Energy of activation for electron transfer

It is commonly assumed that solvent reorganization will dominate electron transfer kinetically. Depending on the thermodynamics of the electron exchange, it is possible to quantitatively predict a relationship between the free energy of activation for electron transfer and the free energy associated with solvent reorganization based on Marcus theory. 

Finally, utilizing a combination cycle for thermal electron transfer and optical charge transfer (Figure 1-19), the relative free energy of activation for electron transfer can be expressed as follows ... 

To be specific, let us consider electron transfer from the reduced form of the reactant to the metal electrode. The electron may be transferred to any empty state on the metal denoting by e the difference in energy between the final state of the electron and the Fermi level, the energy of activation for the transfer is ... 

The energy spacings between levels associated with solvent dipole reorientations are small, 1-10 cm-1. Since the spacings are well below kBT at room temperature ( 200 cm-1), the contribution of the solvent to the energy 6f activation for electron transfer can be treated classically. The results of classical treatments, where the solvent is modelled as a structureless dielectric continuum, will be discussed in later sections. 

Formation of bands in solids by assembly of isolated atoms into a lattice (modified from Bard, 1980). When the band gap Eg kT or when the conduction and valence band overlap, the material is a good conductor of electricity (metals). Under these circumstances, there exist in the solid filled and vacant electronic energy levels at virtually the same energy, so that an electron can move from one level to another with only a small energy of activation. For larger values of Eg, thermal excitation or excitation by absorption of light may transfer an electron from the valence band to the conduction band. There the electron is capable of moving freely to vacant levels. The electron in the conduction band leaves behind a hole in the valence band. 

The energy of activation for thermal electron transfer is related to A and AE in equation (54). Equations (70) and (71) relate Eop to the same variables. It follows that, in the classical limit, the energy of activation for thermal electron transfer can be calculated from op using equation (70) for a symmetrical case or equation (72) for an unsymmetrical case. 

Various theories have been proposed for prediction of rate constants for electron transfer quenching k. Most of the theories are based on the relationship between the free energies of activation for photoinduced electron transfer and the free energy changes, AG, associated with radical ion pair formation through photoinduced electron transfer. 

Moreover, from the data in Table 2 it is possible to estimate the fi ee energy of activation of the reaction studied. In order to do this we must assume, above all, that the optical electron transfer, to which the band correspond, is the same as the themud electron transfer, to which the k values correspond. However, the data in Table 3 cannot be used directly for estimating the activation free energy of the thermal electron transfer reaction. The first obvious reason comes from the fact that the band corresponds to the (Co(NH3)4(pzC02)] -[Ru(CN) ion-pair instead of to the [Co(NH3)4(pzC02)] -[Fe(CN) J "... 

The free energy of activation for the electron transfer is the difference between the free energies of the transition-state configuration and the equilibrium configuration of the reactants. 

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