The Ionic model

Arrhenius success in science must be credited not only to his brilliance as a scientist but also to his conviction in his views. His understanding of the electrical properties of aqueous solutions nus so far ahead of contemporary thought that it would have been ignored but for his confidence in the usefulness of his theory and his refusal to abandon it. It is fitting tribute that the ionic model of aqueous solutions has changed permanently the face of inorganic chemistry. 

The model for the liquid phase may be obtained by analogy with the solid phase. Equation (11) is the ionic model reaction for... 

The ionic model, the description of bonding in terms of ions, is particularly appropriate for describing binary compounds formed from a metallic element, especially an s-block metal, and a nonmetallic element. An ionic solid is an assembly of cations and anions stacked together in a regular array. In sodium chloride, sodium ions alternate with chloride ions, and large numbers of oppositely charged ions are lined up in all three dimensions (Fig. 2.1). Ionic solids are examples of crystalline... 

The ionic model describes a number of metal halides, oxides, and sulfides, but it does not describe most other chemical substances adequately. Whereas substances such as CaO, NaCl, and M 2 behave like simple cations and anions held together by electrical attraction, substances such as CO, CI2, and HE do not. In a crystal of Mgp2, electrons have been transferred from magnesium atoms to fluorine atoms, but the stability of HE molecules arises from the sharing of electrons between hydrogen atoms and fluorine atoms. We describe electron sharing, which is central to molecular stability, in Chapters 9 and 10. 

On the basis of the shell model, two apparently different models of the chemical bond were proposed, the ionic model and the covalent model. 

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. 

The ionic model, developed by Bom, Lande, and Lennard-Jones, enables lattice energies (U) to be summed from inverse square law interactions between spherically symmetrical charge distributions and interactions following higher inverse power laws. Formation enthalpies are related to calculated lattice energies in the familiar Bom-Haber cycle. For an alkali fluoride... 

We shall briefly discuss the electrical properties of the metal oxides. Thermal conductivity, electrical conductivity, the Seebeck effect, and the Hall effect are some of the electron transport properties of solids that characterize the nature of the charge carriers. On the basis of electrical properties, the solid materials may be classified into metals, semiconductors, and insulators as shown in Figure 2.1. The range of electronic structures of oxides is very wide and hence they can be classified into two categories, nontransition metal oxides and transition metal oxides. In nontransition metal oxides, the cation valence orbitals are of s or p type, whereas the cation valence orbitals are of d type in transition metal oxides. A useful starting point in describing the structures of the metal oxides is the ionic model.5 Ionic crystals are formed between highly electropositive... 

The ionic models discussed in section 1.12 involve some sort of empiricism in the evaluation of repulsive and dispersive potentials. They thus need accurate parameterization based on experimental values. They are useful in predicting interaction energies within a family of isostructural compounds, but cannot safely be adopted for predictive purposes outside the parameterized chemical system or in cases involving structural changes (i.e., phase transition studies). 

Covalent contribution to the bonding is confirmed by analysis of the components of V2p. The average values of 2, and X2, representing the contraction of the density in the directions perpendicular to the bond (chapter 6), are found to be — 9eA"s, compared with —4eA 5 for the independent-atom model (IAM) density and — 6eA"5 for the ionic model. In addition, the density at the bond critical point ph is l.leA"3, higher than 0.85 eA"3 and 0.68 eA"3 calculated for the IAM and ionic models, respectively. Results for the borosilicate danburite CaB2Si208, are similar, with ph(SiO) 0.95 eA-3, and large positive values of V2p for the Si—O bonds (Downs and Swope 1992). 

FIG. 11.11 Electron-density difference maps on Li2BeF4 calculated with all reflections < sin 6/1 = 0.9 A"1 (81 K). (a) Based on the neutral atom procrystal model, (b) based on the ionic model. Contour levels are drawn at intervals of 0.045 eA"3.1 Full lines for positive density, dashed lines for negative and zero density. The standard deviation, estimated from [2Lff2(F0)]1/2N, is 0.015 eA-3. Source Seiler and Dunitz (1986). 

Seiler and Dunitz point out that the main reason for the widespread acceptance of the simple ionic model in chemistry and solid-state physics is its ease of application and its remarkable success in calculating cohesive energies of many types of crystals (see chapter 9). They conclude that the fact that it is easier to calculate many properties of solids with integral charges than with atomic charge distributions makes the ionic model more convenient, but it does not necessarily make it correct. 

A more complete and much more rigorous description of bonding in complexes would be provided by a quantum mechanical treatment. Such a treatment is especially needed in the case of departures from the ionic model and increasing contribution of covalent bonding (ion pairs, soft donors and acceptors). However only a few studies have been reported. They are mainly concerned with cation hydration and use either semi-empirical 19—21) or non-empirical methods 22—24). A non-empirical treatment of cation NH3 systems has also been performed recently (25). However the present state of the computations is still far from providing a complete description of the system including the medium. The latter may be taken into account by a Bom-type "solvaton (27,26). Heats of hydration may then be calculated (27). A discussion of this aspect of the problem is deferred to a later date, awaiting especially a more complete analysis of non-empirical calculations. In the course of the discussion of... 

If hybridization is taken into account, nx can be provided only by band calculations. This is true for metals (where T inicates only the orbital) e.g. when hybridization between the f state and the (s, p, d) band is considered. In the case of cation-anion hybridization (ii.), covalency sets up. The complete charge transfer of the ionic model is reduced some charge sharing occurs between cation and anion. 

It is important to note that the good agreement achieved between the Born-Haber and calculated values for lattice energy, do not in any way prove that the ionic model is valid. This is because the equations possess a self-compensating feature in that they use formal charges on the ions, but take experimental internuclear distances. 

Figure 1.4 Actual structures of alkali halides compared with the predictions of the ionic model. The figure is divided into three regions by lines corresponding to rjr = 0.414 and 0.732. The regions correspond to four-, six- and eight-coordinated structures. Filled circles denote six-coordinated structures, open circle, six- or eight-coordinated structure and filled squares, eight-coordinated structures. Note that the predictions of the ionic model do not entirely correspond with the actual structures of alkali halides (Following Phillips, 1973f>).

Nonbonded radii enable us to rationalize aspects of crystal chemistry that cannot be understood in terms of the ionic model. For instance, it is difficult to understand why silicon is four-coordinated in most oxides. This is unlikely to be because of the radius ratio of the classical ionic model 81 is too small to have four oxygens around it. Six-coordinated silicon is known in certain cases (e.g. SiP207) silicon is octahedrally coordinated in fluorides, although the ionic radii of and F are similar. The reason... 

The usually accepted approach is to adopt an ionic model for the superoxide ion on the surface. In this model, an electron is transferred from the surface to the oxygen to form 02, and there is an electrostatic interaction between the cation at the adsorption site and the superoxide ion. A calculation of the g tensor based on this model (Section 111,A,1) accounts for nearly all the data from adsorbed 02 and is consistent with the evidence that the spin density on both oxygen nuclei is the same (Section III,A,2). However, there are examples of oxygen adsorbed on the surface where the g values do not fit the predictions of the ionic model (Section IV,E) and also a few cases where the spin density on the two oxygen nuclei is found to be different. In these situations it seems likely that a covalent model in which a a bond is formed between the cation and the adsorbed oxygen, is more relevant. 

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