Kinetic Analysis of Discrete Path Sampling Stationary Point Databases

TL;DR

This paper introduces new methods for analyzing large stationary point databases in kinetic studies, improving accuracy and efficiency by removing steady-state assumptions and optimizing minima grouping.

Contribution

It presents two novel approaches that enhance kinetic analysis accuracy and speed by eliminating steady-state assumptions and optimizing minima grouping.

Findings

Steady-state assumption removal improves kinetic analysis accuracy.

Leapfrog moves prevent oscillations in kinetic Monte Carlo trajectories.

Grouping minima speeds up analysis at low temperatures.

Abstract

Analysing stationary point databases to extract phenomenological rate constants can become time-consuming for systems with large potential energy barriers. In the present contribution we analyse several different approaches to this problem. First, we show how the original rate constant prescription within the discrete path sampling approach can be rewritten in terms of committor probabilities. Two alternative formulations are then derived in which the steady-state assumption for intervening minima is removed, providing both a more accurate kinetic analysis, and a measure of whether a two-state description is appropriate. The first approach involves running additional short kinetic Monte Carlo (KMC) trajectories, which are used to calculate waiting times. Here we introduce `leapfrog' moves to second-neighbour minima, which prevent the KMC trajectory oscillating between structures separated by low barriers. In the second approach we successively remove minima from the intervening set, renormalising the branching probabilities and waiting times to preserve the mean first-passage times of interest. Regrouping the local minima appropriately is also shown to speed up the kinetic analysis dramatically at low temperatures. Applications are described where rates are extracted for databases containing tens of thousands of stationary points, with effective barriers that are several hundred times kT.