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I recently read two books, "space groups for solid state scientists" by Burns
and Glazer, and "Crystalline Solids" by McKIE.    What I learned from the books
is that a screw axis n(m) is without hand if m=1/2n.  Thus crystals
possessing, P4(2),
for example, can not be optically active.
On the other hand, space groups such as P2(1)2(1)2(1) are obviously chiral, 
because, potassium hydrogen D-tartrate and L-tartrate crystalize in it
(listed in a paper by H. D. Flack, Acta Cryst. A39, 876-881).
So my question is:
Can crystals in P2(1) or  P4(2) or P6(3) be optically active?  If not,
why P2(1)2(1)2(1) is chiral whereas P2(1) is not.
Any comments (or references) are welcome.
-- 
Xianhui Bu                    E-mail:  xianhui@sbxray.ucsb.edu
Chemistry Department          Phone :  (805)-893-2399
University of california      Fax   :  (805)-893-4120
Santa Barbara, CA 93106

Xianhui Bu (xianhui@sbxray.ucsb.edu) wrote:
: I recently read two books, "space groups for solid state scientists" by Burns
: and Glazer, and "Crystalline Solids" by McKIE.    What I learned from the books
: is that a screw axis n(m) is without hand if m=1/2n.  Thus crystals
: possessing, P4(2) for example, can not be optically active.
: On the other hand, space groups such as P2(1)2(1)2(1) are obviously chiral, 
: because, potassium hydrogen D-tartrate and L-tartrate crystalize in it
: (listed in a paper by H. D. Flack, Acta Cryst. A39, 876-881).
: So my question is:
: Can crystals in P2(1) or  P4(2) or P6(3) be optically active?  If not,
: why P2(1)2(1)2(1) is chiral whereas P2(1) is not.
A chiral space group, as I understand it, is one which will contain
only a single enantiomer of a chiral substance or may cause macro-
scopic chirality in a substance which is not chiral in solution
(i.e. the _packing_ arrangement of the molecules causes the crystal
to be chiral where the molecules themselves are not).
It is obvious that the only symmetry operations allowed in these
space groups are rotation and translation. Any other operations
involve inversion of the structure or reflection -- this includes
centers of symmetry, mirrors planes and/or glide planes. This can
be simplified -- only those space groups which contain only numbers
(other than the Bravais lattice indicator) are chiral. No bars, nor
any of n, m, a, b, c, or d. This gives us the subset of space groups
of which P1, C2, P21, P21212, P212121, P3, P31, etc... are members.
All enantiomerically pure chiral materials crystallize in one of
these space groups -- unless there is some disorder which causes
an averaged centrosymmetric structure.  
The quote that you cite above says that the screw axis is "without
hand". That is true -- there is no inherent directionality of the
screw if the pitch is half the translation. I _believe_ that what
this is saying rather is that these polar/chiral space groups cannot
cause macroscopic chirality of non-chiral molecules. The structures
will still be polar (i.e. the crystal will be different when viewed
from the 'top' of the screw as opposed to the view from the 'bottom'
because all of the molecules will be facing in the same direction)
but the crystals will not rotate polarized light.
If the molecules which make up the crystal are chiral, then the
crystals of these substances will also be chiral (as well as
polar). However, if the molecules are non-chiral but just happen
to crystallize in one of these P2n(n) space groups, then the
crystals won't be chiral, but will be polar.
I think... I've never actually seen an experiment which tested
the ability of a crystal to rotate plane-polarized light.
--
Bev Vincent
Molecular Structure Corporation
The Woodlands, TX
http://www.msc.com/

 I would like to purchase 10 to 15 pairs of cheap cardboard
stereoscopes to view standard ORTEP-style stereopairs. 
I've seen these in the past in books, but have had no luck
in finding a supplier. Any suggestions?
 thanks
 larry henling
 lmh@cco.caltech.edu

