Electronic Distortion Model

It was first suggested by Itoh and Yamagata [247] that the same effects which cause shielding changes of halide ions in solution also may affect quadrupole relaxation. This possibility was investigated in detail by Deverell [245 246] and recently a systematic theoretical treatment 

Here AE is the mean electron excitation energy and a the fine struc- 

A comparison of the results for the electronic distortion theory with experiment [245 246] is difficult since especially the mean excitation energy is not easy to estimate with sufficient accuracy. Furthermore, no direct determinations of the nuclear magnetic shielding, relative to the free ions, of hydrated chloride, bromide or iodide ions have yet been performed (cf. Section 6.1). 

One weak point in the work of Deverell [245 246], is the identification of the correlation time with the water reorientational corre- 

The contribution to the total relaxation rate from one water molecule is expected to be proportional to the square of the field gradient in position a, V, to the residence time at a and to the 

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In conclusion, it appears that quantitative tests of the electronic distortion model for the quadrupole relaxation resulting from ion-solvent interactions are presently not possible since neither the field gradient nor the correlation time may be reliably estimated. A more fruitful approach of investigating if electronic distortion effects contribute to halide ion quadrupole relaxation at infinite dilution would probably be to test the predicted relationship between... 

Although no definite stand-point can be reached it appears that these sequences provide some support for the electrostatic model. Especially for aqueous LiCl solutions the electronic distortion model seems not to apply. Thus in this case the halide ion shielding becomes diamagnetic (relative to infinite dilution) at high concentrations [250], whereas marked increases in the halide ion relaxation rate divided by either water relaxation rate or viscosity take place. 

No attempts, corresponding to those described above for the alkali halides, have been made to separate the relaxation rates for the alkaline earth halides into ion-ion and ion-solvent contributions and to analyze these in terms of the electrostatic and electronic distortion models of ion quadrupole relaxation. To do so, certain presently lacking information would be needed such as halide ion chemical shift data. It can, however, be said from the well-established structure-stabilizing effect on water of the alkaline earth ions and from studies of water translational [281] and rotational motions [79] in aqueous alkaline earth halide solutions that a modification of the ion-solvent contribution to halide ion relaxation due to the cations is of great importance. In line with this, in their analyses based on the macroscopic viscosity, Deverell et al. [52] found the ion-ion contributions to Br relaxation to be small at least at not too high electrolyte concentration. Such an interpretation is also suggested by the... 

As demonstrated in Ref. [327] both slow overall and fast local motions may, on the basis of an electrostatic model, produce relaxation rates of the observed order of magnitude. It is to be expected that in particular studies of the change in counterion relaxation rate with phase structure and length of the surfactant ion, as well as comparisons between quadrupole splittings and quadrupole relaxation rates, will come to be very helpful in attempts to elucidate the detailed relaxation mechanism in surfactant systems. It can finally be noted that electronic distortion effects on relaxation, as was discussed above for simple halides, have not been considered for halide ion quadrupole relaxation in surfactant systems. It appears that the electronic distortion model (see above) cannot provide a good rationalization of the observations quoted above. 

The spherical shell model can only account for tire major shell closings. For open shell clusters, ellipsoidal distortions occur [47], leading to subshell closings which account for the fine stmctures in figure C1.1.2(a ). The electron shell model is one of tire most successful models emerging from cluster physics. The electron shell effects are observed in many physical properties of tire simple metal clusters, including tlieir ionization potentials, electron affinities, polarizabilities and collective excitations [34]. 

The model shown in Scheme 2 indicates that a change in the formal oxidation state of the metal is not necessarily required during the catalytic reaction. This raises a fundamental question. Does the metal ion have to possess specific redox properties in order to be an efficient catalyst A definite answer to this question cannot be given. Nevertheless, catalytic autoxidation reactions have been reported almost exclusively with metal ions which are susceptible to redox reactions under ambient conditions. This is a strong indication that intramolecular electron transfer occurs within the MS"+ and/or MS-O2 precursor complexes. Partial oxidation or reduction of the metal center obviously alters the electronic structure of the substrate and/or dioxygen. In a few cases, direct spectroscopic or other evidence was reported to prove such an internal charge transfer process. This electronic distortion is most likely necessary to activate the substrate and/or dioxygen before the actual electron transfer takes place. For a few systems where deviations from this pattern were found, the presence of trace amounts of catalytically active impurities are suspected to be the cause. In other words, the catalytic effect is due to the impurity and not to the bulk metal ion in these cases. 

In the bond valence model quantum effects are treated classically by including them in the interatomic repulsion described by eqn (3.1) or (3.2). There are, however, a number of cases where quantum effects are directly responsible for deviations from the higher symmetry that would otherwise be expected. Such electronically distorted structures were discussed in Chapter 8. 

An important group of cations that shows electronically distorted environments are those of the main group elements in lower oxidation states. These contain nonbonding electron pairs in their valence shells, the so-called lone pairs . Such atoms are usually found displaced from the center of their coordination sphere so as to form between 3 and 5 strong bonds and a number of weaker ones. The effect can be described using the Valence Shell Electron Pair Repulsion (VSEPR) Model [43] in which it is assumed that the cation is surrounded uniformly by between 4 and 7 electron pairs occupying valence shell orbitals. One or more of these is a lone pair... 

The premise of the distortion model of Gregorian et al. [187] is that there is a one-to-one relation between the PrClg coordination polyhedron and the 4f electronic barycenter energies of Pr +. As a result, equivalence of barycenter energies of Pr + in various isostructural host lattices at different pressures indicates equi-... 

A small, positively charged ion (a cation) in an ionic compound can attract the electrons of a neighbouring negatively charged ion (an anion) towards it and distort the anion. When this happens, the anion is said to be poiarized. This distortion can be better represented by using the electron density model of an ionic compound, rather than using Lewis symbols. The outer electron density contours of a purely ionic bond, and an ionic bond which is polarized, are shown in Fig. 4.7. 

The present paper focuses on the application of the electron gas model to the calculation of mineral properties, particularly crystal structures, cohesive energies, electron densities, compressibilities, and pressure-induced phase transitions. The effects of partial covalent bonding, or equivalently the non-spherical distortions of the ions, on these properties are addressed. 

Figure 3. Enthalpy of silica in quartz and stishovite structures as a function of pressure Key squares quartz, circles stishovite open symbols distorted ion electron gas model closed symbols spherical ion electron gas model.

Figure 5. Enthalpies of phases in Magnesium Silicate system as a function of pressure, relative to the binary oxides (stishovite and periclase). (a) distorted ion electron gas model (b) spherical ion electron gas model.

We have already described attempts to correlate the relaxation rates with other properties of the solutions and thereby to obtain information on the mechanism of relaxation. It can be seen that such a path is difficult to follow and it has led to conflicting results. However, there are also theoretical approaches to this problem and these will now be described. As with the ion-solvent interactions two models have been considered, one electrostatic and one electronic distortion. 

Another observation which may be understood in terms of an electrostatic model but is more difficult to reconcile with electronic distortion effects, is the observation of pronounced minima in plots of Rb" relaxation rate versus concentration [261]. For other inorganic salts, large increases in relaxation rate have been observed to be accompanied by diamagnetic shifts over the whole concentration range [246]. 

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