Stochastic formalism for thermally driven distribution frontier: A nonempirical approach to the potential escape problem

TL;DR

This paper introduces a non-empirical stochastic method to identify minimum-energy escape paths from potential minima to saddle points, relying solely on local gradient and Hessian information, applicable to rare event simulations.

Contribution

The paper presents a novel stochastic algorithm that finds escape paths without empirical variables, using only local potential derivatives, advancing first-principles rare event simulations.

Findings

Successfully applied to a 2D model potential

Demonstrated effective path finding to saddle points

Potential for first-principles rare event simulations

Abstract

We develop a non-empirical scheme to search for the minimum-energy escape paths from the minima of the potential surface to unknown saddle points nearby. A stochastic algorithm is constructed to move the walkers up the surface through the potential valleys. This method employs only the local gradient and diagonal part of the Hessian matrix of the potential. An application to a two-dimensional model potential is presented to demonstrate the successful finding of the paths to the saddle points. The present scheme could serve as a starting point toward first-principles simulation of rare events across the potential basins free from empirical collective variables.