Optimizing reaction coordinate by flux maximization in the transition path ensemble

Abstract

The transition path ensemble is a collection of reactive trajectories, all of which largely keep going forward along the transition channel from the reactant state to the product one, and is believed to possess the information necessary for the identification of reaction coordinates. Previously, the full coordinates (both position and momentum) of the snapshots in the transition path ensemble were utilized to obtain the reaction coordinate [W. Li and A. Ma, J. Chem. Phys. 144, 114103 (2016) and W. Li, J. Chem. Phys. 148, 084105 (2018)]. Here, with the conformational (or position) coordinates alone, it is suggested that a meaningful one-dimensional representation of the reaction coordinate can be obtained by maximizing the flux (the net number of transitions through the dividing surface) of a given coordinate in the transition path ensemble. In the application to alanine dipeptide in vacuum, dihedral angles ϕ and θ were identified to be the two best reaction coordinates, which was consistent with the results in the existing studies. A linear combination of these two coordinates gave a better reaction coordinate, which is highly correlated with the committor. Most importantly, the method obtained a linear combination of pairwise distances between heavy atoms, which was highly correlated with the committor as well. The standard deviation of the committor at the transition region defined by the optimized reaction coordinate is as small as 0.08. In addition, the effects of practical factors, such as the choice of transition path sub-ensembles and saving interval between frames in transition paths, on reaction coordinate optimization were also considered.