Deformation density maps

Static deformation density maps can be compared directly with theoretical deformation densities. For tetrafluoroterephthalonitrile (l,4-dicyano-2,3,5,6-tetra-fluorobenzene) (Fig. 5.13), a comparison has been made between the results of a density-functional calculation (see chapter 9 for a discussion of the density-functional method), and a model density based on 98 K data with a resolution of (sin 0//)max = 1.15 A -1 (Hirshfeld 1992). The only significant discrepancy is in the region of the lone pairs of the fluorine and nitrogen atoms, where the model functions are clearly inadequate to represent the very sharp features of the density distribution. 

The distinction between the two states is readily illustrated in a deformation density section perpendicular to the porphyrin plane through the iron atom. Because of the transfer of an electron into the d2z orbital in going from 3EgA, and to 3A2g, the former configuration shows a deficiency and the latter an excess of density above and below the nitrogen atom. This is confirmed by theoretical deformation density maps (Fig. 10.10) (Rohmer 1985). The experimental map for FePc shows the deficiency along the z axis, as expected from the 4-orbital populations listed in Table 10.10. 

Metal-metal bonding in transition metal complexes of low nuclearity (i.e., with only a few metal atoms) tends to be more directed and therefore stronger than the bonding in metals discussed in chapter 11. Accordingly, the metal-metal bonds in transition metal complexes are often localized and considerably shorter than those in most extended solids. Charge accumulations are frequently observed in metal-metal bonding regions of deformation density maps. 

The study of the nature of the Si—O bond through analysis of its charge density is based on net ionic charges, heights of peaks in atom deformation density maps, and, more recently, topological analysis of the total charge density. 

This conclusion is confirmed by both experimental and theoretical deformation density maps. The experimental maps show a positive peak of height... 

To examine the reliability of X-ray charge densities at a time of rapid development of new methods, the Commission on Charge, Spin and Momentum Densities of the lUCr organized a project under which a single substance, a-oxalic acid dihydrate, was studied in a number of laboratories using X-ray, neutron, and theoretical methods. The report by Coppens on the study, published in 1984, established unequivocally the qualitative reproducibility of chemically significant features in deformation density maps, which had not been generally accepted. 

Irngartinger et al. 1977), and the hydro-bis(squarate) anion (Lin et al. 1994). Even in the deformation density maps of the five-membered pyrrole rings in transition metal tetraphenyl porphyrins (chapter 10), bond bending is visible. 

The redistribution of the valence electron density due to chemical bonding may be obtained from summing the multipole populations or Fourier transforming appropriately calculated structure factors, having removed the contribution from neutral spherical atoms, to produce a so-called deformation density map [2], This function was introduced by Roux et al. [23] and has been widely used since then. The deformation electron density represents the difference between the electron density of the system, p(r), and the electron... 

Fig. 3. Charge density ill diisocyanomethane deformation density maps in die molecular plane (a) experimental (b) theoretical (contours at 0.1 t A-3). The non-bonded regions of C(2) and C(3) are more depleted in (a) with the density migrating to the inside of the molecule. The corresponding Laplacians (range - 20 to 250 eA"5) are shown in (c) and (d), respectively (reproduced with permission from Koritsanszky et al.

Fig. 7. Polymorphic forms of o-ethoxy cinnamic acid molecular diagrams and deformation density maps close to the mean plane of the molecules in the a- and the y terms (contours at 0.12 eA 3). Subtle differences in the cinnamoyl bond and the hydrogen bond region are noticeable. The Laplacians of the intermolecular hydrogen bonds in the acid dimer are shown in the relief maps along side (range -250 to 250 eA 5).

Once the multipole analysis of the X-ray data is done, it provides an analytical description of the electron density that can be used to calculate electrostatic properties (static model density, topology of the density, dipole moments, electrostatic potential, net charges, d orbital populations, etc.). It also allows the calculation of accurate structure factors phases which enables the calculation of experimental dynamic deformation density maps [16] ... 

The distinction between hydrogen-bond donors, i.e., N-H, and nondonors, i.e., C-H, is often not apparent in deformation density maps. This distinction appears much more clearly on the electrostatic potential maps, such as illustrated in Fig. 3.4 [218]. Such maps may therefore provide a more effective means of quantitatively analyzing the electronic differences between the different donor-acceptor hydrogen-bond combinations which is manifested by the different mean bond lengths described in Part IB, Chapter 7 [222- 226]. It has been suggested that hydrogen-bond strengths can be at least qualitatively compared from the values of the electrostatic potentials at fixed distances from the donor and acceptor atoms, i.e., 2.0 A [227]. 

Deformation density maps have been used to examine the effects of hydrogen bonding on the electron distribution in molecules. In this method, the deformation density (or electrostatic potential) measured experimentally for the hydrogen-bonded molecule in the crystal is compared with that calculated theoretically for the isolated molecule. Since both the experiment and theory are concerned with small differences between large quantities, very high precision is necessary in both. In the case of the experiment, this requires very accurate diffraction intensity measurements at low temperature with good thermal motion corrections. In the case of theory, it requires a high level of ab-initio molecular orbital approximation, as discussed in Chapter 4. 

Hydrogen bonding must have an effect on the electron density distribution of a molecule. In principle, this should be observed in the deformation density distributions discussed in Chapter 3. There are, in fact, two methods available. One is purely theoretical, in which the calculated deformation density for a hydrogen-bond dimer or trimer is compared with that of the isolated molecule. The other method compares the experimental deformation density of a hydrogen-bonded molecule in a crystal structure with the theoretical deformation density of the isolated molecule. Formamide has been studied by both methods [298, 380], and there appear to be significant differences in the results which are not well accounted for. Theoretical difference (dimer vs. monomer) deformation density maps have been calculated for the water dimer and the formaldehyde-water complex [312]. When those for the water dimer are decomposed into the components described in Chapter 4, a small increase in the charges on the atoms in the O-H -O bond due to the charge-transfer component is predicted [312]. 

Fig. 5.35. Electron-density distributions in borates — deformation density maps for corner-sharing BO, planar triangular units (a) calculated density map for planar H4B,0, (b) experimental density map for LiBOj (contour interval 0.1 electrons A dashed contour is zero negative contours are dotted) (after Zang et al., 1985 reproduced with the publisher s permission).

Fig. 7.8. Calculated (using ab initio SCF Hartree-Rock-Roothaan MO methods) deformation density maps for various Si202 ring-containing molecules (a) H4Si206 in the plane of the Si-O-Si-0 ring (b) H6Si20, in the Si-O-Si plane. The contour interval is 0.05 e A with negative contours dashed and the zero contour dotted (after O Keeffe and Gibbs, 1985 reproduced with the publisher s permission).

The electron density distribution in the Se02Cl anion of [ (CH3)4N ][Se02Cl ] has been studied by an X-X deformation density analysis using high-angle diffraction data at 120 K (405, 406). The deformation density maps clearly reveal the presence of lone-pair (E) density (maximum of 0.40 0.04 e x at a distance of ca. 0.75 A from Se) consistent with model predictions for an approximately i )-tetrahedral Se02ClE arrangement with additional tt density in the Se-0 bonds and with a rather polar Se-Cl bond. 

Deformation density maps these types of maps are calculated when intensity data have been measured to very high resolution (high values of sm0/X). Peaks and valleys in such maps indicate the deformation of the true electron density from the model in which an ellipsoidal peak is placed at each atomic position. The picture of such deformations provided by these maps may contain some evidence of bonding electrons or of lone-pair electrons, that is, the true electron density at very high resolution. The map, is, however, really only the difference between the model and the map from the diffraction data. 

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