Local charge concentrations and partial localization of the Fermi hole

It is demonstrated through a study of the Fermi hole density that the local decrease in the potential resulting from the approach of each ligand to the central atom does result in a partial condensation of the pair density to yield 

The Fermi hole for the reference electron at a bonded maxima in the VSCC of the carbon atom has the appearance of the density of a directed sp hybrid orbital of valence bond theory or of the density of a localized bonding orbital of molecular orbital theory. Luken (1982, 1984) has also discussed and illustrated the properties of the Fermi hole and noted the similarity in appearance of the density of a Fermi hole to that for a corresponding localized molecular orbital. We emphasize here again that localized orbitals like the Fermi holes shown above for valence electrons are, in general, not sufficiently localized to separate regions of space to correspond to physically localized or distinct electron pairs. The fact that the Fermi hole resembles localized orbitals in systems where physical localization of pairs is not found further illustrates this point. 

It should be borne in mind that the resemblance of a Fermi hole density to that of a localized valence orbital is obtained only when the reference electron is placed in the neighbourhood of a local maximum in the VSCC. The Fermi hole and hence the density of the reference electron are much more delocalized for general positions throughout the valence region (see Fig. E7.4(f)). Localized molecular orbitals thus overemphasize electron localiz-ability and do not provide true representations of the extent to which electrons are spatially localized. 

There is partial localization of the valence density in methane. The condensation into four partially localized pairs of electrons arranged along four tetrahedral axes is a result of the combined effects of the ligand field and the Pauli exclusion principle described above. Most important is that this partial localization of the pair density is reflected in the properties of the VSCC of the carbon atom which undergoes a corresponding condensation into four local concentrations of electronic charge. These properties of the pair density are not just the result of the tetrahedral symmetry of the ligand field in methane because, as we will now see, the Fermi hole exhibits the same behaviour in the ammonia molecule. 

VSEPR model maximize the interpair separations or, equivalently, maximize the separations between the local maxima in the VSCC of the central atom. 

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Local charge concentrations and partial localization of the Fermi hole... 

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