[cctbxbb] real-space symmetry operators

[Oleg Dolomanov]

Hi Nat,
it should be something like this:1. Symmetry operation on fractional coordinates: Yfrac = S*Xfrac2. 'Fractionalisation' operation: Xfrac = G^t*Xcart3. 'Orthoganalisation' of the result: Ycart = G*Yfrac4. All together: Ycart = G*S*Xfrac = G*S*G^t*Xcart
where S is a symmetry operator G is the orthogonalisation matrix and G^t is it's transpose. So you can pre-compute G*S*G^t,
Cheers,
o.
From: nechols at lbl.gov
Date: Sun, 17 Aug 2014 15:36:00 -0700
To: cctbxbb at phenix-online.org
Subject: [cctbxbb] real-space symmetry operators

Hi all--
I'm trying to figure out how to orthogonalize symmetry operators given a unit cell, which doesn't seem to be something we have code for.  These appear in PDB files in the REMARK 290 section but I haven't been able to find any other software that generates them, and the relationship between the symops and the real-space equivalents is unclear.  I assume this is conceptually similar to orthogonalizing fractional coordinates, but unit_cell.orthogonalize() does not quite do what I wanted.  In the PDB, for P63 it has this (excerpted):


REMARK 290       2555   -Y,X-Y,Z
...REMARK 290   SMTRY1   2 -0.500000 -0.866025  0.000000        0.00000REMARK 290   SMTRY2   2  0.866025 -0.500000  0.000000        0.00000

REMARK 290   SMTRY3   2  0.000000  0.000000  1.000000        0.00000
which looks like it should be relatively straightforward, but I'm not very good with matrices.  Does anyone know the correct math for this?  The corresponding rt_mx object from sgtbx looks like this:


r=(0.0, -1.0, 0.0, 1.0, -1.0, 0.0, 0.0, 0.0, 1.0) t=(0.0, 0.0, 0.0)

(Yes, I realize that there are much easier ways to apply symmetry operators to coordinates, but I want to limit the number of matrix multiplications involved when starting from Cartesian coordinates.)


thanks,Nat

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