
  • Figure 5: