Probability Of Electron Transfer Research Articles

Theory of near-resonant charge-exchange in gas-surface reactions

A theory is presented for describing near-resonant charge-exchange processes occurring in gas-surface collisions. The surface is represented by a cluster of atoms and its electronic properties are obtained from the Diatomics in Molecules procedure. The Polyatomics in Molecules approach is used to calculate the gas-surface interaction potentials and couplings. Trajectories for the transition probabilities and nuclear variables are obtained from the common eikonal formalism. Preliminary results are presented for Na scattering from a W(110) surface. The surface consists of five W atoms. The approach of the sodium atom is perpendicular to the surface and it collides with the center W atom. Generally, it is found that the probability of electron transfer increases with the initial kinetic energy of the sodium atom (5–60 eV) and can attain values larger than 40%.

Oxidation of cytochrome c 2 by photosynthetic reaction centers of Rhodospirillum rubrum and Rhodopseudomonas sphaeroides in vivo. Effect of viscosity on the rate of reaction

In Rhodospirillum rubrum and Rhodopseudomonas sphaeroides it is shown that the oxidation of cytochrome c 2 involves a diffusion limited process. From analysis of the results it follows that the electron transfer probability must be very low. This is corroborated by in vitro studies using the isolated components.

Reorientation of impurity-vacancy dipoles in europium-doped alkali halides from a reaction-rate viewpoint

Previous experimental ITC data dealing with the relaxation of impurity- vacancy dipoles in europium-doped alkali halides are analyzed in terms of the reaction-rate theory of nonradiative transitions in polar solids. The temperature dependence of the dipolar relaxation time is obtained in this investigation by portional integration of the ITC bands without appealling to any classical reorientational process. It was found that according to the reaction rate theory the dipoles rotate classically and nonadiabatically with very low electron-transfer probabilities. In most of the hosts. However in KCl the dipoles reorientate via nearly equal-weight classical jumps and subbarrier tunneling with a high electron-transfer expectancy within the temperature range of the ITC band.

Classical motion of the charge asymmetry in slow atomic collisions. I. Single-electron motion derived from Ehrenfest's theorem

The time evolution of the quantum mechanical mean value for the charge asymmetry (or the longitudinal dipole moment) of a diatomic collision system is described by classical equations of motion. These equations are derived from a modified Ehrenfest's theorem for a single-electron system. Trajectories as a function of the internuclear separation and the charge asymmetry are calculated for the collision system p+H. The electron transfer probability computed by sampling over trajectories with different initial conditions in its impact parameter dependence reflects the charge oscillations in the reaction zone.

Electron transfer rate and molecular orbital structure

The connection between electron structure and electron transfer probability is examined. The electronic factor in non-adiabatic transfer is found to depend on MO coefficients and energies of the electron exchanging molecular groups as well as on bridge parameters. Some examples are given.

The role of davydov solitons in the molecular chains with cubic anharmonicity in the electron transfer from the donor to the acceptor molecule

This paper is concerned with the study of electron transfer from a donor molecule (D) to an acceptor molecule (A) along a one-dimensional molecular chain to which D and A are joined. It is shown that, in the case when the chain vibrations are with cubic anharmonicity, the probability of electron transfer has analogous form as well as in a previous paper.

A self-consistent eikonal treatment of diabatic rearrangement: Model H++H2 calculationsa)

An eikonal treatment of nonadiabatic reactions, in which nuclear positions and momenta are self-consistently coupled to electronic transition amplitudes in a Hamiltonian formalism, is applied to H++H2 collisions where both electron transfer and nuclear rearrangement may occur. The approach is based on the diabatic electronic representation and uses potential energy surfaces and momentum couplings obtained within the method of diatomics-in-molecules. Equations of motion are obtained for hyperspherical coordinates in a model collinear treatment. Calculations carried out at collision energies 1 eV above the n=4 threshold of H2 illustrate reactive and nonreactive processes, electron transfer, and translational-vibrational energy transfer. Results for total electron transfer probabilities are compared with other calculations within the same model.

