Collective Coupling Effect. The current theory k VSC (Eq. 15) also shows collectiveness of the rate constant modification, originating from the collective coupling between R 0 and {Q j } through ĤRPV in Eq. 2, and the light-matter couplings between q c and {Q j } through ĤLM (see Eq. 4). We use the spectral density theory to explore the collective effective effect inherent by the Hamiltonian through the analytic expression of J eff (ω), with details provided in Supplementary Note 5. We consider that N solvent DOF Q j have identical frequency ω Q . When C j are identical, and there is no disorder in the light-matter coupling angles, only the polaritonic states show up in J eff (ω) meaning that the N -1 dark states present are completely decoupled from the reaction coordinate and will not affect the rate of reaction. This can also be understood from a normal mode analysis approach shown in Supplementary Note 7. As such, the dark vibrational modes are no longer directly coupled to R 0 and will not influence the rate constant. When there are certain disorders in C j and also in cos θ j , the dark vibrational modes will have a finite spectral density contribution (see Fig. -S6 in Supplementary Note 5), and will gradually diminish the VSC collective effect.