Nuclear spin relaxation in paramagnetic systems ( S = 1) in the slow-motion regime for the electron spin. IV. Motional anisotropy and noncoinciding dipole-dipole and zero-field splitting tensors

Abstract

In this work, a paramagnetic complex in which the interacting electron ( S) and nuclear ( I) spins are connected by a vector not coinciding with the principal coordinate system of the zero-field-splitting (ZFS) tensor of the electron spin is considered as a model system. It is shown that the behavior of the dipole-dipole (DD) nuclear spin relaxation in such a system changes drastically when the electron spin enters the slow-motion regime. The effect of the slow motion is shown to be strongly dependent on the angle between the DD vector and the z axis of the principal coordinate system of the ZFS tensor. The present theory is valid for all possible values of the experimental variables and gives the Solomon equations as a limit of lowest order. The relation of the new theory to the modified Solomon-Bloembergen (MSB) equations is also discussed. If the anisotropic reorientation is incoporated (coinciding ZFS and diffusion tensors), the present theory, to the lowest order, yields the same results for the DD interaction of two interacting spins as obtained by Woessner ( J. Chem. Phys. 37, 647 (1962) . The internal diffusion can also be easily incorporated. The differences between the traditional theory and the slow-motion results, as well as the effects on relaxation in some interesting experimental situations are demonstrated by appropriate diagrams.