Computing the Committor with the Committor: an Anatomy of the Transition State Ensemble

The study of the kinetic bottlenecks that hinder the rare transitions between long-lived metastable states is a major challenge in atomistic simulations. We propose a method to explore the transition state ensemble, which is the distribution of configurations that the system passes as it translocates from one metastable basin to another. We base our method on the committor function and the variational principle to which it obeys. We find its minimum through a self-consistent procedure that starts from information limited to the initial and final states. Right from the start, our procedure allows sampling very many transition state configurations. With the help of the variational principle, we perform a detailed analysis of the transition state ensemble, ranking quantitatively the degrees of freedom mostly involved in the transition and enabling for a systematic approach for the interpretation of simulation results and the construction of efficient physics-informed collective variables.探究阻碍长寿命亚稳态间稀有跃迁的动力学瓶颈，是原子尺度模拟（atomistic simulations）领域的核心难题之一。我们提出一种用于探索过渡态系综（transition state ensemble）的方法：该系综指代系统从某一亚稳态势阱跃迁至另一亚稳态势阱时所途经的全部构型的分布。我们的方法以归属函数（committor function）及其所遵循的变分原理（variational principle）为基础构建。仅依托初始态与终态的有限信息，我们即可通过自洽流程求得其极小值。该流程从初始阶段便可实现大量过渡态构型的采样。借助变分原理，我们可对过渡态系综开展精细化分析：定量排序出跃迁过程中占主导地位的自由度，并为模拟结果的系统化解读以及高效物理引导型集体变量（collective variables）的构建提供了系统性可行方案。