As such, we conclude that the FGR expressions in Eq. 41 (as well as the small τ c limit in Eq. 44) are theoretically valuable because they predict the correct scaling relations and semiquantitatively predict the accurate VSC-modified rate constants. Nevertheless, the numerical behavior of the FGR expression is not perfect, as one can see that it will overestimate the rate by 2.5 times for the model system we studied when FGR is valid, and will eventually breakdown for large light-matter coupling strength η c and large cavity lifetime τ c . That said, when FGR is valid, the rate expression provides a nearly perfect trend when changing ω c , η c , and τ c .