Nonadiabatic ring-polymer instanton rate theory: a generalised dividing-surface approach

TL;DR

This paper develops a generalized nonadiabatic ring-polymer instanton rate theory that uses a tunable dividing surface to accurately approximate quantum rates across different electronic coupling regimes, providing new mechanistic insights.

Contribution

It introduces a novel dividing-surface approach that bridges existing limits in nonadiabatic instanton theories, enabling accurate rate calculations for arbitrary electronic couplings.

Findings

Accurately approximates quantum rates for studied systems.

Provides a new mechanistic perspective on nonadiabatic reactions.

Bridges the gap between weak and strong electronic coupling regimes.

Abstract

Constructing an accurate approximation to nonadiabatic rate theory which is valid for arbitrary values of the electronic coupling has been a long-standing challenge in theoretical chemistry. Ring-polymer instanton theories offer a very promising approach to solve this problem, since they can be rigorously derived using semiclassical approximations and can capture nuclear quantum effects such as tunnelling and zero-point energy at a cost similar to that of a classical calculation. A successful instanton rate theory already exists within the Born--Oppenheimer approximation, for which the optimal tunnelling pathway is located on a single adiabatic surface. A related instanton theory has also been developed for nonadiabatic reactions using two weakly-coupled diabatic surfaces within the framework of Fermi's golden rule. However, many chemical reactions do not satisfy the conditions of either limit. By employing a tunable dividing surface which measures the flux both along nuclear coordinates as well as between electronic states, we develop a generalised nonadiabatic instanton rate theory that bridges between these two limits. The resulting theory approximates the quantum-mechanically exact rates well for the systems studied and, in addition, offers a novel mechanistic perspective on nonadiabatic reactions.