On the Breakdown of the Ehrenfest Method for Molecular Dynamics on Surfaces

TL;DR

This paper investigates the limitations of the Ehrenfest method in molecular dynamics on surfaces, identifying conditions under which it fails due to electronic state interactions, thereby informing the applicability of related friction theories.

Contribution

The study provides a clear criterion for when the Ehrenfest approach breaks down in surface molecular dynamics, based on models and the Landau-Zener formula.

Findings

Ehrenfest method fails under specific electronic state conditions.

Derived a breakdown criterion using the Massey parameter.

Validated the criterion with exactly solvable models.

Abstract

Due to a continuum of electronic states present in periodic systems, the description of molecular dynamics on surfaces poses a serious computational challenge. One of the most used families of approaches in these settings are friction theories, which are based on the Ehrenfest (EH) approach. Yet, a mean-field treatment of electronic degrees of freedom in the EH method makes this approach inaccurate in some cases. Our aim is to clarify when EH breaks down for molecular dynamics on surfaces. Answering this question provides limits of applicability for more approximate friction theories derived from EH. We assess the EH method on one-dimensional, numerically exactly solvable models with a large but finite number of electronic states. Using the Landau-Zener formula and the Massey parameter, an expression that determines when EH breaks down is deduced.