Water as a Levy rotor

TL;DR

This paper introduces a Lévy rotor model to describe water's angular dynamics, validated by molecular simulations, revealing a transition from Brownian to anomalous motion and quantifying its impact on NMR relaxation rates.

Contribution

The paper derives a simple probability density function for water's angular motion using a Lévy rotor model, incorporating two key parameters, and validates it with molecular dynamics simulations.

Findings

Water's rotational dynamics are approximately Brownian at sub-picosecond timescales.

Anomalous rotational behavior emerges at longer times due to hydrogen-bond dynamics.

Intra-molecular interactions account for about 65% of the NMR relaxation rate in water.

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.