Solvent reorganization model

In order to simplify the expression for G, one has to employ a sufficiently simple model for the vibrational modes of the system. In the present case, the solvent contribution to the rate constant is expressed by a single parameter E, the solvent reorganization energy. In addition, frequency changes between the initial and final states are neglected and it is assumed that only a single internal mode with frequency co and with the displacement Ar is contributing to G. Thus the expression for G reduces to [124] ... 

In the case where the bond coordinate can be treated as classical, and when the electronic interaction A is much smaller than the solvent reorganization, the energy of activation can be calculated explicitly in Saveant s [1993] model ... 

As with the Marcus-Hush model of outer-sphere electron transfers, the activation free energy, AG, is a quadratic function of the free energy of the reaction, AG°, as depicted by equation (7), where the intrinsic barrier free energy (equation 8) is the sum of two contributions. One involves the solvent reorganization free energy, 2q, as in the Marcus-Hush model of outer-sphere electron transfer. The other, which represents the contribution of bond breaking, is one-fourth of the bond dissociation energy (BDE). This approach is... 

In the framework of the Landau-Zener model, P is related to H by means of equation (75). These equations are also valid when both the stretching and solvent reorganization coordinates are taken into account as in the case of dissociative electron transfer. 

Coming back to solvent reorganization, the reduction of aromatic hydrocarbons in an aprotic solvent such as DMF provides a series of data that may be used for testing the Marcus-Hush model of solvent reorganization13,61-63... 

The coordinate pertaining to solvent reorganization, z, is the same fictitious charge number as already considered in the Hush-Marcus model of outer-sphere electron transfer (Section 1.4.2), and so is the definition of 2q [equation (1.27)] and the difference between the Hush and Marcus estimation of this parameter. The coordinated describing the cleavage of the bond is the bond length, y, referred to its equilibrium value in the reactant, yRX. Db is the bond dissociation energy and the shape factor ft is defined as... 

The fit of the LH model to the remaining kinetic data for the nitrile solvents employed only two fitting parameters, the low-frequency promoting mode, ooq, and the solvent reorganization energy, Es. A factor determining the magnitude of... 

We have investigated the ferrocene/ferrocenium ion exchange to determine the effects of different solvents on electron-transfer rates. There is probably only a very small work term and very little internal rearrangement in this system. Thus the rates should reflect mostly the solvent reorganization about the reactants, the outer-sphere effect. We measured the exchange rates in a number of different solvents and did not find the dependence on the macroscopic dielectric constants predicted by the simple model [Yang, E. S. Chan, M.-S. Wahl, A. C. J. Phys. Chem. 1980, 84, 3094]. Very little difference was found for different solvents, indicating either that the formalism is incorrect or that the microscopic values of the dielectric constants are not the same as the macroscopic ones. 

Both the electronic couphng matrix element and the outer-sphere component of the nuclear reorientation parameter are thought to vary with donor-acceptor separation and orientation [29, 49]. It has been shown in studies of Os and Ru-ammines bridged by polyproline spacers that the distance dependence of X can be greater than that of [50]. Dielectric continuum models of solvent reorganization predict that Xg will increase with... 

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