Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Orbital Surface Hopping with an Electron Thermostat Yields Accurate Dynamics and Detailed Balance

Yongtao Ma, Wenjie Dou

TL;DR

The paper addresses the failure of discretized metal electronic continua in mixed quantum-classical surface dynamics to reproduce energy dissipation and detailed balance. It introduces an electronic thermostat within the Orbital Surface Hopping framework, derives the governing equations under open-system assumptions, and benchmarks the method against numerically exact HEOM results. The authors show that OSH with the electronic thermostat accurately reproduces long-time dynamics and equilibrium populations, aligning with HEOM, and provide comparisons with Tully’s thermostat under varying coupling and friction conditions. The work offers a scalable, physically consistent approach for simulating nonadiabatic dynamics near metal surfaces across multiple electronic states, with guidance on method choice depending on the system’s open- vs closed-system nature.

Abstract

In mixed quantum-classical simulations of molecule-metal surface interactions, the discretization of the metallic electronic continuum typically results in a closed-system representation that fails to capture the open-system nature of the true physical process. This approximation can introduce significant artifacts, including deviations in the dynamical evolution and a violation of the principle of detailed balance. To address this fundamental challenge, we introduce an electronic thermostat into our previously developed orbital surface hopping (OSH) framework, generalizing the method to efficiently handle many discrete electronic states. We first outline the derivation of electronic thermostat orbital surface hopping, where the amplitude of the electronic thermostat is well justified. We then demonstrate that this method can reproduce accurate dynamics and detailed balance in long time, whereas without electronic thermostat the detailed balance is violated. Thus, this method offers a reliable tool for studying nonadiabatic dynamics near metal surfaces.

Orbital Surface Hopping with an Electron Thermostat Yields Accurate Dynamics and Detailed Balance

TL;DR

The paper addresses the failure of discretized metal electronic continua in mixed quantum-classical surface dynamics to reproduce energy dissipation and detailed balance. It introduces an electronic thermostat within the Orbital Surface Hopping framework, derives the governing equations under open-system assumptions, and benchmarks the method against numerically exact HEOM results. The authors show that OSH with the electronic thermostat accurately reproduces long-time dynamics and equilibrium populations, aligning with HEOM, and provide comparisons with Tully’s thermostat under varying coupling and friction conditions. The work offers a scalable, physically consistent approach for simulating nonadiabatic dynamics near metal surfaces across multiple electronic states, with guidance on method choice depending on the system’s open- vs closed-system nature.

Abstract

In mixed quantum-classical simulations of molecule-metal surface interactions, the discretization of the metallic electronic continuum typically results in a closed-system representation that fails to capture the open-system nature of the true physical process. This approximation can introduce significant artifacts, including deviations in the dynamical evolution and a violation of the principle of detailed balance. To address this fundamental challenge, we introduce an electronic thermostat into our previously developed orbital surface hopping (OSH) framework, generalizing the method to efficiently handle many discrete electronic states. We first outline the derivation of electronic thermostat orbital surface hopping, where the amplitude of the electronic thermostat is well justified. We then demonstrate that this method can reproduce accurate dynamics and detailed balance in long time, whereas without electronic thermostat the detailed balance is violated. Thus, this method offers a reliable tool for studying nonadiabatic dynamics near metal surfaces.

Paper Structure

This paper contains 9 sections, 21 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Results and discussion
  4. Simulation details
  5. Benchmarked with HEOM methods
  6. Comparison under pure electron thermostat
  7. Comparison with external friction
  8. Conclusion
  9. Compare parameters for external fiction

Figures (4)

  • Figure 1: Time evolution of the impurity hole population and kinetic energy, comparing the standard OSH, OSH with electronic thermostat (OSH-ETS), and HEOM methods. The inset shows the short-time evolution of the same quantities.
  • Figure 2: Kinetic energy (top) and impurity hole population dynamics (bottom) as a function of time. Results are shown for three methods: OSH, OSH-ETS, and OSH with Tully's electronic thermostat approach ($\tau$ = 100), across a range of coupling strengths: (left) $\Gamma = 6.4 \times 10^{-3}$, (middle) $\Gamma = 1.6 \times 10^{-3}$, and (right) $\Gamma = 4.0 \times 10^{-4}$. The insets zoom in on the short-time behavior.
  • Figure 3: Impurity hole population dynamics as a function of time for OSH, OSH-ETS and OSH ($\tau =$ 100 and 500 for Tully's electronic thermostat method).
  • Figure 4: Impurity hole population dynamics and kinetic energy as a function of time for OSH, OSH-ETS and OSH with Tully's electronic thermostat approach ($\tau$ = 100 and 500).