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

The central idea observes a recursive mapping of [Formula: see text]-body intramolecular interactions to [Formula: see text]-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 [Formula: see text]-body potentials. In particular, the method yields a complete characterization of [Formula: see text]-body interactions. The hierarchical structure of atomic index lists for each interaction order [Formula: see text] 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 [Formula: see text]-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.