Electron transfer rate constants, semiclassical

The Landau-Zener expression is calculated in a time-dependent semiclassical manner from the diabatic surfaces (those depicted in Fig. 1) exactly because these surfaces, which describe the failure to react, are the appropriate zeroth order description for the long-range electron transfer case. As can be seen, in the very weak coupling limit (small A) the k l factor and hence the electron transfer rate constant become proportional to the absolute square of A ... 

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... 

A recently proposed semiclassical model, in which an electronic transmission coefficient and a nuclear tunneling factor are introduced as corrections to the classical activated-complex expression, is described. The nuclear tunneling corrections are shown to be important only at low temperatures or when the electron transfer is very exothermic. By contrast, corrections for nonadiabaticity may be significant for most outer-sphere reactions of metal complexes. The rate constants for the Fe(H20)6 +-Fe(H20)6 +> Ru(NH3)62+-Ru(NH3)63+ and Ru(bpy)32+-Ru(bpy)33+ electron exchange reactions predicted by the semiclassical model are in very good agreement with the observed values. The implications of the model for optically-induced electron transfer in mixed-valence systems are noted. 

Since the phonon energy quantum hu> does not explicitly appear in both Eqs. 35 and 36, these formulas for the rate constant in the semiclassical regime should be derived without the single-mode model being relied on. That is, we should not neglect that various phonon modes contributing to the reaction coordinate Q have, in reality, various energy quanta. In this case, the phonon Hamiltonian in the reactant state (where the electron to be transferred is at the donor) consists of various normal modes. 

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. 

Theoretical efforts beginning in the late 1950s and continuing to the present day have provided a remarkably detailed description of ET reactions [3]. The semiclassical model (Eq. 1) describes the first-order rate constant for electron transfer from a donor... 

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... 

Attention has been shifted to a more detailed understanding of the electron transfer process. It is accepted that solvent molecules affect the charge separation and charge recombination processes [506-511]. An interesting approach for estimating the solvent effect on the electronic and nuclear terms in the semiclassical Marcus equation [Eq. (14)] was reported [502,503]. Temperature dependence on the rate constant of electron transfer ( t) could differentiate them as the first term (electronic) and the second term (nuclear) in Eq. (25). 

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