Tables for
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 9.7, p. 902

Section 9.7.3. Empirical space-group frequencies

A. J. C. Wilson,a V. L. Karenb and A. Mighellb

aSt John's College, Cambridge CB2 1TP, England, and bNIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

9.7.3. Empirical space-group frequencies

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Empirical space-group frequencies are based on two major collections of structural data for organic substances, in Cambridge and Moscow, respectively.

The Cambridge Structural Database (Allen et al., 1991[link]) contains assignments of space groups for a variety of different types of organic compounds. The file can be computer searched in many ways; it is easy, for example, to trace all structures having a particular space group, or those having a particular space group and a particular number of formula units per unit cell. For the present purpose, a selection has to be made, omitting space groups not substantiated by a full structure determination or dubious because of disorder in the crystal. The packing considerations discussed in previous paragraphs would not apply to crystals in which the intermolecular binding was ionic rather than van der Waals or the like, so that space groups of ionic structures (for example salts of organic acids) are also rejected. Unfortunately, as it is implemented at present (early 1995), it is not possible to search for structures with molecules occupying general positions or specified special positions, so that, in particular, the frequency data of Wilson (1993d[link]) are inflated by the inability to distinguish between single occupation of a general position and multiple occupation of special positions.

The file compiled by V. A. Belsky at the L. Ya. Karpov Institute of Physical Chemistry in Moscow is the source of the data used by Belsky, Zorkaya & Zorky (1995[link]). This file differs in objective from the Cambridge file; the latter includes all reasonably established organic structures short of proteins and high polymers, whereas the former concentrates on structures containing only a single type of molecule (`homomolecular structures'). It thus contains appreciably fewer entries than the Cambridge file, even if structures of the types mentioned in the previous paragraph are excluded from the latter. The Moscow file is, of course, the primary source for the data of Belsky, Zorkaya & Zorky (1995[link]), in which the occupation of general and special positions is explicitly presented.


Allen, F. H., Davies, J. E., Galloy, J. J., Johnson, O., Kennard, O., Macrae, C. F., Mitchell, E. M., Smith, J. M. & Watson, D. G. (1991). The development of versions 3 and 4 of the Cambridge Structural Database system. J. Chem. Inf. Comput. Sci. 31, 187–204.
Belsky, V. K., Zorkaya, O. N. & Zorky, P. M. (1995). Structural classes and space groups of organic homomolecular crystals: new statistical data. Acta Cryst. A51, 473–481.
Wilson, A. J. C. (1993d). Space groups rare for organic structures. III. Symmorphism and inherent molecular symmetry. Acta Cryst. A49, 795–806.

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