Rotational-Diffusion Propagator of the Intramolecular Proton–Proton Vector in Liquid Water: A Molecular Dynamics Study

The rotational motion of water molecules plays the dominant role in determining NMR spin-relaxation properties of liquid water and many biological tissues. The traditional theory of NMR spin relaxation predominantly uses the assumption that the reorientational dynamics of water molecules is described by a continuous-time rotational-diffusion random walk with a single rotational-diffusion coefficient. However, recent experimental and theoretical studies have demonstrated that water reorientation occurs by large, discrete angular jumps superimposed on a continuous-time rotational-diffusion process. We have investigated the rotational-diffusion propagator of the proton-proton (H-H) vector of water molecules in liquid water at 298 K using molecular dynamics (MD) simulations. Analysis of the MD-simulated reorientational trajectories reveals that reorientation of the intramolecular H-H vector occurs through a combination of the two mechanisms: rotational diffusion proper and discrete large-angle jumps. We demonstrate that, empirically, the rotational-diffusion propagator of the intramolecular H-H vector in liquid water can be described in terms of multiple rotational-diffusion coefficients. A model with two rotational-diffusion coefficients was found to provide a reasonable (albeit imperfect) fit of the MD-simulated propagator on the time scales relevant to NMR spin relaxation near room or physiological temperature (picoseconds to nanoseconds). We report the apparent values of the two rotational-diffusion coefficients determined from the propagator analysis at 298 K and discuss their physical meaning.