Valences matching

Rule 4.2 (Valence matching principle). The most stable compounds are formed between cations and anions that have the same bonding strength ... 

Many examples of the valence matching principle will be found in the following chapters, but a couple of examples are given here to illustrate its power. 

The first step in any chemical approach to crystalline structure is to determine the short-range order, i.e. which atoms are bonded. The most convenient way of doing this is by means of the bond graph described in Section 2.5. In many cases all or most of the bond graph can be determined from first principles, since, except for the weakest bonds created in the post-crystallization stage, the bond graph is determined by the rules of chemistry, particularly the hierarchical principle (Rule 11.5), the valence matching principle (Rule 4.2), and the principle of maximum symmetry (Rule 3.1). 

Since the electron density is a continuous function across the interatomic surface, the two atoms that form the surface must have the same distribution of electrons over this face. The most stable structures will be those which require the least amount of redistribution of electron density when the free atoms come together, that is, they will be formed between atoms that have similar surface electron densities. This idea is related to the valence matching principle (Rule 4.2) which states that the most stable bonds are formed between ions that have similar bonding strengths. The bonding strength is thus related to the surface electron density of the ion. 

The particular virtue of these definitions is that the Lewis acid and the Lewis base strengths are both estimates of the valence of the bond that links the cation with the anion. The most effective bonds will therefore occur between a cation whose Lewis acid strength (Sg) is close to the Lewis base strength (Sb) of the anion. This is known as the Valence Matching Principle. Compounds between badly matched ions, i.e. Be (Sa = 0.5 v.u.) and ClO j" (Sb = 0.08 v.u.), are difficult if not impossible to form as both the cation and the anion will be forced into unusual coordination. If they... 

The Valence Matching Principle not only allows one to predict chemical stability and solubility, but also suggests ways in which the bonding graph of a compound can be constructed, as described in Section 10.5.1. 

Fig. 10.9. Known silicate compounds as a function of the Lewis acid and base strengths of their ions. Points are from Reference [42]. The thick diagonal line corresponds to a perfect valence match...

Since the bonding strength of both the cation and the anion is an estimate of the valence of the bond formed between them, a cation will preferentially bond to an anion that has the same bonding strength. The valence matching principle, which is useful in determining which cations and anions will bond to each other, states that ... 

The valence matching principle is used in the modelling of structures by ensuring that strong cations bond to strong anions and weak cations bond to weak anions, as discussed below. 

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