Abstract
A probability density function describing the angular evolution of a fixed-length atom-atom vector as a Lévy rotor is derived containing just two dynamical parameters: the Lévy parameter α and a rotational time constant τ. A Lévy parameter α<2 signals anomalous (non-Brownian) motion. Molecular dynamics simulation of water at 298 K validates the probability density function for the intramolecular ^{1}H─^{1}H dynamics. The rotational dynamics of water is found to be approximately Brownian at subpicosecond time intervals, becomes increasingly anomalous at longer time intervals due to hydrogen-bond breaking and reforming, before becoming indistinguishable from Brownian dynamics beyond about 25 ps. The Lévy rotor model is used to estimate the intramolecular contribution to the longitudinal nuclear-magnetic-resonance (NMR) relaxation rate R_{1,intra}. It is found that R_{1,intra} contributes 65%±7% to the overall relaxation rate of water at room temperature.