Charge variation

Further development of the basic model and the detailed analysis of the dependence of the symmetry factor on the potential and the temperature54 have shown that there are additional factors which can affect the elementary act of this reaction. These investigations led to the formulation of the charge variation model (CVM)55 which will be discussed in the next section. 

The effects of charge variation may also play a certain role in other processes involving adsorbed atoms, in particular, in electron transfer processes.59 The physical nature of these effects is to some extent similar to that of the effects of polarization of the electron plasma of the metal by vibrations in a polar medium considered in Ref. 60. 

Figure 3.34 Atomic-charge variations AQ= Q(R) - Q(oo) for boron (circles) and nitrogen (squares) atoms of the

Figure 3.35 Atomic-charge variations AQ = Q(R) — Q(oo) in dative bonds of H3NO (solid lines), H3PO (dotted lines), and H3AsO (dashed lines). Circles mark oxygen squares mark A atoms of 0 A dative bonds.

Figure 4.32 Mirror-image atomic charge variations AQ = Q(R) — Q(oo) for Os (circles) and nitrogen (squares) atoms of the ctosN dative bond (Req = 2.087 A) of the OsH2NH3 coordination complex (see Fig. 3.34).

The role of atomic charges—or, more precisely, of charge variations—manifests itself in the term + 2T ) that will be used in the derivation of the bond... 

The meaning of n can be inferred from Eq. (5.4) where a measures, in a way, the sensitivity of charge variations to substituent effects. Small n values indicate strong substituent effects. If inductive effects did no exist, the charges would be those corresponding to n = oo (i.e., a = 0), and all H atoms would carry the same charge. No theoretical method leads to this extreme result. 

There is one particular n that merits special attention. It reflects simple customary ideas The electron-attracting power of otherwise similar atoms decreases as their electron populations increase, thus opposing charge separation. This concept views local charge variations as events occurring most reluctantly, suggesting that the carbon atoms found in alkanes should be very similar to one another, conceivably differing as little as possible from one another. 

This rough estimate is to be taken cum grano salts (with a grain of salt)— it follows from energy calculations and bmte-force fits with experimental energy data [44]. It is probably not precise, because the contributions of the ip -carbon charge variations are rather small and likely to be blurred by uncertainties of the experimental energy data. 

See = 69.633 and 8ch = 106.806 kcal/mol. Charge normalization terms are inadvertently treated as part of bond energy Both 8 and 8 are metaphors, not physical entities. In the final count. A, which is usually interpreted as being due to steric effects, is simply a function of local charge variations. 

The CC and CH bonds of ethane (Example 10.1), and the final selection See = 69.633 and 8ch = 106.806 kcal/mol, are used to get the CC and CH bonds found in unsaturated hydrocarbons by retaining both the contribution of Fkh Eq. (11.12), and the effect of charge variations described by Eq. (10.37). The reference CC double bond of ethylene and the reference CC bonds of benzene, however, roughly estimated along the lines described in Example 10.1, are deduced from the appropriate CH bond energies and the energy of atomization of the corresponding molecule, AE, obtained from experimental data. 

Direct estimates using the appropriate SCE potentials at the nuclei suggest 181 kcal/mol [141]. The CC and CH parameters are treated the usual way. A general formula is developed as follows. The hydrogen charge variations are expressed relative to q = —W.l me. Charge normalization, (X) c +... 

These equations are in line with Eq. (30), such that kx denotes the ring-opening rate constant of the protonated carbonato complex and / 2 is the decarboxylation rate constant of the ring-opened bicarbonato complex. Values of these rate constants and the acid dissociation constants of some protonated carbonato complexes of cobalt(TII) (see Table III) reflect the ligand dependence with respect to charge variations, steric constraint, and donor properties of the non-labile ligands. 

Perhaps the earliest system to be described as an Anderson transition was cerium sulphide (Cutler and Mott (1969), on the basis of observations by Cutler and Leavy (1964)). The material in question can be written Ce3 xvxS4, where v is a cerium vacancy, the vacancies being distributed at random. The field near a cerium vacancy repels electrons, because they are negatively charged. Variation of x, then, changes the number of electrons and the number of scatterers. Figure 1.25 shows some results on the conductivity. At that time the present author believed... 

The main questions which arise with respect to the Glueckauf model discussed above concern the uniqueness and the physical justification of the postulated local charge variation represented by Eq. (44). With reference to the former question, some model calculations of SN for f(CFL) distributions of different shapes and widths may be noted 122,123). it was shown that the magnitude and form of the deviation from EVM behaviour for a given B/A ratio is determined largely by the shape of the f(CFL) function near the lower limit A. The precise form of f(CFL) in the higher CFL region appears to have a relatively minor effect on the conformity of SN to the power law of Eq. (46) or the value of q. 

The function of the metal ions in Ihc reactions listed is lo attract electrons from the substrate. When this elTex t takes the form of simple polarization of the functional groups of the substrate, charge variations and electron shifts in these groups facilitate the chemical reactions listed under solvolysis and acid catalysts. When the meial ion removes completely one or more electrons from the substrate, the first step in an oxidation reaction occurs. 

Intriguing evidence for an inductive effect comes from computations that treat nuclei quantum mechanically.11 This takes account of anharmonicity and leads to bond lengths and atomic charges that vary with isotopic substitution. Whether those charge variations are large enough to account for the IEs on acidity, independently of changes of vibrational frequencies, is not yet clear. 

The iterative method is very sensitive to the cavity quality, especially for CPCM and IEFPCM in which the interaction between two tesserae depends on the inverse of the distance. Some unpublished tests performed by the author on slowly convergent iterative calculations have shown that in the last steps almost all the error norm is due to a few charges that still have very large variations with respect the previous iteration cycle, whereas all the other charge variations are several orders of magnitude smaller. 

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