On 21 April 2014 21:57, Bernhard Rupp <hofkristall...@gmail.com> wrote:
> > > So the point is to use a meaningful qualifier that, applied as an > adjective to a space group, describes what happens if that space group acts > on a chiral object. Now the ‘enantio’ creeps in: enantio means other, > opposite, and morphos, gestalt, form or so. (Where is Tassos when you need > him…) so: The adjective of those 65 who are "not possessing improper > rotations" as "enantiomorphic", is completely illogical. They are exactly > the ones which do NOT change the ‘morph’ of any ‘enantio’. They, > logically I maintain, are ‘non-enantiogen’ because they generate no > opposite. The 11 pairs of non-enantiogenic SGs that that exist however > indeed form enantiomorphic pairs, even as groups in absence of the need to > act on a (chiral) object. One then can argue, as Ian did, that they form > chiral pairs. However, that is not necessarily a justification to call > these individual SGs themselves chiral. > > To me, the only satisfactory statement is that the 65 space groups “not > possessing improper rotations” are non-enantiogenic, and 22 of them form > enantiomorphic pairs. None of them change the handedness of a chiral object. > Bernhard, Sorry ignore previous empty message (must have accidentally hit a keyboard shortcut for 'Send': Gmail should make it much harder to hit Send accidentally!). I was going to say that I didn't quite follow your argument. The point I was making in my reply was that 'enantiomorphic' refers to the unit cell contents, _not_ to merely the unit cell including its space-group symmetry elements, which is what I meant by 'space-group diagram'. The latter of course possesses the symmetry of the Cheshire group which has additionally symmetry elements, e.g. additional inversion centre and translational elements in many cases. 'Enantiomorphic' means "that for which an enantiomorph (non-superposable mirror image) exists". So the 65 space groups, including their unit-cell contents, are enantiomorphic by that definition, because there exists for each one an enantiomorph of the unit cell contents. We are after all talking only about a mirror-inverted image of an object not the mirror-inverted object (one can argue about whether an image in a mirror 'exists' since it's merely a mathematical construct). In fact in this sense there's no difference between enantiomorphic and chiral (since that also means "having a non-superposable mirror image"). The fact that the enantiomorph (i.e. with D-amino acids and left-handed alpha helices) can't actually exist in Nature is irrelevant, the point is that it's only a mathematical construct. As I said there's really no distinction between 'enantiomorphic' and 'chiral'. However in the sense in which 'chiral' is being used to described the 11, it is clearly being applied to the space-group diagram only, so the space-group diagrams for P1, P21, P212121, P4, P622 etc. are achiral (and non-enantiomorphic in this limited sense), whereas those for P31, P41212 etc are chiral (and enantiomorphic). The unit-cell contents are in all these cases enantiomorphic in the wider sense defined above. This is why I said you need to take care about what objects the words are describing: enantiomorphic and chiral mean the same but they are being used to desscribe 2 different objects! Cheers -- Ian
