Graph-set analysis of hydrogen-bond patterns: some mathematical concepts

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 toot the arrowed T-labeling, has been developed to deal with si tuations in which pattern-forming moieties are located on crystallographic special positions. To demonstrate the utility and various features of these concepts they are applied in detail to two particular structures, polymorp hic iminodiacetic acid [N-(carboxymethyl)glycine] and trans-tetraamminedini trocobalt(III) acetate. To facilitate the application and use of graph sets many of these developments have already been incorporated into the softwar e of the Cambridge Structural Database, as described in the accompanying pa per.