Behavior of the VSC-modified Rate Constants. We further explored how the VSC-modified rate constant would be influenced by the light-matter coupling strength η c (Eq. 7) and by the cavity lifetime τ c (Eq. 32). Our numerical results suggested that as η c increased, the VSCmodified rate constant also increased, and a numerical fitting suggested that the rate constant enhances quadratically with η c when η c < 0.05 (or Ω R < 25 cm -1 , red curve in Fig. ). Using this observation, we also find that the modification of the free energy barrier does not scale linearly with the Rabi splitting Ω R , but rather exhibits a logarithmic scaling of Ω R (blue curve in Fig. ). This numerical behavior exhibits the essential feature of the nonlinear relationship between Ω R and the modification of the free energy barrier. Although there are not many experimental studies on the relationship between VSC-modified rate constants and light-matter coupling strength, there is experimental evidence suggesting a nonlinear relation between the rate constant and the light-matter coupling strength (Rabi splitting) in Ref. 4. Further experimental efforts are needed to investigate the scaling relation between the VSC rate constant and the light-matter coupling strength.