Crystal symmetries molecular packing

Order and dense packing are relative in tire context of tliese systems and depend on tire point of view. Usually tire tenn order is used in connection witli translational symmetry in molecular stmctures, i.e. in a two-dimensional monolayer witli a crystal stmcture. Dense packing in organic layers is connected witli tire density of crystalline polyetliylene. 

Considerations of complementarity in molecular packing culminated in the works of Kitaigorodskii. His most important contribution was the prediction that three-dimensional space groups of lower symmetry should be much more frequent than those of higher symmetry among crystal structures. This was a prediction at a time when few crystal structures had been determined experimentally. 

The macrocyclic phthalocyanine ligand will form a complex Pt(phthalocyanine).1106 The crystal structure shows two polymorphs present because of molecular packing.1107 The platinum is in a square planar coordination geometry with a mean Pt—N distance of 1.98 A. The complex can be partially oxidized with iodine to give conducting mixed valence solids.1108 Eighteen fundamental and overtone combination bands are observed in the resonance Raman spectrum of platinum phthalocyanine, and from this data the symmetry of the excited singlets are found to be Dy.. Qlv or D2.1109... 

Fig. 11.2 A view of molecular packing in the Ni(NCS)2(4-methylpyridine)4 layered structure [2] (host molecules shown in the capped sticks mode, hydrogen atoms are omitted for the sake of clarity). Guest azulene molecules are shown in the space filling mode, the two layers of the guest non-related by crystal symmetry are distinguished by different colors...

Based on molecular packing calculations with and without symmetry constraints the lattice dimensions for RDX crystal have been reproduced to within 0.9% deviation relative to experimental results and with a very small translation and rotation (less than 1.1°) of the molecules inside the unit cell. Additionally, the lattice energy was found to be practically identical to the static lattice energy estimated based on the experimental enthalpy of sublimation (E AH S0M + 2RT). 

As molecular packing calculations involve just simple lattice energy minimizations another set of tests have focused on the finite temperature effects. For this purpose, Sorescu et al. [112] have performed isothermal-isobaric Monte Carlo and molecular dynamics simulations in the temperature range 4.2-325 K, at ambient pressure. It was found that the calculated crystal structures at 300 K were in outstanding agreement with experiment within 2% for lattice dimensions and almost no rotational and translational disorder of the molecules in the unit cell. Moreover, the space group symmetry was maintained throughout the simulations. Finally, the calculated expansion coefficients were determined to be in reasonable accord with experiment. 

Molecular packing in the crystal structure of e-oxygen the solid and open lines indicate covalent and weak bonds, respectively, (a) C-centered layer of (02)4 clusters viewed along the c axis (b) the same layer viewed along the b axis. Symmetry codes Ax, y, z B x, y, z Cx, y, z. 

The symmetry of the crystal structure is a direct consequence of dense packing. The densest packing is when each building element makes the maximum number of contacts in the structure. First, the packing of equal spheres in atomic and ionic systems will be discussed. Then molecular packing will be considered. Only characteristic features and examples will be dealt with here, following Kitaigorodskii [38]. ... 

As is obvious in Fig. 10, there are common features of molecular packing in photo-reactive crystals. In all the photopolymerizable crystals in Table 4, nearly planar molecules are piled up and displaced in the direction of the molecular longitudinal axis by about half a molecule to form a parallel plane-to-plane stack. The periodicity in the stack is about 7 A. The shortest intermolecular distance between the double bonds in photopolymerizable crystals is about 3.9 A (Table 4) and it is found between molecules related to the center of symmetry in the stack. The second shortest distance between molecules in different stacks is more than 5 A. Therefore, the double bonds in the stack react to form a cyclobutane ring consequently, polymer chains should grow in the direction of the stack. The crystal axis along the stack in each photopolymerizable crystal, i.e. the presumed chain-growth direction, is indicated by c) in Table 4. 

In spite of the close similarity of molecular geometry and the fact that the arsenic and ruthenium compounds crystallize with the same space group symmetry, the unit cell shapes are dissimilar and, moreover, the molecular packing is quite different. In FXeFAsF, the long dimensions of the formula units are all nearly parallel to each other, while in FXeFRuF, there are two orientations nearly perpendicular to each other. The molecular volumes differ by less than 3%, reflecting the... 

Fig. 5. The arrangement of the electron density in a tetragonal crystal of human serum albumin. Prominent features of the molecular packing arrangement are large (90 x 90 A) solvent channels (shown in white) that pass through the crystal parallel to the crystallographic c axis. The unit cell and symmetry operations parallel to the c axis are illustrated. Reproduced with permission from Carter et al. (1989) American Association for the Advancement of Science (AAAS).

The crystal and molecular structure of eight different complexes was established by X-ray analysis, indicating three types of disulfide arrangements in the crystal lattice. All crystals are built up from DGTD molecules packed along the twofold symmetry axes and solvent molecules located around the twofold... 

In the crystalline state, the site symmetry is in general lower than the symmetry of the free molecule. The preferred lattice structures of sulfur homocycles are of the orthorhombic and monoclinic crystal systems. The molecular packing arrangements of the soKd allotropes are quite different In orthorhombic Si2, for example, the asymmetric unit is given by one quarter... 

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