In this work, we consider two particular sets of parameters, which we refer to as Model I and Model II. The parameters in the molecular Hamiltonian ĤM are tabulated in Table . In Model I, when strongly coupled to the cavity, the ground polariton potential will approach the diabatic state |C ; for model II, the ground polariton potential approaches the acceptor and donor diabatic states |A and |D , depending on the nuclear configuration. This will modify the reaction barrier on the ground state. In both cases, the molecular model is coupled to a highly off-resonant cavity with ω c = 3 eV (thus operating outside the vibrational strong coupling regime ), and the number of Fock states was treated as a convergence parameter (converged with at most 50 Fock states for Model I and 20 Fock states for Model II). , whereas the ground adiabatic electronic states |Φ 0 (R) at three nuclear configuration are depicted below the diabatic states. In this model, the covalent diabatic state is lower in energy than the donor and acceptor diabatic states, as shown in Fig. ). As a result, the character of the ground adiabatic state is dominated by the covalent diabatic state |C , especially near the top of the potential barrier (where R ≈ 0). In this case, the proton and the electron are transferred simultaneously from the donor ion to the acceptor ion, making this process an adiabatic hydrogen atom transfer reaction. This is schematically illustrated in Fig. , where the adiabatic (bottom panels) and diabatic (top panels) ground state electron distributions are illustrated at the donor (R = -5.5), barrier (R = 0), and acceptor (R = 5.5) nuclear configurations. This shows how the electron follows the proton along the proton transfer coordinate. In Fig. , the adiabatic and diabatic potential energy surfaces are plotted. It can be seen that the two wells in the adiabatic ground state potential energy surface come from the coupling between the donor/acceptor diabats |D and |A with the covalent diabatic state |C through the diabatic couplings V DC (R) and V AC (R).