Quantum-static approximation in outer-sphere electron transfer

Abstract The outer-sphere electron transfer probability has been determined in the quantum-static approximation taking into account consistently the role of quantum modes of the medium. The real dielectric loss spectrum of water has been employed to calculate numerically the reorganization energy and the tunneling factor of the reaction. Limitations have been found on the applicability of the quantum-static approximation, associated with the influence of the isolated modes and the quantum part of the continuous spectrum upon the transfer probability as a function of the free reaction energy.

On the role of the soliton mechanism in the electron transfer along the quasi‐one‐dimensional molecular structures

AbstractAn expression for the probability of electron transfer from a donor molecule (D) to an acceptor molecule (A) along a quasi‐linear molecular chain (biopolymer), to which D and A are attached is derived. Investigated is the case with an indirect interaction caused by modification of Coulomb interaction due to electron transition from D to A and vice versa via a periodical structure, in addition to the direct, resonant interaction of D and A. The indirect interaction may lead to the electron capture by a soliton wave. The one‐way transfer of an electron caused by relaxation phenomena for the dynamical system in contact with a thermostat (T = 0 K) is discussed.

Electron transfer to the L-shell following double K-shell ionization of fluorine in ionic solids

Spectra of Kα hypersatellite X-rays excited in alkali and alkaline earth fluorides by 22 MeV carbon ions have been measured and used to deduce average probabilities for electron transfer to the L-shell. It was found that the average electron transfer probabilities for the double K-vacancy states are about a factor of 2 lower than those for the single K-vacancy states.

Electron Capture of He2+ from Gas Target Atoms at around a Few keV

The single- and double-electron capture cross sections of He 2+ have been measured for targets of Ne, Ar, Kr, Xe and N 2 in the energy range from 0.7 to 4.5 keV. The cross section curves obtained are almost flat except the double-electron capture cross section for the He 2+ –Ne case, which increases rapidly in the energy range studied. A simplified model of statistical electron transfer is introduced with the concept of interaction range and electron transfer probability to consider the collision mechanism. The He 2+ –Ar, –Kr and –N 2 collisions show that single-electron capture proceeds within the interaction range of 2×10 -8 cm, mostly accompanying ionization. In the He 2+ –Xe interaction, single-electron capture is considered to be quite predominant and double-electron capture with ionization also a major process. These transfers occur with the interaction range of 4∼6×10 -8 cm.

Thermal and optical electron transfer probabilities in biological systems

Electron transfer reactions are perhaps the most important elementary chemical processes. In ionizing solution, the rates of the simplest of such exchanges (outer-sphere self-exchange between solvated or complex ions) vary enormously — in fact by a factor of ∼10 9. The reasons for this very striking behaviour, and also for variation in the rates of cross-reactions, are now thought to be basically understood, as a result of work over the last two decades [1]. It is also known that there is an intimate connection between the probability of thermal exchange and of the corresponding optical or photon-assisted exchange (intervalence transfer) [2];in principle, the thermal probability can be calculated from the optical transfer probability and vice versa. Intramolecular transfer in polynuclear complexes [3] and solid-state transfer ( e.g. in organic or organometallic semiconductor/metals) can be interpreted within a very similar framework. Electron transfer processes are very important in biological systems. In these, we are usually faced with the problem that the precise pathway is not known. However, it is known that the overall donor-acceptor distance is often much greater ( e.g.15–20Å) than is usual in simpler systems. There has (mainly as a result of this) been much discussion of the role of tunnelling in biological electron transfer [4], often with the implication that this is of greater importance here than in simpler chemical processes. It is therefore of interest to ask whether one can, at this stage, make useful generalizations about this and other possible determinants of biological transfers. In order to attempt to do so, one must first focus attention on the basic parameters governing transfer probabilities. The most important of these are: 1. the coupling of electronic to intramolecular vibrational and to phonon modes of the system, and the frequencies involved, 2. the nature and magnitude of the transfer integral (J) coupling the reactant and product hypersurfaces, 3. the overall free energy change, 4. steric factors. The interplay of factors (1) and (2) will firstly be illustrated by reference to optical transfer in iron-sulphur proteins. The (thermal) frequency factors for transfer rates over large distances will then be discussed with particular attention to the anticipated form of the distance-dependence of J. This is very important, as the electronic transmission of coefficient multiplying the frequency factor is (for J ⪡ k BT) proportional to J 2. It will be shown that there is good reason to suppose that the decrease of J with increasing donor-acceptor distance R in important systems is typically much less than exponential, and may be a fairly low inverse power of R. The magnitude of expected electron-phonon coupling energies and frequencies will also have an important effect in increasing the electronic transmission coefficients. It will be concluded that while nuclear tunnelling plays a significant but minor role at ordinary temperatures, there is at present no need to invoke electron tunnelling as a rate-determining step in typical large-distance biological electron-transfer processes in order to account for their moderate to rapid rates.

