Reaction rate calculation with time-dependent invariant manifolds

TL;DR

This paper introduces a method to compute time-dependent invariant manifolds in phase space to efficiently identify reactive trajectories and calculate reaction rates in systems influenced by a heat bath, avoiding extensive simulations.

Contribution

It presents a novel approach to determine invariant manifolds in time-dependent systems, enabling exact reaction rate calculations without full dynamical simulations.

Findings

Invariant manifolds can be computed for time-dependent systems.

Reactive trajectories can be identified from initial conditions alone.

Reaction rates can be calculated exactly using perturbation theory.

Abstract

The identification of trajectories that contribute to the reaction rate is the crucial dynamical ingredient in any classical chemical reactivity calculation. This problem often requires a full scale numerical simulation of the dynamics, in particular if the reactive system is exposed to the influence of a heat bath. As an efficient alternative, we propose here to compute invariant surfaces in the phase space of the reactive system that separate reactive from nonreactive trajectories. The location of these invariant manifolds depends both on time and on the realization of the driving force exerted by the bath. These manifolds allow the identification of reactive trajectories simply from their initial conditions, without the need of any further simulation. In this paper, we show how these invariant manifolds can be calculated, and used in a formally exact reaction rate calculation based on perturbation theory for any multidimensional potential coupled to a noisy environment.