W. Lorenz

Quantum chemical studies of the chemisorption of water and of unhydrated and hydrated halide ions on mercury

Abstract Local structures on electrode interfaces can be explored by quantum chemical investigation of medium-sized systems consisting of a cluster of substrate (metal) atoms, one or several solvent molecules, and/or at least one ion to be adsorbed at the interface. For the study of water adsorption and halide ion adsorption (unhydrated as well as hydrated) on a mercury surface, we have used the standard CNDO method together with geometrical optimization of the atom positions. In this paper, the following topics have been treated: (a) adsorption of a single water molecule in different positions on a close-packed plane cluster of seven mercury atoms; (b) adsorption of unhydrated halide ions (Cl−, Br−, I−) in the “on-top” or hollow position on the mercury surface; (c) adsorption of monohydrated halides on the mercury surface. Further studies including solvation by six water molecules are discussed. The calculations provide information about minimum-energy geometries, energetic data, and local charges. Furthermore, they allow some conclusions about water mobility and reorientation on a close-packed metal surface, water orientation under the combined influence of an adsorbed ion and the metal surface, and trends of charge distribution in the halide series to be drawn. Calculations are critically discussed in the light of experimental and other quantum chemical data.

Developments in charge transfer theory

Abstract Basic problems of chemistry at interfaces are connected with the exploration of elementary processes of charge transfer. Multistep and chemical bond formation processes involved in such phenomena have been treated in terms of partial charge transfer models. Related developments since the mid-seventies are briefly addressed in the first part of this paper. These include: the extension of partial charge transfer models to semiconductors; quantum chemical studies of metal and semiconductor electrode processes; developments in the quantum theory of chemical conversion rates in condensed systems; calculation of electronic non-equilibrium related to semiconductor photoelectrochemistry; lastly a brief look is taken at charge transfer on biomembranes. With reference to these topics, the characteristics of λ-, l - and m -type charge transfer are once more explained. In the second part, the problem of chemical processes in electronic non-equilibrium has been taken up, strating from previously developed charge injection considerations. In order to accomplish a connection of quantum theoretical Franck-Condon transition models of chemical species conversion with electronic non-equilibrium of the surrounding medium, a radical reconsideration of basic kinetics proves to be inevitable, even in the limit of integral charge transfer. As a result, a new type of kinetic equations for charge transfer in electronic non-equilibrium has been introduced. The application of these kinetics to light-driven processes on semiconductor surfaces is outlined; as an example of multistep charge transfer, the hydrogen evolution sequence has been considered.

Dynamic theory of the alternating current response of semiconductor electrodes under illumination

Abstract A photoinduced admittance enhancement has been observed on n-GaAs and n-GaP electrodes in the potential range between flatband and stationary photocurrent onset. In order to provide a theoretical evaluation, the alternating current response of a semiconductor electrode under illumination has been investigated on the basis of non-equilibrium treatment of the carrier balance in the semiconductor and of the interfacial charge transfer kinetics. Superposition of an irreversible stationary and small-amplitude periodic rate has been treated for the following cases of charge transfer at the interface: (a) one-step electrochemical process; (b) two-step electrochemical process including an adsorbed intermediate and partial charge transfers; (c) parallel couple of one-step electrochemical and partial charge transfer chemisorption process. Empirical criteria for preference of charge transfer over surface recombination have been considered. In connection with the present development, the general equivalent circuit of a semiconductor electrode has been briefly derived from the dynamical charge balance. The theoretical approach of the stationary photocurrent-voltage curve has been discussed and refined.

Electronic non-equilibrium charge transfer mechanisms in alternating photocurrents on semiconductor electrodes

Abstract The theoretical treatment of alternating photocurrents on semiconductor electrodes has been extended, taking into account electronic non-equilibrium charge transfer kinetics of chemical processes at the interface. Some basic mechanisms of charge transfer processes under illumination are investigated, including anodic irreversible one- to multistep redox processes, anodic or cathodic chemisorption, and superposition of chemisorption with irreversible redox processes. Computational examples are given for alternating photocurrent peaks due to n-III-V-semiconductor dissolution, and to light-driven chemisorption. As possibly interfering processes, electron or hole transport-controlled surface charging, and a non-equilibrium contribution to space charge capacity are considered, as well as the quantum-chemical and dynamical criteria for the distinction of charge transfer and surface charing. In the experimental field, some further alternating photocurrent data on n-GaP and n-GaAs are supplied, including the first phase-sensitive measurements; light-pulsed measurements are discussed briefly.

