On Committor Functions in Milestoning

TL;DR

This paper presents exact formulas for committor functions within Milestoning, enabling efficient computation and adaptive refinement of transition states in high-dimensional systems, validated through model examples.

Contribution

It introduces novel exact expressions for committor functions at different coarse-graining levels within Milestoning, facilitating accurate and efficient calculations.

Findings

Exact formulas for CFPP and CFMM are derived.

An adaptive algorithm improves transition state identification.

Model examples demonstrate the accuracy of the formulations.

Abstract

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.