On the origin of the redshift of the OH stretch in Ice Ih: evidence from the momentum distribution of the protons and the infrared spectral density

Recent measurements of the momentum distribution in water and ice have shown that the proton is in a considerably softer potential in ice Ih than in water or the free monomer. This is broadly consistent with the large red shift observed in the vibrational spectrum. We show that existing water models, which treat the intramolecular potential as unchanged by the hydrogen bonding are unable to reproduce the momentum distribution. In addition, even if they can substantially explain the red shift they are unable to explain the large increase in intensity observed in the infrared spectrum in going from the monomer to ice Ih. We show that the inclusion of a bond dipole derivative term is essential to explain the observed intensities in the infrared spectrum. Though this term is partially responsible for the softening of the effective potential of the proton we show that best agreement with the observed momentum distribution requires a further softening of the harmonic component of the intramolecular potential. We introduce an efficient normal-mode molecular dynamics algorithm for calculating the momentum distribution with path-integrals.