with the broadening parameter ] ). The FGR rates using kVSC in Eq. 10 (thick solid lines) are compared to the HEOM results (open circles with thin guiding lines) under a variety of τc values. (b) The values of k/k0 under the resonance condition ωc = ω0 as a function of τc. The results of HEOM (blue open circles), FGR rates using kVSC in Eq. 10 (red solid line), FGR rates using kVSC in Eq. 17 (blue solid line), and FGR rates using k int VSC in Eq. 20 (gold dashed line) are presented. (c) Resonance peaks of k/k0 for VSC effect under the lossless regime (τc ≫ Ω -1 R ). The FGR rates using kVSC in Eq. 17 where