Igor G. Medvedev

A model of the surface molecule for adiabatic electrochemical electron transfer including electron correlation effects: the exact solution

Abstract A theory of the adiabatic interfacial electron transfer reactions is presented based on the exactly solvable surface molecule limit of the Anderson–Newns model. Unlike the other papers on this subject, the electron correlation effects are taken into account from the very beginning and exactly. It is shown that the electron correlation effects play an important role in the region of parameters describing adiabatic electron transfer and lead not only to quantitative corrections to the results obtained earlier in the spinless model or in the Hartree–Fock approximation but also to new qualitative effects. The critical regions, which correspond to different types of electron transfer processes, are obtained within the space of parameters of the model and classified. The corresponding kinetic regime diagram is constructed and presented. Examples of the adiabatic Gibbs energy surfaces for a number of characteristic, electrochemical electron transfer reactions are given and discussed.

Coulomb repulsion effect in two-electron nonadiabatic tunneling through a one-level redox molecule

We investigated Coulomb repulsion effects in nonadiabatic (diabatic) two-electron tunneling through a redox molecule with a single electronic level in a symmetric electrochemical contact under ambient conditions, i.e., room temperature and condensed matter environment. The electrochemical contact is representative of electrochemical scanning tunneling microscopy or a pair of electrochemical nanoscale electrodes. The two-electron transfer molecular system also represents redox molecules with three electrochemically accessible oxidation states, rather than only two states such as comprehensively studied. It is shown that depending on the effective Coulomb repulsion energy, the current/overpotential relation at fixed bias voltage shows two narrow ( approximately k(B)T) peaks in the limit of strong electron-phonon coupling to the solvent environment. The system also displays current/bias voltage rectification. The differential conductance/bias voltage correlation can have up to four peaks even for a single-level redox molecule. The peak position, height, and width are determined by the oxidized and reduced states of both the ionization and affinity levels of the molecule and depend crucially on the Debye screening of the electric field in the tunneling gap.

Electric double layer effect on observable characteristics of the tunnel current through a bridged electrochemical contact

Scanning tunneling microscopy and electrical conductivity of redox molecules in conducting media (aqueous or other media) acquire increasing importance both as novel single-molecule science and with a view on molecular scale functional elements. Such configurations require full and independent electrochemical potential control of both electrodes involved. We provide here a general formalism for the electric current through a redox group in an electrochemical tunnel contact. The formalism applies broadly in the limits of both weak and strong coupling of the redox group with the enclosing metal electrodes. Simple approximate expressions better suited for experimental data analysis are also derived. Particular attention is given to the effects of the Debye screening of the electric potential in the narrow tunneling gap based on the limit of the linearized Poisson-Boltzmann equation. The current/overpotential relation shows a maximum at a position which depends on the ionic strength. It is shown, in particular, that the dependence of the maximum position on the bias voltage may be nonmonotonous. Approximate expressions for the limiting value of the slope of the current/overpotential dependence and the width of the maximum on the bias voltage are also given and found to depend strongly on both the Debye screening and the position of the redox group in the tunnel gap, with diagnostic value in experimental data analysis.

A Born-Oppenheimer approach to adiabatic electrochemical charge transfer processes

An approach for the construction of the Hamiltonians and free energy surfaces for adiabatic electrochemical reactions accompanied by a considerable reorganization of the intramolecular structure is presented. For one-electron processes it reproduces the results of Koper and Voth (Chem. Phys. Lett. 282 (1998) 100) without an a priori introduction of a switching function transforming the bonding molecular potential into an antibonding one. The present approach is extended to two-electron processes, which are of importance for the dissociative adsorption and electrocatalysis.

An infinite bandwidth limit model for adiabatic electrochemical electron transfer including electron correlation effects: the exact solution

Abstract A theory of the adiabatic interfacial electron transfer reactions is presented based on the exactly solvable infinite bandwidth limit of the Anderson–Newns model which can be applied to the s–p metals. Unlike the other papers on this subject, the electron correlation effects are taken into account from the very beginning and exactly. It is shown that the electron correlation effects play an important role in the region of parameters describing adiabatic electron transfer and lead not only to quantitative corrections to the results obtained earlier in the spin-less model or in the Hartree–Fock approximation but also to new qualitative effects. The critical regions which correspond to different types of electron transfer processes are obtained within the space of parameters of the model and classified. The corresponding kinetic regime diagram is constructed and presented. Examples of the adiabatic Gibbs energy surfaces for a number of characteristic electrochemical electron transfer reactions are given and discussed. The results are compared with those for the surface molecule model.

