Paulings electrostatic valence model

A coordinated polyhedron of anions is formed about each cation, the cation anion distance being determined by the radius sum and the coordination number of the cation by the radius ratio. 

In a stable coordination structure the electric charge of each anion tends to compensate the strength of the electrostatic valence bonds reaching to it from the cations at the centers of the polyhedra of which it forms a corner that is, for each anion 

The presence of shared edges, and particularly shared faces, in a coordinated structure tends to decrease its stability this effect is large for cations with large valence and small coordination number, and is especially large in case the radius ratio approaches the lower limit of stability of the polyhedron. 

In a crystal containing different cations those with large valence and small coordination number tend not to share polyhedron elements with each other. 

The rule of parsimony. The number of essentially different kinds of constituents in a crystal tends to be small. 

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The concept of bond valence, which, as will be shown below, is the same as the bond flux derived in Chapter 2, grew out of attempts to refine Pauling s principles determining the structures of complex ionic crystals (Section 1.7). In this empirical evolution of Pauling s model, both the electrostatic and short-range components were developed simultaneously. Only later did it become apparent that it was also possible to derive the properties of the electrostatic component independently using the ionic theory. 

Soon after the development of the quantum mechanical model of the atom, physicists such as John H. van Vleck (1928) began to investigate a wave-mechanical concept of the chemical bond. The electronic theories of valency, polarity, quantum numbers, and electron distributions in atoms were described, and the valence bond approximation, which depicts covalent bonding in molecules, was built upon these principles. In 1939, Linus Pauling s Nature of the Chemical Bond offered valence bond theory (VBT) as a plausible explanation for bonding in transition metal complexes. His application of VBT to transition metal complexes was supported by Bjerrum s work on stability that suggested electrostatics alone could not account for all bonding characteristics. 

Actually, the recent studies of transition-group spectra have shown that two different models cherished by many theorists— the electrostatic ligand field model and the valency-bond description (more specifically, the Pauling hybridization theory)—cannot be applied to the observed distribution of energy levels. On the other hand, the molecular orbital (M.O.) configurations give an excellent classification of all energy levels of all complexes and a unified description is obtained of all polyatomic molecules. 

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