A general non-adiabatic quantum instanton approximation

TL;DR

The paper introduces the non-adiabatic quantum instanton (NAQI) method for calculating reaction rates in systems with two electronic states, unifying previous theories and demonstrating accuracy through comparisons with exact solutions.

Contribution

The paper develops a general NAQI approach that bridges Wolynes theory and the projected quantum instanton method, applicable to complex non-adiabatic reactions.

Findings

NAQI reduces to Wolynes theory in the golden rule limit

NAQI reduces to the projected quantum instanton in the adiabatic limit

Accurate rate calculations for one-dimensional scattering problems

Abstract

We present a general quantum instanton approach to calculating reaction rates for systems with two electronic states and arbitrary values of the electronic coupling. This new approach, which we call the non-adiabatic quantum instanton (NAQI) approximation, reduces to Wolynes theory in the golden rule limit and to a recently proposed projected quantum instanton (PQI) method in the adiabatic limit. As in both of these earlier theories, the NAQI approach is based on making a saddle point approximation to the time integral of a reactive flux autocorrelation function, although with a generalised definition of the projection operator onto the product states. We illustrate the accuracy of the approach by comparison with exact rates for one dimensional scattering problems and discuss its applicability to more complex reactions.