As such, experimental evidence strongly suggests that the VSC modification needs to be studied by treating the vibrational states quantum mechanically, such that the knowledge of ω 0 is included. The similarity of the optical profile of vibrational absorption and the cavitymodified rate constant also strongly suggests that both have a common origin, both of which correspond to the |ν L → |ν L transition. This is because the optical transition is caused by -μ • E(t), where μ is the transition dipole operator, and E(t) is the classical laser field, whereas the molecule-cavity coupling is caused by μ(â † + â) ∝ μ • qc , where â † and â are cavity field operators and qc = /2ω c (â † + â) is the photonic coordinate that is proportional to the displacement field intensity inside the cavity. Indeed, using the numerically exact hierarchical equations of motion (HEOM) method to investigate the model reaction coupled to the cavity and by treating vibrational states and cavity Fock states quantum mechanically as the quantum subsystem, Reichman and co-workers in Ref. 25 indeed found resonance behavior of the rate profile, which is similar to the absorption spectra of the bare molecule outside the cavity (with similar features of narrow width and centered around ω 0 ). This numerically exact simulation provides invaluable insights into the mechanism of how the cavity modifies reaction rate constants. Nevertheless, an analytic theory to explain the VSC-enhanced rate constant is still missing.