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

International Tables for Crystallography (2006). Vol. C, ch. 9.7, p. 904

## Section 9.7.5. Structural classes

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

### 9.7.5. Structural classes

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As developed so far (Belsky, Zorkaya & Zorky, 1995), structural classes relate primarily to homomolecular structures – structures in which all molecules are the same. Nevertheless, they are important in a study of the space-group distribution of molecular organic structures, as structures belonging to the same space-group type but to different structural classes are found to have very different frequencies. The germ of the idea is implicit in Kitajgorodskij's subdivision of his four categories by molecular symmetry.

In its general form, the symbol of a structural class has the form where is the standard space-group symbol, n is the number of molecules in the unit cell, are the symbols of the point-group symmetries of the Wyckoff positions occupied, and are the numbers of occupied Wyckoff positions of those symmetries. An example will make this clearer. There is a structural class This indicates that the space group is and that there are 32 molecules in the unit cell occupying four positions of symmetry mm, four of symmetry m, and one general position. On consulting the multiplicity of the special positions for this space group in Volume A of International Tables for Crystallography (Hahn, 2005), one finds that the 32 molecule total is accounted for as (4 × 2) + (4 × 4) + (1 × 8). If (as is usually the case) the square brackets are unnecessary, they are omitted, as in Occasionally, two distinguishable structural classes will lead to the same symbol. As yet, Belsky, Zorkaya & Zorky prefer to deal with this problem on an ad hoc basis, rather than by attempting to devise any general rules.

Belsky, Zorkaya & Zorky divide the structural classes into six groups, in accordance with the number of examples found. The groups are anomalous' (up to five examples, 199 structural classes); rare' (up to 19 examples, 55 classes); small' (up to 49 examples, 24 classes); big' (13 classes); giant' (eight classes); and supergiant' (six classes). The last three are not explicitly defined, but examination of the tables shows that the dividing line between big' and giant' is about 250, and between giant' and supergiant' is about 750. All these statistics, of course, are subject to modification as the number of known structures increases.

### References

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.
Hahn, Th. (2005). Editor. International tables for crystallography, Vol. A, Space-group symmetry, fifth edition. Heidelberg: Springer.