Anionic repulsion

It is furthermore to be anticipated that the cation-cation repulsion will operate in some cases to displace the cations from the centers of their coordinated polyhedra. This action will be large only in case the radius ratio approaches the lower limit for stability, so that the size of the polyhedron is partially determined by the characteristic anion-anion repulsive 21 Linus Pauling, Z. Krist., 67, 377 (1928). 

From Fig. 4.49(d) and the last row of Table 4.32 one can see that the quadruply hyperbonded [PtFg]2- dianion is indeed a (meta)stable local equilibrium species, formally of 20e count at the metal atom. Owing to highly unfavorable anion-anion repulsion, the binding of F to [PtF ]- is endothermic, but this species is nevertheless atrue local equilibrium structure (Rptp = 2.04 A, all positive frequencies) of Oh... 

Equations (87)-(89) apply in aqueous solutions of two electrolytes in which the interaction potentials are conformal. For example, the assumptions utilized in the extensions of the Debye-Hiickel theory (e.g. water is considered as a continuous dielectric medium of dielectric constant D, that the cation-anion repulsive potential is that of hard spheres, and that all the... 

The stacking sequence of cation layers is clearly a consequence of anion... anion repulsion any different sequence of the eutactic layers would result in face-sharing between (at least some) OLa octahedra and OLa4 tetrahedra. As it is, only ei/ge-sharing occurs given the La203 stoichiometry and the interstices occupied, the anions are as far... 

M(l)M(2)j tetrahedra] structures. It is worth pointing out that the real and ideal structures differ in the former the O... O distances are greater and the M... M distances smaller so that, in this instance, it is anion... anion repulsions that provide the driving force for departure from the ideal . This is not surprising as in the ideal structure the metal-atom array is the most efficient packing of c.c.p. whereas the anion array is the very open one of three-quarters of the sites of a simple-cubic array. 

At the second level the question arises as to why such simple and well-known cation arrangements appear in oxides. It seems to us plausible that this is a consequence of important non-bonded repulsions between the cations. Om belief is that these are frequently greater than anion... anion repulsions. And certainly this is consistent with the observed regularity of the cation arrays - which is often greater than that of the anion arrays. (Good examples are provided by various olivines and humites, an extreme case being that of the chondrodite type 2Cd2Si04 Cd(OH)2 which is shown in Fig. 25.)... 

Finally, we are not saying that anion... anion repulsion is always negligible, and that cation... cation repulsion alone determines the nature of an oxide structure see, for example, Sect. 3.5. (But neither would we agree with the reverse statement.) However, for compounds with stoichiometric ratios anion/cation 2 and with first row anions, cation... cation repulsion is likely to dominate. 

This chapter focuses primarily on the influence of anion-anion repulsion and on the anion bonding strength. The other factors are described briefly in Section 6.4 but are developed in more detail in later chapters. The special case of is discussed in Chapter 7 and effects that depend on details of the electronic structure of the cation are treated in Chapter 8. The influence of space and symmetry are discussed in Part III. For simplicity, unless otherwise stated, the discussion is confined to compounds in which the anion is oxygen or an oxyanion. Any conclusions will be applicable, mutatis mutandis, to other kinds of anion. 

Fig. 6.4. Effective valence, s versus 0-0 distance for various regular MO coordination environments. Coordination environments shown in bold are known, those in italics are not known. The solid line represents the observed itmin given by eqn (6.3). The broken line represents Ztunstrained> the distance at which the anion-anion repulsion becomes negligible.

Anion-anion repulsion places an upper limit on the coordination number that a cation can adopt but, since the 0 ions do not behave like hard spheres, the size of the limiting 0-0 distance depends on the effective valence of the bonds. Either Fig. 6.4 or eqn (6.3) can be used to decide whether or not a particular coordination number is physically possible. 

The primary constraint on the coordination number is the anion-anion repulsion. Clearly this determines the maximum possible coordination number and, for hard cations, this is normally the coordination number that is observed. However, if the cation is soft or if the maximum possible coordination number gives rise to very small bonding strengths, other coordination numbers may be found as discussed in Section 6.3. A number of examples will illustrate how these various factors work together. 

The crystal chemistry of the H ion is so anomalous that it is usually considered to be qualitatively different from other cations, yet its anomalous properties can be derived in a perfectly rational way by assuming that H is, in principle, no different from other cations except for its small size. H" " is the only cation where the anion-anion repulsion predicts a maximum regular coordination number of less than 2, as can be seen in Fig. 6.4, where the point for regular two-coordinate H ( = 0.5 vu) lies well to the left of the line. However, as... 

The bulge in the centre of the bond flux-bond length correlation in Fig. 7.1 is, however, unexpected and is quite unlike the behaviour shown by any other cation (cf. Fig. 3.1). As pointed out below, the reason for this bulge is the repulsion between the donor and acceptor 0 ions. The bulge is an artefact of anion-anion repulsion and is not intrinsic to the H-O bond itself. The thin line in Fig. 7.1 represents a reasonable interpolation between the two ends of the bond flux-bond length curve and indicates the correlation that might be expected if there were no anion-anion repulsion. 

However, under appropriately constrained conditions, symmetric hydrogen bonds are known (Section 7.4), but not with the predicted 0-0 distance of 220 pm (point E). Since the shortest 0-0 distance allowed by the anion-anion repulsion is 244 pm (point C), the O-H bonds are stretched from 110 to 122 pm and, because they are stretched, the valence sums at H+ are less than 1.0 vu and the bonds are constrained to be linear. 

NO2 ). When the dipole is present the flux lines, hence the ligands, are shifted towards the positive axis, leading to a reduction in the O-M-O angle. This reduction in NO2 is limited by the repulsion between the ions whose separation cannot be less than This, taken from Fig. 6.4, is 213 pm and corresponds to the observed O-M-O angle of 115°. In this case the non-existence of NOj", as well as the geometry of NO2, are both determined by anion-anion repulsion. For all the other ions, the 0-0 distance exceeds so the geometry is primarily determined by other factors. 

Parts I and II of this book focused on the chemistry of inorganic compounds but only briefly considered how the atoms might arrange themselves in space to form a solid. The spatial constraints imposed by anion-anion repulsions were discussed in Section 6.2, but in Part III of this book we look at the much more stringent constraints that appear when atoms come together to form a crystal. As will become apparent, these constraints play an extremely important role in the chemistry of inorganic solids. 

Brown, I. D. (1995). Anion-anion repulsion, coordination numbers and the asymmetry of the hydrogen bond. Can. J. Phys. 73, 616-il. 

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