An improved path-integral method for golden-rule rates

TL;DR

This paper introduces an improved path-integral method for calculating reaction rates in the Fermi golden-rule limit, effectively capturing tunnelling and zero-point energy effects, and is reliable for condensed phase systems.

Contribution

The authors develop a modified golden-rule quantum transition state theory that is size consistent and applicable to complex condensed phase systems, improving upon previous methods.

Findings

Accurately predicts quantum rates in one-dimensional models.

Remains reliable for multi-dimensional spin-boson models.

Effective in the Marcus inverted regime without analytic continuation.

Abstract

We present a simple method for the calculation of reaction rates in the Fermi golden-rule limit, which accurately captures the effects of tunnelling and zero-point energy. The method is based on a modification of the recently proposed golden-rule quantum transition state theory (GR-QTST) of Thapa, Fang and Richardson. While GR-QTST is not size consistent, leading to the possibility of unbounded errors in the rate, our modified method has no such issue and so can be reliably applied to condensed phase systems. Both methods involve path-integral sampling in a constrained ensemble; the two methods differ, however, in the choice of constraint functional. We demonstrate numerically that our modified method is as accurate as GR-QTST for the one-dimensional model considered by Thapa and coworkers. We then study a multi-dimensional spin-boson model, for which our method accurately predicts the true quantum rate, while GR-QTST breaks down with an increasing number of boson modes in the discretisation of the spectral density. Our method is able to accurately predict reaction rates in the Marcus inverted regime, without the need for the analytic continuation required by Wolynes theory.