Ji Xiaojun, Wang Ru, Wang Hao, Liu Wenjian
Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao, Shandong 266237, People's Republic of China.
Frontiers Science Center for Nonlinear Expectations (Ministry of Education), Shandong University, Qingdao, Shandong 266237, People's Republic of China.
J Chem Phys. 2023 Dec 28;159(24). doi: 10.1063/5.0180513.
As an optimal one-dimensional reaction coordinate, the committor function not only describes the probability of a trajectory initiated at a phase space point first reaching the product state before reaching the reactant state but also preserves the kinetics when utilized to run a reduced dynamics model. However, calculating the committor function in high-dimensional systems poses significant challenges. In this paper, within the framework of milestoning, exact expressions for committor functions at two levels of coarse graining are given, including committor functions of phase space point to point (CFPP) and milestone to milestone (CFMM). When combined with transition kernels obtained from trajectory analysis, these expressions can be utilized to accurately and efficiently compute the committor functions. Furthermore, based on the calculated committor functions, an adaptive algorithm is developed to gradually refine the transition state region. Finally, two model examples are employed to assess the accuracy of these different formulations of committor functions.
作为一种最优的一维反应坐标，反应几率函数不仅描述了从相空间某点出发的轨迹在到达反应物状态之前先到达产物状态的概率，而且在用于运行约化动力学模型时能保留动力学信息。然而，在高维系统中计算反应几率函数面临重大挑战。本文在里程碑法的框架内，给出了两个粗粒化层次上反应几率函数的精确表达式，包括相空间点到点的反应几率函数（CFPP）和里程碑到里程碑的反应几率函数（CFMM）。当与从轨迹分析获得的转移核相结合时，这些表达式可用于准确高效地计算反应几率函数。此外，基于计算得到的反应几率函数，开发了一种自适应算法来逐步细化过渡态区域。最后，通过两个模型示例来评估这些不同形式的反应几率函数的准确性。
