Equilibrium molecular-dynamics simulations have been performed for liquid water, and on metastable sI and sII polymorphs of empty hydrate lattices, in addition to ice Ih, in order to study the dynamical properties of librational motion (rotation oscillation) depicted by protons in water molecules. In particular, hydrate lattices were found to display prominent "bifurcated" features, or peaks, at circa 70 and 80-95 meV (or ∼560 and 640-760 cm(-1), respectively), also displayed by ice, in essentially quantitative agreement with experimental neutron-scattering data. However, observed differences in dispersion between these librational modes between these two structures (both hydrate polymorphs vis-à-vis ice), owing primarily to density effects, have been decomposed into contributions arising from angular-velocity dynamics about axes in the local molecular frame of water molecules, with in-plane "wagging" and "twisting" rationalising one mode at ∼70 meV, and out-of-plane motion for the higher-frequency band. This was confirmed explicitly by a type of de facto normal-mode analysis, in which only immediate layers of water molecules about the one under consideration were allowed to move. In contrast, liquid water displayed no marked preference for such local in- or out-of-plane modes characterising librational motion, owing to the marked absence of rigid, pentamers or hexamers therein.