Nuclear spin relaxation due to paramagnetic species in solution: Effect of anisotropy in the zero field splitting tensor

Abstract

The NMR (nuclear magnetic resonance) paramagnetic relaxation enhancement (NMR-PRE) that is produced by paramagnetic solutes in solution has been investigated theoretically with respect to the influence of zero field splitting (zfs) interactions in the electron spin Hamiltonian, in particular with respect to the effects of anisotropy in the zfs tensor. These effects are a physical consequence of the influence of the zfs on the motion of the electron spin vector S̄. When the zfs energy is large compared to the Zeeman energy (the zfs limit), the precessional motion of S̄ is quantized in the molecule-fixed coordinate system that diagonalizes the zfs tensor. The uniaxial portion of the zfs tensor influences the NMR-PRE primarily through its influence on the quantization axes of S̄; the characteristic behavior of the NMR-PRE under the influence of a uniaxial zfs has been described in detail previously. Anisotropy in the zfs tensor induces oscillatory motion in Sz. This motion has a profound influence on the NMR-PRE, the major part of which normally arises from low frequency components of the local magnetic field that are associated with Sz, rather than from the rapidly precessing local fields that are associated with the transverse components S±. For this reason, the NMR-PRE is a sensitive function of zfs anisotropy, which acts to lower the NMR-PRE below the value that occurs in the uniaxial situation. The magnitude of this effect depends on the ratio (E/D) of the anisotropic and uniaxial zfs parameters, on the reduced dipolar correlation time, and on the location of the nuclear spin in the molecular coordinate frame. A second physical effect of zfs anisotropy on the NMR-PRE arises from a resonance between the electron spin precessional motion in the transverse plane with the precessional motion that is perpendicular to the transverse plane (the latter due to zfs anisotropy). Resonance of these motions, which occurs spin energy levels crossings, gives rise to low frequency transverse components of S̄ which result in a resonant increase in the NMR-PRE within a restricted range of E/D ratios.