Reorganization inner shell

Figure 12.3 Regions of the electromagnetic spectrum in terms of both frequency (hertz) and wavelength (m). The visible region is a very narrow band between 400 and 700 nm. The lower labels show which part of the atom the various radiations correspond to, i.e., X-rays result from reorganization of the inner shell electrons, UV from the valence electrons, etc. From PSSC PHYSICS, second edition, copyright 1965 by D. C. Heath and Company. Used by permission of Houghton Mifflin Company.

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),... 

As shown by the cyclic voltammetric response in Fig. 10, the peak potential separation of the initial Mn(II,II) — Mn(II,III) electrode reaction is much larger than that of the other steps. This suggests significant inner-shell reorganization and a small rate of heterogenous electron transfer for oxidation of the fully reduced Mn(II,II) state. Similar kinetic sluggishness is observed for Mn(III)/Mn(II) electron-transfer reactions of some mononuclear complexes (see Sects 16.1.2 and 16.1.3). 

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,... 

Secondly, the intrinsic barrier is usefully separated into so-called "inner-shell and "outer-shell components, AG and AG, respectively. The former is associated with reorganization of the internal reactant coordinates (e.g. changes in metal-ligand bond distances, reactant conformation), whereas the latter arises from alterations in the polarization of surrounding solvent molecules. The former can be estimated on the basis of a simple harmonic oscillator model from [la]... 

Recent theoretical treatments, however, suggest instead that the dynamics of solvent reorganization can play an important and even dominant role in determining vn, at least when the inner-shell barrier is relatively small [43-45]. The effective value of vos can often be determined by the so-called longitudinal (or "constant charge ) solvent relaxation time, rL [43, 44]. This quantity is related to the experimental Debye relaxation time, rD, obtained from dielectric loss measurements using [43]... 

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. 

As large as this this value is, it corresponds to an electron exchange rate between CpMo(CO)3NCCH3+ and CpM(CO>3 of only -lO L moP s. The small value signals a large inner-shell reorganization the two sptedes differ by one coordinated molecule of solvent. 

The reorganization parameter is usually broken down into inner-shell (vibrational) and outer-shell (solvational) components. 

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. 

To illustrate the approach used to calculate the iimer-shell contribution to the reorganization barrier we consider the symmetrical stretching vibrations of the two reactants in the Fe(H20)6 " -Fe(H20)6 + self-exchange reaction (Eq. la). The inner-shell reorganization term is the sum of the reorganization parameters of the individual reactants, i.e. ... 

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. 

Similar considerations apply to the inner-shell reorganization. When initial-state delocalization is present d2° - df) is scaled by (1 - 2c f) ... 

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