Distortions Caused by Spatial Constraints

The second type of distortion arises from the difficulty of mapping the ideal bond lengths calculated using the network equations into real space, either because of constraints of crystal symmetry or because of non-bonding repulsions. For example, if an atom is placed in a cavity that is too large for it, its valence sum will be too small. The Distortion Theorem (Section 10.2.2) predicts that the valence sum will be increased if the environment of the atom is distorted to give bonds of different lengths. 

The Bond Valence Model has its roots in the ionic models of Pauling, but it can be equally well derived from the covalent models of Lewis. It thus spans the full range between ionic and covalent bonds without making any distinction between them. In the formal development of the model, a chemical structure is treated as a network of bonds in which each bond is associated with a valence that expresses its strength. The two network equations, viz the Valence Sum Rule (Equation 10.5) and the Equal Valence Rule (Equation 10.6), can be used to predict bond valences, and hence bond lengths, when the bond network is known. The influence of one part of the structure on another is transmitted through the network by application of the network equations. 

In the Bond Valence Model, atoms are characterized by their atomic valence (oxidation state) and by their Lewis acid or Lewis base strength, the latter two quantities correlating with electronegativity and respectively. The acid and base strengths are both estimates of the valence of the bonds formed by the atoms. Hence, for a 

The model is restricted to compounds that display acid-base bonding and therefore it cannot be used to describe metallic or organic bonding. Within these limits, the Valence Sum Rule is found to be widely obeyed and has proved remarkably useful in the analysis of inorganic structures. The Equal Valence Rule is less universal and fails when the environment of an atom is distorted as a result of its internal electronic structure or as the result of the application of the Distortion Theorem in constrained structures. In some highly constrained structures the Valence Sum Rule may also be violated, indicating the presence of internal strain and flagging the possible existence of a complex crystal chemistry. 

Taken together, the rules of the Bond Valence Model provide a powerful tool for modelling and understanding the structures of compounds containing acid-base bonds. 

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