Anharmonic Nuclear Motion and the Relative Stability of Hexagonal and Cubic ice

Abstract

We use extensive first-principles quantum mechanical calculations to show that, although the static lattice and harmonic vibrational energies are almost identical, the anharmonic vibrational energy of hexagonal ice is significantly lower than that of cubic ice. This difference in anharmonicity is crucial, stabilizing hexagonal ice compared with cubic ice by at least 1.4 meV/H_{2}O, in agreement with experimental estimates. The difference in anharmonicity arises predominantly from molecular O-H bond-stretching vibrational modes and is related to the different stacking of atomic layers.