Measurements of the proton momentum distribution np in water from ambient conditions to above the supercritical point are compared with theoretical calculations based on a recently developed polarizable water model. The np along the H-bond direction is narrower in the dense phases, and approaches that of the isolated molecule in the more dilute phases. The theoretical model, which includes only electrostatic interactions, is unable to explain the softening of the local potential experienced by the proton in the dense phases, but it accurately predicts the np for the dilute phases.

T he structure and dynamics of liquid water are directly influenced by quantum mechanics, not only in terms of the electronic structure and chemical bonding but also at the level of the nuclear motion. So-called nuclear quantum effects (NQEs) include zero-point energy, tunnelling, isotope effects in the thermodynamic properties, and, what is most relevant to the present work, large deviations from the classical, Maxwell− Boltzmann behavior of both the average nuclear kinetic energy ⟨E K ⟩ and the momentum distribution n(p).Even though NQEs are very large (the zero-point energy content of an O−H stretching vibration is in excess of 200 meV), it is often the case that their net effect on macroscopic properties is relatively small. For instance, the melting temperatures of light and heavy water differ by less than 4 K, and the boiling temperatures differ by just 1 K. Recent theoretical analyses 1,2 have suggested that this could stem from a partial cancellation between quantum effects in the intra-and intermolecular components of the hydrogen bond, so that the net effect is small even if the individual contributions are large. In particular, the competition between quantum effects can be seen very clearly when decomposing the changes in the quantum kinetic energy of protons and deuterons along different molecular axes. 3,4 The mechanism that underlies the competition between changes in the different components of the quantum kinetic energy can be understood by considering as an analogy a twolevel quantum system with an environment-dependent offdiagonal coupling β. A small change in the coupling Δβ, arising from a phase transition or some other change in the environment of the system, will shift its eigenvalues by the same amount proportional to Δβ, but in opposite directions. Even though this picture is clearly oversimplified, it is consistent with a diabatic state model of the hydrogen bond, 5 it demonstrates that the notion of competing quantum effects is nothing exotic, and explains why it returns in many circumstances in the study of water and other hydrogenbonded systems.Competing quantum effects have in fact been identified in a diverse variety of simulations, 1−4 and it seems entirely plausible