Ionic model, limitations

Formal charge and oxidation number are two ways of defining atomic charge that are based on the two limiting models of the chemical bond, the covalent model and the ionic model, respectively. We expect the true charges on atoms forming polar bonds to be between these two extremes. 

As is obvious from the table, Tc is almost doubled upon deuteration. These isotope effects are one of the largest observed in any solid state system. The question arises about isotope effects in non-hydrogen-bonded ferro- and antiferroelectrics. As already mentioned in the Introduction, within a mean-field scheme and in a purely ionic model it was predicted that these systems should not exhibit any isotope effect in the classical limit, which has been verified experimentally. Correspondingly, there was not much effort to look for these effects here. However, using a nonlinear shell-model representation it was predicted that in the quantum limit an isotope effect should... 

All density functional models exhibit similar behavior with regard to dipole moments in diatomic and small polyatomic molecules. Figures 10-6 (EDFl) and 10-8 (B3LYP) show clearly that, except for highly polar (ionic) molecules, limiting (6-311+G basis set) dipole moments are usually (but not always) larger than experimental values. 

This book is divided into four parts. Part I provides a theoretical derivation of the bond valence model. The concept of a localized ionic bond appears naturally in this development which can be used to derive many of its properties. The remaining properties, those dependent on quantum mechanics, are, as in the traditional ionic model, fitted empirically. Part II describes how the model provides a natural approach to understanding inorganic chemistry while Part 111 shows how the limitations of three-dimensional space lead to new and unexpected properties appearing in the inorganic chemistry of solids. Finally, Part IV explores applications of the model in disciplines as different as condensed matter physics and biology. The final chapter examines the relationship between the bond valence model and other models of chemical bonding. 

The ionic model is of limited applicability for the heavier transition series (4d and 5d). Halides and oxides in the lower oxidation states tend to disproportionate, chiefly because of the very high atomisation enthalpies of the elemental substances. Many of the lower halides turn out to be cluster compounds, containing metal-metal bonds (see Section 8.5). However, the ionic model does help to rationalise the tendency for high oxidation states to dominate in the 4d and 5d series. As an example, we look at the fluorides MF3 and MF4 of the triad Ti, Zr and Hf. As might be expected, the reaction between fluorine gas and the elemental substances leads to the formation of the tetrafluorides MF4. We now investigate the stabilities of the trifluorides MF3 with respect to the disproportionation ... 

The present review therefore puts much weight on the assessment of the low-temperature thermodynamics of selenium in aqueous solution and makes independent analyses of the available literature in this area. The standard method used for the analysis of ionic interactions between components dissolved in water (see Appendix B) allows the general and consistent use of the selected data for modelling purposes, regardless of the type and composition of the ground water, within the ionic strength limits given by the experimental data used for the data analyses in the present review. 

Calculations of the type reported here are relatively simple and inexpensive. There are clear limitations in that they are based on an ionic model which cannot serve the role of appropriate ab initio electronic structure studies, particularly for electronic defects. Neither can aspects related to the magnetism be addressed. Nevertheless, the approach is highly specific and versatile. It is clear from the results presented here that its particular strength lies in the insight that can be gained from comparative studies of interrelated families of materials with related structures and other similarities in their chemical or physical behaviour. It seems likely that simulation techniques will continue to provide valuable information on these complex materials and in particular on the new superconducting phases prepared by novel synthetic strategies. 

The authors questioned the value of E° (Th" /Ttf, -3.0 V, chosen by [1997KLA/SCH] from the estimation of [1986BRA/LAG] based on an ionic model which took account the stabihsation of d electrons by crystal field effects. A re-evaluation of the crystal field stabilisation effects by [199810N/MAD] led these authors to propose -3.82 V and-3.35 V as limiting values for this potential, consistent with the earher estimate -3.7 V by [1973NUG/BAY]. 

If the reader has actually made it up to this point, he or she will have the impression that the whole universe of solid-state materials, i.e., insulators, semiconductors, metals, and intermetallic compounds can nowadays be studied by electronic-structure theory, and predictive conclusions are really in our own hands. Indeed, the numerical limitations of most classical approaches - in particular, the ionic model of everything - have been overcome. While the computational methods of today include very different quantum-chemical methods, their varying levels of accuracy and speed are due to differences in their atomic potentials and the choice of the basis sets that are involved. The latter may either be totally delocalized (plane waves) or localized (atomic-like), adapted to the valence electrons only (pseudopotentials) or to all the electrons. In order to understand structures and compositions of solid-state materials, the results of electronic-structure theory are typically investigated in terms of some quantum-chemical analysis. 

In the second section this electron counting scheme is rationalized in terms of recent band structure calculations. The limitations of the ionic model as well as a variety of structural and electronic relationships for metal-rich halides are also discussed using these theoretical treatments. 

For the rare earth metal halides and their interstitial derivatives, a simple ionic model related to the aforementioned electron counting rules has been successful to rationalize a number of structural and physical observations. This model, which has been repeatedly used in the preceding section, assigns to each halide an oxidation state of — 1, and to the highly electropositive rare earth metal, usually its maximum oxidation state, which in most cases is trivalent. If interstitial species occurs, these accept any excess electrons to the extent of becoming closed shell ions. Any additional electrons will then enter the metal-centered band. The following examples will address the validity and the limitations of such a treatment. 

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