Resonance Theory and Quantum Dynamics Simulations of Vibrational Polariton Chemistry

We present numerically exact quantum dynamics simulations using the hierarchical equation of motion (HEOM) approach to investigate the resonance enhancement of chemical reactions due to the vibrational strong coupling (VSC) in polariton chemistry. The results reveal that the cavity mode acts like a ``rate-promoting vibrational (RPV) mode" that enhances the steady-state population of the vibrational excited states, leading to an enhanced product population at the resonant condition, when the cavity mode frequency matches the vibrational transition frequency. Based on the numerical observations, we present an analytic rate theory to explain the observed sharp resonance peak of the rate profile when tuning the cavity frequency to match the quantum transition frequency of the vibrational ground state to excited states. This rate theory further explains the origin of the broadening of the rate profile. Both the analytic rate constant and the exact simulation predict that the VSC-modified rate constant will change quadratically as the light-matter coupling strength increases and this effect will magnify as the cavity lifetime increases. To the best of our knowledge, this is the first analytic theory that is able to explain the sharp resonance behavior of the VSC-modified rate profile when coupling an adiabatic ground state chemical reaction to the cavity. We envision that it will offer invaluable theoretical insights to unravel the mysteries of the experimentally observed vibrational strong coupling-induced rate constant modification.