Just a short contribution on the global optimisation messages that
have appeared recently since our names came into the frame.
Our publication (Z. Kirst 212 (1997) 550-552) simply demonstrates
the first application of a GA-based global optimisation strategy
to the problem of determining structures from powders.
In that paper, we do all the things that Armel does at the beginning
of the problem: namely getting the best lattice constants and peak
widths. We do a Pawley analysis and extract the integrated
intensities and their associated covariances. Yes, they are
correlated and the Pawley analysis gives the correct statistical
correlations.
We then go on to work with the extracted intensities in the structure
solution for reasons that should be obvious - fitting to the
extracted intensities (with the associated covariance matrix) is
mathematically equivalent to fitting to the pattern. Ted Prince
showed this a few years ago - (E. Prince in "Structure and
Statistics in Crystallography" pp. 95-103 ed. A.J.C. Wilson, Adenine
Press (1985)). Fitting to intensities is, however, substantially
faster - at least an order of magnitude quicker. This is, of course,
important for global optimisation since many structures have to be
sampled and compared with the data. Such speed-ups allow much harder
problems to be tackled - we should also point out that the structure
of ibuprofen, solved in our Z. Krist paper, is considerably more
complex in terms of its intramolecular flexibility than
ortho-thymotic acid.
The notion that has arisen in certain papers that extracting
intensities is problematical and that fitting a model to a pattern
somehow circumvents the overlap problem is, as Armel has stated,
simply erroneous. We're surprised that it continues to be accepted
at face value. Clearly Armel is not refereeing those papers !!
On the global optimisation versus direct methods issue, you pay your
money and take your choice! The important thing is to solve the
structure. Our experience is that the incorporation of prior chemical
information can only be a good thing and that there is nothing
particularly magical about genetic algorithms.
Bill David and Kenneth Shankland