How to avoid unnecessarily low symmetry in crystal structure determinations

Abstract

A check of recent volumes of Acta Crystallographica and Crystal Structure Communications shows that about 3% of all recently published crystal structures were described with too low symmetry. Three categories of error are recognized: (1) both Laue class and crystal system are wrong; (2) only the Laue class is wrong; (3) Laue class and crystal system are correct, but an inversion center is missing. Category (1) cases can be most easily diagnosed by calculating the reduced cell and its Niggli matrix. Category (3) cases are most easily recognized during full-matrix leastsquares refinement from singularities, high correlations between parameters and poor convergence. The omission of an inversion center will not result in a singular matrix when all atoms in the centrosymmetric cell are in special positions which become general positions in the noncentrosymmetric cell. Once the refinement is completed structures with a missing inversion center can be recognized by unusually high e.s.d.'s, especially for the highly correlated parameters, and by large distortions of observed bond * Present address: Mineralogisches Institut, Universitiit Wiirzburg, Am Hubland, D-8700 Wiirzburg, Federal Republic of Germany. distances and angles from accepted values. Such distortions often show up as splitting of the centrosymmetrically related atomic positions into positions whose average is close to the true centrosymmetric positions. A mechanical application of the R-ratio test should be avoided; it can easily lead to wrong conclusions. Proof of higher symmetry must be obtained from the diffraction data. The presence of more than one effective formula per asymmetric unit should always be reason to check for higher symmetry. Cases in all three categories can be checked for the occurrence of higher symmetry by searching for regularities in bond lengths and angles or in the positional coordinates of the atoms. The most systematic way for such searches is the simple, but powerful method of topological analysis of crystal structures. For six structures which previously had been described with too low symmetry higher-symmetry descriptions are provided.

Space-group frequencies of proteins and of organic compounds with more than one formula unit in the asymmetric unit

“…metry. Several crystal structure determinations had been performed with space groups of incorrectly low symmetry (Baur & Tillmanns, 1986) and there are instances of wrong space-group assignments which lead to more than one molecule in the asymmetric unit of the reported low-symmetry space group. For example, N-methylacetamide hemihydrochloride [originally described as C2, Z = 8; Jaber, Guilhem & Loiseleur (1983)] is correctly described as orthorhombic, Fdd2, with one molecule in the asymmetric…”

“…Space-group frequencies for protein crystal structures from the Protein Data Bank, Brookhaven, have been calculated and are compared with those of chiral small molecules. (Baur & Tillmanns, 1986;Marsh, 1986 We report here the frequency for each of the 230 Ima2 46 1 space groups for all compounds which have more than one formula unit in the asymmetric unit. The analysis was made on the Cambridge Structural Database (CSD: release of 1987; see e.g.…”

Rietveld Refinement of the Kaolinite Structure at 1.5 K

“…However, with a distance least-squares (DLS) structure of kaolinite as a starting model (Bish and Von Dreele, 1989), the resulting refined structure was crystal-chemically reasonable and the weighted profile residuals were significantly lower (18.0% for the P1 starting model vs. t2.3% with the DLS starting model). Baur and Tillmanns (1986) suggested that these aspects are characteristic of refinements conducted using unnecessarily low symmetry. Thus, the refinement and partial structure solution of kaolinite were conducted using space group C1; there is no substantive evidence for lower space group symmetry.…”

Single-crystal X-ray diffraction and variable-temperature MAS NMR study on the heterogeneous network clathrate Na[N(CH3)4]7[Si8O20].54H2O

“…Baur & Tillmanns, 1986;Marsh, 1986) we believe that the structure is better described, at 153 K also, in the higher-symmetry space group R3 with disordered (instead of ordered) NMeg cations, at least as long as H atoms are not being considered and special attention is paid to the weak reflections. Suzuki, Shin, Hayamizu & Yamamoto, 1985;Derouane & Nagy, 1987).…”