where Γ ν is the line width, ω 0 is the peak position (the same as Eq. 25). The infrared (IR) spectra of the baremolecule system are numerically calculated by HEOM, in which Γ ν ≈ 30 cm -1 (see Fig. ). Details on the calculation of IR spectra using HEOM are presented in Sec. I-D of the Supplementary Material. In recent studies of VSC rate enhancement, the bare molecular absorption has a line width of 25 ∼ 30 cm -1 (see Fig. of Ref. 4 or Fig. of Ref. 5). Note that this line width includes both homogeneous (captured by J ν (ω) and inhomogeneous broadenings (static disorder, not modeled here). As such, the choice of the parameter for J ν (ω) is in line with what was observed in experiments, even though the phonon bath friction η ν for the molecule is in the energy diffusionlimited regime. We must emphasize that it is currently unknown in which regime VSC reactions 7 operate. It could be either the spatial or energy diffusion-limited regime or some intermediate regime. Chemical reactions in the liquid phase are typically expected to take place in the spatial diffusion-limited regime (with strong solvent friction, also known as the plateau regime or the Kramers overdamped regime), whereas those in the gas phase are expected to take place in the energy diffusionlimited regime (with weak solvent friction, also known as the Kramers underdamped regime). However, the energy diffusion-limited regime is more prevalent than is commonly assumed for chemical kinetics in liquid solvents . It is also possible for chemical reactions to be energy diffusion-limited even if the solvent friction is large, as long as the bath DOFs are slow. To answer this question, one can perform a direct molecular dynamics simulation to extract the solvent spectral density. Because all VSC experiments use a cavity that has a finite lifetime τ c , we need to briefly discuss the connection between the cavity loss rate Γ c and the photon bath spectral density J c (ω). We assume J c (ω) to be the Drude-Lorentz form as follows (cf. Eq. 13)