The influence of crystallographic inhomogeneity of a polycrystalline electrode surface on the behavior of the electric double-layer

The specific features of the electric double-layer structure at polycrystalline electrodes in the absence of specific ion adsorption have been examined for two different models: Model I and Model II. In the case of Model I each of the faces showing on the surface of a polycrystalline electrode retains its own Helmholtz and diffuse double layers. In the case of Model II the faces retain only their own Helmholtz layer, whereas the diffuse layer is common to the entire electrode surface. The difference of zero charge potentials of the faces is defined both by their dissimilar hydrophilic properties and by different work functions. The experimental data available at present on the electric double-layer structure at polycrystalline electrodes for which the potentials of zero charge of the faces differ significantly are described by Model I.     

Solvent dynamics in a model system

We report herein a study of the solvent reorganization process in an electron transfer reaction. The calculations are based on a model consisting of 26 or 62 solvent particles. Molecular dynamics simulations are performed to calculate the electric field fluctuations during the orientational and translational motion of the solvent molecules. The changes in the electric fields at various points near the reacting sites in the system are evaluated as a function of time. From these electric fields, electric field time correlation functions are calculated. The main conclusion in this work is that it requires nearly 3 ps for the model solvent to reorient during the charge transfer. These results suggest ways of incorporating solvent dynamics based on molecular models into theoretical studies of electron transfer rates in condensed media.     

Impact of Electron–Electron Collisions on the Spatial Electron Relaxation in Non-Isothermal Plasmas

The impact of electron–electron collisions on the spatial relaxation of electrons in the column-anode plasma of a glow discharge, acted upon by a space-independent electric field and initiated by a constant influx at the cathode side of the plasma, is investigated in inert gas plasmas. The investigations are based on a new method for numerically solving the one-dimensional inhomogeneous Boltzmann equation of the electrons including electron–electron interaction in weakly ionized, collision-dominated plasmas. A detailed analysis of the spatial behaviour of the velocity distribution function and relevant macroscopic properties of the electrons is given for various degrees of ionization and electric field strengths. A significant impact of the electron–electron collisions on the relaxation structure and the resultant relaxation length already at relatively low ionization degrees has been found for low to medium electric fields.     

Calculation of the Stark effect of neon I usingjl coupled wave functions

A method to calculate the Stark shifts and splittings in noble gases is described and results for neon I are presented. The energy values in a static homogeneous electric field are found by diagonalizing the energy matrix numerically. This matrix consists of the energy values of the free atom taken from experiment and of off-diagonal matrix elements of the electric field operator. The latter are computed using wave functions consisting of a radial function of the excited electron found by numerical integration, and of a two-particle (core+electron) spin-orbital part represented by rigorousjl coupling. As an example, the splitting of the levels 6s to 6p is shown and is explained in terms of atomic level positions, the relative size of matrix elements and of selection rules. A nomenclature for the high field Stark effect is developed in accord with group theory.     

Solution of periodic Poisson's equation and the Hartree–Fock approach for solids with extended electron states: Application to linear augmented plane wave method

We formulate a Hartree–Fock‐LAPW method for electronic band structure calculations. The method is based on the Hartree–Fock–Roothaan approach for solids with extended electron states and closed core shells where the basis functions of itinerant electrons are linear augmented plane waves. All interactions within the restricted Hartree–Fock approach are analyzed and in principle can be taken into account. In particular, we obtained the matrix elements for the exchange interactions of extended states and the crystal electric field effects. To calculate the matrix elements of exchange for extended states, we first introduce an auxiliary potential and then integrate it with an effective charge density corresponding to the electron exchange transition under consideration. The problem of finding the auxiliary potential is solved by using the strategy of the full potential LAPW approach, which is based on the general solution of periodic Poisson's equation. Here, we use an original technique for the general solution of periodic Poisson's equation and multipole expansions of electron densities. We apply the technique to obtain periodic potentials of the face‐centered cubic lattice and discuss its accuracy and convergence in comparison with other methods. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Substituent effect on a family of quinones in aprotic solvents: an experimental and theoretical approach

