The Electronic Factor

The electronic factor in the sum j(r, R) arises from the familiar BO electronic Hamiltonian defined for a fixed R. Since this Hamiltonian is independent of the nuclear set Xk(R) cany the e label. As is well known, with each k... 

In this equation, AG°CS is taken to be negligible for p- and y-cyclodextrin systems and to be constant, if there is any, for the a-cyclodextrin system. The AG W term is virtually independent of the kind of guest molecules, though it is dependent on the size of the cyclodextrin cavity. The AG dw term is divided into two terms, AG°,ec and AGs°ter, which correspond to polar (dipole-dipole or dipole-induced dipole) interactions and London dispersion forces, respectively. The former is mainly governed by the electronic factor, the latter by the steric factor, of a guest molecule. Thus, Eq. 2 is converted to Eq. 3 for the complexation of a particular cyclodextrin with a homogeneous series of guest molecules ... 

The Role of the Electronic Factor in the Kinetics of Charge-Transfer Reactions German, E. D. Kuznetsov, A. M. 24... 

A systematic NMR spectroscopic study of these adducts suggests that the steric repulsion between the trimethyl aluminum Lewis acid and the phosphane Lewis base rather than the electronic factors account for the detected changes in the P-NMR spectroscopic chemical shifts (Table 1). The change in the chemical shift (A) of the phosphanes on coordination to AlMe3 has been correlated to the... 

EPR studies on electron transfer systems where neighboring centers are coupled by spin-spin interactions can yield useful data for analyzing the electron transfer kinetics. In the framework of the Condon approximation, the electron transfer rate constant predicted by electron transfer theories can be expressed as the product of an electronic factor Tab by a nuclear factor that depends explicitly on temperature (258). On the one hand, since iron-sulfur clusters are spatially extended redox centers, the electronic factor strongly depends on how the various sites of the cluster are affected by the variation in the electronic structure between the oxidized and reduced forms. Theoret-... 

The analysis of the regioselective reactivity of olefins in identical topochemical environments by three computational methods concludes that both steric factors (cavity and potential energy) and electronic factors (perturbation energy from orbital interactions) play important cooperative roles in determining which C—C double bond in a molecule reacts first in [2-1-2] photodimerization. The steric factor is considered to be effective in the movement of olefins at an early stage of the reaction, whereas the electronic factors are effective in the adduction of olefins at a later stage of the reaction. 

Gold forms a continuous series of solid solutions with palladium, and there is no evidence for the existence of a miscibility gap. Also, the catalytic properties of the component metals are very different, and for these reasons the Pd-Au alloys have been popular in studies of the electronic factor in catalysis. The well-known paper by Couper and Eley (127) remains the most clearly defined example of a correlation between catalytic activity and the filling of d-band vacancies. The apparent activation energy for the ortho-parahydrogen conversion over Pd-Au wires wras constant on Pd and the Pd-rich alloys, but increased abruptly at 60% Au, at which composition d-band vacancies were considered to be just filled. Subsequently, Eley, with various collaborators, has studied a number of other reactions over the same alloy wires, e.g., formic acid decomposition 128), CO oxidation 129), and N20 decomposition ISO). These results, and the extent to which they support the d-band theory, have been reviewed by Eley (1). We shall confine our attention here to the chemisorption of oxygen and the decomposition of formic acid, winch have been studied on Pd-Au alloy films. 

We first consider the electronic factors responsible for conformational preference in tetraatomic molecules of the type X—Y—Y—X. Our model compound is 02F2 and the two conformations we will compare are shown below ... 

In this section, we shall discuss the electronic factors which determine conformational preferences in CH3CH=X systems. We shall attempt to predict the relative energy of the staggered and eclipsed conformations shown below as well as its dependence upon the nature of X. 

The fundamental unit of proteins is the peptide linkage. An understanding of the electronic factors dictating conformational preference in the peptide linkage, therefore, can lead to further insight into polypeptide and protein torsional isomerism. 

Thus, relation (18) gives directly the value of lTab(Q ) as half the difference between the energies of the two stationary states /i and xJ/j, caleulated at the nuclear configuration Q = Q. We shall see in Sect. 2.2.3 some examples of theoretical calculations of the electronic factor which are based on this property. 

The electronic factor of the reaction rate is obtained by evaluating (19) and (20) at the nuclear configuration Q = Q where haa bb equal. Expression (20) is readily generalized to a sequence of n orbitals bridging cp and tp. For Q = Q, the main term can be written ... 

The preceding many-electron formulation is useful to separate the different contributions to T b, and could be easily improved to include the whole set of valence electrons of the system. However, it is not certain that this method is the most convenient for the effective calculation of the electronic factor. Actually, in the very few many-electron calculations that have been reported in the literature, Tjb was evaluated globally. These studies are summarized below. 

For the time being, qualitative or semi-quantitative analysis of the influence of the medium on the electronic factor value rest on the description given by the... 

In a first type of systems, redox centers are randomly distributed in a rigid matrix, glass or polymer [73, 74, 75], Donor or acceptor centers are initially created photochemically or by pulse radiolysis, and the study of the return to equilibrium of the system allows the determination of the law k(R) giving the rate variation as a function of the intercenter distance R. The experimental data are well described by an exponential law, which is considered as reflecting an exponential variation of the electronic factor ... 

Another method used to vary the AG° of the recombination reaction without chemical modification of the centers, consists of placing the system in an electric field whose orientation and intensity are well defined [141]. However, the energy level shifts induced by the field also change the electronic factors, so that the interpretation of the experimental results is not straightforward. Bixon and Jortner have proposed using electric field effects to elucidate the nature of the primary electron step in bacterial photosystems [142], a problem that will be discussed in Sect. 3.5. One basic difficulty encountered in this method is the evaluation of the internal field effectively seen by the redox centers in the membrane. 

---