Solvent reorganization energy in ET

Electron transfer (ET) reactions in condensed matter continue to be of considerable interest to a wide range of scientists. The reasons are twofold. Firstly, ET plays a fundamental role in a broad class of biological and chemical processes. Secondly, ET is rather simple and very suitable to be used as a model for studying solvent effects and to relate the kinetics of ET reactions to thermodynamics. Two circumstances make ET reactions particularly appealing to theoreticians  

For outer-sphere ET the solvent component of the reorganization energy 

Nowadays, theories of ET are intimately related to the theories of optical transitions. While formerly both issues have developed largely independently, there is now growing desire to get a rigorous description in terms of intermolecular forces shifting the research of ET reactions toward model systems amendable to spectroscopic methods. It is the combination of steady state and transient optical spectroscopy that becomes a powerful method of studying elementary mechanisms of ET and testing theoretical concepts. The classical treatments of ET and optical transition have been facing a serious problem when extended to weakly polar and eventually nonpolar solvents. Values of E p (equal to E, in eq [13.1.25]) as 

It should be mentioned that the two contributions can be completely separated because they have different symmetries, i.e., there are no density/orientation cross terms in the perturbation expansion involved in the calculations. The density component comprises three mechanisms of ET activation (i) translations of permanent dipoles, (ii) translations of dipoles induced by the electric field of the donor-acceptor complex (or the chromophore), and (iii) dispersion solute-solvent forces. On the other hand, it appears that in the orientational part only the permanent dipoles (without inductions) are involved. 

A maximum in the Arrhenius coordinates follows from the fact that the two terms in eq. [13.1.28] depend differently on temperature. Density fluctuation around the reacting pair is determined mainly by the entropy of repacking hard spheres representing the repulsive part of the intermolecular interaction. Mathematically, the entropy of activation arises 

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Electron transfer (ET) reactions are analyzed by Newton in terms of continuum solvation models. Their role in the determination of the ET critical parameters (i.e. the solvent reorganization energy and the electronic coupling between the initial and final states) is analyzed using both an equilibrium and nonequilibrium solvation framework. 

Throughout the literature, many authors argue for the high reduction potential of hydroxyl radicals being responsible for the oxidative reactions observed in AOPs. However, simple electron transfer reactions such as those of Eq. 6-21 seem to be unlikely because of the large solvent reorganization energy involved in the formation of the hydrated hydroxide ion (Buxton et al., 1988). Instead, in the case of halide ions X or pseudo-halide ions, the formation of intermediate adducts with hydroxyl radicals is observed (Eq. 6-24). 

There is an additional, more fundamental, issue involved in applying the standard diabatic formalism. The solvent reorganization energy and the solvent component of the equilibrium free energy gap are bilinear forms of A ab and (Fav (Eqs. [45] and [47]). A unitary transformation of the diabatic basis (Eq. [27]), which should not affect any physical observables, then changes A b and v, affecting the reorganization parameters. The activation parameters of ET consequently depend on transformations of the basis set ... 

Numerical strategies for computing both the electronic and nuclear components of the ET rate are now rather advanced (see the chapter by Newton). For example, in both proteins and small molecules, finite-difference Poisson-Boltzmann methods are widely used for computing the outer-sphere component of the solvent reorganization energy Aq [9, 10, 11, 12] ... 

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