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: 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.     

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.     

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.     

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.     

Calculation of adiabatic free energy surfaces in the case of electrochemical tunneling microscopy of redox systems

A method of adiabatic (infinitely slow) switching-on of interaction of the reactant with the electrode and the tip of a tunneling microscope at a bias voltage other than zero is used to derive expressions for the average number of electrons in the valence orbital of the reactant, the current passing through the valence orbital of the reactant at fixed values of coordinates of the slow subsystem of the solvent, and the electronic contribution to an expression that describes the adiabatic free energy surface (AFES) of the electrode-reactant-tip of the tunneling microscope system. The derived expressions are the same that had already been obtained in a Kuznetsov-Schmickler work, by a not-quite-correct method, though. Relationships that link the AFES corresponding to the opposite signs of the bias voltage are deduced. Examples of calculations of AFES and a current for a number of characteristic sets of parameters of the system are presented.Translated from Elektrokhimiya, Vol. 41, No. 3, 2005, pp. 259–272.Original Russian Text Copyright © 2005 by Medvedev.     

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.     

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.     

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.     

Effects of Electron Correlations in a Simple Model for Adiabatic Electrochemical Reactions: The Diagram of Kinetic Regimes

In the framework of the surface-molecule model for adiabatic electrochemical reactions of electron transfer previously suggested by the authors, a diagram of kinetic regimes (DKM) in the space of model parameters is obtained. The diagram comprises critical regions that correspond to various feasible electron transfer processes (transfer of one electron, simultaneous transfer of two electrons, transfer of two electrons in the presence of an intermediate state) and a region corresponding to electroadsorption of the reagent in certain charge states. Analytical expressions for boundary curves of DKM are obtained for a number of simple cases. A DKM for the general case of the surface-molecule model with an exact allowance for electron–electron correlations is constructed and analyzed.     

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.     

A semiclassical model of polarisation forces in atomic scattering

Low-energy elastic, differential and integral, collision cross sections for electron scattering from rare gas atoms are calculated using a simplified model treatment of the short-range polarisation forces already applied successfully to helium atoms (De Fazio et al., 1994). Static and exchange contributions to the total interaction are treated exactly, while a global semiclassical model provides a simple procedure for the short-range damping of all the long-range adiabatic terms which asymptotically lead to the polarisation forces. The results are compared with several available experimental findings for Ne and Ar atoms. The higher order terms in the perturbation expansion are found to have little effect on the cross sections and then only at low energies and in the small-angle region.Von Humboldt Stiftung Forschungspreisträger (1992)     

Proton-coupled electron transfer versus hydrogen atom transfer: generation of charge-localized diabatic states

The distinction between proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) mechanisms is important for the characterization of many chemical and biological processes. PCET and HAT mechanisms can be differentiated in terms of electronically nonadiabatic and adiabatic proton transfer, respectively. In this paper, quantitative diagnostics to evaluate the degree of electron-proton nonadiabaticity are presented. Moreover, the connection between the degree of electron-proton nonadiabaticity and the physical characteristics distinguishing PCET from HAT, namely, the extent of electronic charge redistribution, is clarified. In addition, a rigorous diabatization scheme for transforming the adiabatic electronic states into charge-localized diabatic states for PCET reactions is presented. These diabatic states are constructed to ensure that the first-order nonadiabatic couplings with respect to the one-dimensional transferring hydrogen coordinate vanish exactly. Application of these approaches to the phenoxyl-phenol and benzyl-toluene systems characterizes the former as PCET and the latter as HAT. The diabatic states generated for the phenoxyl-phenol system possess physically meaningful, localized electronic charge distributions that are relatively invariant along the hydrogen coordinate. These diabatic electronic states can be combined with the associated proton vibrational states to generate the reactant and product electron-proton vibronic states that form the basis of nonadiabatic PCET theories. Furthermore, these vibronic states and the corresponding vibronic couplings may be used to calculate rate constants and kinetic isotope effects of PCET reactions.     

Modified electron transfer model for excitation functions of the type M + RX → MX + R and M+ + RX− (M = alkali,R = alkyl group,X = halogen) and M′ + N2O → MO* + N2 (M′= Ba OR Sm)

A one-dimensional model is described for the excitation functions of reactions that are initiated by an electron transfer at close range. The process is governed by a barrier in the entrance channel, the abortive reflection of trajectories at higher energies and by the competition of an adiabatic and a diabatic channel for the reactive flux. The model is fitted to measured cross sections for the (K.Rb)+CH₃I, K+C₂H₅Br and (Ba.Sm)÷ N₂O reactions and the electron transfer cross section for K+CH₃I → K⁺ + CH₃I^- is successfully predicted from the fitting parameters of the reactive channel.     

