Controlling the nonadiabatic electron-transfer reaction rate through molecular-vibration polaritons in the ultrastrong coupling regime

TL;DR

This paper explores how ultrastrong coupling of molecular vibrations to an optical cavity can modify electron-transfer reaction rates, revealing the roles of energy level shifts and vibrational state mixing, with effects depending on system size.

Contribution

It provides a theoretical analysis of reaction rate control via molecular-vibration polaritons in the ultrastrong coupling regime, highlighting the dominant factors and their dependence on system parameters.

Findings

Energy level shifts can increase reaction rates.

Vibrational state mixing can decrease reaction rates.

Effects vary with the number of molecules in the system.

Abstract

Recent experiments showed that the chemical reaction rate is modified, either increased or decreased, by strongly coupling a nuclear vibration mode to the single mode of an optical cavity. Herein we investigate how the rate of an electron-transfer reaction depends on the molecule-cavity coupling in the ultrastrong coupling regime, where the coupling strength is comparable in magnitude with both the vibrational and the cavity frequencies. We found two main factors that determine the modification of the reaction rate: the relative shifts of the energy levels induced by the coupling and the mixing of the ground and excited states of molecular vibration in the ground state of the hybrid molecule-plus-cavity system through which the Franck-Condon factor between the initial and final states of the transition is altered. The former is the dominant factor if the molecule-cavity coupling strengths for the reactant and product states differ significantly from each other and gives rise to an increase in the reaction rate over a wide range of system's parameters. The latter dominates if the coupling strengths and energy levels of the reactant and product states are close to each other and it leads to a decrease in the reaction rate. The effect of the mixing of molecular vibrational states on the reaction rate is, however, suppressed in a system containing a large number of molecules due to the collective nature of the resulting polariton, and thus should be observed in a system containing a small number of molecules. In contrast, the effect of the relative shifts of the energy levels should be essentially independent of the number of molecules coupled to the cavity.