The electronic states of completely polarized cubic ice are studied using as an expansion set the Bloch sums formed with water molecular orbitals. A complete symmetry analysis appropriate for the nonsymmorphic group of cubic ice is given for a simplified model. The band structure of cubic ice is obtained at high-symmetry points and high-symmetry lines of the Brillouin zone. The calculated energy gap of 7.8 eV is in good agreement with experimental data and corresponds to a critical point of type $M_0$ at $\overrightarrow{\mathrm{k}}=0\mathrm{}$. The critical points of type $M_1$ occurring at the point $L$ of the Brillouin zone are interpreted as responsible for the strong peak in the ultraviolet optical constants at 8.7 eV. The broad absorption band at higher energy (≅ 15 eV) is interpreted as due to transitions from valence bands derived from lone-pair orbitals to the lowest excited bands.

• Received 20 October 1972

DOI:https://doi.org/10.1103/PhysRevB.8.3009