Fig. presents k/k 0 with N = 10 4 at various Ω R . The overall collective coupling between {Q j } and R 0 is kept fixed at Λ = 1.71 cm -1 (see Eq. 3). Note that as √ N always pair up with η c in k VSC , the results are thus identical to the case of N = 1 with a much larger η c . The theory predicts a sharp resonance suppression when ω c = ω Q , which can not be captured by previous rate theories . Fig. further present k/k 0 as a function of increasing N , while keeping the lightmatter coupling strength Ω R / √ N constant. The results present the fundamental scaling relation in Eq. 18. Our theory demonstrates the same essential feature of the collective coupling effects observed in the experiments , which is the rate constant suppression as increasing the number of molecules (or concentration of the molecules). Under the collective coupling regime, the effect scales as k VSC ∝ 1/N and is caused by the light-matter hybridization induced splitting of J eff (ω). It must be emphasized that the values of C j depend on the chemical environment of the reactive molecule. One usually expects the solventsolute coupling involves N ≈ 10 3 -10 4 molecules , which will couple to both R 0 and q c . Note that the lightmatter coupling strength per molecule η c ∝ Ω R / √ N used in Fig. is still much larger than the VSC experiments. Future work is required to fully address the collectiveness that emerged from coupling at least N = 10 6 molecules to the cavity that leads to the rate constant changes. Fig. further explores the effects of having disorders in C j , using the exact expression for J eff (ω) (see Eq. 34).