Re: [ccp4bb] anisotropic displacement parameter matrix shelxl

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CCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999

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Subject: anisotropic displacement parameter matrix shelxl
From: artis {- at -} CHEMISTRY {- dot -} MONTANA {- dot -} EDU artis {- at -} CHEMISTRY {- dot -} MONTANA {- dot -} EDU
Date: 2007-07-08

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Subject: Re: how to convert matrix to angle
From: "Douglas L {- dot -} Theobald" dtheobald {- at -} BRANDEIS {- dot -} EDU
Date: 2007-07-08

Subject: Re: anisotropic displacement parameter matrix shelxl
From: Gerard Bricogne gb10 {- at -} GLOBALPHASING {- dot -} COM
Date: 2007-07-08

Dear Arti,

The sign

in this case means "determinant", not "absolute value".
Upon expanding that 3x3 determinant by Cramer's rule you get a cubic
polynomial in lambda, which can indeed be solved by Cardan's formula. You
should definitely give it a try. Condensed algebraic notation like

can
be confusing.

Best of luck,

Gerard.

--
On Sun, Jul 08, 2007 at 01:06:51PM -0600, artis@CHEMISTRY.MONTANA.EDU wrote:
> Hello all,
>
> I am trying to understand how the anisotropic displacement parameters
> output by shelxl in the form U11 U22 U33 U23 U13 U12 relate with the
> displacement in the x, y and z directions of say an ellipsoid in ORTEP.
> So far I tried to find the eigenvalues for the matrix using the relationship
>
>
Ucart - (lambda)I
=0
>
> where lambda would give the eigenvalues along the three principal axis. In
> the above relationship, I assumed the

to stand for absolute value and
> used just basic algebra to find the value of lambda, which will be the
> inverse matrix for Ucart in this case. I used the reference
>
> On the handling of atomic anisotropic displacement
> parameters
> R. W. Grosse-Kunstleve* and P. D. Adams
> J. Appl. Cryst. (2002). 35, 477±480
>
> to look up the above relationship. In the paper it is mentioned that
>
>
Ucart - (lambda)I
=0
>
> is solved using Cardan's formula.
>
> So I probably oversimplified my solution and have it wrong.
>
> Can anyone please help me on this? Is there a simple way of knowing the
> displacement along a major axis on the ellipsoid itself in terms of
> Angstrom?
> Thank you.
>
> Arti S. Pandey
> Chemistry and Biochemistry
> Montana State University
> Bozeman,MT 59717

--

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CCP4bb navigation

CCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999

Next message:
Subject: Re: how to convert matrix to angle
From: "Douglas L {- dot -} Theobald" dtheobald {- at -} BRANDEIS {- dot -} EDU
Date: 2007-07-08