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Bin,
To get from your (4a, 16l, 8h) sites in I4/mcm to (4d, 16i, 8e) in
I-4c2, you need to shift the origin by adding (0,1/2,1/4). The shifted
(16l) sites will then have coordinates (x,x,z+1/4), etc., and all sites
will satisfy the symmetry of I-4c2. (16i) in I-4c2 is the general
position (x,y,z). So, the coordinates for atom B in the original
structure should be close to your transformed coordinates, but with x
and y not exactly equal.
Hope this clarifies things a little,
Marian Szebenyi
Staff Scientist, MacCHESS
Petrus H Zwart wrote:
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The Bilbao crystallographic server might be of some use.
(http://www.cryst.ehu.es/)
Check for instance the Wykoff splitting when going to a lower symmetry:
I4/mcm (140) -> I-4c2 (120)
wykoff splitting table:
I4/mcm I-4c2
32m -> 16i 16i
16l -> 16i
16k -> 16i
16j -> 16i
16i -> 8e 8e
8h -> 8h
8g -> 8g
8f -> 8f
8e -> 8e
4d -> 4d
4c -> 4b
4b -> 4c
4a -> 4a
(Looking at this table, I do not understand the splitting in positions
you observe, unless I am missing a transformation somewhere ....)
The coset decomposition between the two spacegroup gives a clue of
which symmetry element is missing between the two spacegroups:
A representative elements of the left cosets of I4/mcm and I-4c2 are
1. x,y,z (of course)
2. (-y,x,z) (a 4 fold along z)
HTH
Peter
----- Original Message -----
From: Bin Li <[EMAIL PROTECTED]>
Date: Wednesday, August 2, 2006 8:48 pm
Subject: RE: [ccp4bb]: Question about symmetry relationship
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Dear BR:
Thank you for your quick reply.
From my data and my experience I believe my refinement with high
symmetry space group is right.
The problem is that if I assume both structures are right, how I
can
describe the atom site relationship in both structures in terms of
symmetry, such as removing inversion center , or mirror planes.
By the way, if I transfer my high symmetry space group (I4/mcm) to
lower symmetry space group (I-4c2, which is also a subgroup of
I4/mcm), I got the atom sites of A, B, and D at 4a, 16i, and 8h
sites, respectively, in stead of the one reported in the
literature
(4d, 16i and 8e sites). Is this a problem or not?
I hope I am not confusing you.
Your help is highly appreciated!
Best Regards!
Bin Li
At 10:24 PM 8/2/2006, you wrote:
The first thing I would look at is the |E**2-1| number
in the intensity distributions.
This should indicate whether centrosymmetric or not.
0.736 for acentric and 0.968 for centric structures.
If this is not decisive in small molecules, suspicion
is in order, but w/o more stats it is hard to say.
BR
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
Behalf Of Bin
Li
Sent: Wednesday, August 02, 2006 7:47 PM
To: [email protected]
Subject: [ccp4bb]: Question about symmetry relationship
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Dear:
I have a question about symmetry relationship between two space
groups.>In the literature, there is a compound AB4C2. It was
refined with
I-4c2 space group and A, B, and C are at 4d, 16i and 8e sites,
respectively.>I got a new compound AB4D2 which can be refined very
well with high symmetry
space group, I4/mcm. In my compound A, B, and D are 4a, 16l, and
8h sites,
respectively. If I draw both structures, they look same, except
some bond
distances change.
The high symmetry space group is central symmetry and the another
one in
non-central symmetry, but both have very similar Wyck positions.
How do I figure out the symmetry relationship between these two
structures?>Your help is highly appreciated!
Thank you for your time!
Best Regards!
Bin Li
Bin Li, Ph.D
Ames Lab., Iowa State University
Ames, IA, USA
