Effects of Electronic Correlations for Adiabatic Electrochemical Reactions of Electron Transfer in Electrode Models with Nearly Empty and Nearly Filled Conduction Bands: General Relationships

Expressions for the calculation of the adiabatic free energy surfaces (AFES) and average number of electrons in the valence orbital of the reagent for adiabatic electrochemical reactions of electron transfer are obtained in terms of exactly solved models for a metal electrode with nearly empty and nearly filled conduction bands. The models are extreme cases of the Anderson model, which account exactly for the electron–electron correlation effects. In particular, the electrode model with a nearly filled conduction band can be applied to transition metals of Group VIII in the periodic table. Exact relationships connecting AFES and diagrams of kinetic modes (DKM) for electrodes with symmetric position of Fermi levels relative to the conduction band center are obtained. Two characteristic functions for analyzing the role of electron–electron correlation effects in the system under consideration are proposed and calculated. The results form a basis for calculating AFES and studying correlation effects in adiabatic electrochemical reactions of electron transfer and constructing DKM that would correspond to different electron transfer modes.     

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.     

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.     

On the possibility of an STM-induced dissociative electron transfer

The process of dissociative adsorption of a molecule on an electrode in a system of the type in situ scanning tunneling microscopy (STM) is investigated theoretically. It is shown that, in the case of fully nonadiabatic or partly adiabatic electron transfer, the presence of the tip of STM may either accelerate (or even induce) or decelerate the process of dissociation of the molecule, depending on the sign of the bias voltage. The maximum effect takes place in the case of strong interaction of the molecule with both electrodes (fully adiabatic electron transfer). In this limit, diagrams of kinetic modes, which mark off the boundaries between processes of different types possible in a given system, are constructed.Translated from Elektrokhimiya, Vol. 41, No. 3, 2005, pp. 273–284.Original Russian Text Copyright © 2005 by Kuznetsov, Medvedev.     

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.     

Simulation of scanning tunneling microscope images of 1,3-cyclohexadiene bound to a silicon surface

Scanning tunneling microscope (STM) images of 1,3-cyclohexadiene bound to silicon are interpreted using a nonequilibrium Green's function method. The resolution of the carbon-carbon double bond for positive bias voltages but not for negative bias voltages is explained using a quasiprobability density analysis. The asymmetry in the images arises from the system's voltage dependent electronic structure. A pi* orbital is found to be responsible for the empty state STM images of the carbon-carbon double bond, which is observed experimentally. The pi orbital relevant for the opposite bias does not produce an STM image sharply localized in the bond region because the molecule induces a Si-surface dipole dependent on the bias. The dipole voltage dependence arises from molecular charging. This result emphasizes the importance of simulating the molecule as an element in an open quantum system.     

Symmetry properties of adiabatic free energy surfaces and a diagram of kinetic modes in the case of electrochemical tunneling microscopy of redox systems

The symmetry properties of adiabatic free energy surfaces, which describe redox and dissociative electron transfer reactions in systems of the type in situ STM, are investigated. A notion of an effective overvoltage, which is a generalization of a traditional overvoltage to the case where the bias voltage is other than zero, is introduced. Diagrams of kinetic modes, which describe processes that can occur in systems of the type in situ STM under consideration, are constructed in the space of model parameters. It is shown that, in some cases, with the bias voltage other than zero, there may emerge DKR of a sufficiently complicated structure with several critical regions.__________Translated from Elektrokhimiya, Vol. 41, No. 4, 2005, pp. 419–432.Original Russian Text Copyright © 2005 by Medvedev.     

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.     

Effects of Electronic Correlations for Adiabatic Electrochemical Reactions of Electron Transfer in Electrode Models with Nearly Empty and Nearly Filled Conduction Bands: Adiabatic Free Energy Surfaces

Adiabatic free energy surfaces (AFES) for adiabatic electrochemical reactions of electron transfer (ARET) are computed with exact allowance for electron–electron correlation effects (EECE) in models of electrode with nearly empty and almost filled conduction bands and analyzed on the basis of a diagram of kinetic modes obtained earlier. The EECE role in ARET for an electrode with an arbitrary Fermi level in a conduction band of an arbitrary width is discussed. In the general case, allowing for EECE gives at some model parameters results other than for the Fermi level coinciding with the conduction band center (model of a surface molecule, MSM). As in the case of MSM considered previously, EECE considerably reduce activation free energies and at some model parameters give qualitatively different AFES.     

Kramers problem for nonequilibrium current-induced chemical reactions

We discuss the use of tunneling electron current to control and catalyze chemical reactions. Assuming the separation of time scales for electronic and nuclear dynamics we employ Langevin equation for a reaction coordinate. The Langevin equation contains nonconservative current-induced forces and gives nonequilibrium, effective potential energy surface for current-carrying molecular systems. The current-induced forces are computed via Keldysh nonequilibrium Green's functions. Once a nonequilibrium, current-depended potential energy surface is defined, the chemical reaction is modeled as an escape of a Brownian particle from the potential well. We demonstrate that the barrier between the reactant and the product states can be controlled by the bias voltage. When the molecule is asymmetrically coupled to the electrodes, the reaction can be catalyzed or stopped depending on the polarity of the tunneling current.     

