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Re: [Imgcif-l] ImgCIF Densiry Maps



Joe Krahn wrote:

>I was looking over the Hall notation. If I understand it right, it only
>defines origin choices which are symmetry equivalents of the normal
>origin choice. There are cases where it is useful to shift a C2221
>origin to align symmetry operators with those of P212121. 
>
The Hall symbol allows one to select any origin that is related to the 
symmetry operations.  One can specify the translational part of the 
symmetry matrix in terms of the translations 0, 1/4 or 1/2 as well as 
the intrinsic translations of the screw axes.  The standard setting for 
P212121 is P 2ac 2ab.  The first element describes the c screw axis 
displaced 1/4 from the origin along a, the second element is the a screw 
axis displaced 1/4 along b.  The symbols a, b and c represent 
translations of 1/2 along the a, b and c axes resspectively and the 
order by convention gives the c axis first, then a. The standard setting 
for C2221 is C 2c 2 incdicating a c screw axis and an a 2-fold axis both 
passing through the origin.  To choose an origin for C2221 that is 
compatible with P212121 requires the origin to be shifted so that the c 
screw axis is lies at 1/4,0,z and the a 2-fold axis lies at x,0,1/4.  
This would be achieved using the symbol C 2ac 2c.  Of course the 2-fold 
axis is not present in P212121 but this shift puts the a screw axis at z 
= 1/4.

>I don't think
>the standard Hall notation handles this sort of case, at least not as
>tabulated in the International tables.
>
The original description of this symbol (which I used to work out the 
above illustration) is found in Syd Hall's paper in Acta Cryst. (1981) 
A37, 517-525.  This discusses how to create the symbol for all the 
non-standard situations.

>
>The other issue is that interactions may need to define a specific
>symmetry operation. Is there a standard way to derive the symmetry
>operators in a specific order from Hall notation?
>
This is algorithm dependent which is why Acta Cryst. requires the 
symmetry operations to be listed explicitly since they are addressed 
individually in the _geom categories.  Syd wrote a simple program to 
expand the symbol and one could use this to provide a consistent 
ordering of the operations.  As far as I know no one has proposed a 
standard algorithm for ordering the symmetry operations.  I know 
definitely that there is no algorithm that will order the special 
positions in a way that consistently matches the ordering given for the 
standard space group settings in International Tables and the same may 
be true of the operations themselves.


David Brown
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