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

The central idea observes a recursive mapping of n-body intramolecular interactions to (n + 1)-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 n-body potentials. In particular, the method yields a complete characterization of 4-body interactions. The hierarchical structure of atomic index lists for each interaction order n 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 n-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.