DFT calculations of the energies and stabilities

The energies and stabilities of guest-free clathrates and selected ice phases were investigated by DFT calculations with the VASP 5.3 software package (44). The electron-ion interactions were described by the projector augmented wave (PAW) potential (45). To account for the intermolecular dispersion interactions, the exchange-correlation interaction was described by the vdW-DF2 functional (46), with inclusion of a long-range term of the correlation energy. The electron wave function was expanded by plane-wave basis up to 700 eV, and the Brillouin zones were sampled by k point grids with a uniform spacing of 2π × 0.04 Å⁻¹.