Exact identities between values of the tunnel current in the redox-mediated tunneling contacts and the positions of the extrema of the tunnel current/overvoltage characteristics

Two exact identities for the tunnel current through a redox-mediated tunneling contact are obtained. These identities are valid for arbitrary temperatures, electrodes, strengths of the redox group-electrodes coupling, interaction of the valence electrons with the phonon modes and values of the Coulomb repulsion U between electrons at the valence level. They permit to obtain the expression which relates the positions of different maxima (minima) of a given tunnel current/overvoltage characteristic in the case of the symmetric tunneling contact defined below or relates the positions of maxima (minima) of two tunnel current/overvoltage characteristics where one of them corresponds to the transposed parameters describing two working electrodes and their coupling to the redox group. For the symmetric tunneling contacts and under the other general conditions we also obtain the expression for the position of one of the extremal points of the tunnel current/overvoltage characteristic. It is shown that this point is the point of the maximum in the case of the redox-mediated tunneling contacts considered at room temperature within the spin-less model or the model with U = 0. The tunnel current/overvoltage characteristics are calculated both for the fully diabatic and fully adiabatic limits and it is shown that the positions of the points of the maxima (minima) are indeed given by the derived expressions.