  One of the many peculiar properties of water is the pronounced deviation of
the proton momentum distribution from Maxwell-Boltzmann behaviour. This
deviation from the classical limit is a manifestation of the quantum mechanical
nature of protons. Its extent, which can be probed directly by Deep Inelastic
Neutron Scattering (DINS) experiments, gives important insight on the potential
of mean force felt by H atoms. The determination of the full distribution of
particle momenta, however, is a real tour de force for both experiments and
theory, which has led to unresolved discrepancies between the two. In this
Letter we present comprehensive, fully-converged momentum distributions for
water at several thermodynamic state points, focusing on the components that
cannot be described in terms of a scalar contribution to the quantum kinetic
energy, and providing a benchmark that can serve as a reference for future
simulations and experiments. In doing so, we also introduce a number of
technical developments that simplify and accelerate greatly the calculation of
momentum distributions by means of atomistic simulations.
