Water as a Levy rotor

Abstract

A probability density function describing the angular evolution of a fixed-length atom-atom vector as a L\'{e}vy rotor is derived containing just two dynamical parameters: the L\'{e}vy parameter $\alpha$ and a rotational time constant $\tau$. A L\'{e}vy 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 L\'{e}vy rotor model is used to estimate the intra-molecular contribution to the longitudinal nuclear-magnetic-resonance relaxation rate $R_{1,{\rm intra}}$ due to dipolar $^1$H--$^1$H interactions. It is found that $R_{1,{\rm intra}}$ contributes $65\,\pm 7$\% to the overall relaxation rate of water at room temperature.