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.