Topological identification of multi-cage water clusters

The most stable configurations of clusters with tetrahedral bond coordination are often polyhedral or have the form of several adjacent polyhedra. This paper proposes a new approach to the topological identification of such structures, which is distinguished by the use of explicit formulas for calculating n-membered cycles in the structural graph. Furthermore, a formula that is a generalization of the Euler formula for adjacent polyhedra is used for the first time. Methods for identifying multi-cage structures can find application in working with cluster databases, in probabilistic methods for generating cluster structures, and in interpreting the results of computer simulations aimed at understanding the self-organization processes of molecular systems. The Database of Water Cluster Minima is used as the main dataset [Rakshit et al., J. Chem. Phys. 151, 214307 (2019)].