Computing the committor with the committor to study the transition state ensemble

Abstract

The study of the kinetic bottlenecks that hinder the rare transitions between long-lived metastable states is a major challenge in atomistic simulations. Here we propose a method to explore the transition state ensemble, which is the distribution of configurations that the system passes through as it translocates from one metastable basin to another. We base our method on the committor function and the variational principle that 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 the sampling of 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 a systematic approach for the interpretation of simulation results and the construction of efficient physics-informed collective variables. A self-consistent iterative procedure is proposed to compute the committor function for rare events, via a variational principle, and extensively sample the transition state ensemble, allowing for the identification of the relevant variables in the process.