Fluctuating energy level model

The Fluctuating-Energy-Level Model Proposed by Gerischer... 

The diagram shown in Fig. 3.10 is now widely used to describe electron transfer processes at electrodes, and it has the merit that it can be extended readily to the discussion of electron transfer at semiconductor and insulator electrodes [16]. The theoretical basis for the diagram is to be found in the fluctuating energy level model of electron transfer which has been discussed by Marcus [12,13], Gerischer [17-19], Levich [20], and Dogonadze [21]. 

The fluctuating energy level model of electron transfer... 

The application of the fluctuating energy level model to the symmetrical reaction (Equation (3.54)) is of particular interest since it suggests that it should be possible to compare heterogeneous and homogeneous rate constants. The expressions for the rate constant in each case are... 

Molecules with small spin have also been discussed. For example, time-resolved magnetization measurements were performed on a spin 1/2 molecular complex, so-called V15 [81]. Despite the absence of a barrier, magnetic hysteresis is observed over a time scale of several seconds. A detailed analysis in terms of a dissipative two-level model has been given, in which fluctuations and splittings are of the same energy. Spin-phonon coupling leads to long relaxation times and to a particular butterfly hysteresis loop [58, 82],... 

In the present author s view, the Gaussian distribution function based on the solvent fluctuation model, which is developed for a simple redox couple, is used too often even when the basic assumption is not valid. For example, this type of distribution function is often drawn for the hydrogen evolution reaction where the oxidized state is H+ and reduced state is H2.105 Certainly the nature of the solvation is completely different between H+ and H2. Moreover, when one considers the kinetics of the hydrogen evolution reaction, one should consider not the energy level of H+/H2 but that of H+/H(a) as Gurney did. 

Considerations of interfacial electron transfer require knowledge of the relative positions of the participating energy levels in the two (semiconductor and solution) phases. Models for redox energy levels in solution have been exhaustively treated elsewhere [27, 28]. Besides the Fermi level of the redox system (Eq. 6), the thermal fluctuation model [27, 28] leads to a Gaussian distribution of the energy levels for the occupied (reduced species) and the empty (oxidized species) states, respectively, as illustrated in Fig. 5(a). The distribution functions for the states are given by... 

Fig. 1. Schematic energy level diagram of the in-terconfigurational fluctuation (ICF) model describing valence fluctuations between two 4f configurations (4r, 4r ), characterized by their /multiplet level structure. The basic parameters of the ICF model and denote the interconfigurational excitation energy and interconfigurational mixing width, respectively.

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