Analytical expression for the tunnel current through the redox-mediated tunneling contact in the case of the adiabatic electron transfer at one of the working electrodes and any possible type of the electron transfer at the other electrode.

We study the tunnel current through a one-level redox molecule immersed into the electrolyte solution for the case when the coupling of the molecule to one of the working electrodes is strong while it is arbitrary to the other electrode. Using the Feynman-Vernon influence functional theory and the perturbation expansion of the effective action of the classical oscillator coupled both to the valence level of the redox molecule and to the thermal bath representing the classical fluctuations of the polarization of the solvent, we obtain, following the canonical way, the Langevin equation for the oscillator. It is found that for the aqueous electrolyte solution, the damping and the stochastic forces which arise due to the tunnel current are much smaller than those due to the thermal bath and therefore can be neglected. We estimate the higher-order corrections to the effective action and show that the Langevin dynamics takes place in this case for arbitrary parameters of the tunneling junction under the condition of the strong coupling of the redox molecule to one of the working electrodes. Then the steady-state coordinate distribution function of the oscillator resulting from the corresponding Fokker-Planck equation is the Boltzmann distribution function which is determined by the adiabatic free energy surface arising from the mean current-induced force. It enables us to obtain the expression for the tunnel current in the case when the coupling of the redox molecule to one of the working electrodes is strong while it is arbitrary to the other electrode.