Stability of the Minimum Energy Path

TL;DR

This paper proves the stability of minimum energy paths (MEPs) under landscape perturbations, advancing understanding of their robustness and aiding the convergence analysis of numerical methods like nudged elastic band and string methods.

Contribution

It introduces a new theoretical result demonstrating the stability of MEPs when the energy landscape is perturbed, which is essential for numerical approximation convergence.

Findings

Establishes the stability of MEPs under perturbations.

Provides a theoretical foundation for convergence of numerical methods.

Enhances understanding of transition path robustness.

Abstract

The minimum energy path (MEP) is the most probable transition path that connects two equilibrium states of a potential energy landscape. It has been widely used to study transition mechanisms as well as transition rates in the fields of chemistry, physics, and materials science. In this paper, we derive a novel result establishing the stability of MEPs under perturbations of the energy landscape. The result also represents a crucial step towards studying the convergence of various numerical approximations of MEPs, such as the nudged elastic band and string methods.