Setting up Constraints in GSAS

>From: "Brian H. Toby [Brian.Toby@NIST.GOV]" 
>Date: Fri, 8 Aug 1997 14:13:56 -0400
>To: RIETVELD_L Distribution List [rietveld_l@ill.fr]
>Subject: Re: GSAS constraints

> Subject: GSAS functions
>  I try to find the explanation for "Soft constraint" and "Rigid body
>  constraints" function of GSAS but I can't find in manual.  Does
>  anybody know where the explanation or document for these functions?

Soft constraints in GSAS consist of adding a set of new "observables" to the
experiment: one defines a set of distances between atoms and their standard
deviations along with an overall weighting factor. The GENLES program will then
try to improve both the agreement between the observed and calculated
diffractogram(s) as well as the presumed and calculated interatomic distances.
To use soft constraints, go to the soft constrain menu in least-squares set up.
Use the commands
	R 1.2
	I 2.0 0.1 1:3 8:10
to search for distances between atoms 1,2 & 3 to 8,9 & 10 that are between
2.0/1.2 A and 2.0*1.2 A. You will then be presented with a list of matching
interatomic distances and the choice to add a constraint on that distance.
Use the F command to set a weight. This number may need to be quite high
(100-5000, even more on occasion) at the beginning of a refinement, but one
wants to set F to 0 at the final stages of a refinement, if possible.

A note on use of soft constraints (S-C's): purists don't believe in their use:
in part appropriately -- because while you may think you know a bond distance,
in reality all that you know is what your have measured (the diffractogram)
Everything you think you know is merely prejudicing your result. It is possible
to refine to a false minimum through use of S-Cs.  I don't agree with this
philosophy in its entirety.  What crystallographers do for a living is
determine models. We call our models "crystal structures" but there are always
implicit assumptions made in fitting our models to data. In some cases (for
example nearly all macromolecular crystallography) there is simply not enough
data to completely determine all bond distances etc. In these cases, it is
valid to model data as a spectroscopist would -- by presenting a model and
showing that it is consistent with the observations. It may or may not be
right, but it is an honest interpretation.

It is important to document in any eventual publication how the constraints
were used. If they were used in the beginning and then removed, say so. If they
could not be removed, report the relative contribution of the S-Cs to the total
CHI^2 in the final stages of refinement. Don't report interatomic distances
with Standard Uncertainties (esd's) for constrained distances as if the
distances were fitted in your model -- they were assumptions that went into
building your model.

Rigid bodies are used by defining a group of atoms in terms of cartesian
coordinates. One then specifies six parameters (an origin and Euler angles) to
locate the body within your model. The location and orientation can then be
refined, as well as potentially rather sophisticated group temperature factors
and even some optional scaling variables. GSAS allows for pretty complex rigid
bodies; it is possible to set up (for example) a benzene ring where the
carbon-carbon and carbon-hydrogen distances are refined but their relative
geometry is fixed. Rigid bodies can be rather complex to set up. How to do it
is not the sort of thing I would try to explain in an e-mail message or even
over the phone, but I can say that I have used them several times -- they can
be very helpful.

Brian

-- 
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Brian H. Toby                      Center for Neutron Research E151/235
Brian.Toby@NIST.gov        National Institute of Standards & Technology
voice: 301-975-4297  FAX: 301-921-9847           Gaithersburg, MD 20899
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