A simple model for electron-transfer reactions

To develop these ideas into a quantitative theory, we require models for the inner and outer sphere and their reorganization. The problem is similar to that encountered in infrared and Raman spectroscopy, where 

A is a measure for the energy required to reorganize the inner and outer sphere during the reaction. The energy of activation for the oxidation is the saddle point energy minus the initial energy ered, which gives  

The same relations axe more easily obtained from a very simple one-dimensional model, in which only one degree of freedom is considered in this case the two potential energy surfaces reduce to parabolas, and the energy of activation is simply calculated from their intersection point (see Problem 1). 

At the standard equilibrium potential eox = ered changing the electrode potential by an overpotential r/ lowers the energy of the oxidized state, where the electron has been transferred to the electrode, by — 

The exact form of the pre-exponential factor A (see Chapter 5) is still being debated from the preceding considerations it is apparent that we must distinguish two cases If the reaction is adiabatic, the pre-exponential factor will be determined solely by the dynamics of the inner and outer sphere if it is nonadiabatic, it will depend on the electronic overlap between the initial and final state, which determines the probability with which the reaction proceeds once the system is on the reaction hypersurface. 

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