Electronic States and Optical Properties in Cubic Ice

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.