Reorganization nuclear

So far, only the nuclear reorganization energy attending electron transfer has been discussed, yielding the expressions above of the free energy of activation in the framework of classical transition state theory. A second series of important factors are those that govern the preexponential factor, k, raising in particular the question of the adiabaticity or nonadiabaticity of electron transfer between a molecule and the electronic states in the electrode. 

Nuclear reorganization or the rehybridization of the carbon is a main factor in the retardation of proton transfer involving carbon acids, and solvation changes have much less impact (7). 

Statement number 6 has to do with carbon acids and is supported by reference (7). There are, in fact, other references that suggest solvent plays a much more direct role in the kinetics of protonating carbanions than statement number 6 would imply. For example, there is evidence that nuclear reorganization and rehybridization of the carbon atom are too rapid to have much kinetic importance when compared with solvent reorientation. The strong dependence of carbanion protonation rates on the solvent supports this view. These rates are typically much faster in organic solvents, such as DMSO, than in water. A particular reaction that was studied in different solvents (17) is... 

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),... 

So far the attention has been on the nuclear reorganization barrier. Nevertheless, other important factors previously hidden in the pre-exponential factor (and ultimately in the standard rate constant) have to be considered, namely, the fundamental question of the magnitude of the electronic interaction between electroactive molecules and energy levels in the electrode (i.e., the degree of adiabaticity) and its variation with the tunneling medium (electrode-solution interface), the tunneling distance, and the electrode material. Thus, within the transition-state formalism, the rate constant for electron transfer can be expressed as the product of three factors [39—42] ... 

On the basis of the Franck-Condon principle, photoelectron transfer between a donor and acceptor molecule proceeds as follows (Fig. 10). Initially, the donor and acceptor are dispersed randomly in a solution. On light absorption, the donor (or acceptor) undergoes a rapid transition to form a Franck-Condon state, which rapidly undergoes nuclear relaxation to an equilibrated state. A further nuclear reorganization takes place before electron transfer. After electron transfer, there is nuclear relaxation to the final, equilibrated product state. 

Nuclear reorganization consists of changes in the internal or vibrational modes of the reactants as well as changes in the nuclear polarization of the surrounding solvent molecules. The distinction between these two classes of nuclear barriers is fundamental in understanding reactivity in photoelectron transfer. With this in mind, we shall now proceed to evaluate the barriers in electron transfer (Fig. 11). The classical theory, to be discussed in the next section, emphasizes the Coulombic and nuclear, whereas in the nonclassical, nonadiabatic theories, which are discussed in Sect. 3.3, emphasis is on electronic and nuclear barriers. 

In the classical theory of Marcus, the rate determining factors involve nuclear reorganization. We write the first-order rate constant, ke, as [37]... 

X is thus related to the entire nuclear reorganization of an electron-transfer reaction. These nuclear barriers, which precede the actual electron transfer, involve bond-length changes within the reactants, and reorientation of the surrounding solvent dipoles. 

The other model parameters entering Eq. [66] are the nuclear reorganization energies defined through the second cumulants of the reaction coordinate... 

For example, the faster rate of reaction from of cyclobutanones relative to cyclopentanones can be qualitatively understood on the basis of greater relief of strain in for the four-membered ring versus the five membered ring. Furthermore, since the 1,4-biradical is produced cis and in the singlet state, all of the observed reactions can occur with relatively minor nuclear reorganization and with no prohibitions. 

The interfacial kinetics processes at semiconductor/liquid contacts for reactions with one-electron, outer-sphere, redox species can be understood in a conventional theoretical framework. The rate constant can be broken down into a term representing the attempt frequency, Vn, a term representing the electronic coupling between the electrons in the conduction band of the semiconductor and the redox acceptor state, k x, and a term representing the nuclear reorganization energy in the transition state from reactants to products, For outer-sphere electron transfer processes, the nuclear term is well-known to be ... 

Application of the Marcus equation for electron transfer affords the electron exchange rate of the molybdenum radical/anion couple. The value is fcge = 3 X 10 L mol s. The high value argues that very little nuclear reorganization is needed to add an electron to the SOMO of the 17e radical. 

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