Dominant Reaction Pathways in High Dimensional Systems

TL;DR

This paper introduces a theoretical and computational framework to efficiently identify and analyze the most probable reaction pathways in high-dimensional systems governed by Langevin dynamics, accounting for thermal fluctuations.

Contribution

It develops a novel method to sample significant reaction pathways and compute fluctuation corrections, enhancing understanding of transition states in complex systems.

Findings

Successfully applied to a 2D diffusion model with a funnel potential.

Able to generate transition state conformations.

Provides predictions for observable evolution during reactions.

Abstract

This paper is devoted to the development of a theoretical and computational framework to efficiently sample the statistically significant thermally activated reaction pathways, in multi-dimensional systems obeying Langevin dynamics. We show how to obtain the set of most probable reaction pathways and compute the corrections due to quadratic thermal fluctuations around such trajectories. We discuss how to obtain predictions for the evolution of arbitrary observables and how to generate conformations which are representative of the transition state ensemble. We present an illustrative implementation of our method by studying the diffusion of a point particle in a 2-dimensional funneled external potential.