The normal mode frequencies can be obtained by solving Eq. 226 and the transmission coefficient κ can be computed by plugging these normal mode frequencies into Eq. 201. Fig. shows the trend of κ/κ 0 , where κ is the transmission coefficient inside the cavity and κ 0 is the transmission coefficient outside the cavity, concerning different light-matter coupling strengths. When the total number of solvent molecules is fixed (N = 2500), the reaction rate is suppressed at all tested coupling strengths, and there is a clear resonant structure for the cavity frequency. However, the minima in all cases have a much smaller red-shift from ω ‡ compared to the results from Ref. 69. Fig. 29f shows the cavitymodified reaction rate with respect to the number of solvent molecules, while the cavity frequency is fixed at ω c = 200 cm -1 . At a certain per-molecule light-matter coupling strength, increasing the number of molecules will further suppress the reaction rate, similar to the observations in the single-molecule case. Additionally, the authors also explored the effects of cavity loss and found that cavity loss can further enhance the dissipation capability of the cavity mode, which will lead to more suppression of the reaction rate. Note that the setup of this model system is not directly related to the experimental setups shown in Fig. . Here, N denotes the number of solvent DOF (which are also collectively coupled to the cavity) directly coupling to the reactive molecule, while the experiments in Fig. suggest the reactivity depends on the number of reactive molecules (or their concentration in Fig. ) collectively coupled to the cavity. Nevertheless, there are VSC experiments that directly couple cavity mode to the solvent DOF, whereas the solvents are then coupled to a solute molecule that undergoes reactions. In Fig. , the rate constant is enhanced when the cavity mode is collectively coupled to the solvents, which are also coupled to the reactive molecules. In a very recent experiment of VSC modified Urethane Addition Reaction, 367 it was also found that when collectively coupling the solvent DOF with the cavity mode (where the solvent also interacts with the reactive molecule), the rate constant is suppressed, which is in favor to the theoretical results proposed here. We should emphasize that by no means does this theoretical work provides the ultimate answer to the mysteries of the VSC modification of the reactivities. We envision that this theoretical work brings us one step closer to finally resolving the mysteries of VSC enabled chemistry demonstrated in recent experiments by demonstrating both the collective coupling effect and the cavity frequency dependent modification of the rate constant.