The control of difficult refinements

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 over-complex 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.