Vol. 11, No. 2, 2016

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
Analysis of estimators for Adaptive Kinetic Monte Carlo

David Aristoff, Samuel T. Chill and Gideon Simpson

Vol. 11 (2016), No. 2, 171–186
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.

Keywords
kinetic Monte Carlo, molecular dynamics, stopping time
Mathematical Subject Classification 2010
Primary: 65C05, 65C20, 82C80
Milestones
Received: 30 June 2015
Accepted: 21 September 2016
Published: 20 December 2016
Authors
David Aristoff
Department of Mathematics
Colorado State University
221 Weber Hall
Fort Collins, CO 80523-1894
United States
Samuel T. Chill
QuantumWise A/S
Austin, TX 78749
United States
Gideon Simpson
Department of Mathematics
Drexel University
Korman Center
33rd and Market Streets
Philadelphia, PA 19104
United States