Analysis of estimators for adaptive Kinetic Monte Carlo
For researchers using Adaptive KMC to simulate metastable systems, this provides theoretical validation of existing stopping criteria and a new criterion when Eyring-Kramers law fails.
This work analyzes stopping criteria for saddle point searches in Adaptive Kinetic Monte Carlo, proving that two estimators based on reaction rate fraction have mean square errors that vanish as simulation continues.
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.