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 298K 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 25ps. 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.
Highlights
A probability density function describing the angular evolution of a fixed-length atom-atom vector as a Levy rotor is derived containing just two dynamical parameters: the Levy parameter α and a rotational time constant τ
The dynamics of water may be probed by 1H nuclear magnetic resonance (NMR) techniques
The longitudinal relaxation rate R1 is exquisitely sensitive to the relative motion of pairs of 1H spins due to the collective effects of all water dynamical processes including vibration, bond stretching, libration, tumbling, collisions and the breaking and reforming of H-bonds [1]
Summary
A probability density function describing the angular evolution of a fixed-length atom-atom vector as a Levy rotor is derived containing just two dynamical parameters: the Levy parameter α and a rotational time constant τ. The intra-molecular contribution is associated with the rotation of the fixed-length 1H–1H vector in the applied magnetic field and the inter-molecular contribution is due to the relative translational motion of pairs of 1H spins on different molecules and includes changes in both vector length and angle. The Levy model for intra-molecular rotational assumes that the distance between the two 1H spins on the same water molecule is fixed and that the rotational evolution is described by the probability density function P (ψ, t) given by Eq (1).
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