Pauling valency

Where Q is the formal ion charge and C its coordination number. For the Mg2+ ion, the Pauling valency equals... 

On the surface the charge excess of an ion is defined as the formal charge Q of the ion considered plus the sum of the Pauling valencies, computed with respect to the other ion ... 

At the present stage of theoretical development it is hardly possible to go far enough, in terms of either band theory or the Pauling valence bond approximation, with a quantitative treatment of crystals involving free electrons and a relatively large electronegativity difference between the components. Nevertheless, the matter merits more attention. 

Surface Lewis acidic or basic sites are created on ionic surfaces because surface atoms have a lower coordination number compaired to their bulk values. A condition for surface stability is that the sum of the charges over the surface unit cell is zero and the surface is overall neutral. A useful method to estimate the degree of coordinative unsaturation on an ionic surface is to use Pauling valencies and to compute charge excesses. The Pauling valency, v, is defined as ... 

For metals and metal alloys in particular, relationships have been sought between collective properties and catalytic behavior. The metallic state was generally described by the simple band model or the Pauling valence structure theory. 

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... 

The remainder of this book will be devoted to the modem ideas of bonding in several important classes of molecules. The emphasis will be on the molecular-orbital theory, with comparisons made from time to time to the valence-bond theory. Of the many scientists involved in the development of these theories, the names of R. S. Mulliken (molecular-orbital theory) and Linus Pauling (valence-bond theory) are particularly outstanding. 

This increased-valence description of electron conduction combines features of both the delocalized molecular orbital and the Pauling valence-bond and theories. The simplest increased-valence theory need use only the 2s orbitals for bonding (cf the simplest form of delocalized molecular orbital theory), and it uses localized bonds as does the valence-bond theory. 

The increased-valence theory represents a natural extension of the more familiar Lewis-Pauling valence-bond theory. Therefore an understanding of it may be useful for all chemists who have an interest in qualitative valence-bond descriptions of electronic structure. It will be shown that all Lewis-type valence-bond structures with lone-pairs of electrons can be stabilized easily via one-electron delocalizations from doubly-occupied atomic orbitals into diatomic bonding molecular orbitals when the relevant atomic orbitals overlap, as is shown here for the two sets of oxygen n electrons of N2O. 

Very recently, Singleton has suggested a new way of calculating isotope effects illustrated by the bromonium ion [61]. This method could possibly also be used for tautomeric systems. Another new approach is the multicomponent molecular orbital method for direct treatment of nuclear quantum effects [62]. The basic idea is to incorporate the nuclear wave function and in particular the proton wave function directly into the electronic structure calculation. This approach has great potential but has so far been tested only for secondary isotope effects on chemical shifts [63]. The geometric isotope effect has also been looked into based on Pauling valence-bond orders [20]. 

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