Atomistic simulations of rare events using gentlest ascent dynamics

TL;DR

This paper extends the gentlest ascent dynamics (GAD) method to finite temperature conditions, enabling efficient sampling of saddle points in complex energy landscapes, demonstrated on surface defect systems.

Contribution

The paper introduces a finite temperature extension of GAD for sampling saddle points, improving simulation of rare events in high-dimensional energy surfaces.

Findings

Successfully applied to surface vacancy and ad-atom pair

Effectively sampled low barrier saddle points

Demonstrated on copper (111) surface systems

Abstract

The dynamics of complex systems often involve thermally activated barrier crossing events that allow these systems to move from one basin of attraction on the high dimensional energy surface to another. Such events are ubiquitous, but challenging to simulate using conventional simulation tools, such as molecular dynamics. Recently, Weinan E et al. [Nonlinearity, 24(6),1831(2011)] proposed a set of dynamic equations, the gentlest ascent dynamics (GAD), to describe the escape of a system from a basin of attraction and proved that solutions of GAD converge to index-1 saddle points of the underlying energy. In this paper, we extend GAD to enable finite temperature simulations in which the system hops between different saddle points on the energy surface. An effective strategy to use GAD to sample an ensemble of low barrier saddle points located in the vicinity of a locally stable configuration on the high dimensional energy surface is proposed. The utility of the method is demonstrated by studying the low barrier saddle points associated with point defect activity on a surface. This is done for two representative systems, namely, (a) a surface vacancy and ad-atom pair and (b) a heptamer island on the (111) surface of copper.