In this work a comparison between redox potentials, obtained by constructing current-potential plots from chronoamperometric measurements, and the parameter sigma(x), as proposed by Zuman in terms of the Hammett substituent parameters, was performed for several quinone compounds. This study shows the limitations of this approach and proves that methods based on quantum chemistry can be used to study the substituent effect in quinone systems. By using the Density Functional Theory, in the Kohn-Sham context with three exchange-correlation functionals, BLYP, B3LYP, and BHLYP, it was found that the electron affinity is good enough to give a useful relationship with experimental redox potentials of quinone systems. This conclusion is reached when the basis set functions involve diffuse functions, and also when the Hartree-Fock exchange energy is included in the exchange-correlation functional. The Fukui function, to describe preferential sites involved at initial stages of a system that bind an electron, is analyzed when electron donor and electron acceptor groups are present as substituents in quinone systems. The methods applied in this work are valid for any kind of quinone compound and will be used in further analysis of the electron reorganization in semiquinone species.     

Thermodynamic Foundation for High Temperature Electrochemistry

Thermodynamic concepts required for the thermodynamic calculation of the potentials of electrodes for high temperature applications are briefly reviewed. A thermodynamic approach to the calculation of half cell potentials and the standard chemical potential of an electron at high temperatures which are related to the Standard Hydrogen Electrode(SHE) is discussed. As examples, an external Ag/AgCl reference electrode and a YSZ(Ag|O2) pH sensor for high temperature applications are analyzed by using the thermodynamic ap-proach to derive a high temperature pH measurement equation. The two electrodes are employed to measure high temperature pH and the measured pH was compared with the calculated pH by using a solution chem-istry method. Concepts and principles for electrode kinetics are also briefly introduced and a modification to the Tafel equations is suggested.     

Microwave Diagnostics in Diffusive and Constricted Medium-Pressure Discharges

The high-frequency (HF) electron current induced in a dc discharge plasma bysuperimposing a HF electric field presents a useful tool for the diagnosticsof the time-dependent electron behavior of the plasma. This response to theHF field has been recently studied in diffusive discharge plasmas at lowergas pressures and discharge currents. These studies are extended tomedium-pressure plasmas operating in the diffusive as well as in theconstricted mode. In particular, the impact of the electron–electroninteraction on the phase delay between the HF field and electron current inconstricted column plasmas has been experimentally and theoreticallyanalyzed. Furthermore, the problem has been studied if, under the conditionsof pronounced electron–electron interaction, the determination of theelectron density will further on be possible by using the phase delay. Themeasurements of the delay have been performed by means of the microwaveresonator method in a medium-pressure krypton glow discharge operating inthe diffusive as well as the strongly constricted mode. In addition, thedelay has been theoretically determined by treating the appropriatetime-dependent electron kinetic equation at high frequencies of thesuperimposed microwave field.     

A bulk adjusted linear combination of atomic orbitals (BA-LCAO) approach for nanoparticles

We describe a bulk adjusted linear combination of atomic orbitals (BA-LCAO) approach for nanoparticles. In this method, we apply a many-body scaling function (in similar manner as in the environment-modified total energy based tight-binding method) to the DFT-derived diatomic AO interaction potentials (like in the conventional orbital-based density-functional tight binding approach) strictly according to atomic valences acquired naturally in a bulk structure. This modification, (a) facilitates all atom orbital-based electronic structure calculations of charge carrier dynamics in nanoscale structures with a molecular acceptor, and (b) allows to closely match high-level density functional calculation data (previously adjusted to the available experimental findings) for bulk structures. To advance practical application of the BA-LCAO approach we parameterize the Hamiltonian of wurtzite CdSe by fitting its band structure to a high-level DFT reference, corrected for experimentally measured band edges. Here, unlike in conventional DFTB approach, we: (1) use hydrogen-like AOs for the basis as exact atomic eigenfunctions, while orbital energies of which are taken from experimentally measured ionization potentials, and (2) parameterize the many-body scaling functions rather than the atomic wavefunctions. Development of this approach and parameters is guided by our goals to devise a method capable of simultaneously treating the problems of (i) interfacial electron/hole transfer between finite, variable size nanoparticles and electron scavenging molecules, and (ii) high-energy electronic transitions (Auger transitions) that mediate multi-exciton decay in quantum dots. Electronic structure results are described for CdSe quantum dots of various sizes. © 2018 Wiley Periodicals, Inc.     