Dependence of alternating photocurrent on n-GaAs electrodes upon frequency and illumination intensity

Abstract The photoinduced alternating current enhancement on semiconductor electrodes in the potential range between flatband and stationary photocurrent onset has been investigated on n-GaAs, taking into consideration the dependences upon frequency and illumination intensity. The alternating photocurrent peak at the onset potential turned out to be nearly frequency-independent, whereas the additional structure of the alternating photocurrent curve between the onset the flatband potential depended strongly on the frequency. These observations are in agreement with the predictions of charge transfer theory for the case of chemisorption of solute (particularly protolytic) species. The theory of chemisorption-controlled alternating photocurrent has been extended by considering partial charge transfer both over the valence and conduction band (fractional-hole and fractional-electron transfer). Peculiarities of a light-driven chemisorption state have been taken into account.

Non-equilibrium Fermi energy profiles of electrons and holes over the semiconductor space charge layer at stationary dark or photocurrents

Abstract The properties of semiconductor electrodes at larger band bending and under stationary dark or photocurrents, may be discussed in terms of non-equilibrium Fermi energy profiles of electrons and holes over the space charge layer, which were calculated from balance and classical Nernst-Planek transport equations. In this paper particularly the anodic regime of n-type semiconductors has been investigated. The features of non-equilibrium Fermi energy profiles of majority and minority carriers are elucidated. The problem of termination of the Mott-Schottky range at large band bending is again considered and the effects of competition of classical transport and tunnelling are qualitatively discussed.

Chemical conversion rates for interfacial processes with bond formation and partial charge transfer: Effects of anharmonicity of species potential surfaces upon Arrhenius and Tafel-Brönsted parameters

Abstract A survey is given of calculations of rate processes connected with chemical bond formation and partial charge transfer in condensed systems or at interfaces. In order to allow for partial charge transfer, local adiabatic potential surfaces (in the sense of the Born-Oppenheimer approach) of a reactive subsystem have been subjected to a unitary transformation which yields quasi-adiabatic species potential surfaces and renders possible the application of the common T-matrix formalism. The influence of anharmonicity of transformed species potentials upon phonon-assisted chemical conversion rates has been extensively studied. Anharmonic Franck-Condon overlap can be calculated numerically with the aid of recursive construction of vibration state vectors: this procedure allows us to calculate thermally averaged vibration transitions, including these for heavy-atom motions. The constraints for a working definition of temperature-dependent Arrhenius and Tafel-Bronsted parameters have been considered in greater detail, and the anharmonicity effect upon these quantities has been investigated. Comparison has been made with relevant empirical properties of electrochemical processes on metals.

Some remarks on the theory of chemical elementary processes with charge transfer in condensed systems

Abstract In this paper we discuss some questions concerning quantum theory of rate processes, particularly in electrochemical systems: (a) the role of quantum theoretical and macroscopic charge conservation conditions of elementary charge transfer processes; (b) the general kinetic problem of dividing quantum statistical transition probabilities into Arrhenius factors and the introduction of Gibbs energies of activation; (c) application of the transition matrix model to interfacial processes.

Zur anwendung der transformations—impedanzspektrometrie

Abstract Besides other modern techniques of impedance measurement, such as the automatic digital balance of impedance bridges, or multichannel measurement of impedance components, the frequency dependent impedance of electrochemical systems can be determined by Laplace-transformation of linear perturbation and response functions from the time domain: Laplace-transform—impedance spectrometry. In this paper, some results of our current work on the development of the transform method are treated. Chapter 2 gives a short summary of the theoretical basis of the method, including different variants of evaluation (s-transformation; transformation of impedance components). The main types of perturbation are (a) the (ideal or nonideal) potential step function, (b) the charge injection (current-δ-function). Both types of perturbation are complementary with respect to the decay behaviour of the associated response (Chap. 3). In Chapter 4 possible errors of transformation are discussed in some detail: (a) error of synchronization of perturbation and response; (b) linear distortion of perturbation and response because of limited band width of measuring receivers; (c) breaking off the time integration at a finite time; (d) errors of numerical integration. While the errors (a, b, d) generally increase with increasing frequency, error (c) increases with decreasing frequency. Details of the error characteristics depend on the type of perturbation and on the form of impedance spectrum. Some points of the computer programs for numerical transformation and correction, and of the measuring devices are mentioned shortly in Chapters 5 and 6. In the low frequency limit, true experimental information (without simulated extrapolation) is obtainable up to about the reciprocal measuring time of response function. Of course, the main advantage of transform—impedance spectrometry should lie in the possibility of an extremely fast measurement. Experimental work, including molecule adsorption processes and study of time dependent impedance spectra in mixed adsorption systems, is in progress.

Stationary and alternating photocurrents on n-InP electrodes

Abstract Stationary and alternating dark and photocurrents have been investigated on n-InP in alkaline and acidic aqueous solutions. Due to the larger distance between the potential ranges of semiconductor photodissolution and of hydrogen evolution, a weaker interaction of both processes than on n-GaAs or GaP is expected, which favours the onset of strong inversion under illumination. New alternating photocurrent patterns beyond the stationary photocurrent onset are observed on n-InP and discussed qualitatively in terms of electronic non-equilibrium dynamics.