In this paper, we consider a reaction using a thermal barrier crossing model. Fig. presents the first few vibrational states of the double well model, where |𝜈 L ⟩ denotes the vibrational ground state of the reactant (left well), |𝜈 ′ L ⟩ denotes the vibrationally excited state of the reactant, and similar for the product (right well). The red arrow represents the thermal activation process from the vibrational ground state, |𝜈 L ⟩, to the vibrationally excited state, |𝜈 ′ L ⟩ in the reactant well. Then, through the coupling between |𝜈 ′ L ⟩ and |𝜈 ′ R ⟩, a chemical reaction occurs. Finally, the vibrational excited state |𝜈 ′ R ⟩ relaxes to the ground state of the product |𝜈 R ⟩. The presence of the cavity mode qk explicitly enhances the transition |𝜈 L ⟩ → |𝜈 ′ L ⟩. The symmetric double-well model is used to model the reaction, with details in Supplementary Material, Sec II. Fig. shows the phonon spectral density 𝐽 𝜈 (𝜔) (blue) adapted from Ref. 39 as well as the effective spectral density 𝐽 eff (𝜔) (red) of the cavity and its associated photon bath environment that accounts for loss. Note that 𝐽 eff (𝜔) resembles the Brownian oscillator spectral density that centers at a particular frequency. When its peak frequency is in resonance with the quantum vibrational frequency 𝜔 0 , 𝐽 eff (𝜔) could potentially accelerate the state-to-state quantum transitions |𝜈 L ⟩ → |𝜈 ′ L ⟩ (as indicated by the red arrows in Fig. ).