On Sunday, 20 April 2014 01:35:33 AM Bernhard Rupp wrote:
> Hi Fellows,
>
>
>
> because confusion is becoming a popular search term on the bb, let me admit
> to one more:
>
> What is the proper class name for the 65 space groups (you know, those):
>
>
>
> Are
>
> (a) these 65 SGs the chiral SGs and the 22 in the 11 enantiomorphic pairs
> the enantiomorphic SGs?
>
> Or
>
> (b) the opposite?
>
>
>
> In other words, is (a) enantiomorphic a subclass of chiral or (b) chiral a
> subclass of enantiomorphic?
I am not sure it is possible to reconcile conflicting uses
of the term "chiral" in formal theory and common use.
My recollection from group theory is that a chiral group is one
that contains a chiral operator as one of its generators.
Removing this chiral operator creates 2 smaller groups which are
not themselves "chiral" because they do not contain the chiral
operator. Each is a subgroup of the original chiral group.
Translating to crystallography, this would mean that a chiral
group necessarily contains a mirror or inversion operator.
Strangely, this is exactly opposite to what I think most
crystallographers want the term to mean.
I don't recall encountering the term "enantiomorphic group" when
learning group theory, but as used in crystallography it would
logically describe one of the two groups, call them SL and SR,
whose composition SL x SR yields a chiral group containing both
SL and SR as subgroups.
Ethan
>
> Small molecule crystallography literature seems to tend to (b) whereas in
> macro I often find (in terms of number of class members) chiral >
> enantiomorphic. Interestingly, did not find an authoritative definition in
> ITC-A.
>
>
>
> Logical is neither. The 65 are perhaps enantiostatic because they do not
> change handedness (as opposed to enantiogen), and the 22 are enantiodyadic
> (or so). I am sure Tassos will enlighten us on that one..
>
>
>
> So, (a) or (b) or ?
>
>
>
> Happy Easter, BR
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--
mail: Biomolecular Structure Center, K-428 Health Sciences Bldg
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