Analysis of estimators for Adaptive Kinetic Monte Carlo

Abstract

Adaptive Kinetic Monte Carlo combines the simplicity of Kinetic Monte Carlo (KMC) with a saddle point search algorithm based on Molecular Dynamics (MD) 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 criterion of S. T. Chill and G. Henkelman (J. Chem. Phys. 140 (2014), no. 21, 214110), which 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.