Recursion formula for electron repulsion integrals over Hermite polynomials

A method for computing electron repulsion integrals over contracted Gaussian functions is described in which intermediate integrals over Hermite polynomials are generated by a “pre‐Hermite” recursion (PHR) step before the conversion to regular integrals. This greatly reduces the floating‐point operation counts inside the contraction loops, where only simple “scaling”‐type operations are required, making the method efficient for contracted Gaussians, particularly of high angular momentum. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

A New Method of the Microwave Diagnostics for Determining the Electron Density

A improved method of the microwave diagnostics for the determination of the electron density in the column plasma of dc glow discharges is presented. This method overcomes significant limitations involved in the conventional method. The latter is mainly based on the measurement of the resonance frequency shift of the resonator cavity caused by the presence of the dc column plasma and is strictly valid only in the so-called high field frequency limit of the resonator operation. Of significant importance with respect to the improved method is the additional inclusion of the measurable phase delay between the electric hf field, superimposed on the dc plasma by the microwave field of the resonator, and the induced hf electron current. This new method has been critically evaluated with respect to its extended applicability and has been successfully applied to the experimental determination of the electron density in dc plasmas of neon and molecular nitrogen.     

Evaluation of multicenter one-electron integrals of noninteger u screened Coulomb type potentials and their derivatives over noninteger n Slater orbitals

Multicenter integrals over noninteger n Slater type orbitals with integer and noninteger values of indices u of screened Coulomb type potentials, f(u)(eta,r)=r(u-1)e(-etar), and their first and second derivatives with respect to Cartesian coordinates of the nuclei of a molecule are described. Using complete orthonormal sets of Psi(alpha) exponential type orbitals and rotation transformation of two-center overlap integrals, these integrals are expressed through the noncentral potential functions depending on the molecular auxiliary functions A(k) and B(k). The series expansion formulas derived for molecular integrals of screened Coulomb potentials and their derivatives are especially useful for the computation of multicenter electronic attraction, electric field, and electric field gradient integrals. The convergence of series is tested for arbitrary values of parameters of potentials and orbitals.     

Electrochemical nanoimprint lithography directly on n-type crystalline silicon (111) wafer

Here we report spontaneous redox reactions at the Pt/Si/electrolyte three-phase interface and propose an electrochemical method for nanoimprint lithography on a crystalline Si wafer that does not require thermoplastic and photocuring resists. When the Pt metallized imprint mold is compacted on the n-type Si (111) wafer, electrons will transfer from the n-type Si to Pt due to their different electron work functions. At equilibrium, the Fermi levels of the electrons in each phase become equal, resulting in an electric field and a contact potential at the Pt/Si interface. When immersed in an electrolyte solution, the potentials of the Pt/electrolyte interface and the Si/electrolyte interface are observed to shift in opposite directions. Hydrogen peroxide is spontaneously reduced on the Pt surface. Meanwhile, the electrons in Si will tunnel to Pt and the residual holes will oxidize Si along the three-phase interface. In this way, the micro-/nanostructures on the Pt metallized imprint mold are transferred to the Si wafer.     

