where σ c = 2ω 3 c A 0 µ DA ⟨q 2 c ⟩ with ⟨q 2 c ⟩ = 1/βω 2 c for classical distribution of the photon mode. Thus, the reaction rate is enhanced, (as shown in Fig. ) when coupled to the cavity. This is due to the modification of the diabatic coupling due to the photonic mode serving as a fluctuating DOF that mediates the donor-to-acceptor coupling (commonly referred to as the Peierls coupling). It must be noted that while these works show the modification of the non-adiabatic electron transfer reactions for photon frequencies in the IR regime, the photon mode is coupled to the transition dipole between the donor and acceptor diabatic states (or a give permanent dipole), not any explicit vibrational excitation in the system.