Symmetry and chirality in crystals

A classification scheme relating the chirality of molecules to the type of crystal structures (chiral or achiral) they may form is presented. With respect to similar classifications proposed in the past, some corrections and extensions are introduced. In particular, (1) it is shown that chiral crystal structures from achiral molecules can occur in 28 types of space group having screw axes n_p, with p ≠ n/2, not in any Sohncke type of space group; (2) it is shown that the restriction on Z′ > 1 for kryptoracemates is contradicted by examples with Z′ = 1; and (3) the case of scalemic enantioenriched solutions, absent from most classifications, is included. Chiral crystal structures from purely inorganic (non-molecular) compounds are addressed too.