Inner-shell reorganization energy

In semiclassical ET theory, three parameters govern the reaction rates the electronic couphng between the donor and acceptor (%) the free-energy change for the reaction (AG°) and a parameter (X.) related to the extent of inner-shell and solvent nuclear reorganization accompanying the ET reaction [29]. Additionally, when intrinsic ET barriers are small, the dynamics of nuclear motion can limit ET rates through the frequency factor v. These parameters describe the rate of electron transfer between a donor and acceptor held at a fixed distance and orientation (Eq. 1),... 

The free energy required to reorganize the solvent molecules around the reactants (the outer coordination shell) and to reorganize the inner coordination shell of the reactants. These are termed and X, respectively. 

Here V is the matrix element which describes the coupling of the electronic states of reactants and products, S is known as the electron-vibration coupling constant which is equal to the inner-shell reorganization energy X- expressed in units of vibrational quanta,... 

Good models for such studies are also metallocenes (M = Mn, Fe, Co) and Cr(CgHg)2 °, which were studied by Weaver and Gennett [148] in seven solvents. The authors compared the experimental data with two sets of calculated results. In the calculations of the first set of data, v was identified with the inner-shell vibration frequency V and it was assumed that the reaction is adiabatic (/c = l). In the second set the authors assumed that the frequency of surmounting the free energy barrier is controlled entirely by the dynamics of solvent reorganization. It was found that the second set of calculated data was much closer to the experimental results. 

It was found that in the overall energy of reorganization, there is a significant contribution from the inner-shell component, roughly comparable with the outer-shell reorganization. 

The inner-shell reorganization energy is generally treated within an harmonic approximation [18], The outer-shell reorganization energy depends upon the properties of the solvent. When a continuum model for the solvent is used Aout is a function of the dielectric properties of the medium, the distance separating the donor and acceptor sites, and the shape of the reactants. 

The relationship between the vertical reorganization parameter and the activation energy and the effect of using different criteria for the inner-shell reorganization have recently been considered in some detail [15]. The reorganization energy and the contributions of the individual reactants turn out to be quite sensitive to the model used. 

Analogous to the case of the inner-shell reorganization, energy conservation requires that the transition-state charges for the solvent reorganization be equal. 

The free-energy barrier for the thermal-electron transfer AG is made up of two parts, the inner-shell and the outer-shell (solvent) reorganization energy " ... 

The energy required to reorganize the inner-coordination shells of the reactants can be estimated using a harmonic-oscillator approximation as follows. The potential energy needed to change the metal-ligand bond distances in [ML ] and from their equilibrium values, d and d°, to the values appropriate to the intersection region, dj and dj, respectively, is ... 

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