Benchmarks of graph invariants for hydrogen-bond networks in water clusters of different topology

Abstract

The diversity of the various forms of water stems from systems of hydrogen bonds. Cooperative behaviour of hydrogen-bond networks gives rise to unique properties of water systems. A number of approaches to understand and model the collective behaviour of hydrogen bonds and predict their properties on the basis of a small number of calculations have been put forward. Among them, the concept of graph invariants provides most general descriptors for hydrogen-bond networks, which are routinely used to predict properties of water systems. In the present work, we examine the formalism of graph invariants and propose its modification which may be beneficial for water structures with defects. To benchmark graph invariants, we carried out quantum-chemical calculations of more than 10⁷ water clusters with different hydrogenbond configurations. The quality of the approximation is studied as a function of the type of graph invariant and its order. The results demonstrate that the method is applicable only to cage-like structures without significant strains.

Published as part of the special collection of articles “Festschrift in honour of P. R. Surjan.”