Nonadiabatic instanton rate theory beyond the golden-rule limit

TL;DR

This paper develops a first-principles semiclassical theory extending the golden-rule instanton rate to account for stronger diabatic couplings, including recrossing effects and potential energy changes, with minimal additional computational effort.

Contribution

It introduces the first-principles derivation of the next-order correction beyond the golden-rule instanton rate, incorporating new pathways and effects of diabatic coupling.

Findings

Derivation of a sum of three components for the next-order rate correction.

Identification of new instanton pathways that include recrossing effects.

The theory requires little additional computational effort.

Abstract

Fermi's golden rule describes the leading-order behaviour of the reaction rate as a function of the diabatic coupling. Its asymptotic $(\hbar \rightarrow 0)$ limit is the semiclassical golden-rule instanton rate theory, which rigorously approximates nuclear quantum effects, lends itself to efficient numerical computation and gives physical insight into reaction mechanisms. However the golden rule by itself becomes insufficient as the strength of the diabatic coupling increases, so higher-order terms must be additionally considered. In this work we give a first-principles derivation of the next-order term beyond the golden rule, represented as a sum of three components. Two of them lead to new instanton pathways that extend the golden-rule case and, among other factors, account for the effects of recrossing on the full rate. The remaining component derives from the equilibrium partition function and accounts for changes in potential energy around the reactant and product wells due to diabatic coupling. The new semiclassical theory demands little computational effort beyond a golden-rule instanton calculation. It makes it possible to rigorously assess the accuracy of the golden-rule approximation and sets the stage for future work on general semiclassical nonadiabatic rate theories.