Symmetry elements from XYZ

islam islam at icrf.icnet.uk
Thu Apr 17 05:45:36 EST 1997

I would be grateful for any ideas, comments or software to deal
with the following problem please:

Given an orthogonal dataset of coordinates for 2 identical
molecules is it possible to derive the symmetry operator relating
them or determine if one exists ?

Am I correct in thinking:

 * the problem is equivalent to least squares fitting the
   two molecules to derive a transformation matrix and then
   decomposing/examining the derived matrix to its "simplest
   form" e.g. rotation about a 3D axis

 * in a sense as long as a transformation matrix can be obtained
   to fit one molecule exactly onto another, then a symmetry op 
   always exists defined by the matrix ?

Can the above idea be extended to derive the crystallographic
symmetry operator relating the two molecules (obviously given
the appropriate cell,space group etc).  (An alternative here,
I guess, would be to generate unit cells to find which symmetry
elements related to the 2 molecules).

Suhail A Islam
Biomolecular Modelling Laboratory
Imperial Cancer Research Fund, P.O. Box 123
44 Lincoln's Inn Fields, London WC2A 3PX
Tel: (0171) 269 3380, Fax: (0171) 269 3479
email: islam at icrf.icnet.uk

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