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 Anderson's 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.     

Does the electron spin affect the rates of electron tunneling in electrochemical systems?

An effect of spin degeneracy of electron energy levels in the metal electrode on the observable characteristics of electrochemical systems in the absence of magnetic field is discussed. Single-electrode outer-sphere electron transfer reactions are considered as well as redox-mediated electron tunneling in electrochemical contacts. Particular attention is paid to the difference between the spin-less model and the limit of infinitely large Coulomb repulsion of the electrons occupying the same valence orbital in the redox group. Adiabatic and non-adiabatic regimes of the transitions are studied and the expressions for the tunnel current are obtained.     

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 surface hopping method for chemical reaction dynamics in solution described by diabatic representation: an analysis of tunneling and thermal activation

We present a surface hopping method for chemical reaction in solution based on diabatic representation, where quantum mechanical time evolution of the vibrational state of the reacting nuclei as well as the reaction-related electronic state of the system are traced simultaneously together with the classical motion of the solvent. The method is effective in describing the system where decoherence between reactant and product states is rapid. The diabatic representation can also give a clear picture for the reaction mechanism, e.g., thermal activation mechanism and a tunneling one. An idea of molecular orbital theory has been applied to evaluate the solvent contribution to the electronic coupling which determines the rate of reactive transition between the reactant and product potential surfaces. We applied the method to a model system which can describe complex chemical reaction of the real system. Two numerical examples are presented in order to demonstrate the applicability of the present method, where the first example traces a chemical reaction proceeded by thermal activation mechanism and the second examines tunneling mechanism mimicking a proton transfer reaction.     

Effect of electron-electron correlations on the activation free energy of adiabatic electrochemical reactions of dissociative electron transfer

Adiabatic free energy surfaces for adiabatic electrochemical reactions of dissociative electron transfer are calculated with exact allowance for the effects of electron-electron correlations in a model of an electrode with an infinitely broad conduction band. The role of correlation effects in these reactions is discussed. It is shown that, as in common adiabatic electrochemical reactions of electron transfer, correlation effects play a substantial role and lead to a considerable decrease in the activation free energies.__________Translated from Elektrokhimiya, Vol. 41, No. 4, 2005, pp. 412–418.Original Russian Text Copyright © 2005 by Kuznetsov, Medvedev, Sokolov.     

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.     

Effect of Coulomb interaction between the electrons on two-electron redox-mediated tunneling

Two-electron non-adiabatic redox-mediated tunneling through a symmetric electrochemical contact with a bridge molecule having one electron energy level participating in tunneling is considered under ambient conditions. It is shown that the current/overpotential dependence in this system can disclose two distinct or overlapping clear-cut maxima depending on the value of the effective Coulomb repulsion energy. This new effect is due to the opening of the channel for tunneling of second electron with the variation of the electrode potential. The system manifests also a rectification effect in the current/bias voltage curve which depends on the value of the effective Coulomb repulsion energy.     

Effects of Electron Correlations in a Simple Model for Adiabatic Electrochemical Reactions: The Application to Particular Reactions

Adiabatic free-energy surfaces (AFES) for some typical electrode processes are calculated in the framework of the surface-molecule model for adiabatic electrochemical reactions of electron transfer previously suggested by the authors. The surfaces are analyzed using the proposed diagrams of kinetic modes. It is shown that correlation effects play a substantial role in the reactions and not only considerably diminish the free energy of activation but also lead to qualitatively different shapes of AFES in some regions of modeling parameters.     

Excitation energies expressed as orbital energies of Kohn–Sham density functional theory with long-range corrected functionals

A new simple and conceptual theoretical scheme is proposed for estimating one-electron excitation energies using Kohn–Sham (KS) solutions. One-electron transitions that are dominated by the promotion from one initially occupied orbital to one unoccupied orbital of a molecular system can be expressed in a two-step process, ionization, and electron attachment. KS with long-range corrected (LC) functionals satisfies Janak's theorem and LC total energy varies almost linearly as a function of its fractional occupation number between the integer electron points. Thus, LC reproduces ionization energies (IPs) and electron affinities (EAs) with high accuracy and one-electron excitation energies are expressed as the difference between the occupied orbital energy of a neutral molecule and the corresponding unoccupied orbital energy of its cation. Two such expressions can be used, with one employing the orbital energies for the neutral and cationic systems, while the other utilizes orbital energies of just the cation. Because the EA of a molecule is the IP of its anion, if we utilize this identity, the two expressions coincide and give the same excitation energies. Reasonable results are obtained for valence and core excitations using only orbital energies.