Rate expression, for electron transfer

The technique of complex-valued dielectric functions was originally applied to solvation problems by Ovchinnikov and Ovchinnikova [2] in the context of the electron transfer theory. They reformulated in terms of s(k, to) the familiar golden rule rate expression for electron transfer [3], This idea, thoroughly elaborated and extended by Dogonadze, Kuznetsov and their associates [4-7], constitutes a background for subsequent nonlocal solvation theories. 

V. RATE EXPRESSIONS FOR ELECTRON TRANSFER AT ILLUMINATED SEMICONDUCTOR/ELECTROLYTE INTERFACES... 

The expression in equation (25) gives the rate constant for electron transfer from a particular vibrational distribution of the reactants to a particular distribution of the products. In order to calculate the total electron transfer rate constant it is necessary to include two additional features. One is all possible transitions from a particular vibrational distribution of the reactants to all of the possible vibrational distributions of the products. In addition, it is necessary to recognize that a statistical distribution exists in solution amongst the various vibrational distributions of the reactants. The total transition rate will include contributions from each distribution of the reactants to all distributions of the products. 

Equation (36), which attempts to include both t and re, has been proposed as a more general expression for et.48 Note that in the limit, when Te -4 t , the expression for the electron transfer rate constant (equation 37) no longer depends on the extent of electronic coupling since vel > vn. In this limit the rate constant for electron transfer for a vibrational distribution near the intersection region is dictated by rates of repopulation of those intramolecular and/or solvent modes which cause the trapping of the exchanging electron. 

From the expression for ket in equation (55), assuming the appropriateness of the dielectric continuum approximation so the AE can be replaced by AGet0, the rate constant for electron transfer in the classical limit is given by equation (59). 

So far the attention has been on the nuclear reorganization barrier. Nevertheless, other important factors previously hidden in the pre-exponential factor (and ultimately in the standard rate constant) have to be considered, namely, the fundamental question of the magnitude of the electronic interaction between electroactive molecules and energy levels in the electrode (i.e., the degree of adiabaticity) and its variation with the tunneling medium (electrode-solution interface), the tunneling distance, and the electrode material. Thus, within the transition-state formalism, the rate constant for electron transfer can be expressed as the product of three factors [39—42] ... 

R. D. Harcourt, G. D. Scholes and K. P. Ghiggino, Rate expressions for excitation transfer. II. Electronic considerations of direct and through-configuration exciton resonance interactions, J. Chem. Phys., 101 (1994) 10521-10525. 

Marcus has recently returned to this problem [133] and, by analogy with the problem of donor-acceptor electron transfer at the interface between two immiscible liquids, has derived the following expression for ka, the heterogeneous rate constant for electron transfer from a semiconductor to a species in a contacting electrolyte ... 

The relative rates of the reactions leading to formation of either ground-state or excited-state products can be evaluated in terms of formalisms developed by Marcus [26], Hopfield [27], Jortner [28], and others [29]. The development of the semiclassical and quantum-mechanical expressions for electron transfer are discussed in Chapters. 3-5 (Volume I, Part 1). A general expression for the rate constant of a non-adiabatic electron-transfer process is given below. 

Treating the solvent classically yields the following expression for the rate constant for electron transfer ... 

Both involve high-pressure electrochemistry. One is the measurement of the pressure dependence of the rate constant for electron transfer in a given couple at an electrode, but it is not immediately clear how feg] and the corresponding volume of activation relate to feex and AV, respectively, for the self-exchange reaction of the same couple. This is a major theme of this chapter, and is pursued in detail below. The other method involves invocation of the cross relation of Marcus [5], which expresses the rate constant ku for the oxidation of, say, A by B+ in terms of its equilibrium constant and the rate constants kn and fe22 for the respective A+/A and B+/B self-exchange reactions ... 

When the standard rate constant for electron transfer kP is very small, kf and are also both very small. Moreover, kf, becomes negUgible as the electrode potential is made increasingly negative to drive the reduction of O. In this case, the voltammogram is said to be totally irreversible and equation (11.2.50) reduces to equation (11.2.51). After substitution of kf and further rearrangement, the potential is expressed in terms of the current (equation (11.2.52)) ... 

Meisel has demonstrated (16) good agreement between the predictions of the Marcus theory (17) and the rate data for electron-transfer reactions involving quinones. The approximate dependence of k upon AG ] may be predicted from the Marcus expressions ... 

In our simple model, the expression in A2.4.135 corresponds to the activation energy for a redox process in which only the interaction between the central ion and the ligands in the primary solvation shell is considered, and this only in the fonn of the totally synnnetrical vibration. In reality, the rate of the electron transfer reaction is also infiuenced by the motion of molecules in the outer solvation shell, as well as by other... 

A powerful application of outer-sphere electron transfer theory relates the ET rate between D and A to the rates of self exchange for the individual species. Self-exchange rates correspond to electron transfer in D/D (/cjj) and A/A (/c22)- These rates are related through the cross-relation to the D/A electron transfer reaction by the expression... 

Further research in improving the BDS activity of the biocatalysts was targeted towards the search of co-catalysts and co-factors to enhance overall desulfurization rates as well as promoters to enhance enzyme expression. This research resulted in identification of NADH and FMNH2 as co-factors essential for electron transfer and related oxidoreductase enzymes as co-catalysts as described in detail below. Additionally, other bacterial strains were also investigated as hosts and are reported below. 

The individual forward rate constant for the transfer of one electron from one electron state in the metal to the acceptor (oxidized form of the redox couple) in the solution may be expressed as... 

If more than two electrons should be involved, these expressions can be extended accordingly. The transfer rate kel for electronic excitation energy... 

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