Nonadiabatic Dynamics of Molecules Interacting with Metal Surfaces: Extending the Hierarchical Equations of Motion and Langevin Dynamics Approach to Position-Dependent Metal-Molecule Couplings

TL;DR

This paper extends the hierarchical equations of motion and Langevin dynamics methods to include position-dependent metal-molecule couplings, enabling more accurate simulations of nonadiabatic molecular dynamics at metal surfaces.

Contribution

It introduces a novel extension of electronic friction theory to models with position-dependent couplings within the hierarchical equations of motion framework.

Findings

New expressions for electronic forces accounting for position dependence

Applicable to both equilibrium and nonequilibrium conditions

Demonstrated on various molecular models

Abstract

Electronic friction and Langevin dynamics is a popular mixed quantum-classical method for simulating the nonadiabatic dynamics of molecules interacting with metal surfaces, as it can be computationally more efficient than fully quantum approaches. Previous approaches to calculating the electronic friction and other forces, however, have been limited to either noninteracting molecular models or position-independent metal-molecule couplings. In this work, we extend the theory of electronic friction within the hierarchical equations of motion formalism to models with a position-dependent metal-molecule coupling. We show that the addition of a position-dependent metal-molecule coupling adds new contributions to the electronic friction and other forces, which are highly relevant for many physical processes. Our expressions for the electronic forces within the Langevin equation are valid both in and out of equilibrium and for molecular models containing strong interactions. We demonstrate the approach by applying it to different models of interest.