Shannon Robin, Glowacki David R
Mechanical Engineering, Stanford University , Stanford, California 94305, United States.
School of Chemistry, University of Bristol , Bristol, BS8 1TS, United Kingdom.
J Phys Chem A. 2018 Feb 15;122(6):1531-1541. doi: 10.1021/acs.jpca.7b12521. Epub 2018 Jan 31.
The chemical master equation is a powerful theoretical tool for analyzing the kinetics of complex multiwell 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.
化学主方程是一种强大的理论工具，用于分析复杂多阱势能面的动力学，适用于化学动力学的广泛不同领域，包括燃烧、大气化学、气-固表面化学、溶液相化学和生物化学。求解化学主方程有两种成熟的方法：一种是随机的“动力学蒙特卡罗”方法，另一种是基于矩阵的方法。原则上，这两种方法得出的结果是相同的；哪种方法更适合特定研究取决于所研究特定系统的细节。在本文中，我们提出了一种将随机方法加速几个数量级的严格方法，以及一种对加速结果进行无偏处理以恢复“真实”值的方法。我们在本文中采用的方法受到所谓“盒装分子动力学”（BXD）方法的启发，该方法此前仅用于加速分子动力学模拟中的罕见事件。在这里，我们扩展了BXD方法，以设计一种简单的算法策略来加速随机动力学模拟中的罕见事件。对多个系统的测试表明，使用BXD罕见事件策略获得的结果与无偏结果高度一致。为了进行这些测试，我们在MESMER中实现了一种动力学蒙特卡罗方法，MESMER是一个跨平台、开源且免费可用的主方程求解器。
