Electron transfer semiclassical theory

Chemical and electrochemical reactions in condensed phases are generally quite complex processes only outer-sphere electron-transfer reactions are sufficiently simple that we have reached a fair understanding of them in terms of microscopic concepts. In this chapter we give a simple derivation of a semiclassical theory of outer-sphere electron-transfer reactions, which was first systematically developed by Marcus [1] and Hush [2] in a series of papers. A more advanced treatment will be presented in Chapter 19. 

In semiclassical ET theory, three parameters govern the reaction rates the electronic couphng between the donor and acceptor (%) the free-energy change for the reaction (AG°) and a parameter (X.) related to the extent of inner-shell and solvent nuclear reorganization accompanying the ET reaction [29]. Additionally, when intrinsic ET barriers are small, the dynamics of nuclear motion can limit ET rates through the frequency factor v. These parameters describe the rate of electron transfer between a donor and acceptor held at a fixed distance and orientation (Eq. 1),... 

Overall, the outer-sphere electron-transfer reactions of transition metal complexes reactions are consistent with the expectations of the semiclassical Marcus-Hush theory. h22,25,32,43,57,7i,75 78 agreement... 

According to the semiclassical Marcus theory [6], the rate of electron transfer depends on the reduction potential (AGq), the electronic coupling matrix element Hda), and the reorganisation energy (A) ... 

The theoretical description of the kinetics of electron transfer reactions starts fi om the pioneering work of Marcus [1] in his work the convenient expression for the free energy of activation was defined. However, the pre-exponential factor in the expression for the reaction rate constant was left undetermined in the framework of that classical (activate-complex formalism) and macroscopic theory. The more sophisticated, semiclassical or quantum-mechanical, approaches [37-41] avoid this inadequacy. Typically, they are based on the Franck-Condon principle, i.e., assuming the separation of the electronic and nuclear motions. The Franck-Condon principle... 

The nontraditional example of applying the AMSA theory is connected with the treatment of electrolyte effects in intramolecular electron transfer (ET) reactions [21, 22], Usually the process of the transfer of the electron from donor (D) to acceptor (A) in solutions is strongly nonadiabatic. The standard description of this process in connected with semiclassical Marcus theory [35], which reduces a complex dynamical problem of ET to a simple expression of electron... 

Kuznetsov, A.M. and Kharkats, Y.L (1975) Semiclassical theory of adiabatic and nonadiabatic electron-transfer bridging reactions. Soviet... 

Iron and copper redox centers facilitate the transfer of electrons through proteins that are part of the respiratory and photosynthetic machinery of cells. Much work has been done with the goal of understanding the factors that control electron flow through these proteins. The results of many of the key experiments have been interpreted in terms of semiclassical theory. 

Equation (2.2.15) poses an obvious problem that is, it predicts that the electron transfer approaches zero as the temperature approaches zero, which is at variance with experiment. The reason for such a discrepancy is that the classical theory does not account for tunneling effects that occur at low temperature. A semiclassical treatment can overcome this problem it leads to an equation of the form [25] ... 

The adiabatic redox reactions at electrodes were first considered by MARCUS /40a,145/ in a classical (semiclassical) framework. lEVICH, DOGONADZE and KUSNETSOV /146,147/, SGHMICKLER and VIELSTICH /169/ a.o. have developed a quantum theory for non-adiabatic electron transfer electrode reactions based on the oscillator-model. The complete quantum-mechanical treatment of the same model by CHRISTOV /37d,e/ comprises adiabatic and non-adiabatic redox reactions at electrodes. 

At the microscopic level, polaron hopping can be viewed as a self-exchange electron-transfer reaction where a charge hops from an ionized oligomer or chain segment to an adjacent neutral unit. In the framework of semiclassical Marcus theory, the electron-transfer rate is written as... 

Are the rate constants estimated from the Bloch type treatment consistent with expectations based on theory The -1 mixed valence state of complex (Id) is a Robin-Day class II complex, and thus its electron transfer rate constant can be independently estimated from Marcus theory. The semiclassical expression for the rate constant for intramolecular electron transfer, k, in a symmetric mixed valence complex with no net free energy change is given by... 

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