In article , xianhui@sbxray.ucsb.edu 
(Xianhui Bu) wrote:
>I recently read two books, "space groups for solid state scientists" by Burns
>and Glazer, and "Crystalline Solids" by McKIE.    What I learned from the books
>is that a screw axis n(m) is without hand if m=1/2n.  Thus crystals
>possessing, P4(2),
>for example, can not be optically active.
>
>On the other hand, space groups such as P2(1)2(1)2(1) are obviously chiral, 
>because, potassium hydrogen D-tartrate and L-tartrate crystalize in it
>(listed in a paper by H. D. Flack, Acta Cryst. A39, 876-881).
>
>So my question is:
>
>Can crystals in P2(1) or  P4(2) or P6(3) be optically active?  If not,
>why P2(1)2(1)2(1) is chiral whereas P2(1) is not.
>
>Any comments (or references) are welcome.
>
Crystals in P2(1) etc AND P2(1)2(1)2(1) would be achiral if the asymetric 
units (molecules or whatever) which crystallize in these space groups were 
also truly achiral. If the molecules are chiral, then the crystals must be 
too. Of course, even molecules which would be achiral in the gas phase, would 
likely become ever so slightly chiral due to packing forces in these space 
groups.
Space groups P3(1) etc are inherently chiral even if the asymmetric units are 
not, because they will be arranged in a helical pattern in the crystal.
Hope I've helped
Peter Bird
Chemistry and Biochemistry, Concordia University
Montreal

Hi,
Does anybody have an idea what the difference in total intensity between
line focus and point focus would be of one and the same source?
Thanks
Bart Meert

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Larry M. Henling wrote:
> 
>  I would like to purchase 10 to 15 pairs of cheap cardboard
> stereoscopes to view standard ORTEP-style stereopairs.
Larry,
    I have a cardboard stereoviewer on my desk here called a
taylor-merchant Stereopticon 707.  I found one reference that indicates
it's a New York-based company.  But I'd be surprised if Polycrystal
doesn't have this item (polybook@dnaco.net)   Our stockroom stocks them
(or at least used to) so if you get stuck let me know and I'll see if I
can find out where they got them from.
Steve Geib
-- 
Steven J. Geib
Department of Chemistry, University of Pittsburgh
E-mail:  geib+@pitt.edu
http://www.pitt.edu/~geib

Chirality is a molecular geometric property and the term is not usually
applied to crystals or space groups. For crystals one speaks of
enantiomorphs.
Two molecules are in a chiral relationship or two crystals are enantio-
morphs if they are isometric (identical bond distances and angles) but
are not supposable. This definition leads to symmetry restrictions on
molecules which may be chiral or crystals which may display 
enantiomorphism. For a molecule to be chiral or a crystal to display
enantiomorphism it must NOT contain any IMPROPER (-1, m, -3,-4, -6)
symmetry operation as this leads to the two objects being supposable. 
 In short any improper symmetry operation leads chirality or
enantiomorphism to be forbidden.
The symmetry restrictions on optical activity are completely different.
Optical activity is represented by a second-rank axial tensor called the
gyration tensor. Such tensors must take zero values for ALL components
(i.e. no optical activity) if the object (molecule or crystal) contains
a centre of symmetry. For other improper symmetry operations some terms
of the tensor must be zero but others may take arbitrary values (i.e.
optical activity is possible). For example a crystal or molecule in
the point group m can show optical activity and the symmetry of the 
tensor is such that if for a particular direction of transmission of the
light the rotation is +alpha, there will be a related direction where
the rotation is -alpha. So it is quite possible to observe optical 
activity on a crystal with point symmetry m in a fixed orientation. In
principle the same is true of a single molecule but you need to hold it
still and have a sufficiently intense interaction.
 In solution, in addition to the molecular point symmetry one has to
consider the statistical symmetry due to the tumbling of the molecules.
This leads to the symmetry restriction on the optical activity of
molecules IN SOLUTION being that optical activity is forbidden in the
presence of any molecular improper symmetry operation. Hence there is 
a one-to-one correspondence on the conditions for chirality and those
for optical activity IN SOLUTION.
H.
-- 
From:
 H. D. Flack
 Telephone   [+[41] 22] 702 62 49         | Laboratoire de
Cristallographie
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