Graph-set analysis of hydrogen-bond patterns: some mathematical concepts. Erratum (vol B55, pg 1030, 1999)

To provide a foundation for further theoretical and software development of the application of graph sets to patterns of hydrogen bonding and other in termolecular interactions a number of mathematical concepts and tools are d efined, developed and demonstrated. Following a review of the basic definit ions and uses of graph sets, the directional properties of hydrogen bonds a re now included in the treatment. The concepts of a constructor graph and c ovalent distance matrix have been developed to aid in the generation of a q ualitative descriptor for the straightforward, consistent and ultimately au tomatic (with appropriate software) definition of patterns. An additional m athematical tool, the arrowed T-labeling, has been developed to deal with s ituations in which pattern-forming moieties are located on crystallographic special positions. To demonstrate the utility and various features of thes e concepts they are applied in detail to two particular structures, polymor phic iminodiacetic acid [N-(carboxymethyl)glycine] and trans-tetraamminedin itrocobalt(III) acetate. To facilitate the application and use of graph set s many of these developments have already been incorporated into the softwa re of the Cambridge Structural Database, as described in the accompanying p aper.