VSC rate constant modifications. To validate the k VSC theory in Eq. 16, we perform numerical simulations of the rate constants for a single molecule (N = 1) coupled to a single cavity mode, where the details are provided in Methods. The parameters used for V ( R0 ) set the well frequency ω 0 ≈ 1189.7cm -1 . For N = 1, the RPV mode could be either an intermolecular vibration or a nearby solvent that has a frequency ω Q = ω 0 . Further, we set χ = 1 that corresponds to a vibrational dipole aligned to the cavity mode. All the simulations are performed at T = 300 K and a cavity lifetime τ c = 500 fs. The exact quantum dynamics propagation is done by using the hierarchical equations of motion (HEOM) approach .