A polarizable molecular dynamics model for adiabatic electron transfer across the electrode\electrolyte interface is presented. The electronic polarizability of the water and of the metal electrode is accounted for by a dynamical fluctuating charge algorithm, image charges, and the Ewald summation adapted for a conducting interface. The effects of the solvent electronic polarizability are studied by computing the diabatic and adiabatic free energy curves for both polarizable and non-polarizable water models. This represents the first effort to compute the adiabatic free energy curves from simulation for a fully polarizable electrochemical system.