Fig. presents the results of k/k 0 using both the numerically exact HEOM simulations (open circles with thin guiding lines) and the analytic FGR rate theory (thick solid curves), with the light-matter coupling strength η c = 0.05 a.u. For the analytic FGR rate theory, we present the results k/k 0 = 1+0.5 k VSC /k 0 , where k VSC is evaluated using Eq. 10 and k 0 is directly obtained from HEOM simulations, and an empirical re-scaling factor 0.5 is applied (see Method, Rate Constant Calculations). One can see that Eq. 10 provides an excellent agreement with the HEOM results when τ c < 100 fs. Both the resonance peak position and the width of the rate constant modifications are well captured.