The numerical result of FGR rates using k int VSC in Eq. 20 is presented in Fig. (golden dashed line), with a rescaling factor of 0.5 applied to both k VSC (Eq. 10) and kVSC (Eq. 17). One can see that Eq. 20 correctly captured the turnover behavior in the τ c -dependence of VSC rate constant, which maximizes at around τ c = 200 fs and agrees with the HEOM simulations, although being less accurate than either Eq. 2 in the lossy regime or Eq. 17 in the lossless regime. As a corollary of k int VSC , the maximum enhancement of the VSC rate constant can be reached when τ c = Ω -1 R . This is because under the resonance condition ω c = ω 0 , Eq. 20 becomes (c.f. Eqs. 9 and 19)