The control of difficult refinements

Abstract

Each year, many single-crystal structure analyses are reported that show evidence of over-or under-refinement.Often, the refinement strategies have been naive or overcomplex and alternative strategies might have been more effective. The many descriptions of crystallographic and numerical techniques suitable for assisting with the control of difficult refinements are distributed widely in the literature and so are not always easily accessible. Without being a review of these procedures (which would require a substantial book), this article attempts to list readily available procedures, together with a brief outline of their backgrounds and examples of their applications to organic and organometallic compounds. The analysis of extended-lattice materials (usually inorganic materials) often raises problems in addition to those covered here. The particular aim of this article is to remind the reader that X-ray structure analysis is a modelling process and that, while standard models may be adequate for most analyses, more care and imagination must be applied to the treatment of difficult cases. Principles of methods are described without detailed mathematical derivations, although sufficient references to the literature are provided to permit careful study. Future requirements for refinement processes are outlined, including the use of new machine architectures, applications of sparse-matrix methods and the development of expert systems.

Pyridine-2-selenolate and -2-tellurolate as ligands: a multinuclear (77Se, 119Sn, 125Te) magnetic resonance study of some tin(IV) complexes, and X-ray structural analyses of Sn(SPh)2(2-Se-C5H4N-N,Se)2 and Sn(SPh)1.85(2-Se-C5H4N)2.15

“…The agreement factors, estimated standard deviations, residual electron density, thermal parameters, etc. indicate that this is a very good X-ray analysis (34,35). Indeed, if considered in isolation, the X-ray analysis could easily be mistaken for that of 1; only the NMR and elemental analytical data (see experimental section) tell us that the compound is not 1.…”

Refinement of Macromolecular Structures by the Maximum-Likelihood Method

“…[For reviews on refinement and a more complete set of references see Bricogne (1993);Watkin (1994). ]…”

SVDdiagnostic, a program to diagnose numerical conditioning of Rietveld refinements

“…Authoritative literature about the analysis of numerical stability in matrix inversion based on SVD exists in books about numerical analysis, but we found very little crystallographic work where SVD is used, in line with remarks about SVD by Watkin (1994). Consequently, we developed the corresponding tools needed for assessing the conditioning of crystallographic least-squares matrices by SVD.…”