Instanton formulation of Fermi's golden rule in the Marcus inverted regime

TL;DR

This paper extends semiclassical instanton theory to the Marcus inverted regime, enabling more accurate quantum tunnelling rate calculations for molecular transitions in this regime, which was previously limited to the normal regime.

Contribution

The authors develop an instanton method applicable to the Marcus inverted regime, incorporating negative imaginary-time trajectories for improved tunnelling rate predictions.

Findings

Extended instanton method to the inverted regime.

Analyzed properties of the periodic orbit in the inverted regime.

Enhanced understanding of tunnelling in molecular transitions.

Abstract

Fermi's golden rule defines the transition rate between weakly coupled states and can thus be used to describe a multitude of molecular processes including electron-transfer reactions and light-matter interaction. However, it can only be calculated if the wave functions of all internal states are known, which is typically not the case in molecular systems. Marcus theory provides a closed-form expression for the rate constant, which is a classical limit of the golden rule, and indicates the existence of a normal regime and an inverted regime. Semiclassical instanton theory presents a more accurate approximation to the golden-rule rate including nuclear quantum effects such as tunnelling, which has so far been applicable to complex anharmonic systems in the normal regime only. In this paper we extend the instanton method to the inverted regime and study the properties of the periodic orbit, which describes the tunnelling mechanism via two imaginary-time trajectories, one of which now travels in negative imaginary time. It is known that tunnelling is particularly prevalent in the inverted regime, even at room temperature, and thus this method is expected to be useful in studying a wide range of molecular transitions occurring in this regime.