Pauling valency strength

In 1929 Pauling proposed as the second of his Principles Determining the Structures of Complex Ionic Crystals [1], that a cation-anion bond could be characterized by the oxidation state (atomic valence) of its cation divided by its coordination number. He showed that the total amount of this quantity, usually now called the Pauling Bond Strength, received by the anion was approximately equal to the anion oxidation state. He called this the Electrostatic Valence Principle, but it is now commonly referred to as Pauling s Second Rule. 

The Pauling valency or the strength of an electrostatic bond with a cation or anion is defined as... 

By way of example we use the concepts of Pauling valency to describe the reactivity of MgO. MgO takes on a rock-salt structure. In the bulk each cation or anion has six neighbors. For the Mg + ion, the Pauling bond strength equals... 

In these equations is the valence of the anion, Z, is the valence, and Vi the coordination number of the fth cation, and is the strength of the bond between the anion and cation i. This equation defines the Pauling bond strength as the valence of the cation divided by the number of bonds the cation forms. 

Pauling, L., Herman, Z.S., Kamb, B.J. Reliability of the Pair-Defect-Sum Approximation for the Strength of Valence-Bond Orbitals Proc. Natl. Acad. Sci. (USA) 1982, 79, 1361— 1365. 

The coordination of an O2- ion is three Al3+ ions within an A1404 cube and one Mg2+ ion outside of this cube. This way it fulfills the electrostatic valence rule (Pauling s second rule, cf p. 58), i.e. the sum of the electrostatic bond strengths of the cations corresponds exactly to the charge on an O2- ion ... 

Pauling (1929) introduced the concept of mean strength of the bond (Si) as a ratio of the valence with coordination number. He also formulated the principle of electrostatic valence, which establishes that the sum of the mean bond strengths for a given coordination polyhedron (P) coincides with the valence state—i.e.. 

Pauling s second mle is the electrostatic valence mle. It states that the charge on an ion must be balanced by an equal and opposite charge on the surrounding ions. A cation, coordinated by n anions, has an electrostatic bond strength (BBS) for each bond defined as ... 

There are now quite a sizeable number of high superconductors, and in the plot [33] shown in Fig. 15 it is apparent that the Cu-O distance is a useful parameter to describe their superconducting properties. A connection can be made between these Cu-O distances and the number of holes in the CuOj layer by consideration of the bond valence sum, v, at the copper atoms. This concept dates from Pauling s idea of the electrostatic bond sum rule and has been refined in the intervening period [34]. Modern usage defines it as the sum of the bond strengths over all bonds coordinated to copper in the following way. The bond valence sum, u = E, exp(r, - r(,)/0.37, where the parameter depends on the... 

We prefer an empirical approach to bonding as opposed to any complex theories of binding [4] or bonding [5, 6, 7], The bond valence method for determining the strength of bonds in crystals has developed from Pauling s concept of bond strength [8] and recently has been documented extensively [9, 10, 11]. 

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. 

---