Nonadiabatic ring-polymer instanton rate theory: A generalized dividing-surface approach

Abstract

Constructing an accurate approximation to nonadiabatic rate theory that 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 tunneling 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 tunneling 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 that measures the flux both along nuclear coordinates and between electronic states, we develop a generalized 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.