Mikhail V. Kirov

Ice and gas hydrates exhibit extraordinary structural diversity, which is superimposed by exponential proton disorder caused by the ambiguous arrangement of hydrogen atoms (protons) in hydrogen bonds. In many water clusters and finite ice nanostructures, the relative energy variation due to proton disorder is much greater than in bulk samples. Two-layer ices are a separate class of water nanostructures, in which the variation in the stabilization energy is also large and, per water molecule, comparable with the heat of fusion of ice. An important feature of some bilayer ices is the presence of large cavities, which, in the presence of confining walls, allows them to be considered as frameworks of 2D clathrate hydrates. To study the stability of different ice bilayers, taking into account proton disorder, computer simulations were performed using the non-additive intermolecular potential AMOEBA. Emphasis was placed on bilayers whose individual layers predominantly form pentagonal rings. The factors determining the stability of bilayer ices were identified. The necessary topological condition for the assembly of planar 3-coordinated lattices and corresponding ice bilayers from individual fragments is established. Self-assembly methods that yield the most stable bilayer configurations are discussed.

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)].

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.

Euler's formula for polyhedra is one of the most famous mathematical results. It is also widely used outside mathematics. In particular, it is used in the analysis of molecular structures, many of which have a polyhedral shape. Generalizations of Euler's formula for non-simply connected and multidimensional polyhedra are well known. This article presents a generalization of Euler's formula for adjacent polyhedra. Various cases of adjacency are considered: face-sharing, edge-sharing and vertex-sharing connections. For a system of adjacent polyhedra, a single formula relates the number of vertices, edges and faces in the form V – E + F = N + 1, where N is the number of polyhedra.

Euler's formula for polyhedra is one of the most famous mathematical results. It is also widely used outside mathematics. In particular, it is used in the analysis of molecular structures, many of which have a polyhedral shape. Generalizations of Euler's formula for non-simply connected and multidimensional polyhedra are well known. This article presents a generalization of Euler's formula for adjacent polyhedra. Various cases of adjacency are considered: face-sharing, edge-sharing and vertex-sharing connections. For a system of adjacent polyhedra, a single formula relates the number of vertices, edges and faces in the form V – E + F = N + 1, where N is the number of polyhedra.

A simple model to study the stability of multi-cage clathrate-like structures.