Singh Aditya N, Limmer David T
Department of Chemistry, University of California, Berkeley, California 94720, USA.
Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
J Chem Phys. 2024 Aug 7;161(5). doi: 10.1063/5.0203840.
The committor constitutes the primary quantity of interest within chemical kinetics as it is understood to encode the ideal reaction coordinate for a rare reactive event. We show the generative utility of the committor in that it can be used explicitly to produce a reactive trajectory ensemble that exhibits numerically exact statistics as that of the original transition path ensemble. This is done by relating a time-dependent analog of the committor that solves a generalized bridge problem to the splitting probability that solves a boundary value problem under a bistable assumption. By invoking stochastic optimal control and spectral theory, we derive a general form for the optimal controller of a bridge process that connects two metastable states expressed in terms of the splitting probability. This formalism offers an alternative perspective into the role of the committor and its gradients in that they encode force fields that guarantee reactivity, generating trajectories that are statistically identical to the way that a system would react autonomously.
在化学动力学中，反应坐标是主要关注的量，因为它被认为编码了罕见反应事件的理想反应坐标。我们展示了反应坐标的生成效用，即它可以被明确地用于生成一个反应轨迹系综，该系综表现出与原始过渡路径系综在数值上精确的统计特性。这是通过将解决广义桥接问题的反应坐标的时间相关类似物与在双稳假设下解决边界值问题的分裂概率联系起来实现的。通过调用随机最优控制和谱理论，我们推导出了一个桥接过程最优控制器的一般形式，该桥接过程连接两个用分裂概率表示的亚稳状态。这种形式主义为反应坐标及其梯度的作用提供了另一种视角，因为它们编码了保证反应性的力场，生成的轨迹在统计上与系统自主反应的方式相同。
