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

Grell1, Bernstein, Tinhofer

  • 1Institute of Freshwater Ecology and Inland Fisheries, Department of Ecohydrology, Rudower Chaussee 6a, D-12489 Berlin, Germany.

Acta Crystallographica. Section B, Structural Science
|August 6, 2000
PubMed
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This study introduces new mathematical tools, including constructor graphs and arrowed T-labeling, to analyze hydrogen bonding patterns. These methods enable consistent and automatic identification of intermolecular interaction patterns in crystal structures.

Area of Science:

  • Crystallography
  • Chemical Physics
  • Computational Chemistry

Background:

  • Graph sets are utilized for analyzing patterns in intermolecular interactions.
  • Existing methods require enhancement to incorporate directional properties of hydrogen bonds.
  • Mathematical formalisms are needed for consistent and automated pattern definition.

Purpose of the Study:

  • To develop and demonstrate mathematical concepts and tools for applying graph sets to hydrogen bonding and intermolecular interactions.
  • To establish a foundation for theoretical and software development in pattern analysis.
  • To enable the straightforward, consistent, and automatic definition of interaction patterns.

Main Methods:

  • Review of basic definitions and uses of graph sets.

Related Experiment Videos

  • Inclusion of directional properties of hydrogen bonds.
  • Development of constructor graphs and covalent distance matrices.
  • Introduction of arrowed T-labeling for moieties on crystallographic special positions.

    • Main Results:

    • Defined and demonstrated mathematical concepts and tools for graph set application.
    • Developed constructor graphs and covalent distance matrices for qualitative descriptor generation.
    • Created arrowed T-labeling to address special crystallographic positions.
    • Applied the developed concepts to polymorphic iminodiacetic acid and trans-tetraamminedinitrocobalt(III) acetate structures.

    Conclusions:

    • The developed mathematical tools provide a robust framework for analyzing hydrogen bonding and intermolecular interactions.
    • These methods facilitate consistent and automated pattern definition in crystal structures.
    • The concepts are integrated into Cambridge Structural Database software for practical application.