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

Source: [A simple Boxed Molecular Kinetics approach to accelerate rare events in the stochastic kinetic master equation](<https://www.sota2.com/research/paper/68fa38c81e209131ce8bd0f2>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T23:07:48.316Z

Authors: Robin J Shannon, David R Glowacki

Published: 2018-11-26T12:37:30.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1811.10324>)

[PDF](<https://arxiv.org/pdf/1811.10324.pdf>)