Energetics of ice nanotubes and their encapsulation in carbon nanotubes from density-functional theory

We have performed total-energy electronic-structure calculations based on the density-functional theory that clarify atomic and electronic structures of ice nanotubes encapsulated in carbon nanotubes. We have found that three tubular structures of ice are stable in carbon nanotubes. The structural characteristics of these ice nanotubes is a straight stacking or helical arrangement of polygonal units consisting of water molecules. In these stable ice nanotubes, each water molecule is fourfold coordinated with neighboring water molecules through hydrogen bonds. The energy gain upon encapsulation of ice nanotubes in carbon nanotubes is found to be an order of $10\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ per water molecule, whereas the energy gain to form ice nanotubes from isolated water molecules is about a half eV per molecule. Carbon nanotubes act as a template to form the new polymorph of ice. Detailed structural analysis has revealed a role of hydrogen-bond angles in determining energetics of the ice nanotubes. We have also clarified that energy gaps of ice nanotubes are comparable with the gap of the most stable ice polymorph Ih and that the electronic structure of ice nanotubes encapsulated in carbon nanotubes is a superposition of the energy bands of the constituents.