A. M. Kuznetsov

Approximate method for calculation of electron transition probability for simple outer-sphere electrochemical reactions

The probability of an elementary act in an outer-sphere electrochemical electron transfer reaction is calculated with arbitrary values of the parameter of reactant-electrode electron interaction for diabatic freeenergy surfaces of the parabolic form. The dependence of effective transmission coefficient on the Landau-Zener parameter is found. Interpolation formulas are obtained that describe this dependence and allow calculating the electron transition probability using the results of quantum chemical calculations of the electronic matrix element as a function of distance.

Theory of the shot noise in electrochemical bridge contacts

Correlation functions of the current and the noise power for a redox-group-containing electrochemical tunnel contact are calculated under the assumption on a shot character of the electron tunneling. Weak and strong interaction between the redox group and electrodes is considered. Overvoltage dependence of the Fano factor at different bias-potentials is found. The conditions of passing of the calculated dependences into the Schottky law are formulated.

Elementary act of dissociative adsorption of two-atom molecules on a solid surface in a polar solvent

A model is suggested for the description of an elementary act of dissociative adsorption of molecules of the X2 type at a solid surface in a polar solvent. Within this model, the potential energy of interaction between the molecule and the surface and the intramolecular energy of X2 are approximated by Morse functions. The model accounts for the reorganization of the substrate and polar solvent structures. The model is compared with other approximations.

On the applicability of the Born-Oppenheimer approximation in a theory of nonadiabatic charge transfer reactions: An exactly solvable model

The question concerning the applicability of the Born-Oppenheimer approximation (BOA) for the calculation of the transition probability for a nonadiabatic process of charge transfer in a polar environment with allowance made for temperature effects is investigated theoretically. Considered is the transfer of a quantum particle (proton) that interacts with a local vibration mode in a model of bound harmonic oscillators. The model admits an exact solution for wavefunctions of the initial and final states. A calculation shows that BOA is applicable even for very large distances of the proton transfer. At the same time, the exact result and the BOA result severely differ from a probability calculated in a crude Condon approximation. It is demonstrated that the non-Condon effects are in a general case temperature-dependent and may substantially influence the calculated values of the transition probability.

Effects of electron correlations in a surface-molecule model for the adiabatic electrochemical electron transfer reactions with allowance for the electrostatic repulsion of electrons on an effective orbital of metal

Within the framework of a surface-molecule model for the adiabatic electrochemical electron transfer reactions, exact expressions for the adiabatic free energy surfaces are obtained and the diagrams of kinetic modes are constructed with allowance made for the electrostatic repulsion between electrons with the opposite spin projection both on the valence orbital of the reactant and on the effective electron orbital of the metal. It is shown that taking into account the electrostatic repulsion on the effective orbital of the metal and the correlation effects connected with it is very substantial for a number of electrochemical electron-transfer reactions and leads not only to an alteration of the activation free energies but also to qualitatively different forms of adiabatic free energy surfaces in some regions of values of the model’s parameters.

Fully adiabatic dissociative electrochemical electron transfer reactions induced by scanning tunneling microscopy

A theory of fully adiabatic dissociative electrochemical processes of the electron transfer that are induced by scanning tunneling microscopy is constructed. Adiabatic free energy surfaces are calculated and properties of their symmetry are examined under various conditions. Diagrams of kinetic regimes, which characterize possible kinetic processes, which may proceed in the system under consideration, are constructed in the space of model parameters. Dependence of activation free energy on the bias voltage, overvoltage, physical properties of a molecule, and intensity of interaction of a molecule with an electrode and the tip of the scanning tunneling microscope is explored.

Effects of Electron Correlations in a Simple Model for Adiabatic Electrochemical Reactions: The General Relationships

General relationships for adiabatic free-energy surfaces (AFES) for electrochemical reactions of electron transfer are derived in the framework of exactly solvable model of the so-called surface molecule, which is a limiting case of Andersons Hamiltonian and may be applied to transition metals. As opposed to earlier models for adiabatic reactions, the model exactly allows for the effects of electron–electron correlations. The obtained results constitute a basis for calculating AFES and plotting diagrams that correspond to different kinetic regimes of one- and two-electron processes.

Theory of nonadiabatic electron transitions in symmetrical two-center tunnel electrochemical contact

Passage of current through two-center bridge contact is studied theoretically for a nonadiabatic mechanism of electron transfer. General expressions for steady-state current as a function of overvoltage and bias voltage are obtained. For a symmetrical contact, a simple approximate expression is derived for current in the limit when electron transfer between bridge redox-groups is the slow stage. It is shown that the current as a function of overvoltage passes through a maximum near the equilibrium potential. The shape of the maximum does not depend on the medium reorganization energy.

Electron correlation effects for adiabatic electrochemical reactions of electron transfer in a model for an electrode with an infinitely wide conduction band: Computing adiabatic free energy surfaces

The adiabatic free energy surfaces for adiabatic electrochemical reactions of electron transfer are calculated in a model for an electrode with an infinitely wide conduction band with exact allowance for electron–electron correlations. The surfaces are analyzed on the basis of a diagram of kinetic modes obtained earlier. It is shown that, as in a surface-molecule model for these reactions, the correlation effects play an essential role and lead to a considerable decrease in the activation free energies and to qualitatively different forms of adiabatic free energy surfaces in certain ranges of model parameters.

Electron Correlation Effects for Adiabatic Electrochemical Reactions of Electron Transfer in a Model for an Electrode with an Infinitely Wide Conduction Band: Diagrams of Kinetic Modes

For adiabatic electrochemical reactions, within the framework of a model for an electrode with an infinitely wide conduction band, exact results are obtained for critical regions that correspond to different possible types of electron transfer processes (transfer of a single electron with and without an intermediate state, simultaneous transfer of two electrons) and regions that correspond to electroadsorption of the reactant in certain charge states. These regions form a diagram of kinetic modes (DKM) in the space of model parameters. Analytical expressions for outermost curves of DKM are obtained for some extreme cases. For the general case of a model for an electrode with an infinitely wide conduction band, a DKM is constructed and investigated with exact allowance for the effects of electron–electron correlations.