Fig. presents the ω c -dependence of k/k 0 from the numerically exact HEOM results (open circles with thin guiding lines), and the FGR rate constant using kVSC in Eq. 17 (thick solid lines). One can see that kVSC agrees well with the exact results for τ c > 500 fs, and the resonance peak positions are well captured by FGR (with a re-scaling factor of 0.5 applied). In addition, the widths given by kVSC are in agreement with the HEOM results for a wide range of τ c . We also note that the long tails towards lower cavity frequencies in the FGR results disagree with the HEOM results, due to the Lorentzian lineshape function decays slowly while n(ω c ) increases fast when decreasing ω c .