more opinions were invited on "Molecule location, a distinct topic in
crystallography ?", and I present mine in all modesty. Since I have not
previously introduced myself to this list, I will say that I am a
crystallographer at RAL, and I previously held a position at the ILL. I am
mainly interested in oxides (crystal and magnetic structures), and I have
very little or no personal interest for the type of structures concerned
with "molecular location" techniques. This is mainly because I like
symmetry, and I just cannot get excited about P1. Also, I don't have a
single paper in Acta Cryst. (take it as the ultimate infamy or as a badge of
honor, depending on who you are).
Nevertheless, I find the idea of a distinct topic for heavily constrained
refinements quite outrageous. From the statistical point of view, we are
dealing in every case with nonlinear least-square minimization of a set of
variables against powder data, and it does not make any difference
whatsoever whether the variables are free atomic coordinates, constrained
atomic coordinates or torsional angles. Provided that one is reasonably
close to the statistical limit, the accuracies of the refined variables are
rigorously expressed in terms of well-defined statistical quantities, and,
in general, have nothing to do with Nhkl/Nxyz (if anything, the useful
parameter is Nhkl/Nf, where Nf is the number of degrees of freedom). Also,
the addition of new variables can be rigorously justified (Hamilton test or
the like). The big problem arises in the presence of systematic errors,
due to the inaccuracy of the starting model, whereby the statistical
indicators become meaningless. Arguably, heavily constrained refinements
are more prone to systematic errors than free refinements, simply because
the starting model is more complex and more assumptions are made.
Nevertheless systematic errors and complex models are by no means exclusive
to "molecular locators". For instance, there is an extensive literature on
defects in inorganic compounds, in which very complex models are used,
including site substitutions associated with local atomic displacements.
This is, admittedly, a little shakier than an unconstrained refinement of a
perfectly homogeneous structure, but simple problems like those were all
solved 50 years ago.
I would argue that sophisticated modeling is *the* mainstream of the
Rietveld community. In this context, placing "molecular locators" in a kind
of getto would be all but absurd. On the contrary, what distinguishes them
from the rest of us is that they have found clever ways to perform the
least-square minimization (our common problem), which we should try to learn
and apply to higher symmetry structures. I am afraid the point about the
hexoterism of current codes in this field is well taken. However,
segregation of their community is not the answer.
By the way, while I am at it, let me take side also an a previous discussion
about Rietveld vs. "Intensities + correlations". The formal equivalence
between the two can be readily demonstrated from matrix algebra, provided
that **lattice constants and profile parameters are not refined in the final
Rietveld fit**. This may seem like a big difference, but is not, because,
usually, it hardy makes any difference on the internal coordinates (and
associated variances) if you fix these parameters at your last Rietveld
cycle. Whether the "Rietveld" lattice constants and profiles are better
than the "Pawley" ones, it is a matter of debate, but if they come out very
different one should worry. The error bar issue is a red herring, because
the Hessian matrix is identical in the two cases, and the error bars only
depend on how you define chi^2 (on the profile or on the integrated
intensities). You will get the same error bars if you define chi^2 in the
same way. The "Intensities + correlations" method is only useful if the
number of observations can be lowered with respect to the number of profile
points. This is not obvious, but is usually the case for high-resolution
data and simple background.
Best
Paolo G. Radaelli
Dr. Paolo G. Radaelli
ISIS Facility
Rutherford Appleton Laboratory, Bldg. R3
Chilton, Didcot
Oxon. OX11 0QX
United Kingdom
Phone : (+44) 1235-44 6290
FAX : (+44) 1235-44 5642
e-mail: P.G.Radaelli@rl.ac.uk
pgr@isise.rl.ac.uk