Symmetry elements from XYZ

Jonathan Epstein epstein at gold.nlm.nih.gov
Fri Apr 18 13:16:43 EST 1997

I believe that what you are looking for is called singular value
decomposition.  See

 - Jonathan 

 Jonathan Epstein                                epstein at ncbi.nlm.nih.gov
 National Center for Biotechnology Information   Phone: (301)496-2477 x254
 National Library of Medicine                    Building 38A, Room 8N805
 National Institutes of Health                   8600 Rockville Pike
						 Bethesda, MD 20894

islam (islam at icrf.icnet.uk) wrote:
> 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).

> Thanks.
> ____________________________________________
> 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
> http://www.icnet.uk/bmm/
> ____________________________________________

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