Spectral/structural data of helium atoms with exponential‐cosine‐screened coulomb potentials

Atomic systems with exponential‐cosine‐screened Coulomb (ECSC) or static screened Coulomb (SSC) potentials have drawn considerable attention recently due to the possible applications to atoms in plasma environments. In this work, we develop a computing scheme to deal with the electron–electron correlation terms with the screened Coulomb interactions instead of the conventional expansion method using the Gegenbauer's addition theorem. Based on this approach, we investigate the helium atom with the ECSC potentials. Bypassing the complex expansion functions for electron–electron interactions, the proposed approach simplifies the calculations greatly and provides an advantage on programming. The results are found to be in good agreement with the existing data. Bound‐state energies, oscillator strengths, and multipole polarizabilities varying with the screening parameters are presented. Comparisons of the ECSC potentials are made with the SSC potentials. The influence of screening effect on the energies, oscillator strengths, and polarizabilities is discussed. © 2015 Wiley Periodicals, Inc.     

Photoinduced electron transfer in ion pairs of cation-anion polymethine dyes

Photoinduced electron transfer in ion pairs of cation-anion polymethine dyes was studied by flash photolysis. The formation of radicals, which are the products of photoinduced transfer of an electron from an anion to a cation in the ion pairs, was observed during photoexcitation of a number of cation-anion dyes in nonpolar and some weakly polar solvents (in particular, in toluene and chloroform). Photoinduced electron transfer is also observed during triplet sensitization of ion pairs of the cation-anion dyes. The redox potentials of the cations and anions constituting the dyes were measured; the radical yields were compared with the free energies of photoinduced electron transfer. Photoinduced electron transfer in the systems under study was compared with similar process in cyanineborate ion pairs.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 878–884, May, 1995.The authors thank I. Ya. Levitin for help in measuring redox potentials.This work was financially supported by the Russian Foundation for Basic Research (Project No. 93-03-4217).     

Modeling exact exchange potential in spherically confined atoms

In this work, local exchange potentials corresponding to the Hartree–Fock (HF) electron density have been obtained using the Zhao–Morrison–Parr method for a number of closed‐shell confined atoms and ions. The exchange potentials obtained and the resulting density were compared with those given by the Becke–Johnson (BJ) model potential. It is demonstrated that introducing a scaling factor to the BJ potential allows improving the quality of the resulting density. The optimum scaling factor increases with decreasing confinement radius. The performance of Karasiev and Ludeña's SCα‐LDA method as well as of the Becke‐88 exchange potential for reproducing the HF electron densities in confined atoms has been also examined. © 2015 Wiley Periodicals, Inc.     

One-center expansion method with model potentials. I. Formulation and test calculations

The one-center expansion (OCE ) method is extended to evaluate molecular wave functions for molecules with heavy off-center nuclei. This extension is achieved through the use of model potentials (MP ) to approximate the highly bound core orbitals. The remaining diffuse valence charge distribution is then rather easy to simulate using OCE . The formulation of the method is described. New molecular integrals are solved to a high degree of accuracy. Successful results are reported for H₂O, H₂S, and N₂. The valence electron distributions and orbital energies are in good agreement with those obtained from more complete calculations. The method combines the computational economy of both OCE and MP procedures, resulting in a potentially useful package for further chemical applications.     

Electrostatic potentials and fields in the vicinity of engineered nanostructures

We have developed a method for calculating the electrostatic potentials and fields in the vicinity of geometrically complex engineered nanostructures composed of varying materials in electrolytes of arbitrary pH and ionic strength. The method involves direct summation of charged Debye-Hückel spheres composing the nanostructural surfaces and, by including charge redistribution on the surface of conducting materials held at constant potential, is applicable to mixed boundary conditions. The method is validated by comparison to analytical solutions for an infinite plane (Gouy-Chapman), an infinite cylinder (Bessel functions), and an infinite plane which contains a hole and which is held at constant potential. Excellent agreement between the potentials obtained by our numerical method and the closed form solutions is found for these conditions. The method is applied to the calculation of the electric field enhancement in the vicinity of a nanomembrane whose pore wall is held at constant charge and whose membrane surfaces are held at constant potential. The electric field is found to be enhanced by the charge buildup in the rim of the hole of the nanomembrane; the buildup results from the potential being held constant in the conducting region. Ion concentrations are also calculated. Positive ion rejection is found to be enhanced by this charge buildup in the region of the rim when a constant positive potential is applied.