Fig. presents the HEOM results of k/k 0 under various cavity frequency ω c with a strong coupling Ω R = 60 cm -1 . We do not observe any noticeable change of k/k 0 over a wide range of cavity frequency, agreeing with the null experimental results in Ref. . This is opposed to the situation of Fig. . These results can be interpreted from the vibrational population dynamics provided in Fig. in Supplemental Note 4, where the vibrationally excited states do not actively participate in the forward reaction, and tunneling between |ν L ⟩ and |ν R ⟩ is the primary mechanism leading to the formation of for this low barrier reaction. Similarly, in Ref. 70, a range of Ω R were used in the experiments (25 ≤ Ω R ≤ 75 cm -1 ), and one still finds null VSC results. Fig. presents k/k 0 under various Ω R under the resonance condition ω c = ω Q , and predicts the same null effect. These results suggest that the current theory based on the mechanism in Eq. 7 supports the null VSC results recently discovered in the experiments .