Analysis of estimators for adaptive Kinetic Monte Carlo

TL;DR

This paper evaluates and compares estimators used in adaptive Kinetic Monte Carlo simulations, focusing on their mathematical properties and effectiveness in estimating reaction rates.

Contribution

It analyzes a recent stopping criterion based on reaction rate fraction and introduces a related criterion valid without the Eyring-Kramers law.

Findings

Both estimators have well-behaved mean square errors that decrease over time.

The reaction rate-based criterion is effective for adaptive KMC.

Mathematical analysis confirms the estimators' reliability.

Abstract

Adaptive Kinetic Monte Carlo combines the simplicity of Kinetic Monte Carlo (KMC) with a Molecular Dynamics (MD) based saddle point search algorithm in order to simulate metastable systems. Key to making Adaptive KMC effective is a stopping criterion for the saddle point search. In this work, we examine a recent criterion, due to S. Chill and G. Henkelman, that is based on the fraction of total reaction rate found instead of the fraction of observed saddles. The criterion uses the Eyring-Kramers law to estimate the reaction rate at the MD search temperature. We also consider a related criterion that remains valid when the Eyring-Kramers law is not. We examine the mathematical properties of both estimators and prove their mean square errors are well behaved, vanishing as the simulation continues to run.