Edge-sharing water prisms.

Regular-shaped water clusters and nanostructures can be of particular interest for the self-assembly of complex structures and functional materials involving water molecules. Polyhedral water clusters are the most well studied. The low-energy structures of water hexamer, octamer and decamer are shaped like right prisms. The cavities of gas hydrates also have a polyhedral shape. Ice nanotubes are of no less interest both as configurations of global energy minima and in terms of possible applications. This article presents the results of the first systematic study of the structure and properties of a special class of water clusters. It reveals different combinations of three right prisms sharing an edge. According to modern calculations, the configurations of global energy minima of water clusters with the number of molecules being eighteen and twenty have this structure precisely. The topological characteristics of the edge-sharing water prisms are studied and the formulas for estimating the residual entropy are obtained. For these clusters (3-prisms), the usefulness of using a discrete model of intermolecular interaction [strong-weak-effective-bond model], previously developed for polyhedral water clusters, is shown. Calculations of the binding energy were performed using the non-additive Amoeba potential. To understand the relative stability of 3-prisms among other cluster forms, we use the structures recently reported in a published database containing over 3 × 106 unique water cluster networks (H2O)N of size N = 3-25 [Rakshit et al., J. Chem. Phys., 2019, 151(21), 214307, DOI: 10.1063/1.5128378].

Ice structures assembled from cubic water clusters of D2d and S4 symmetry.

The study of self-assembly processes is of key importance for fundamental science and modern technologies. Cubic water clusters of D2d and S4 symmetry show great potential as building blocks for self-assembly. The objective of this paper is to construct possible ice structures formed by hydrogen bonding of these very stable water clusters. A number of such structures are herein presented, including quasi-2D and 3D ices as well as spatial layered and tubular ices. The energetics and structure of many configurations differing in the arrangement of hydrogen atoms in hydrogen bonds have been studied. It was established that the proton disorder of all such ices is of island type. The residual entropy of these ices is equal to ln(3)/4 in dimensionless form. For layered structures formed by the stacking of multiple bilayers, the determining role of the van der Waals interactions is shown. Note that, for all considered ices, the lowest-energy configurations are formed only by clusters of D2d symmetry.

Hydrogen bond arrangements in (H2O)20, 24, 28 clathrate hydrate cages: Optimization and many-body analysis.

We provide a detailed study of hydrogen bonding arrangements, relative stability, residual entropy, and an analysis of the many-body effects in the (H2O)20 (D-cage), (H2O)24 (T-cage), and (H2O)28 (H-cage) hollow cages making up structures I (sI) and II (sII) of clathrate hydrate lattices. Based on the enumeration of the possible hydrogen bonding networks for a fixed oxygen atom scaffold, the residual entropy (S0) of these three gas phase cages was estimated at 0.754 82, 0.754 44, and 0.754 17 · Nkb, where N is the number of molecules and kb is Boltzmann's constant. A previously identified descriptor of enhanced stability based on the relative arrangement and connectivity of nearest-neighbor fragments on the polyhedral water cluster [strong-weak-effective-bond model] also applies to the larger hollow cages. The three cages contain a maximum of 7, 9, and 11 such preferable arrangements of trans nearest dimer pairs with one "free" OH bond on the donor molecule (t1d dimers). The Many-Body Expansion (MBE) up to the 4-body suggests that the many-body terms vary nearly linearly with the cluster binding energy. Using a hierarchical approach of screening the relative stability of networks starting from optimizations with the TIP4P, TTM2.1-F, and MB-pol classical potentials, subsequently refining at more accurate levels of electronic structure theory (DFT and MP2), and finally correcting for zero-point energy, we were able to identify a group of four low-lying isomers of the (H2O)24 T-cage, two of which are antisymmetric and the other two form a pair of antipode configurations.

Thermal stability of water polyhedra with square faces.

The ability to form numerous crystalline modifications of ice and gas hydrate frameworks is a characteristic feature of water. In fact, this structural variety is much wider due to the proton disorder. Configurations with different arrangements of hydrogen atoms (protons) in hydrogen bonds are not equivalent in their properties. Polyhedral water clusters are convenient objects for studying the effect of proton disorder on the properties of ice-like systems. It was previously established that the stability of water polyhedra is determined by the competition of two factors. The geometric factor gives preference to tetrahedrally coordinated structures with a large number of pentagonal faces. The topological factor takes into account the number of energetically most favorable types of H-bonds. This number increases with the number of square faces. It was found that tetrahedrally coordinated structures are not the most stable. However, these calculations were performed without taking thermal effects into account (Kirov M. V., J Phys Chem A, 124:4463 - 4470, 2020). The purpose of the present article is to study the structural stability of various water polyhedra at different temperatures. In the course of modeling, using the Amoeba force field, the advantage of configurations with a large number of square faces is demonstrated. The structure and energetics of surface defects are studied. Several very stable structures of unusual shape were found, including polyhedra which contain 4-coordinated molecules and polyhedra whose O-H groups are directed to the cluster center. The comparative analysis of cluster stability includes the temperature intervals of melting-like transitions.

Energetics of Water Polyhedra with Square Faces.

