Response to off-board mail: >How about [calling them] non-centro-symmetric space groups, as I often tell my >students?
Almost, but not exact enough..... The 65 are only a subset of non-centrosymmetric space groups: Not all enantiogenic (not elements of the 65-set) space groups are centrosymmetric. Simplest example Pm. According to above definition Pm (and many more lacking a center of inversion) would be a ok space group for chiral motifs. (when a space group has the 'center at ....' annotation in the Tables, it has a coi and is a centrosymmetric space group). This implies that there are actually three types of crystal structures (cf. Flack): (a) chiral (non-centrosymmetric) crystal structures (b) centrosymmetric crystal structures (c) achiral non-centrosymmetric crystal structures And just as a reminder, the substructure inversion for 3 members of the 65 is not about the origin (0,0,0): I41, I4122, F4132 are their own enantiomorph, so for them there is no enantiomorphic pair (eg. I41 and I43), in fact no separate space group I43 is even necessary - look at the SG diagram #80 - both, 41 and 43 axes appear in the same SG. (2005 Erice paper of George explains more) Enough yet? Cheers, BR
