Hidden asymmetry of ice

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.

Classification of hydrogen bond flips in small water polyhedra applied to concerted proton tunneling

Recently a new mechanism of proton tunneling in a prism-like water hexamer was revealed [Richardson et al., Science, 2016, 351, 1310]. The tunneling motion involves the concerted breaking of two hydrogen bonds and rotations of two nearest water molecules. Eventually, this structural transformation means flipping one of the hydrogen bonds without the creation of defects in the hydrogen bond network. On the surface of polyhedral water clusters, there are five essentially different types of hydrogen bonds, and only two of them can be changed in this manner. In this article, the topological classification of such transformations for five small water polyhedra: triangular, pentagonal, and hexagonal prisms as well as cube and polyhedron 4⁴5⁴, consisting of four square and four pentagonal faces, is presented. Our classification includes the enumeration of all possible one-bond-flips with consideration of the types of hydrogen bonds on the polyhedral surface. Attention is paid to the most stable proton configurations which can be studied in experiments. It was established that a number of one-bond-flip transitions between the low energy configurations are possible in clusters in the shape of triangular and pentagonal prisms.

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.