# anisotropic temperature factors

Michael Kenneth Davoli mdavoli at eng.auburn.edu
Fri Mar 12 15:31:46 EST 1993

```Hi,

I'm writing a parallel program to perform full-matrix, least-squares refinement
of small molecular structures on a distributed memory multiprocessing system.
The program will be able to refine structures using either individual isotropic
temperature factors or anisotropic temperature factors, depending on which is
supplied with the data file.

I am having no problem with the isotropic case.  My dilemma concerns the
anisotropic case.  During the initial cycles of refinement the positions of the
atoms should change more than the anisotropic temperature factors.  Because of
this,  anisotropic temperature factors are usually "fixed" and only the atomic
positions are refined (This also speeds up the refinement and avoids false
minimums).  After a few refinement cycles, the ansisotropic temperature factors
are then also refined.

My problem is that I'm not sure what is meant by "fixing" the anisotropic
temperature factors and so I'm not sure what to do.  I am considering two
possible approaches:

1.  I have been told that what is done sometimes is to approximate an ISOTROPIC
temperature factor for each atom using that atom's 6 ANISOTROPIC temperature
factors.  I believe this is done by finding the radius of a sphere whose volume
approximates that of the ellipsoid described by the anisotropic temperature
factors, U11, U22, U33, U12, U13, and U23.  After the refinement, the shift to
this approximated ISOTROPIC temperature factor is applied to the ANISOTROPIC
temperature factors.  Any references to how this is done would be GREATLY
appreciated (Acta Cryst.?, J.of App. Cryst.?, Stout & Jensen?).

2.  The other possibility is that "fixing" the anisotropic temperature factors
means truly treating them as constants - they are used to calculate the
structure factors, but not actually refined for the first few cycles.  This
would effectively reduce the least-squares matrix to those elements that involve
just the atomic positional parameters.  While this is *very* appealing
considering the simplicity of implementation, I don't know if this is a valid
approach.  It seems that the anisotropic temperature factors involve the
orientation of the ellipsoid.  Clearly if the atom postions have shifted
appreciably, the orientation of the ellipsoid will no longer be valid.  On the
other hand, this might be corrected in the refinement....

Any references to information on this topic would be greatly appreciated.  Any
suggestions or thoughts on the topic would also be welcome.

Thanks in advance,

Michael Davoli
Computer Science Department
Auburn University
mdavoli at eng.auburn.edu

```

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