Enumerating and indexing many-body intramolecular interactions: a graph theoretic approach

Robert Penfold, Peter J. Wilde

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The central idea observes a recursive mapping of -body intramolecular interactions to -body terms that is consistent with the molecular topology. Iterative application of the line graph transformation is identified as a natural and elegant tool to accomplish the recursion. The procedure readily generalizes to arbitrary -body potentials. In particular, the method yields a complete characterization of -body interactions. The hierarchical structure of atomic index lists for each interaction order is compactly expressed as a directed acyclic graph. A pseudo-code description of the generating algorithm is given. With suitable data structures (e.g., edge lists or adjacency matrices), automatic enumeration and indexing of -body interactions can be implemented straightforwardly to handle large bio-molecular systems. Explicit examples are discussed, including a chemically relevant effective potential model of taurocholate bile salt.

Original languageEnglish
Pages (from-to)1634-1648
Number of pages15
JournalJournal of Mathematical Chemistry
Issue number7
Early online date19 May 2015
Publication statusPublished - Aug 2015


  • Computer simulation
  • Molecular modelling
  • Graph theory

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