So far, we have used the FGR theory in Eq. 44 to qualitatively interpret the VSC rate constant modifications, explain the resonance condition ω c = ω 0 , the basic scaling rule of k/k 0 ∝ 1 + C • η 2 c , as well as the τ c dependence of k/k 0 . Here, we assess the quantitative accuracy of the FGR rate constant in Eq. 41. Note that we are less interested in how to compute the rate outside the cavity k 0 , as there are many accurate theories to describe it in theoretical chemistry. Rather, we want to focus on the performance of k VSC in Eq. 41. As such, we only report the value of k/k 0 = 1 + k VSC /k 0 , where we numerically integrate out dω in Eq. 41 to obtain k VSC , and we directly use the numerical result of k 0 = 1.2672 × 10 -7 a.u. -1 obtained from the HEOM simulation (outside cavity case in Fig. ). We used Eq. A21 to evaluate the convolution integral in Eq. 41, and compare the FGR rate constant with the HEOM results. We found that the simple FGR rate constant overestimates the results by 2.5 times compared to the numerically exact results obtained from HEOM, and will breakdown for large η c and τ c . Nevertheless, this simple FGR theory captures the basic trend of the VSC modified rate constant when η c < 0.05 (or Ω R < 25 cm -1 ) and τ c < 100 fs, as shown in Fig. .