  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,
stabilising hexagonal ice compared with cubic ice by at least 1.4 meV/H2O, 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.
