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 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: Diagram of Kinetic Modes

A diagram of kinetic modes (DKM), whose parts correspond to different electron transfer types, for any electrode's Fermi energy _F and any finite value of its conduction band's width B is studied. Important differences between DKM for any _F and B and DKM in a model of a surface molecule for an electrode-reactant system are pointed out. DKM for electrode models with nearly empty and nearly filled conduction bands proposed earlier are discussed. Expressions for outermost curves of DKM are derived for some special cases within these models.     

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.     

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.     

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.     

Temperature dependence of the electronic factor in the nonadiabatic electron transfer at metal and semiconductor electrodes

The temperature dependence of the electronic contribution to the nonadiabatic electron transfer rate constant (k_ET) at metal electrodes is discussed. It is found in these calculations that this contribution is proportional to the absolute temperature T. A simple interpretation is given. We also consider the nonadiabatic rate constant for electron transfer at a semiconductor electrode. Under conditions for the maximum rate constant, the electronic contribution is also estimated to be proportional to T, but for different reasons than in the case of metals (Boltzmann statistics and transfer at the conduction band edge for the semiconductor versus Fermi–Dirac statistics and transfer at the Fermi level, which is far from the band edge, of the metal).     

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.     

Comparison of Trap‐state Distribution and Carrier Transport in Nanotubular and Nanoparticulate TiO2 Electrodes for Dye‐Sensitized Solar Cells

Dye‐sensitized solar cells (DSCs) with nanotubular TiO₂ electrodes of varying thicknesses are compared to DSCs based on conventional nanoparticulate electrodes. Despite the higher degree of order in one‐dimensional nanotubular electrodes, electron transport times and diffusion coefficients, determined under short‐circuit conditions, are comparable to those of nanoparticulate electrodes. The quasi‐Fermi level, however, is much lower in the nanotubes, suggesting a lower concentration of conduction band electrons. This provides evidence for a much higher diffusion coefficient for conduction band electrons in nanotubes than in nanoparticulate films. The electron lifetime and the diffusion length are significantly longer in nanotubular TiO₂ electrodes than in nanoparticulate films. Nanotubular electrodes have a trap distribution that differs significantly from nanoparticulate electrodes; they possess relatively deeper traps and have a characteristic energy of the exponential distribution that is more than two times that of nanoparticulate electrodes.     

Characterization of solid-state dye-sensitized solar cells utilizing high absorption coefficient metal-free organic dyes

Solid-state dye-sensitized solar cells were fabricated using the organic hole-transporting medium (HTM) 2,2'7,7'-tetrakis-(N,N-di-p-methoxyphenyl-amine)-9,9'-spirobifluorene (spiro-MeOTAD), and three organic indoline-based sensitizer dyes with high molar extinction coefficients. The cells were characterized by several techniques, including spectral response measurements, photovoltage decay transients, intensity modulated photovoltage spectroscopy (IMVS), and charge extraction. The differences in apparent electron lifetime observed for cells fabricated using the three dyes are attributed in part to changes in the surface dipole potential at the TiO2/spiro-MeOTAD interface, which shift the TiO2 conduction band energy relative to the Fermi level of the HTM. These energy shifts influence both the open circuit voltage (as a result of changes in free electron density) and the short circuit current (as a consequence of changes in the overlap between the dye LUMO level and the conduction band). A self-consistent approach was used to derive the positions of the conduction band relative to the spiro-MeOTAD redox Fermi level for cells fabricated using the three dyes. The analysis also provided estimates of the free electron lifetime in spiro-MeOTAD cells. In order to evaluate the possible contribution of the adsorbed dyes to the observed changes in surface dipole potential, their dipole moments were estimated using ab initio density functional theory (DFT) calculations. Comparison of the calculated dipole contributions with the experimentally measured shifts in conduction band energy revealed that other factors such as proton adsorption may be predominant in determining the surface dipole potential.     

Direct measurement of the temperature coefficient of the electron quasi-fermi level in dye-sensitized nanocrystalline solar cells using a titanium sensor electrode

A novel type of dye-sensitized cell (DSC) with a passivated titanium sensor electrode located on top of the nanocrystalline titanium dioxide layer has been used to study the temperature dependence of the electron quasi-Fermi level relative to the I3-/I- redox-Fermi level under short circuit conditions. The results show that the Fermi level decreases with increasing temperature (-1.76 meV K(-1)) as predicted for diffusive electron transport at short circuit. A smaller temperature dependence (-0.25 meV K(-1)) of the position of the TiO2 conduction band relative to the I3-/I- redox-Fermi level was deduced from the shifts in the trap distribution. An expression for the temperature dependence of the open circuit voltage, U(photo), has been derived. The experimentally observed temperature dependence of U(photo) gave values of the activation energy (0.25 eV) and preexponential factor (10(8) s(-1)) for the transfer of electrons from the conduction band of the nanocrystalline TiO2 to triiodide ions.     

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.     

