For a single molecule coupled to a single mode cavity, the theory k VSC (Eq. 16) explains (i) a sharp resonance suppression behavior at ω c = ω Q (Fig. ); (ii) non-linear scaling of k/k 0 with respect to Ω R (Fig. ), as well as the non-linear scaling of ∆∆G ‡ with respect to Ω R ; (iii) modification of both effective activation Entropy and Enthalpy (Fig. ). (iv) The null effect because of a very low reaction barrier (Fig. ), such that the mechanistic in Eq. 7 no longer hold. The analytic theory (using Eq. 8) agrees very well with the numerically exact simulations for all cases.