On the Prevalence of polar and Chiral Space Groups

Abstract

Abstract Previous compilations of space-group frequencies have largely ignored differences in the number of molecules or formula units in the asymmetric unit, i.e., differences in Z′ = Z/N, where N is the number of general positions in the space group. This study demonstrates the importance of the variable Z′. Crystals with space groups that include mirror planes nearly always contain mirror-symmetric molecules located at these special positions; likewise, crystals with space groups that include threefold rotation axes usually contain molecules with threefold symmetry. The relative occurrence of polar and chiral space groups is discussed.