GRAPH THEORETICAL-ANALYSIS OF WATER CLUSTERS

A graph theoretical representation of the hydrogen bond network in a water cluster is developed using the concept of directed graphs. Ab initio STO-3G calculations on a large collection of small linear and branched, open chain and monocyclic water clusters are presented. The invariants of the digraph representations are utilized for a statistical analysis of the ab initio results, and this procedure provides physically meaningful factorizations of the hydrogen bond energies. The usefulness of a graphical analysis of this type is further demonstrated by applying it to (i) the analysis of a previous energy data set (MCY potential/many-body corrections) for highly condensed clusters of water molecules and (ii) the prediction of the cohesive energy of ice. The graph theory parameters based on the many-body calculation results give an ice cohesive energy in good agreement with experiment.