[Imgcif-l] ImgCIF Densiry Maps
David Brown idbrown at mcmaster.caMon Mar 26 17:00:01 BST 2007
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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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