Arrays with Local Centers of Symmetry in Space Groups Pca2₁ and Pna2₁

Abstract

Of the several hundred structures in the Cambridge Structural Database [version 4.6 (1992), Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge, England] having space groups Pca21 or Pna21 and more than one molecule in the asymmetric unit (Z > 4), approximately three-quarters contain local centers of symmetry. These local centers, which are not crystallographic centers, occur predominantly near x = 1\over8, y = 1\over4 in Pca21 or near x = 1\over8, y = 0 in Pna21; this also holds for the limited number of examples we have examined of pseudo-centrosymmetric molecules with Z = 4. Local centers at these points create unusual correlations between corresponding atoms in the two molecules.

Distribution of molecular pairs in Z′ = 2 structures

“…24 and 25) show clearly that there is clustering in the distribution of pair centroids in Z 0 = 2 structures. There is some evidence for the annular distribution of pair centroids, like that observed for Z 0 = 1 structures; this is particularly evident from the apparent curvature of the occupied positions close to (x, y) = ( Again, comparison of these results with those of Marsh et al (1998) shows that the distributions are similar, but with a larger spread of centroid positions in this study resulting from the presence of local operators other than inversion centres.…”

“…These results make for an interesting comparison with the findings of Marsh et al (1998); the distributions are very similar in the xy projection, although here we observe many more structures where the two molecules are centred along a line of x = 1 4 , rather than being restricted to the point (x, y) = (0, 1 4 ). We suggest that this is because the independent molecules are related by operators other than centres of inversion.…”

“…Note that it is possible to locate the pair centroids within the range 0-1 4 by applying origin shifts to a site of identical symmetry within the space group (Marsh et al, 1998); however, keeping the display within the range 0- The histograms for the Z 0 = 2 structures show that the distributions are largely invariant for the different choices of centroid (Fig. 3).…”

“…The positions of local (non-crystallographic) centres of inversion in space groups Pca2 1 and Pna2 1 have also been investigated for structures with Z 0 = 2 (Marsh et al, 1998). In this study, we have investigated the arrangement of pairs of molecules in the most common space groups for structures with Z 0 = 2, and thus there is overlap with those two papers: with the methodology of the former and with the results of the latter.…”

(Chloromethyl)pentacarbonylmanganese(I): a crystal structure with a non-crystallographic centre of symmetry

“…This is a noncrystallographic or local centre of symmetry, but it is not unusual to find such local centres. For example Marsh et al have found several structures, having space group Pca2 1 or Pna2 1 with more than one molecule in the asymmetric unit, containing local centres of symmetry [17], and Dalhus and Henrik report another example, also in Pca2 1 [18]. A situation similar to that observed for 1 was reported for 2-methylpyrazine [19] which crystallizes in the tetragonal space group I-4 with two independent molecules in the asymmetric unit.…”