Polar Bond, Effective Charges of Atoms

The effective charges of atoms in crystals, rather than molecules, can be determined by Szigeti s spectroscopic method [55], which is also described in details in Chap. 11, using the formula 

Another spectroscopic method of measuring bond polarity (or ionicity) f in solids was developed by Phillips and Van Vechten (PVV) [64-67], using the equation 

Most structural methods see either the position of the atomic nucleus (neutron diffraction, NMR spectroscopy), or the atomic center of mass (optical and microwave 

Probably, 99.99 % of all X-ray structure determinations to-date have been done on this approximation. Of course, the real distribution of the electron density in an actual crystal/molecule is different from such model (often called pro-crystal/pro-molecule) its topology can be best understood within the framework of the AIM theory, developed by Bader [8]. Electron density is concentrated between atoms which are linked by a covalent bond, and is depleted between atoms which participate in closed-shell interactions (ionic or van der Waals). A good quantitative measure of such effects is the Laplacian of the electron density (V p), equal to the sum of its principal curvatures (second derivatives) at a given point  

According to the Virial Theorem, the Laplacian of pe is related to the densities of kinetic (G) and potential (V) energies of the electrons, 

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