Computational Approaches and Novelty. We performed numerically exact simulations using hierarchical equations of motion (HEOM) to investigate the effect of vibrational strong coupling (VSC) on the reaction rate constant. With harmonic analysis for the equations of motion, an effective spectral density function was derived to describe the cavity and its associated loss. In the HEOM simulations, only the system's vibrational states were described as the quantum subsystem, whereas the influence of the molecular phonon bath, the cavity mode, and its associated photon-loss bath were described implicitly using spectral density functions. Compared to recent work that treats the photon coordinate qc inside the quantum subsystem and using Fock state description, the current approach describes the cavity mode using an effective spectral density and thus significantly reduces the computational cost due to a much smaller number of states in the quantum subsystem. On the other hand, including qc in the quantum subsystem using Fock states does require truncation of the Fock states, while the current approach that treats qc inside the spectral density description does not explicitly involve any Fock state truncation. With this new description, it becomes possible to extend numerical exact simulations to multimode cases and polymeric systems with arbitrary types of bath TCF, even though in this work we are still under the single-molecule case. Another interesting direction of applying the current approach is to explore the quantum dynamics of a hybrid plasmonic-photonic structure that has few-Mode field quantization with structured spectral densities. Origin of the Resonance Condition. Our numer-ical simulations confirm the results in a recent work which also performs exact quantum dynamics, suggesting that in the energy diffusion-limited regime of chemical reactions, the cavity mode acts like a "rate-promoting vibration (RPV) mode". This "rate-promoting" cavity mode promotes the transition from the reactant ground vibrational state |ν L to the reactant excited vibrational state |ν L , then follows by tunneling to the product vibrational excited state |ν R , and eventually relaxes to the product ground vibrational state |ν R . Our exact quantum dynamics results (Fig. ) suggest that the presence of a resonant cavity mode whose frequency ω c matches the quantum transition frequency ω 0 (corresponding to the |ν L → |ν L transition) will significantly enhance the steady-state populations of the |ν L and |ν R states, thus promoting the forward rate constant.