Electron transfer weakly interacting systems

General Discussion—Electron Transfer in Weakly Interacting Systems... 

Sutin, N. and Brunschwig, B.S. (1982). Electron transfer in weakly interacting systems, in Inorganic Reaction Mechanisms, ACS Symposium Series, Vol. 198, American Chemical Society, Washington, DC, pp. 105-135. 

The systems of the first class afford the closest approach to a simple barrier penetration process, and perhaps they more readily respond to a theoretical analysis. It can reasonably be supposed that for these systems orbital overlap for the two ions is small, so that the frequency of the electronic transition is small, and there is no substantial binding between the two exchanging centers. A model of this kind presumably corresponds to the weak overlap cases as defined and discussed by Marcus (8 ). In attempting to calculate the rates of these reactions, besides the problem of the shape and height of the barrier for the electron transfer, electrostatic interaction of the reactants must be dealt with and the energy necessary to distort the solvent and ionic atmosphere about each ion to make the enei of the electron equal at the two sites. Different workers have emphasized different ones of these factors, and serious differences of opinion are recorded. 

Weakly interacting systems — as is implied by their name — are expected to change only to certain extent in the complex formation. Using some one-electron quantities (including those related to LMOs) comparative studies can thus be done by exploiting transferability. 

The adoption of different localization criteria does not lead to equivalent orbitals, as the given procedure usually applies iterative method. The iteration is repeated until the criterion chosen is fulfilled. In spite of this, LMOs obtained by different algorithms are quite similar. This similarity increases the hope, that a) the LMOs imply a serious, general (even interpretative) significance in the study of molecular electronic structure and b) the use of LMOs (especially their transferability property) might be helpful in studying extended/weakly interacting systems. 

The kinetic energy terms are representative one-electron quantities of molecular orbitals. Although the results are given for molecules, their transferable properties could be shown for weakly interacting systems (dimer of water, e.g.) as well. 

Forces of Adsorption. Adsorption may be classified as chemisorption or physical adsorption, depending on the nature of the surface forces. In physical adsorption the forces are relatively weak, involving mainly van der Waals (induced dipole—induced dipole) interactions, supplemented in many cases by electrostatic contributions from field gradient—dipole or —quadmpole interactions. By contrast, in chemisorption there is significant electron transfer, equivalent to the formation of a chemical bond between the sorbate and the soHd surface. Such interactions are both stronger and more specific than the forces of physical adsorption and are obviously limited to monolayer coverage. The differences in the general features of physical and chemisorption systems (Table 1) can be understood on the basis of this difference in the nature of the surface forces. 

Figure 2.1 (Plate 2.1) shows a classification of the processes that we consider they aU involve interaction of the reactants both with the solvent and with the metal electrode. In simple outer sphere electron transfer, the reactant is separated from the electrode by at least one layer of solvent hence, the interaction with the metal is comparatively weak. This is the realm of the classical theories of Marcus [1956], Hush [1958], Levich [1970], and German and Dogonadze [1974]. Outer sphere transfer can also involve the breaking of a bond (Fig. 2. lb), although the reactant is not in direct contact with the metal. In inner sphere processes (Fig. 2. Ic, d) the reactant is in contact with the electrode depending on the electronic structure of the system, the electronic interaction can be weak or strong. Naturally, catalysis involves a strong...

The methodology of surface electrochemistry is at present sufficiently broad to perform molecular-level research as required by the standards of modern surface science (1). While ultra-high vacuum electron, atom, and ion spectroscopies connect electrochemistry and the state-of-the-art gas-phase surface science most directly (1-11), their application is appropriate for systems which can be transferred from solution to the vacuum environment without desorption or rearrangement. That this usually occurs has been verified by several groups (see ref. 11 for the recent discussion of this issue). However, for the characterization of weakly interacting interfacial species, the vacuum methods may not be able to provide information directly relevant to the surface composition of electrodes in contact with the electrolyte phase. In such a case, in situ methods are preferred. Such techniques are also unique for the nonelectro-chemical characterization of interfacial kinetics and for the measurements of surface concentrations of reagents involved in... 

The magnitude of the electronic interaction between the reactants is exceedingly important. If H g is very small then the coupling of the initial and final states of the system will be very weak, the electron transfer will be slow, and the reaction will be nonadiabatic. The procedures used for estimating H g or k include the following ... 

The scope of this work is to deal with the possible treatments of electron correlation in a localized representation. Several methods will be discussed in detail elaborated by present authors. Special attention will be payed to the analysis of the transferability of certain correlation energy contributions. The use of their transferability will be discussed for extended systems series of hydrocarbons and polyenes will be investigated. The transferable properties of the contributions to the correlation energy, furthermore, turned out to be useful in the study of weakly interacting intermolecular systems. A detailed description of this procedure will be given in the present work. 

The theory of electron transfer in chemical and biological systems has been discussed by Marcus and many other workers 74 84). Recently, Larson 8l) has discussed the theory of electron transfer in protein and polymer-metal complex structures on the basis of a model first proposed by Marcus. In biological systems, electrons are mediated between redox centers over large distances (1.5 to 3.0 nm). Under non-adiabatic conditions, as the two energy surfaces have little interaction (Fig. 5), the electron transfer reaction does not occur. If there is weak interaction between the two surfaces, a, and a2, the system tends to split into two continuous energy surfaces, A3 and A2, with a small gap A which corresponds to the electronic coupling matrix element. Under such conditions, electron transfer from reductant to oxidant may occur, with the probability (x) given by Eq. (10),... 

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