Two-particle random walk simulation of outer-sphere nuclear relaxation

Abstract

We present a two-particle Monte Carlo method for computing the outer-sphere (OS) dipolar time correlation function (DTCF) of the relative position of a nuclear spin I on a diamagnetic molecule M(I) with respect to a nuclear or electronic spin S on a molecule M(S) when both molecules are anisotropic and undergo translational and rotational diffusion. As a first application, we question the validity of the appealing interspin procedure [L. P. Hwang, Mol. Phys. 51, 1235 (1984); A. Borel et al., Chem. Eur. J. 7, 600 (2001)] based on the solutions of a Smoluchowski diffusion equation, which conserve the interspin radial distribution function in the course of time. We show that the true random spatial motion of the interspin vector obtained by simulation can be very different from that given by the Smoluchowski solutions and lead to notable retardation of the time decay of the OS-DTCF. Then, we explore the influence of the solvation properties of M(S) on the decay rate of the DTCF. When M(S) is significantly larger than M(I), its rotation accelerates the decay only weakly, even if M(I) follows M(S) in its Brownian tumbling. By contrast, viscous solvation layers in OS pockets of M(S) can yield an important local slowdown of the relative translational diffusion of M(I), leading to a decay retardation of the DTCF, which adds to that due to the shape anisotropy of M(S). When M(S) is a Gd(3+)-based contrast agent, this retardation leads to a notable increase of the OS contribution to relaxivity even at rather high imaging field.