On the theory of long‐range electron hopping in polar media

AbstractExpressions for the probability of a nonadiabatic electron transfer between a donor‐trap and an acceptor‐trap in a polar medium are obtained. The transition probability is expressed in terms of the zeroth‐order electron densities near the traps. The interaction of the electron with the phonon field is analyzed. A way of definition and calculation of the zeroth‐order electron states with due account for their modulation by the phonon field is suggested. The effects of deviation from the Condon approximation due to the modulation of the electron densities and of the interaction with the phonon field causing the transition are estimated. The effects of this modulation on the kinetic parameters of the transition in the Condon approximation and in the improved Condon approximation are analyzed. It is shown that these effects are rather large for the processes involving solvated, trapped, or weakly bound electrons. The deviations from the Condon approximation should be taken into account for long‐range electron transfer.

Selective Final-State Population in Electron Capture by Low-Energy Highly Charged Projectiles Studied by Energy-Gain Spectroscopy

Energy-gain spectra and total cross sections have been measured for projectiles of 492-eV ${\mathrm{Ne}}^{+10}$ and 443-eV ${\mathrm{Ne}}^{+9}$ capturing electrons from rare-gas targets. For each collision system a single, or at most two, principal quantum numbers on the projectile are found to be populated. The effective electron-transfer probabilities are found to be quite dependent upon the collision system.

Differential cross sections in the impact parameter treatment of charge transfer

The differential cross section for electron capture in the semiclassical impact parameter treatment is written in terms of a classical elastic differential cross section multiplied by an electron transfer probability. The relationship between the phase of the transfer amplitude and the classical differential cross section is stressed. Comparison is made between the exact semiclassical result and the method described above, for the case where the internuclear interaction is purely Coulombic. The effect of electron screening in modifying the classical elastic differential cross section is also illustrated.

Electron transfer in pendant-group and molecularly doped polymers

Utilizing the molecular-ion model previously constructed to describe photoemission and ultraviolet absorption in pendant-group polymers, we derive an expression for the probability of electron transfer between a molecular ion and a neutral molecular species embedded in a frequency-dependent dielectric medium described by the (nonlocal) longitudinal dielectric response function $\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},\ensuremath{\omega})$. The medium is taken to exhibit three branches of its longitudinal polarization excitation spectrum defined by $\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},\ensuremath{\omega}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}))=0$: a low-frequency branch corresponding to intermolecular motions, an infrared branch corresponding to molecular vibrational modes, and a high-frequency branch corresponding to valence-electron excitations. In addition, the linear coupling of the electron to the intramolecular modes of the initial and final molecular ions is incorporated into the model. The electron-transfer probability is evaluated as a function of the spacing, $R$, between the molecular-ion sites and the energy difference between the intitial and final molecular-ion states. Utilizing parameters in $\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},\ensuremath{\omega})$ typical of pendant-group polymers (e.g., polystyrene, polyvinylpyridine) or the matrices utilized in molecularly doped polymers films (e.g., polycarbonates), we find that the electron-transfer process is activated and that the low-frequency dielectric relaxations characteristic of these polymers create this activation. Explicit expressions for the activation energies are derived and evaluated numerically for poly(2-vinylypyridine): a material for which a model of $\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},\ensuremath{\omega})$ is available in the literature. The valence-electron excitations do not influence the electron-transfer activation energies, but both the intramolecular and longitudinal-polarization vibrational modes increase these activation energies above the values predicted using the low-frequency relaxations alone. The energies, $\ensuremath{\hbar}{\ensuremath{\omega}}_{n}$, of many of these vibrational modes are, however, larger than thermal energies, $\mathrm{kT}$. Consequently, the predicted electron-transfer activation energies are smaller than those given by traditional semiclassical models of electron transfer. Moreover, these activation energies also depend explicitly on the spacing, $R$, between the two sites. This $R$ dependence is evaluated for both classical and quantum-mechanical models of the change densities on the molecular ions. Our analysis predicts, therefore, the complete spacing and temperature dependence of the electron-transfer probabilities as functions of the intramolecular molecular-ion vibrational frequencies and electron-vibration coupling constants, and of the frequency and spatial dependence of the dielectric response of the medium in which these ions are embedded. This prediction permits the identification of scaling laws relating both the activation energies and electron-transfer prefactors to molecular and dielectric observables: an identification which provides valuable guidance in the molecular design of efficient electronic transport media.

