Condensed phase chemical reactions often possess complex structures, where the reaction coordinate strongly interacts with a variety of environmental vibrations. These fast dynamical modes, known as rate promoting vibrations (RPV), have been recognized as playing a key role in increasing the chemical reaction rate . Moreover, it has been theoretically shown that the cavity mode could significantly influence the reaction dynamics when it interacts with one of such RPV or solvent degrees of freedom (DOF). We model the interactions between RPV modes and R 0 using the following Hamiltonian