W0231

Z' > 1 Structures: Software for Analysis and Refinement. R.I. Cooper, D.J. Watkin, A. Collins, Chemical Crystallography Laboratory, Univ. of Oxford, 9 Parks Rd., Oxford, OX1 3PD, UK, richard.cooper@chem.ox.ac.uk.

Software tools have been developed for comparing, contrasting, analysing and refining Z' > 1 structures (more than one chemically identical molecule in the asymmetric unit).

These materials can be roughly divided into two types: pseudosymmetric and non-pseudosymmetric. The former poses particular difficulties for the structure analyst. In this case, the independent molecules are related by pseudo-symmetry operators that almost correspond to real operators for a different space group. When the pseudo-operator approximates a centre of inversion [1], or a super lattice translation the refinement is notoriously difficult to handle well.

Refinement of a pseudo-centrosymmetric structure is ill-conditioned and cannot be ‘fixed’ with block matrices or damping restraints. The near singularity means unpredictable parameter shifts distorting the geometry. Once distorted, the structure’s pseudo-centre has been removed and refinement proceeds to a local, but incorrect minimum.

Weak reflections are very important in deciding whether a space group has an inversion centre [2]: Deviations from a true centre contribute to the imaginary term of the structure factor, F, but only in the very weak reflections, where the real component is also small, will these cause a significant change in the magnitude of F. This fact can be used to develop weighting schemes to try to remove the near singularity in pseudo-centrosymmetric refinement.

A closely related problem occurs when pseudo-translations cause near-absences in layers of a diffraction pattern. The refinement problem can be re-parameterised [3] to better fit the problem using combinations and differences of physical parameters.

1. V. Schomaker (1979), Acta. Cryst. B35, 1933-1934

2. R.E. Marsh (1981), Acta Cryst. B37, 1985-1988

3. E. Prince (1982), Mathematical Techniques in Crystallography and Material Science, p. 113