Hybrid atom deformation density

Topological analysis of the total density has a considerable advantage over the use of the deformation densities in that it is reference-density independent. There is no need to define hybridized atoms to analyze the nature of covalent bonding, and the ambiguity when using the standard deformation density, noted above in the discussion on propellanes, does not occur. 

Schneider, Hansen, and Kretschmer (SHK) (1981) have measured the 19 reflections with sin 0/A < 0.7 eA 3 with 0.03 A y-radiation. Deformation densities based on these reflections show a small accumulation of charge of height 0.19 eA 3 at 1/4 1/4 0 and equivalent positions, which is between nearest neighbors located along the [110] directions, as well as an accumulation of similar height, but somewhat more extended, in the voids between the atoms at 1/4 1/4 1/2. This seems fully compatible with a hybrid bonding model. 

To negate this observation, the conviction that covalent interaction mandates an excess bonding density in all cases, prompted the formulation of aspherical atomic densities to reflect the requirements of bonding theory. By multipole expansion of atomic densities, based on real spherical harmonics, in line with traditional models of orbital hybridization, the mandated deformation densities are retrieved. Increased flexibility of the model by the introduction of scaling parameters further ensures the elimination of any discrepancies with the theory. However, it is debatable whether this exercise proofs anything other than the power of well-chosen parameters to improve the fit between incompatible data sets. 

In terms of hybrid-bond theory it appears reasonable that the deformation density could be negative in some bonds. When a p-block atom with n valence electrons forms a bond, the valence shell is polarized into a tetrahedral distribution with n/4 electrons concentrated around each potential... 

The electron density of L-cystine has been accurately measured. The deformation density distribution and AIM analysis clearly reveal disulfide bridge characteristics and sulfur lone pair electron regions in accord with high-level ab initio calculations. In terms of p s topology it is now known that SS bonds are weak single covalent bonds. The almost tetrahedral distribution of the VSCC of the sulfur atom is consistent with sp hybridization. 

The rare-earth atoms in compounds contribute three (5d 6s ) valence electrons per atom which hybridize into bands. Because the 5d-like bands are quite narrow their contribution to the elastic constants should also be considered. This will be done in sect. 3. It is sufficient to mention here that these deformation potential effects have little or no effect on c (T) for the system discussed here, as simple density of states considerations will show (see sect. 3.2). 

More informative deformation maps could be obtained by subtracting a correctly preoriented independent atom, or a reference atom in a corresponding state of hybridization. Features of one particular bond in a molecule can be most highlighted by subtracting the (calculated by MO methods) electron densities of the two fragments, differing from the molecule by the absence of only this bond. 

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