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arXiv · 2104.12897

Water as a Levy rotor

David A. Faux·Arifah A. Rahaman·Peter J. McDonald
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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. 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 $8 \! < \! τ\! < \! 11$\,ps. The Lévy 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.

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David A. Faux, Arifah A. Rahaman, Peter J. McDonald. 2021-09-14. Water as a Levy rotor. https://doi.org/10.1103/physrevlett.127.256001

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