氯化血红素分子对牛血清白蛋白电子传输能级的调控

蛋白质分子的电子传输(ETp)性能,即导带(CB)和价带(VB)的能量差(带隙)是影响蛋白质电子器件性能的主要因素之一。因此,调控蛋白质ETp带隙是提高这些电子器件性能并扩展其应用领域的重要途径。本文报道一种通过外部分子结合调控蛋白质ETp带隙的方法。以氯化血红素(hemin)与牛血清白蛋白(BSA)结合为例,首先运用分子对接方法从理论上确定hemin分子能结合到BSA分子IIA域的疏水口袋中,位于Tpr213附近;然后实验(荧光光谱和吸收光谱)证实hemin与BSA结合后,能形成hemin-BSA复合物,并且没有改变BSA的原有结构;最后将hemin-BSA通过BSA分子表面Cys34的―SH固定在金电极表面,形成有序的分子层,研究其ETp性能;I–V结果表明,BSA表现出半导体的ETp特征,并且hemin的结合能使BSA的带隙由原来的~1.50±0.05e V降低到~0.93±0.05e V。本文的结果为调控蛋白质分子的ETp带隙提供了一种简单有效的方法,通过选择不同的结合分子能使蛋白质分子的带隙调控至所需要的范围,并且形成的蛋白质复合物还能用于各种电子器件的制作。     

Energy‐Level Alignment for Single‐Molecule Conductance of Extended Metal‐Atom Chains

The use of single‐molecule junctions for various functions constitutes a central goal of molecular electronics. The functional features and the efficiency of electron transport are dictated by the degree of energy‐level alignment (ELA), that is, the offset potential between the electrode Fermi level and the frontier molecular orbitals. Examples manifesting ELA are rare owing to experimental challenges and the large energy barriers of typical model compounds. In this work, single‐molecule junctions of organometallic compounds with five metal centers joined in a collinear fashion were analyzed. The single‐molecule i–V scans could be conducted in a reliable manner, and the E_FMO levels were electrochemically accessible. When the electrode Fermi level (E_F) is close to the frontier orbitals (E_FMO) of the bridging molecule, larger conductance was observed. The smaller |E_F?E_FMO| gap was also derived quantitatively, unambiguously confirming the ELA. The mechanism is described in terms of a two‐level model involving co‐tunneling and sequential tunneling processes.     

Investigation of Electron Behavior in Nano‐TiO2 Photocatalysis by Using In Situ Open‐Circuit Voltage and Photoconductivity Measurements

The in situ open‐circuit voltages (V_oc) and the in situ photoconductivities have been measured to study electron behavior in photocatalysis and its effect on the photocatalytic oxidation of methanol. It was observed that electron injection to the conduction band (CB) of TiO₂ under light illumination during photocatalysis includes two sources: from the valence band (VB) of TiO₂ and from the methanol molecule. The electron injection from methanol to TiO₂ is slower than that directly from the VB, which indicates that the adsorption mode of methanol on the TiO₂ surface can change between dark and illuminated states. The electron injection from methanol to the CB of TiO₂ leads to the upshift of the Fermi level of electrons in TiO₂, which is the thermodynamic driving force of photocatalytic oxidation. It was also found that the charge state of nano‐TiO₂ is continuously changing during photocatalysis as electrons are injected from methanol to TiO₂. Combined with the apparent Langmuir–Hinshelwood kinetic model, the relation between photocatalytic kinetics and electrons in the TiO₂ CB was developed and verified experimentally. The photocatalytic rate constant is the variation of the Fermi level with time, based on which a new method was developed to calculate the photocatalytic kinetic rate constant by monitoring the change of V_oc with time during photocatalysis.     

A generalized Landauer-Datta-Lundstrom electron transport model

General problems of electronic conductivity, reasons for a current flow, the role of electrochemical potentials, Fermi functions, the Fermi window for conduction, the elastic resistor model, different electron transport regimes, conduction modes, and transmission coefficients are discussed in terms of the “bottom-up” approach to nanoelectronics. The generalized model of electron transport in the linear response regime developed by R. Landauer, S. Datta, and M. Lundstrom, which can be applied to conductors of any size, scale, and arbitrary dispersion in the ballistic, quasi-ballistic, or diffusive regimes is described.     

Photoinduced electron transfer and interfacial photocatalysis behaviour of ZnS/CdS binary co-colloid system

The interfacial photoinduced electron transfer and related secondary photochemical behaviour in the system of ZnS/CdS co-colloid superfine particles were studied by means of ESR and fluorescence spectroscopy techniques. The photoinduced charge-separation and the radical intermediates produced in the secondary redox reactions initiated via charge separation, as well as the mechanism of reaction processes, were investigated in detail through simultaneous excitation of two colloid components or only one of them. Research results indicated that, as E_(g(ZnS))>E_λ>E_(g(CdS)), only CdS in co-colloid system might be excited. The transfer process of electron from the conduction band of CdS to the conduction band of ZnS is forbidden, and under the excitation wavelength range used, the electron transfer of cocolloid system was impossible, thus the photo redox reactions of the substrate in co-colloid system had no obvious difference from those reactions happening in single colloid system. While the excitation wav     

Elementary Photoelectronic Processes at a Porphyrin Dye/Single‐Walled TiO2 Nanotube Hetero‐interface in Dye‐Sensitized Solar Cells: A First‐Principles Study

A unique one‐dimensional (1D) sandwich single‐walled TiO₂ nanotube (STNT) is proposed as a photoanode nanomaterial with perfect morphology and large specific surface area. We have thoroughly examined the elementary photoelectronic processes occurring at the porphyrin dye/STNT hetero‐interface in dye‐sensitized solar cells (DSSCs) by theoretical simulation. It is desirable to investigate the interfacial photoelectronic processes to elucidate the electron transfer and transport mechanism in 1D STNT‐based DSSCs. We have found that the photoexcitation and interfacial charge separation mechanism can be described as follows. A ground‐state electron of the dye molecule (localized around the electron donor) is first promoted to the excited state (distributed electron donor), and then undergoes ultrafast injection into the conduction band of the STNT, leaving a hole around the oxidized dye. Significantly, the injected electron in the conduction band is transported along the STNT by means of Ti 3d orbitals, offering a unidirectional electron pathway toward the electrode for massive collection without the observation of trap states. Our study not only provides theoretical guidelines for the modification of TiO₂ nanotubes as a photoanode material, but also opens a new perspective for the development of a novel class of TiO₂ nanotubes with high power‐generation efficiency.