Quantum equations for vibrational dynamics on metal surfaces

TL;DR

This paper develops a quantum theoretical framework for vibrational dynamics of molecules on metal surfaces, incorporating electronic friction and quantum noise, and compares it with classical models.

Contribution

It introduces a first-principles quantum Langevin equation approach for vibrational dynamics on metal surfaces, including effects of electronic friction and nonadiabatic coupling.

Findings

Quantum Langevin equation with electronic friction derived

Quantum noise and friction satisfy fluctuation-dissipation theorem

Classical limit aligns with existing models

Abstract

A first-principles treatment of the vibrational dynamics of molecular chemisorbates on metal surfaces is presented. It is shown that the mean field quantum evolution of the vibrational position operator is determined by a quantum Langevin equation with an electronic friction. In the mean field limit, the quantum noise and friction are related by the quantum fluctuation-dissipation theorem. The classical limit of this model is shown to agree with previously proposed models. A criterion is presented to describe the validity of the weak-coupling approximation and equations of motion for the dynamics in the presence of strong nonadiabatic coupling to electron-hole pairs are presented.