The Theory of Homogeneous Electron Transfer

The theory of electron transfer is the most developed of that for any reaction in solution. In addition this type of reaction has been studied extensively by experiment. As a result many of the predictions made by theory have been addressed in the laboratory. As was seen from earlier discussion, simple electron transfer may proceed by two mechanisms, inner sphere and outer sphere. The inner sphere mechanism involves both electron and atom transfer. The discussion here is limited to the outer sphere mechanism, which involves the transfer of a single electron without the formation or breaking of any chemical bonds. 

Within the context of transition state theory there are two problems to be addressed in developing a model to estimate the rate constant for electron transfer. One is the estimation of the Gibbs energy of activation for the process the second is estimation of the pre-exponential factor. The model used to describe the activation barrier is considered first. 

In order to visualize the energy barrier between reactants and products, it is assumed that each system can be represented as a classical harmonic oscillator along the reaction coordinate. This is illustrated in fig. 7.15. The left-hand parabola gives the Gibbs energy of the reactants and the right-hand parabola, that of 

Using the properties of the parabolas shown in fig. 7.15, one can determine a relationship between the Gibbs energy of activation and the shape and position of the parabolas on the reaction coordinate. The equation giving the Gibbs energy of the reactant system is 

In order to simplify the last equation the reorganization energy, E, is introduced, where 

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The theory of homogeneous electron transfer processes, as well as of the closely-related electron exchanges with metallic electrodes, has been the subject of considerable study. The proposal by Hush and by Marcus that these processes are, for simple systems, either usually electronically adiabatic or... 

The theory of homogeneous electron transfer reactions in solution has been formulated in terms of models in which the transferring electron is localized at a donor site in the reactant and at an acceptor site in the... 

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