In ice and other icelike systems, the structural variety of tetrahedrally coordinated systems increases strongly due to proton disorder. Configurations that differ from each other only by the arrangement of hydrogen atoms (protons) in hydrogen bonds are nonequivalent. Polyhedral water clusters are interesting objects of study since the analysis of the energetics of these tetrahedrally coordinated systems reveals very simple regularities. For water polyhedra of the most regular shape, the simplified physical model of strong and weak effective H bonds (the SWEB model) has been developed. This model allows predicting the classes of the most stable proton configurations. The number of H bonds that are more preferable from the point of view of Coulomb interaction is the only classification criterion for this model. For water polyhedra with square faces, this model becomes less accurate. However, for such clusters, there is another essential topological indicator: the number of molecules that are completely located in the planes of square faces. The results of numerous calculations show that these two topological indices largely determine the energetics of a huge number of proton configurations in water polyhedra with square faces.

Proton disorder and elasticity of hexagonal ice and gas hydrates.

This work is devoted to the study of the mechanical properties of hexagonal ice Ih and gas hydrate frameworks sI, sII and sH, taking into account the disorder in the positions of the hydrogen atoms (protons). The article emphasizes the critical role of the elastic energy for the evaluation of the relative energy of the proton configurations. The calculations are performed with the help of the TINKER package using the AMOEBA polarizable force field. The elastic constants, elastic modulus, and anisotropy indices are calculated. It is shown that all gas hydrate frameworks are very isotropic due to their cage-like structure. It was established that one of the reasons for the higher anisotropy of ice Ih is the presence of a large number of highly symmetric proton configurations. The purpose of the article is to overcome the apparent contradiction between the ab initio and force field methods in predicting the relative stability of the proton configurations of ice structures at low temperature. The other purpose is to evaluate the effect of proton disorder on the elastic properties of ice and gas hydrate structures. Graphical abstract Proton configurations in hexagonal ice: fixed (a) and free (b) unit cell parametersᅟ.

Hydrogen-bond-reversal symmetry and its violation in ice nanotubes.

Recently, a new type of generalized symmetry of ice structures was introduced which takes into account the change of direction of all hydrogen bonds. The energy nonequivalence of pairs of configurations with opposite direction of all hydrogen bonds was established in the course of computer simulation of bilayer ice and other four-coordinated structures without `dangling' hydrogen atoms. In this article, the results of detailed investigations of the violation of the hydrogen-bond-reversal symmetry in ice nanotubes consisting of stacked n-membered rings are presented. A comprehensive classification of all possible hydrogen-bonding configurations and their division into two classes (antisymmetrical and non-antisymmetrical) are given. Attention is focused on the most stable configurations that have no longitudinally arranged water molecules. This restriction made the asymmetry very difficult to find. For example, it was established that the asymmetry (non-antisymmetrical configurations) in ice nanotubes with square, pentagonal and hexagonal cross sections appears only when the number of transverse rings in the unit cell is more than six. It is shown that this is related to the well known combinatorial problem of enumerating the symmetry-distinct necklaces of black and white beads. It was found that, among the ice nanotubes that had been considered, hydrogen-bond-reversal asymmetry is most conspicuous in wide nanotubes such as heptagonal and octagonal. In this case the asymmetry is observed for unit cells of any length. In order to verify the results of the symmetry analysis and to confirm the energy nonequivalence of some (non-antisymmetrical) configurations, approximate calculations of the binding energy have been performed using the package TINKER.

Topological crystallography of gas hydrates.

A new approach to the investigation of the proton-disordered structure of clathrate hydrates is presented. This approach is based on topological crystallography. The quotient graphs were built for the unit cells of the cubic structure I and the hexagonal structure H. This is a very convenient way to represent the topology of a hydrogen-bonding network under periodic boundary conditions. The exact proton configuration statistics for the unit cells of structure I and structure H were obtained using the quotient graphs. In addition, the statistical analysis of the proton transfer along hydrogen-bonded chains was carried out.

Hidden asymmetry of ice.

Ice is a very complex and fundamentally important solid. In the present article, we review a new property of the hydrogen-bonded network in ice structures: an explicit nonequivalence of some antipodal configurations with the opposite direction of all hydrogen bonds (H-bonds). This asymmetry is most pronounced for the structures with considerable deviation of the H-bond network from the tetrahedral coordination. That is why we have investigated in detail four-coordinated ice nanostructures with no outer "dangling" hydrogen atoms, namely, ice bilayers and ice nanotubes consisting of stacked n-membered rings. The reason for this H-bonding asymmetry is a fundamental nonequivalence of the arrangements of water molecules in some antipodal configurations with the opposite direction of all H-bonds. For these configurations, the overall pictures of deviations of the hydrogen bonds from linearity are qualitatively different. We consider the reversal of all H-bonds as an additional nongeometric operation of symmetry, more precisely antisymmetry. It is not easy to find the explicit breaking of the symmetry of hydrogen bonding (H-symmetry) in the variety of all configurations. Therefore, this asymmetry may be named hidden.

Low-energy networks of the T-cage (H2O)24 cluster and their use in constructing periodic unit cells of the structure I (sI) hydrate lattice.

Hydrate networks are "host" lattices for the storage of "guest" natural gases. To enhance their physical stabilities near ambient conditions, the most stable clathrate hydrates should be identified. Here we report the lowest-energy networks of the tetrakaidecahedral cage (T-cage) (H(2)O)(24) cluster, a constituent of the unit cell of the structure I [denoted (sI)] hydrate. A four-step screening method was employed to search for the lowest-energy T-cage networks, which were eventually optimized at the MP2 level of theory. We further outline a procedure based on the obtained low-energy isomers of the T-cage for constructing periodic unit cells of the (sI) hydrate lattice.