Molecular electron affinities and the calculation of the temperature dependence of the electron-capture detector response

The use of the electron-capture detector (ECD) to measure molecular electron affinities and kinetic parameters for reactions of thermal electrons is reviewed. The advances of the past decade are emphasized and include the multistate electron-capture detector model and the use of semi-empirical self-consistent field quantum mechanical calculations and half wave reduction potential values to support gas phase experimental results. A procedure for the evaluation of the adiabatic electron affinities of the main group elements and the homonuclear diatomic molecules is presented. Potential excited states are identified for the magnetron (MGN) values for quinones, thermal charge transfer (TCT) values for CS2, C6F6, SF6 and photoelectron spectroscopy (PES) values for O2, NO, nitromethane, and the nucleic acids. Literature electron affinities are then evaluated. The temperature dependence of the electron-capture detector can be calculated using values for kinetic rate constants and electron affinities to optimize response and temperature sensitivity in analytical procedures. The temperature dependence for adenine, guanine, thymine and cytosine are predicted for reactions with thermal electrons. Using the recent advances, the new adiabatic electron affinities are: all in electron volts (eV), 4-F-benzaldehyde (0.57 +/- 0.05) and acetophenones (APs) 4-F-AP (0.52 +/- 0.05); 2-CF3-AP (0.79 +/- 0.05); 3-CF3-AP (0.79 +/- 0.05); 4-CF3-AP (0.89 +/- 0.05); 3-CI-AP (0.67 +/- 0.05); and 4-Cl-AP (0.64 +/- 0.05). The adiabatic electron affinities of chloro and fluorobenzenes range from 0.17 to 1.15 eV and 0.13 to 0.86 eV.     

Model system-bath Hamiltonian and nonadiabatic rate constants for proton-coupled electron transfer at electrode-solution interfaces

An extension of the Anderson-Newns-Schmickler model for electrochemical proton-coupled electron transfer (PCET) is presented. This model describes reactions in which electron transfer between a solute complex in solution and an electrode is coupled to proton transfer within the solute complex. The model Hamiltonian is derived in a basis of electron-proton vibronic states defined within a double adiabatic approximation for the electrons, transferring proton, and bath modes. The interaction term responsible for electronic transitions between the solute complex and the electrode depends on the proton donor-acceptor vibrational mode within the solute complex. This model Hamiltonian is used to derive the anodic and cathodic rate constants for nonadiabatic electrochemical PCET. The derivation is based on the master equations for the reduced density matrix of the electron-proton subsystem, which includes the electrons of the solute complex and the electrode, as well as the transferring proton. The rate constant expressions differ from analogous expressions for electrochemical electron transfer because of the summation over electron-proton vibronic states and the dependence of the couplings on the proton donor-acceptor vibrational motion. These differences lead to additional contributions to the total reorganization energy, an additional exponential temperature-dependent prefactor, and a temperature-dependent term in the effective activation energy that has different signs for the anodic and cathodic processes. This model can be generalized to describe both nonadiabatic and adiabatic electrochemical PCET reactions and provides the framework for the inclusion of additional effects, such as the breaking and forming of other chemical bonds.     

Adiabatic electrochemical electron-transfer reactions involving frequency changes of inner-sphere modes

A Hamiltonian model is formulated for electrochemical electron-transfer reactions involving frequency changes of the inner-sphere modes. The adiabatic free energy surface is calculated and it is shown that this nonlinear coupling leads to a transfer coefficient different from 1/2, and that the transfer coefficient can no longer be identified with the electron occupation probability in the transition state saddle point, as in the linear coupling case.     

Microscopic modelling of the reduction of a Zn(II) aqua-complex on metal electrodes

The mechanism of the Zn(II) reduction from acid aqueous solution at a metal electrode surface has been elucidated at a microscopic level. The Anderson–Newns model was employed in order to construct the adiabatic potential energy surfaces along the solvent coordinate for several reactions as a function of the electrode–reactant distance and the overpotential. A quantum chemical approach was employed to treat the coupling of the reactant to the metal electrode within a cluster model. The reduction of a [Zn(H₂O)₆]²⁺ complex was found to proceed in the adiabatic regime, the transfer of the first electron being rate-determining. Main attention is focused on effects of a qualitative nature, which are discussed in the light of available experimental data. The electrode charge excess and distance of maximal approach were found to affect significantly the Frank–Condon barriers of the reaction. An experimentally observed dependence of the rate constant of Zn(II) reduction upon the electrode material has been interpreted.     

Theory of Interrelated Electron and Proton Transfer Processes

A simple theory of elementary act of interrelated reactions of electron and proton transfer is developed. Mechanisms of synchronous and multistage transfer and coherent transitions via a dynamically populated intermediate state are discussed. Formulas for rate constants of adiabatic and nonadiabatic reactions are derived.     

The influence of the effective potential on the strong collision limiting low–pressure rate coefficients

The influence of the effective potential energy curves on the calculation of the strong collision limiting low-pressure rate coefficients of thermal dissociation-recombination reactions was analyzed in terms of the factorized formalism of Troe. An analysis of 26 reactions employing a Morse potential coupled with a quasitriatomic molecular model and an explicit account of the adiabatic zero-point barriers, as originallyproposed by Troe, was performed. A comparison between calculations realizedwith an exactly fitted looseness parameter, α, and with a standard value of α = 1.0 Å^?1, indicates that the use of this last value is satisfactorily justified in the evaluation of thestrong collision limiting low-pressure rate coefficients. A study interms of restrictive relationships between the looseness and Morse parameters and ab initio, radial potentials (for CH₄, CH₃O₂, and HO₂) was also realized. The uncertainties in the evaluation of termolecular rate coefficients due to the lack of a complete knowledge of the long-range potentials are also briefly discussed.