Convergence of the Discrete Minimum Energy Path

TL;DR

This paper proves the optimal convergence rate of the discrete minimum energy path computed via the nudged elastic band method, linking discretization size to accuracy in reaction mechanism simulations.

Contribution

It establishes a theoretical convergence rate for the discrete MEP in NEB, supported by numerical simulations on model systems.

Findings

Proves optimal convergence rate of discrete MEP in NEB

Numerical simulations confirm theoretical results

Links discretization size to accuracy of reaction pathway calculations

Abstract

The minimum energy path (MEP) describes the mechanism of reaction, and the energy barrier along the path can be used to calculate the reaction rate in thermal systems. The nudged elastic band (NEB) method is one of the most commonly used schemes to compute MEPs numerically. It approximates an MEP by a discrete set of configuration images, where the discretization size determines both computational cost and accuracy of the simulations. In this paper, we consider a discrete MEP to be a stationary state of the NEB method and prove an optimal convergence rate of the discrete MEP with respect to the number of images. Numerical simulations for the transitions of some several proto-typical model systems are performed to support the theory.