Electronegativity Geometric Equalization Principle

Alternatively, one may consider the so called geometrical mean of atoms-in-molecule electronegativity, namely through the relationships (Parr Bartolotti, 1982) 

Together, Eqs. (3.221) and (3.222) can equivalently be written like a geometric mean 

Because of the energy conservation reasons, a similar relation has to be obeyed also by the isolated atoms 

By equating the right hand sides of last two equations the geometrieal general form for the dependence of the atomic electronegativity in molecule results 

In these conditions, applying the equalization principle between the atomic electronegativities in molecules, Z a) X[b) transferred charge that promotes the binding process of the AB molecule casts as 

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Parr RG, Bartolotti L (1982) On the geometric mean principle for electronegativity equalization. J Am Chem Soc 104 3801-3803... 

Datta, D. Geometric Mean Principle for Hardness Eualization A Corollary of Sanderson s Geometric Mean Principle of Electronegativity Equalization. J. Phys. Chem., 1986,90,4216-4217. 

Yang, W. Lee, C. Ghosh, S. K. Molecular Softness as the Average of Atomic Softnesses Companion Principle to the Geometric Mean Principle for Electronegativity Equalization. / Phys. Chem., 1985, 89, 5412-5414. 

Zeolites are composed of various atoms of different electronegativity (refer to Table 2.8). However, their intermediate electronegativity (i.e., geometric mean of the component atoms after redistribution of the electrons in the compound) is reported to be established as demonstrated hy Sanderson s principle of electronegativity equalization (i.e., when two or more atoms initially different in electronegativity combine chemically, they become adjusted to flie same electronegativity within the compound). The intermediate electronegativity can be determined for a compound, Qv, by Eq. (2.1) [59] ... 

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