Deformation density standard

Figure 6.7 shows the calculated electron density distributions for the H2 and N2 molecules in their equilibrium geometry together with the standard deformation densities. There is clearly a buildup of electron density in the bonding region in both molecules. In the N2 molecule there is also an increase in the electron density in the lone pair region and a de-... 

Figure 6.8 Deformation densities for the F2 molecule, (a) Standard deformation density. Note that there is no charge buildup-in the bonding region between the nuclei, (b) Modified deformation density molecular density minus the density of atoms in the (ls)2(2s)2(2px)2(2py)2( 2pe)1 reference state showing a buildup of charge in the bonding region. (Reproduced with permission from P. Coppers [1997].)...

Figure 6.9 (a) Standard deformation density of tetrafluoroterephthalonitrile in the molecular plane. Contour interval is 0.1 e A-3, terminated at 1.5 e A 3. (b) Molecular diagram with a box around the fragment shown in the deformation map (a). (Reproduced with permission from F. L. Hirshfeld, Acta Crystallogr., B40, 613, 1984.)... 

A common reference density, first used by Roux and Daudel (1955), is the superposition of spherical ground-state atoms, centered at the nuclear positions. It is referred to as the promolecule density, or simply the promolecule, as it represents the ensemble of randomly oriented, independent atoms prior to interatomic bonding. It is a hypothetical entity that violates the Pauli exclusion principle. Nevertheless, the promolecule is electrostatically binding if only the electrostatic interactions would exist, the promolecule would be stable (Hirshfeld and Rzotkiewicz 1974). The difference density calculated with the promolecule reference state is commonly called the deformation density, or the standard deformation density. It is the difference between the total density and the density corresponding to the sum of the spherical ground-state atoms located at the positions R... 

An example of a standard deformation density, for oxalic acid dihydrate, obtained at limited resolution using parameters from a high-order refinement, is shown in Fig. 5.2. Oxalic acid dihydrate has been the subject of an extensive study aimed at calibrating the techniques used in different laboratories. The map shows... 

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. 

A complex with an Fe—Fe bond for which the electron density is available is bis(dicarbonyl-7i-cyclopentadienyl iron), [C5H5Fe(CO)2]2 (Fig. 10.13) (Mitschler et al. 1978). The 18-electron rule again requires only a single bond to explain the observed diamagnetism. The combined X-ray and neutron study indicates a complete absence of density accumulation in the metal-metal bonding region of the standard deformation density, in agreement with an SCF theoretical density,... 

---