Electron correlation effects in the adiabatic charge transfer reactions at the metal/polar liquid interface

New simple expressions for average number of electrons in the valence orbital of a reacting ion and the charge susceptibility are obtained that allow one to calculate adiabatic free energy surfaces (AFES) and corresponding kinetic regime diagrams (KRD) for adiabatic processes of electron transfer from the ion, located in a polar liquid, to a metal within the framework of the exactly solvable (in the limit T-->0) model of the metal with the infinitely wide conduction band. This model represents one of limiting cases of the Anderson model that may be applied to s-p metals. Unlike previous studies of the adiabatic reactions in the model of the metal with the infinitely wide conduction band, the present work takes into account the electron-electron correlation effects in an exact manner. General results are illustrated with KRD which determine the regions of the physical parameters of the system corresponding to various types of electron transfer processes. AFES are calculated for some typical parameters sets. The exact AFES are compared with those calculated within the Hartree-Fock approximation. It is shown that the correlation effects are of importance and results not only in a considerable decrease of the activation free energy but also to qualitatively different shapes of AFES in some regions of the system parameters.

Effect of the asymmetry of the coupling of the redox molecule to the electrodes in the one-level electrochemical bridged tunneling contact on the Coulomb blockade and the operation of molecular transistor

Effect of the asymmetry of the redox molecule (RM) coupling to the working electrodes on the Coulomb blockade and the operation of molecular transistor is considered under ambient conditions for the case of the non-adiabatic tunneling through the electrochemical contact having a one-level RM. The expressions for the tunnel current, the positions of the peaks of the tunnel current/overpotential dependencies, and their full widths at the half maximum are obtained for arbitrary values of the parameter d describing the coupling asymmetry of the tunneling contact and the effect of d on the different characteristics of the tunneling contact is studied. The tunnel current/overpotential and the differential conductance/bias voltage dependencies are calculated and interpreted. In particular, it is shown that the effect of the Coulomb blockade on the tunnel current and the differential conductance has a number of new features in the case of the large coupling asymmetry. It is also shown that, for rather large values of the solvent reorganization energy, the coupling asymmetry enhanced strongly amplification and rectification of the tunnel current in the most of the regions of the parameter space specifying the tunneling contact. The regions of the parameter space where both strong amplification and strong rectification take place are also revealed. The obtained results allow us to prove the possibility of the realization of the effective electrochemical transistor based on the one-level RM.

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.

Electron Correlations for Adiabatic Electrochemical Electron Transfer Reactions in a Model for an Electrode with an Infinitely Wide Conduction Band

Fresh general relationships for adiabatic free-energy surfaces (AFES) and corresponding diagrams of kinetic modes for adiabatic electrochemical electron transfer reactions are derived in the framework of an exactly solvable model for a metallic electrode with an infinitely wide conduction band. The model is a limiting case of the Anderson model applicable to the sp metals. In contrast to earlier studies of adiabatic reactions in a model for an electrode with an infinitely wide conduction band, this work accounts for the electron–electron correlation effects exactly. As an illustration, an AFES is calculated and a diagram of kinetic modes is constructed for a special case corresponding to the equilibrium electrode potential of a two-electron reaction. The exact AFES is compared with the AFES computed in the Hartree–Fock approximation and a spinless model. The correlation effects are shown to play a substantial role and lead to a considerable decrease in the activation free energy.

Non-local effects in the kinetics of heterogeneous charge transfer reactions

Abstract The effect of the solvent spatial dispersion and the field penetration into a metal on the kinetic parameters of the heterogeneous charge-transfer reactions is studied. The calculations are based on the exactly solvable ‘sharp boundary model’ of the interface, the Born sphere model of an ion and the Lorentzian form for the dielectric function of the solvent. It is shown that the reorganization Gibbs energy and the activation Gibbs energy decrease with decrease of the electrode–reactant separation in accordance with Marcus theory (in which the non-local effects are neglected) and in contrast with the results of Dzhavakhidze, Kornyshev and Krishtalik [J. Electroanal. Chem. 228 (1987) 329]. The reorganization Gibbs energy is found to be smaller than that given by the Marcus formula. The effect of the overscreening phenomenon on the results obtained is discussed.