DFT calculations were carried out to determine the internal energy (U ) of the reactant and product configurations of the rate limiting step for the reduction reactions detailed in Table as a function of the applied electric fields (Fig. ). By taking the energy difference between the reactants and products, the reduction driving force (eq. 11) is given as a function of electric field (Fig. ). We then determined the shift in Fermi energy of the surface with free charges (Ce ′ Ce or Fe • Fe ) as a function of the appled electric field (Fig. ). The simulated ∆χ -η act relationship for the three systems (Fig. ) considered is given in Table .