Fragment deformation density

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.)... 

If we are particularly interested in the nature of the bonding between the fragments of a molecular complex, a fragment deformation density may be calculated by subtracting fragment densities from the total distribution. In the case of a transition metal complex, the fragment may be a metal atom plus ligand, or just the density... 

Olovsson and coworkers have pointed out that the superposition of the electron density of adjacent molecules in the experimental deformation density may lead to modification of the contours in the lone-pair region of the water molecules (Fernandes et al. 1990, McIntyre et al. 1990). To avoid this complication, it is preferable to partition the crystal density through the multipole analysis, after which comparisons can be based on individual molecule or fragment densities. 

A more realistic outline of a molecular surface can be defined in terms of the outer contours of electron density according to Bader [173]. To avoid excessive computation the densities of large molecules may be built up from previously calculated densities of smaller fragments [213]. The most obvious approach, to approximate molecular density by the sum of atomic densities over the promolecule has also been explored [214]. This approach works well since the deformation density associated with bond formation is small compared to the total density [215]. The total density may therefore be represented by a sum over spherically averaged atomic densities, p(r) = Pa(t)-... 

The first column in Figure 4.17 shows the deformation densities Ap, which are coupled to the donor-acceptor interactions between the most important pairs of occupied and vacant fragment orbitals that are given in the last two columns. The color coding for the charge flow of Ap is red blue. The plots of the density deformations and the orbitals come from the calculations of Si2(NHC =)2. The... 

Bis(dithiocarbamate) complexes have been studied by a variety of other techniques including XPS (523,550,553-555,1490) polarized optical spectra (1491) the electron spin-echo envelope modulation technique (1492) deformation density maps (510) extended Hilckel (1492), quantum mechanical (554), NDDO (1493), and DFT (510) calculations IR spectroscopy (517) and a normal coordinate analysis using Gibov s fragmentation procedure (1494). 

FIG. 20-80 Heckel profiles of the unloaded relative compact density for (1) a material densifying by pure plastic deformation, and (2) a material densifying with contributions from brittle fragmentation and particle rearrangement. 

The approximate transferability of fuzzy fragment density matrices, and the associated technical, computational aspects of the idempotency constraints of assembled density matrices, as well as the conditions for adjustability and additivity of fragment density matrices are discussed in Section 4, whereas in Section 5, an algorithm for small deformations of electron densities are reviewed. The Summary in Section 6 is followed by an extensive list of relevant references. 

Small deformations of electron densities, adjustability and additivity conditions for fragment density matrices... 

The macromolecular density matrix built from such displaced local fragment density matrices does not necessarily fulfill the idempotency condition that is one condition involved in charge conservation. It is possible, however, to ensure idempotency for a macromolecular density matrix subject to small deformations of the nuclear arrangements by a relatively simple algorithm, based on the Lowdin transform-inverse Lowdin transform technique. 

They are, in fact, two possible perturbative approaches. In the first approach, one considers two (or any number) reagents A and B as a single system where A and B are two fragments in interactions. The total density is p(r ) = p4(r/) I p/ (r/) [24]. Displacement of A relative to B is an internal mechanical deformation of the complete system it is related to response function of A I B. For instance, a small displacement U/f of an atom K of B will modify the force on the other atoms by... 

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