Benchmarks of graph invariants for hydrogen-bond networks in water clusters of different topology

  • Andrey M. Tokmachev
  • Andrei L. TchougréeffEmail author
  • Richard Dronskowski
Part of the Highlights in Theoretical Chemistry book series (HITC, volume 12)


The diversity of the various forms of water stems from systems of hydrogen bonds. Cooperative behaviour of hydrogen-bond networks gives rise to unique properties of water systems. A number of approaches to understand and model the collective behaviour of hydrogen bonds and predict their properties on the basis of a small number of calculations have been put forward. Among them, the concept of graph invariants provides most general descriptors for hydrogen-bond networks, which are routinely used to predict properties of water systems. In the present work, we examine the formalism of graph invariants and propose its modification which may be beneficial for water structures with defects. To benchmark graph invariants, we carried out quantum-chemical calculations of more than 107 water clusters with different hydrogenbond configurations. The quality of the approximation is studied as a function of the type of graph invariant and its order. The results demonstrate that the method is applicable only to cage-like structures without significant strains.


Water clusters Hydrogen bonds Graphs Invariants APSG 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Andrey M. Tokmachev
    • 1
  • Andrei L. Tchougréeff
    • 2
    • 3
    • 4
    Email author
  • Richard Dronskowski
    • 4
  1. 1.NBICS CentreNRC Kurchatov InstituteMoscowRussia
  2. 2.Moscow Center for Continuous Mathematical EducationMoscowRussia
  3. 3.Department of ChemistryMoscow State UniversityMoscowRussia
  4. 4.Institut für Anorganische ChemieRWTH Aachen UniversityAachenGermany

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