Note that the top of the barrier frequency, ω b = 1000 cm -1 , the classical bottom of the well frequency, ω cl 0 = 1414 cm -1 , and the quantum vibration frequency, ω 0 = 1172.2 cm -1 , are different. Later in quantum dynamics simulations, we find that the cavity-promoted reaction rate constant is directly related to ω 0 , and the resonance effect is very sharp in frequency space, such that we are sure it is different from both ω cl 0 and ω b . Further, the reaction coordinate R is coupled to a harmonic phonon bath to model the effect of the other vibrational DOFs, where the system-bath coupling is characterized with a spectral density taken in the Drude-Lorentz form,