A Discrete Approach for Finding the Lowest-Energy Configurations of Small Water Polyhedra

The diversity of water clusters is due not only to the different hydrogen (H-) bond network topology but also to the different arrangement of hydrogen atoms (protons) in the H-bonds. The polyhedral shape is typical for the smallest water clusters. Gas hydrate cavities are also polyhedral, which increases the practical interest in studying the properties of polyhedral water clusters. For theory, the structural homogeneity of these clusters, in which all molecules are in equivalent positions, is of particular importance. It is no coincidence that a simple discrete model of intermolecular interactions was initially developed for polyhedral water clusters. The model of strong and weak effective H-bonds (SWEB model) allows classifying the entire set of proton configurations by energy. This article is devoted to the study of the energetics of proton configurations of all three-coordinated water polyhedra with the number of molecules less than 20. The peculiarity of this article is that the selection of candidates for the lowest-energy configurations is carried out using the discrete approach, taking into account the number of the most preferred types of H-bonds, a simplified estimate of the total dipole moment and the number of molecules located in the planes of the square faces.