Section 9.7.4.1. Positions with symmetry 1

The empirical results for `homomolecular structures' with one molecule in the general position are given in Table 9.7.1.2. The classification by arithmetic crystal class and degree of symmorphism follows Wilson (1993d); the numerical data are taken from Belsky, Zorkaya & Zorky (1995). Space groups symmorphic in the technical sense (Wilson, 1993d) are prefixed by an asterisk (*), and in each arithmetic crystal class the space group most nearly antimorphic is followed by an obelus (†). The number of known structures having precisely one molecule in the general Wyckoff position is given as a superscript in brackets. It will be noticed immediately that structures with space groups `fully symmorphic' or `tending to symmorphism' are extremely rare. Most have no examples; three (P4<sub>2</sub>, P4/n and ) are credited with a single example each. The frequency of space groups increases rapidly with increasing antimorphism. In the monoclinic system, the `fully symmorphic' space group P2/m has no examples with one molecule in the general position, the `equally balanced' P2/c has 11 examples, the `tending to antimorphism' C2/c has 587, and the `fully antimorphic' P2<sub>1</sub>/c has 5951. Other systems have fewer examples, but the trend is the same; the really popular space groups are the `fully antimorphic' plus P1 and .

All space groups, of course, possess general positions of symmetry 1, and the data in Table 9.7.2.1 show that 116 of them exhibit structures of some kind, and that 57 exhibit structures in which one or more general positions are used. 13 space groups (P1, P2₁, Pc, Cc, P2₁2₁2₁, Pca2₁, Pna2₁, P4_1,3, P3_1,2, P6_1,5) have no positions with symmetry higher than 1. These space groups contain no syntropic symmetry elements, and all are relatively popular.