Semiconductor‐electrochemical aspects of bacterial leaching. I. Oxidation of metal sulphides with large energy gaps

AbstractThiobacillus ferrooxidans has been cultivated successfully on synthetic metal sulphides with large energy gaps (CdS, ZnS) as the only energy source for many culture generations during a period of 4 years. The results obtained, which were quantitatively evaluated by calculations of electron transfer probabilities, show that a direct electron transfer from the metal sulphide valence band to the bacterial metabolic system (hole injection into the valence band of the sulphide) has to be excluded as the cause for the enhanced oxidative dissolution for energetic reasons. A detailed analysis of the dynamics of the metal sulphide aqueous electrolyte interface reveals that protons are involved in the mechanism on which bacterial activity is based. By reacting chemically with the metal sulphide surface they break chemical bonds and shift electronic states energetically into the forbidden energy gap to produce surface states which can be chemically described as −SH∂ groups. These control the rate of dissolution of the metal sulphide and are removed by bacterial activity. In this way the proton is recycled and its action can be considered catalytic. For sulphides in which the valence band of the semiconductor is derived from metal orbitals instead of from sulphur orbitals, this mechanism is bound to fail. MoS2 and WS2 are discussed as examples of such metal sulphides which are not a suitable energy source for bacteria. Some kinetic aspects of the bacterial surface reaction are discussed.

Outer-sphere electron transfer in polar solvents

The theory of outer-sphere electron transfer reactions in polar solvents is developed. It is based on a description of the solvent by complex dielectric permittivity in the Debye approach. It was shown that the pre-exponential factor of the electron transfer probability in the case of a strong interaction differs from all known pre-exponential factors of earlier works. An activation energy for electron transfer is obtained larger than the well-known expression first obtained by Marcus [1]. A new criterion distinguishing between non-adiabatic and adiabatic reactions is developed. Outer-sphere electron transfer was treated by generalizing and solving the Landau-Zener problem for the case where the system passes the intersection point of electronic terms without velocity and motion in the crossing region is diffusive.

Theory of electron transfer in donor–acceptor pairs

AbstractThe wave functions of donor–acceptor pairs before and after electron transfer are written as a product of the electron‐vibrational wave functions of the donor and acceptor with allowance for the change in the number of electrons on these particles by one after transition. In this approximation, the energy of the initial state is represented as a sum of the electron‐vibrational levels of the donor and acceptor and that of the final state as a sum of donor cation and acceptor anion levels. Formulas for the electron transfer probability of symmetrical and nonsymmetrical donor–acceptor pairs have been derived that express the dependence of this process on the ionization potential difference of the donor and the electron affinity of the acceptor, on the vibrational frequencies of these particles, and on temperature.

Transfer of solvated electrons to some aliphatic halides in ethanol at 77 K. The role of Franck-Condon factors

Electron transfer probabilities of solvated electrons were determined by optical absorption measurements in ethanol at 77 K. Large variations in the electron transfer probabilities were recognized for various kinds of acceptors, being related to the activation energy of the dissociative electron attachments in gases. These were ascribed to the effects of the nuclear contributions of the acceptors, namely, Franck-Condon factors. Treating the nonadiabatic electron transfer process with the Fermi golden rule instead of the simple barrier penetration model, the Franck-Condon factors were calculated in the same manner developed in the theory of predissociation. Using Morse potentials obtained in the gas phase, relationships among the transfer of solvated electrons and dissociative electron attachments in gases and liquids were clarified. 2 tables, 5 figures.