where we have ignored the solvent reorganization energy λ b (see Eq. 9) in the above condition due to its small value. For Fig. , ε n is sampled based on a Gaussian distribution (Eq. 74), while ε = 2.0 eV. For results presented in Fig. ), there is no site energy disorder and ε n = ε = 2.0 eV. The cavity frequency is thus kept at ℏω c = 2.0 eV (zero light-matter detuning). The cavity loss rate was set at Γ = 10 meV. The nuclear time step for verlet propagation was taken to be ∆t = 10 a.u. (≈ 0.25 fs), and the forward and backward coefficients are evolved between nuclear propagation using Eq. 32.