Neutron-scattering measurements of wave-vector-dependent hydrogen density of states in liquid water

Inelastic-neutron-scattering spectroscopy is utilized to probe single-particle excitations as a function of temperature in light and heavy water over an energy range of 50 to 600 meV, covering the librational, bending, and stretch vibrational regions of molecular motion. A computer molecular-dynamics simulation of liquid water based on a simple point-charge model is also carried out to compute the Q-dependent proton density of states $G_s$(Q,E) for direct comparison with the equivalent quantity deduced from experimental measurements on an absolute scale. The calculated classical density of states is lower than the measured one by a factor of 2, indicating the importance of quantum-mechanical corrections at high-energy transfers. The classical simulation fails to predict a combination band at 525 meV which we attribute to a quantum-mechanical process of simultaneous excitation of the stretch vibrational mode and breaking of the adjacent H-O...H hydrogen bond. The temperature dependence of this band is predicted correctly by a quantum-mechanical calculation using a one-dimensional hydrogen-bond model.