> On Tue, 2014-04-29 at 16:12 +0200, Bernhard Rupp wrote: > > > 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 > > >
Not quite, here's a table giving the complete list of the 3 types: http://pd.chem.ucl.ac.uk/pdnn/symm3/allsgp.htm The table heading states: "Space groups possessing a point of inversion are termed *centrosymmetric*; these are shown in the table in red. Some space groups have no symmetry element that can change the handedness of an object; these are termed *enantiomorphic* space groups and are shown in magenta." i.e. your (a) set are the magenta ones, your (b) set are the red ones and your (c) set are the remaining black ones. -- Ian
