Pauling bond strength

Figure 5.35 displays a schematic energy-level diagram for each stationary species along the proton-transfer reaction coordinate. Although Pauling bond strengths... 

All oxygen-based polyhedra with the same Pauling bond strength (cationic charge/coordination number see section 1.10.3) have the same mean polyhedral linear expansion. 

C = anion charge, z = cation charge, v = cation coordination number, 5 = (Pauling) bond strength.]... 

FIGURE 2. A plot of the average bond lengths, , of the XOn coordination polyhedra observed for silicate and oxide crystals vs the Pauling bond strength, s, of the X—O bond. The Roman numeral superscript denotes the coordination number of the X-cation... 

A generally applicable relationship has been developed by Brown and Wu for relating Pauling bond strengths to bond lengths for metal-oxygen bonds ... 

Sveqensky and Sahai [62] found the following correlations between ApK and v Pauling bond 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. 

Only a few attempts have been made to use computational methods for the silanol acidities. Sverjensky and Sahai have developed a method for estimating surface protonation equilibrium constants from the surface dielectric constant and an average Pauling bond strength. Rustad and coworkers [319] have used molecular dynamics methods to estimate the pK, for the reaction >SiOH — >SiO + H+ at 8.5. Tossell [320] used several quantum chemical levels of theory to establish correlations between calculated gas-phase AE and AH values and experimental aqueous solution pK s. Liu et al. [308] have employed both experimental and computation methods to study the gas-pha.se properties of organic silanols. ... 

Pauling bond strength and bond length variations... 

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. 

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