Water as a Levy rotor

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 $\alpha$ and a rotational time constant $\tau$. A Lévy parameter $\alpha <2$ signals anomalous (non-Brownian) motion. A molecular dynamics simulation of water at 298\,K validates the probability density function for the intra-molecular ${}^1$H--${}^1$H dynamics of water. The rotational dynamics of water is found to be approximately Brownian at sub-picosecond time intervals but becomes increasingly anomalous at longer times due to hydrogen-bond breaking and reforming. The rotational time constant lies in the range $8<\tau <11$\,ps. The Lévy rotor model is used to estimate the intra-molecular contribution to the longitudinal nuclear-magnetic-resonance relaxation rate $R_{1,\mathrm{intra}}$ due to dipolar ${}^1$H--${}^1$H interactions. It is found that $R_{1,\mathrm{intra}}$ contributes $65\pm 7$\% to the overall relaxation rate of water at room temperature.

4 pages, 3 figures, for the main paper. Supplementary material included and in the right place