Transition state trajectory stability determines barrier crossing rates in chemical reactions induced by time-dependent oscillating fields

TL;DR

This paper demonstrates that the rate of barrier crossing in chemical reactions driven by periodic external fields can be accurately predicted by analyzing the stability of the time-dependent transition state using Floquet exponents, eliminating the need for extensive trajectory simulations.

Contribution

It introduces a stability-based method to determine reaction rates for time-dependent transition states, linking Floquet exponents to crossing rates.

Findings

Floquet exponents accurately predict crossing rates

Stability analysis matches simulation results

Method reduces computational effort for rate calculation

Abstract

When a chemical reaction is driven by an external field, the transition state that the system must pass through as it changes from reactant to product -for example, an energy barrier- becomes time-dependent. We show that for periodic forcing the rate of barrier crossing can be determined through stability analysis of the non-autonomous transition state. Specifically, strong agreement is observed between the difference in the Floquet exponents describing stability of the transition state trajectory, which defines a recrossing-free dividing surface [G. T. Craven, T. Bartsch, and R. Hernandez, Phys. Rev. E 89, 040801(R) (2014)], and the rates calculated by simulation of ensembles of trajectories. This result opens the possibility to extract rates directly from the intrinsic stability of the transition state, even when it is time-dependent, without requiring a numerically-expensive simulation of the long-time dynamics of a large ensemble of trajectories.