  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.
