Ring-polymer instanton theory of electron transfer in the nonadiabatic limit

TL;DR

This paper introduces a ring-polymer instanton method for calculating electron transfer rates in the nonadiabatic limit, providing a semiclassical approach that improves efficiency and accuracy over existing methods.

Contribution

The paper reformulates the golden-rule instanton method using a ring-polymer approach, enabling efficient numerical computation of electron transfer rates in the nonadiabatic limit.

Findings

The new method allows efficient minimization of multidimensional instanton trajectories.

Comparison shows the semiclassical approach is the steepest-descent limit of Wolynes' quantum instanton.

The approach offers improved accuracy in certain electron transfer scenarios.

Abstract

We take the golden-rule instanton method derived in the previous paper [arXiv:1509.04919] and reformulate it using a ring-polymer approach. This gives equations which can be used to compute the rates of electron-transfer reactions in the nonadiabatic (golden-rule) limit numerically within a semiclassical approximation. The multidimensional ring-polymer instanton trajectories are obtained efficiently by minimization of the action. In this form, comparison with Wolynes' quantum instanton method [P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987)] is possible and we show that our semiclassical approach is the steepest-descent limit of this method. We discuss advantages and disadvantages of both methods and give examples of where the new approach is more accurate.