Resonant Cavity Modification of Ground State Chemical Kinetics

Recent experiments have suggested that ground state chemical kinetics can be suppressed or enhanced by coupling the vibrational degrees of freedom of a molecular system with a radiation mode inside an optical cavity. Experiments show that the chemical rate is strongly modified when the photon frequency is close to characteristic vibrational frequencies. The origin of this remarkable effect remains unknown. In this work, we develop an analytical rate theory for cavity-modified ground state chemical kinetics based on the Pollak-Grabert-H\"anggi rate theory. Unlike previous work, our theory covers the complete range of solvent friction values, from the energy-diffusion limited to the spatial-diffusion limited regimes. We show that the chemical reaction rate can either be enhanced or suppressed depending on the bath friction; when bath friction is weak chemical kinetics is enhanced as opposed to the case of strong bath friction, where chemical kinetics is suppressed. Further, we show that the photon frequency at which maximum modification of chemical rate is achieved is close to the reactant well, and hence resonant rate modification occurs. In the strong friction limit the {\it resonant} photon frequency is instead close to the barrier frequency, as obtained using the Grote-Hynes rate theory. Finally, we observe that the rate changes (as a function of photon frequency) are much sharper and more sizable in the weak friction limit than in the strong friction limit, and become increasingly sharp with decreasing well frequency.