Stochastic Transition States: Reaction Geometry amidst Noise

TL;DR

This paper introduces a stochastic, time-dependent dividing surface in phase space to accurately model reaction rates in noisy environments, addressing limitations of classical transition state theory.

Contribution

It develops a novel stochastic dividing surface that ensures a one-crossing condition for reaction paths in noisy systems, extending TST to fluctuating environments.

Findings

Provides a stochastic dividing surface that avoids recrossings

Enables exact rate calculations in noisy, fluctuating environments

Extends classical TST to stochastic systems

Abstract

Classical transition state theory (TST) is the cornerstone of reaction rate theory. It postulates a partition of phase space into reactant and product regions, which are separated by a dividing surface that reactive trajectories must cross. In order not to overestimate the reaction rate, the dynamics must be free of recrossings of the dividing surface. This no-recrossing rule is difficult (and sometimes impossible) to enforce, however, when a chemical reaction takes place in a fluctuating environment such as a liquid. High-accuracy approximations to the rate are well known when the solvent forces are treated using stochastic representations, though again, exact no-recrossing surfaces have not been available. To generalize the exact limit of TST to reactive systems driven by noise, we introduce a time-dependent dividing surface that is stochastically moving in phase space such that it is crossed once and only once by each transition path.