where k 0 is the outside cavity rate constant, and α is an ad hoc rescaling factor due to the inaccuracy of the FGR level of theory. Practically, we found α = 0.5 will match the numerically exact results from HEOM . Eq. 17 is the first main theoretical result in this work. This analytic theory kVSC (as well as in Eq. 10 for k VSC ) implies that the optical lineshape of the molecule described by A ν (ω-ω 0 ) is intimately connected to the VSC kinetics modifications, due to the fact that both are sensitive to the vibrational quantum transition. The current theory in Eq. 17 provides an analytic answer to the early numerical observations from HEOM simulations. Under the resonance condition (ω c = ω 0 ), Eq. 17 becomes