SPACE-GROUPS RARE FOR MOLECULAR ORGANIC STRUCTURES - THE ARITHMETIC CRYSTAL CLASS MMMP

Packing considerations suggest that within an arithmetic crystal class the number of examples of a space-group type should decrease exponentially with the number of mirror planes [m] and twofold axes [2]. After allowing for various other factors, quantitative agreement (R2 less-than-or-equal-to 0.05) could be obtained, but in the crystal class mmm the discrepancies between observed and calculated frequencies greatly exceeded the statistical sampling errors. Kitajgorodskij's prediction that molecules with inherent mirror symmetry will adopt preferentially certain space groups (in particular Pnma) satisfactorily explains the discrepancy.