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

J. Grell, J. Bernstein, G. Tinhofer

Research output: Contribution to journalArticlepeer-review

215 Scopus citations


To provide a foundation for further theoretical and software development of the application of graph sets to patterns of hydrogen bonding and other intermolecular interactions a number of mathematical concepts and tools are defined, developed and demonstrated. Following a review of the basic definitions and uses of graph sets, the directional properties of hydrogen bonds are now included in the treatment. The concepts of a constructor graph and covalent distance matrix have been developed to aid in the generation of a qualitative descriptor for the straightforward, consistent and ultimately automatic (with appropriate software) definition of patterns. An additional mathematical tool, the arrowed T-labeling, has been developed to deal with situations 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, polymorphic iminodiacetic acid [N-(carboxymethyl)glycine] and trans-tetraamminedinitrocobalt(III) acetate. To facilitate the application and use of graph sets many of these developments have already been incorporated into the software of the Cambridge Structural Database, as described in the accompanying paper.

Original languageEnglish
Pages (from-to)1030-1043
Number of pages14
JournalActa Crystallographica Section B: Structural Science
Issue number6
StatePublished - 1 Dec 1999

ASJC Scopus subject areas

  • General Biochemistry, Genetics and Molecular Biology


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