For the FGR-based theory, we use the value of the k 0 (outside the cavity rate constant) obtained from the HEOM simulation and report k/k 0 ≈ k D /k 0 +α•k VSC /k 0 , where the α = 0.7 is an ad hoc re-scaling factor needed to bring the value of FGR rate constant to the consistent range with the HEOM results for outside cavity situation when η c = 0 It is kept fixed for all the results (and for any finite value of η c ) presented in this work.