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

Abstract

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.

Role of internal motions and molecular geometry on the NMR relaxation of hydrocarbons

“…[1]. The case of water shows two distinct peaks in rotational distribution P R (τ ), which agrees well with previous reports [24,25]. According to Ref.…”

“…According to Ref. [25] for water, the larger peak ( 79 % relative intensity) with longer rotational correlation-time (τ = 3.8 ps) is interpreted as Debye continuous-time rotational diffusion, while the smaller peak ( 21 % relative intensity) with shorter rotational correlation-time (τ = 0.22 ps) is interpreted as large-amplitude discrete jumps. [1], including water (W).…”

“…Such heuristic approaches include a variety of distribution functions for the underlying correlation times, including the Cole-Davidson distribution function [4,22], the generalized gamma function [18], the Kohlrausch-Williams-Watts [4] functions, and the Singer-Hirasaki function [23], each chosen to fit the observations, but without theoretical justification. In the case of bulk water (which exhibits hydrogen-bonding), G R (t) is stretched to a similar extent as n-pentane [1], which may be a result of large, discrete angular-jumps [24] superimposed on a continuous-time rotational-diffusion process [25].…”

Critical Role of Confinement in the NMR Surface Relaxation and Diffusion of n-Heptane in a Polymer Matrix Revealed by MD Simulations

“…Molecular dynamics (MD) simulations have already played a helpful, guiding role in this regard. 20,21 We have already shown that MD simulations of 1 H− 1 H dipole−dipole relaxation can naturally separate intramolecular from intermolecular T 1,2 for liquid-state n-alkanes and water, 22,23 as well as 1 H spin-rotation relaxation for methane. 24 Our MD simulations have also shown the effects of internal motions and molecular geometry on T 1,2 of various hydrocarbons, as well as the differences in T 1,2 between methyl and methylene 1 H's across the n-alkane chain.…”

Molecular dynamics simulations of $^1$H NMR relaxation in Gd$^{3+}$--aqua

“…This feature was also present in liquid alkanes, which was attributed to the fast spinning methyl end-groups [49]. Investigations are underway to better understand the origin of this feature in Gd 3+ -aqua, which can perhaps be explained using a two rotational-diffusion model such as found in bulk water [84].…”