Static deformation density

Figure 3. Static deformation density in Si-O-Si bridge planes Si,-0,-Si2 and Si,-O,o-Sij. Contours as in Figure 1.

For the 2-cyanoguanidine molecule6 the static deformation density has been mapped by least-square refinement against low-temperature X-ray data in order to explain the fact that the C—N bonds around the C atom are almost identical and the fact that a large negative charge (—0.2 e) is on the N(3) atom. Hence one must take all the resonance forms (2) into consideration. 

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. 

Fig. 9. Polymorphism in p-nitrophenol static deformation density in the plane of the phenyl rings for the a- and the (3-forms (contours at 0.1 eA-3). Intramolecular and lone-pair regions exhibit many differences. Relief maps of the Laplacians in the inteimolecular hydrogen bond region are also shown (range -250 to 250 eA-5). In the a-fonn, H(l) bonds not only with 0(3) but also with 0(2) and N(l) of the neighboring nitro group (reproduced with permission from Kulkami et al. [61]).

Fig. 15. (a) Intramolecular hydrogen bonds in urea crystal with displacement ellipsoids at 50% probability, (b) Static deformation density obtained from the multipolar analysis of the experimental data corrected for the thermal diffuse scattering. Theoretical deformation density obtained using (c) the Hartree-Fock method (d) the DFT method by generalized gradient approximation (contours at 0.0675 eA-3) (reproduced with permission from Zavodnik et al. [69]). 

Figure 3. ORTEP view (a) and theoretical static deformation density of H3PO4 in the 0=P-0(H) plane (b). Contours interval 0.1 e A 3 (—) positive contours, ( ) negative contours zero contour omitted.

Having secured a set of n values for phosphorus, the pseudoatom model was fitted to the four simulated data sets to test the effectiveness of the pseudoatoms model s formal deconvolution of multipolar valence density features from thermal vibrations smearing. Results are illustrated in Figure 4 as maps of the model static deformation densities ... 

Figure 4. Model static deformation densities of H3PO4 in the 0=P-0(H) plane from simulated structure factors with U = 0 (a), at 75K (b), at 150K (c), at 300K (d). Contours as in Figure 3.

Figures 6 and 7 give respectively the experimental and theoretical static deformation density in the planes of the C3=C4 double bond and of one of the two peptide links, calculated with the two basis sets, as well as their difference.

Figure 6. Static deformation densities in the plane defined by the C3=C4 double bond in AcPhe Experiment (a), basis set I (b), basis set II (c), (c) - (b) = (d). (continued)...

Hirshfeld, F. L. The static deformation density of tetrafiuoroterephthalonitrile (TFT) from the Ziirich X-ray data at 98 K. Acta Cryst. B40, 484-492 (1984). 

Kg. 4. Static deformation density maps of tetrafluoroterephthalodinitrile in the molecular plane (from [28]). The upper map is unconstrained, the lower one is constrained to satisfy the Hellmann-Feynman theorem (see text). Note the shght dipolar deformation at the atomic positions in the constrained map. 

By adding the static deformation density to the pro-molecule density one obtains the experimental charge density of the molecule in the crystal. In recent years, a fruitful mutual interaction has been established between Bader s interpretation of bonding in terms of the Laplacian of the electron density at its topological critical points [29] and experimental static charge density distributions [26]. To avoid complications due to residual vibrational smearing, the crystal data must refer to the lowest practically attainable temperature. 

Fig. 7 Reactive surface (V p(r) = 0 eA around the boron atoms and the static deformation density at the level of 0.2 eA" for 1 upper row) and 2 bottom row)...

Fig. 18 Dark-green crystals of (TipSi)g (7, Tip=2,4,6-triisopropylphenyl) (a), Laplacian distribution around the silicon atoms of 7 at an isosurface level of — 1.9 eA (b), bond paths in 7 with the BCPs as red spheres and the RCP as yellow spheres (c), static deformation density contour plot of 7, contour lines are drawn at 0.015,0.03,... eA interval level blue positive red negative (d)...

From a single crystal X-ray diffraction study with the data set refined by a multipole expansion model to R = 0.0054 and R = 0.0056, electron density maps have been obtained. The static deformation density distribution resulting from the multipole refinement is depicted in Fig. 4-25, p. 50 [10, 11]. 

Fig. 4-25. Static deformation density distribution for 3-BN in the (110) plane. Contours at 0.05 electrons/A (negative contours are dashed) [10].

Figure 3.3 3D static deformation density maps from experimental and theoretical charge density calculations for C1---C1 intermolecular interactions of the compounds (a) VCLl, (b) VCL2 and (c) VCL3. Blue and red colors represent positive and negative values, respeetively. The Ap(r) iso-surfaces are drawn at 0.01 eA. ... 

Fig. 2.27 a Laplacian maps and b 3D static deformation density maps for C1---F intEamolecular interactions in (i) 4-fluorobenzoyl chloride and (ii) 2,3-difluoiobenzoyl chloride. Contours are drawn at logarithmic intervals in V p (r), eA . Blue lines indicate positive contours, and red lines indicate negative contours. Ap(r) isosurfaces are drawn at 0.1 e A". Reprinted with the permission from Ref. [124]. Copyright 2012 American Chemical Society... 

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