Re: [ccp4bb]: error propagation on anisotropic thermal parameters

[Kevin Cowtan <cowtan@ysbl.york.ac.uk>]

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On Tuesday 03 Sep 2002 6:12 pm, Ulrich K. Genick wrote:
> Has somebody in the past worked out
> how to propperly propagate errors when
> extracting the eigenvectors and eigenvalues
> from the 6 U parameters output by SHELX.
>
> In other words, I know the esds for the
> U parameters and want to calculate the
> esds for the components of the 3
> Eigenvectors and the 3 Eigenvalues.

I'm not sure if the information you need is available without getting into the 
SHELXL internals.

The problem is that the PDB format defines a couple of rather idiosyncratic 
entries: SIGATM and SIGUIJ, which contain the sigmas of the coordinates and 
thermal parameters. And, despite many other improvements, the mmCIF format 
has chosen to continue this, uh, *unusual* practice.

Linear algebra 101: Coordinates form a vector. Vectors don't have sigmas. 
Vectors have variance-covariance matrices.

To get sigmas on derived parameters, such as the eigenvalue components, or 
even such trivial cases as symmetry related atoms, you need not just the 
sigmas on the individual parameters, but also the covariances of the 6 
parameters. Yes, thats right. You can't even get the sigmas on the 
coordinates of symmetry related atoms, let alone Uijs.

This information must be available within SHELXL, and indeed any program which 
does at least a block-diagonal refinement of the aniso U's. But the powers 
that be have decreed that we throw all such information away before putting 
it in a file or a database.

-- 
Department of Chemistry, University of York, Heslington, York YO10 5DD