Recent x-ray Compton scattering experiments in ice have provided useful information about the quantum nature of the interaction between H$_2$O monomers. The hydrogen bond is characterized by a certain amount of charge transfer which could be determined in a Compton experiment. We use ab-initio simulations to investigate the hydrogen bond in H$_2$O structures by calculating the Compton profile and related quantities in three different systems, namely the water dimer, a cluster containing 12 water molecules and the ice crystal. We show how to extract estimates of the charge transfer from the Compton profiles.

16 pages, 7 figures, to appear in Phys. Rev. B