Proton Momentum Distribution and Diffusion Coefficient in Water: Two Sides of the Same Coin?

Water, the prototype of a liquid to ordinary people, is the most anomalous liquid to physicists, showing regions of the temperature-density (T,ρ) plane where its microscopic structure, diffusion coefficient, and density have anomalous behaviors. Structural anomalies occur over a broad bell-shaped T,ρ region. This region contains, as a matryoshka, two smaller regions, one delimiting dynamical and the other delimiting thermodynamic anomalies. Water anomalous behavior in each of these regions manifests itself as a decrease of order or an increase of the diffusion coefficient upon increasing pressure and as a decrease of density upon cooling. Here, we show that the radial momentum distribution of water protons and their mean kinetic energy have a peculiar, theoretically unpredicted anomaly in the region of dynamical anomalies. This anomaly can be rationalized as due to two distinct "families" of water protons, experiencing quite distinct local environments, leading to an enhancement of the momentum fluctuations along with an increase of kinetic energy.