VSC-modified rate constant and the optical lineshape. Apart from predicting the correct resonance condition (ω c = ω 0 ), kVSC in Eq. 17 also predicts that the width of the rate constant profile is determined by the lineshape function of the molecular vibration spectra A ν (ω c -ω 0 ), with width Γ ν (see Eq. 15). Note that kVSC is slightly broader than A ν (ω -ω 0 ) due to the Bose-Einstein distribution function n(ω c ) (see Eq. 3). Fig. presents k/k 0 obtained by HEOM simulations (light blue open circle and shaded area) and FGR from Eq. 17 (dark blue solid line), respectively, as well as the IR spectra of the bare molecule system obtained from HEOM simulation (red solid line with shaded area). The rate profile is the same as the magenta curve in Fig. , where η c = 0.05 a.u. and τ c = 1000 fs. The IR spectra are simulated by HEOM, with details presented in Supplementary Note 6. The optical spectra can be well approximated as A ν (ω -ω 0 ) in Eq. 14 (red open circles), which is visually identical to the HEOM results. The similar trend of the vibration spectra for the molecular system outside the cavity and the VSC-modified rate constant profile are a ubiquitous feature for most of the VSC experiments so far , with the peaks both located at ω c = ω 0 and the widths roughly at Γ ν (although there are counter-examples, such as Fig. of Ref. 2). This feature is observed in current numerical simulations, as well as in the previous work , which can be explained by the kVSC expression in Eq. 17.