First-principles Momentum Distributions and Vibrationally Corrected Permittivities of Hexagonal and Cubic Ice

Three-dimensionally resolved proton momentum distributions and end-to-end distributions have been calculated for hexagonal and cubic water ice. First-principles quantum nuclear wave functions have been used to investigate the impact of vibrational anisotropy, anharmonicity, proton and stacking disorder, temperature, and pressure on these distributions. Moreover, the effects of vibrations on the electronic density in hexagonal ice are shown to lead to a 5% vibrational correction with respect to the static-lattice optical permittivity, and proton disorder is found to be crucial in explaining its experimentally observed temperature dependence.