where k D is the rate constant for the double-well potential without coupling to any RPV modes Q j or the cavity mode q c , and α is a scaling parameter. When FGR is exact and the role of {Q j } and q c are directly additive to k, α = 1. For the previous work of VSC-enhanced rate constant studies, we found that α ∈ [0.5, 1] are needed to bring a quantitative agreement of the FGR expression with the numerically exact results. Throughout the paper, we report the ratio of the rate constant inside and outside the cavity as follows