A simple Boxed Molecular Kinetics approach to accelerate rare events in the stochastic kinetic master equation

Abstract

The chemical master equation is a powerful theoretical tool for analysing the kinetics of complex multi-well potential energy surfaces in a wide range of different domains of chemical kinetics spanning combustion, atmospheric chemistry, gas surface chemistry, solution phase chemistry, and biochemistry. There are two well-established methodologies for solving the chemical master equation: a stochastic kinetic Monte Carlo approach and a matrix-based approach. In principle, the results yielded by both approaches are identical; the decision of which approach is better suited to a particular study depends on the details of the specific system under investigation. In this article, we present a rigorous method for accelerating stochastic approaches by several orders of magnitude, along with a method for unbiasing the accelerated results to recover the true value. The approach we take in this paper is inspired by the so-called boxed molecular dynamics (BXD) method, which has previously only been applied to accelerate rare events in molecular dynamics simulations. Here we extend BXD to design a simple algorithmic strategy for accelerating rare events in stochastic kinetic simulations. Tests on a number of systems show that the results obtained using the BXD rare event strategy are in good agreement with unbiased results. To carry out these tests, we have implemented a kinetic Monte Carlo approach in MESMER, which is a cross platform, open-source, and freely available master equation solver.