Graph invariants: A tool to analyze hydrogen bonding in ice and water clusters

We have studied a wide range of aqueous systems, from the order/disorder in the hydrogen bond network of ordinary ice, a fundamental problem in ice physics for over 70 years, to properties of water clusters. A common theoretical difficulty in these systems is the enormous number of hydrogen bond arrangements that must be considered in these systems, and for which no systematic treatment has been available. Our analytical method based on graph theory and the introduction of graph invariants provides a means for efficient and reliable analysis. Recent investigations of water clusters have demonstrated that graph invariants provide a powerful tool for capturing very complex behavior using only a small number of parameters, and some of our findings have uncovered unknown aspects of the behavior of water clusters. Applications of this analytic method provide insight into the nature of hydrogen bond disorder in ice, and impact our understanding of chemical reactions in water clusters important to environmental chemistry.