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Resources for Crystallographic Software Developers

References, methods, programs and source code for converting Symmetry Operators to Spacegroup Symbols / Spacegroup numbers

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(Corrections, additions, comments appreciated)

References, methods, programs and source code for Converting Symmetry Operators into a Spacegroup Symbol / Spacegroup Number

Date: Wed, 10 Oct 2001 09:28:36 -0700 (PDT)
From: "Ralf W. Grosse-Kunstleve" [rwgk@cci.lbl.gov]
To: l.m.d.cranswick@dl.ac.uk


> Can Sginfo take a set of symmetry operators and then
> determine the spacegroup?

Yes, SgInfo can, but the cctbx is more general. 
You can try both on the web:

    http://cci.lbl.gov/servers/cctbx/explore_symmetry.html

    http://www.csb.yale.edu/user-cgi-bin/sginfo-query

Restriction in both cases:
    - Elements of rotation parts of the symmetry operations must
      be integers.
    - Elements of the translation parts must be multiples of some
      base factor (fixed 1/12 for SgInfo, user-definable for cctbx).
Restrictions in SgInfo:
    - Only the standard lattice translations can be processed
      (P,A,B,C,I,R,F).
    - Symmetry operations must be aligned with certain axes.
      In particular, the primitive setting of some centred
      space groups cannot be processed.

> Are there methods published for doing this?

"Algorithms for deriving crystallographic space-group information",
R. W. Grosse-Kunstleve
Acta Cryst. 1999, A55:383-395
http://journals.iucr.org/a/issues/1999/02/02/au0146/

Ralf


Computational Crystallography Toolbox (CCTBX)


SGInfo (obsolescent - replaced by Computational Crystallography Toolbox (CCTBX)) - Ralf W. Grosse-Kunstleve

Brute Force method of Converting Symmetry Operators into a Spacegroup Symbol / Spacegroup Number

Date: Fri, 12 Oct 2001 09:39:31 +0100
To: Lachlan Cranswick [l.m.d.cranswick@dl.ac.uk]
From: Louis Farrugia [louis@chem.gla.ac.uk]


This functionality is present in SXGRAPH and WinGX. The method used is crude
but it works and on any reasonable PC is computed in a second or so, even for
the cubic space groups. The algorithm  is :

a) convert SHELX symmetry operators into the corresponding Seitz matrices and 
   then expand to full set using inversion operators/lattice translations 
   (if present)

(b) go through all the Hall symbols in the lookup table of Grosse-Kunstleve  
    and calculate the Seitz matrices using the GETSPEC routines

(c) compare with those from (a) until an exact match is found

This brute force method was coded first because it's simplest. Searching 
just a subset of space groups would be easy to implement, but since its 
so fast I have never bothered.



Ton Spek's Platon also uses a similar technique to WinGX's SXGRAPH - 'selective matching with the relevant subset of the 230 spacegroups and its common variants known to PLATON. One of its applications in PLATON is with respect to ADDSYM

Platon - Ton Spek, Bijvoet Center - Utrecht University

Platon - Ton Spek

The Addsym routine within Platon (for finding extra symmetry in crystal structures) makes use of symmetry operator to spacegroup conversion



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