Calculation of reaction constants using Transition Path Sampling with a local Lyapunov bias

TL;DR

This paper introduces a novel method combining transition path sampling with a local Lyapunov bias to efficiently compute reaction rate constants in many-body systems, validated on Lennard-Jones clusters and iron crystals.

Contribution

The paper presents a new approach that enhances sampling of reactive trajectories using Lyapunov bias and estimates reaction rates with MBAR, improving accuracy and efficiency.

Findings

Accurately computed reaction constants for LJ38 cluster.

Estimated vacancy migration rates in alpha-iron at various temperatures.

Compared results with harmonic approximation, showing differences.

Abstract

We propose an efficient method to compute reaction rate constants of thermally activated processes occurring in many-body systems at finite temperature. The method consists in two steps: first, paths are sampled using a transition path sampling (TPS) algorithm supplemented with a local Lyapunov bias favoring diverging trajectories. This enhances the probability of observing rare reactive trajectories between stable states during relatively short simulations. Secondly, reaction constants are eventually estimated from the unbiased fraction of reactive paths, yielded by an appropriate statistical data analysis tool, the multistate Bennett acceptance ratio (MBAR) package. In order to test our algorithm, we compute reaction constants for structural transitions in LJ38, a well studied Lennard-Jones cluster, comparing our results to values previously reported in the literature. Additionally, we apply our method to the calculation of reaction rates for vacancy migration in an {\alpha}-Iron crystal, for temperatures ranging from 300 K to 850 K. Vacancy diffusion rates associated with activation barriers at finite temperature are then evaluated, and compared to values obtained using the standard harmonic approximation.