A schematic illustration of the model system is provided in the top panel of Fig. . Fig. presents the potential V (R) for the ground state along the reaction coordinate R, as well as key quantum states associated with the two different mechanisms of the VSC-modified kinetics. Specifically, Fig. shows the four diabatic matter states |ν L ⟩ (blue), |ν R ⟩ (orange), |ν ′ L ⟩ (red), |ν ′ R ⟩ (green), in which the cavity is included in the bath and described by an effective spectral density J eff (ω) (see Supplementary Note 2, section A). The major VSC enhanced reaction channel is shown in Eq. 1, in which k 1 is the rate-limiting step. This mechanism is confirmed for the lossy regime using the exact quantum dynamics simulations in our previous work . Fig. shows several key photon-dressed vibration states. These states include |ν L , 0⟩ (blue), |ν R , 0⟩ (orange), |ν L , 1⟩ (magenta), |ν R , 1⟩ (green-yellow), |ν ′ L , 0⟩ (red), |ν ′ R , 0⟩ (green) for both the reaction coordinate R and the cavity mode qc , in which the cavity is included in the system and coupled to the photon-loss environment characterized by the spectral density J c (ω) (see Supplementary Note 2, section B). The VSC-enhanced reaction channel is shown later in Eq. 11, in which the photonic excitation |ν L , 0⟩ → |ν L , 1⟩ and the conversion to vibrational excitation |ν L , 1⟩ → |ν ′ L , 0⟩ are sequential steps which together act as the rate-limiting steps. Later, we will see that the FGR rate theory constructed using Eq. 1 works for the lossy regime while using Eq. 11 works for the lossless regime.