τ c leads to a weakening and broadening of J eff (ω). The dependence of τ c on the VSC rate constant profile resonance peak is dictated by the shape of J eff (ω), as shown in Fig. . Under the lossless limit (τ c → ∞), there is no apparent cavity modification effect, as discussed in the previous work in Ref. 25. When gradually decrease the cavity lifetime, the resonance structure in the rate profile shows up and the VSC modifications gradually increase. This trend is in line with the results in Ref. 25 using a similar model, where the cavity mode q c was included in the quantum subsystem system description using Fock states. The rate constant enhancement reaches a maximum intensity when τ c ≈ 200 fs, in which the rate constant is enhanced by 1.35 times. Further decreasing τ c leads to a decreased and broadened rate constant profile. The cavity modification effect gradually disappears at the heavy loss limit τ c → 0.