Nuclear magnetic resonance relaxation enhancements produced by paramagnetic solutes: Effects of rhombicity in the zero field splitting tensor with the S=2 spin system as an example

Abstract

Effects due to the nonuniaxial part of the zero field splitting (ZFS) tensor on NMR relaxation enhancements produced by paramagnetic species in solution (the NMR PRE) has been studied theoretically and experimentally in the ZFS limit, i.e., in the limit where the ZFS energy is large compared to the Zeeman energy. In the ZFS limit, the precessional motion of the electron spin is quantized with respect to molecule-fixed coordinate axes. The uniaxial part of the ZFS tensor induces precessional motion in the transverse (x,y) components of the electron spin vector S, and x,y anisotropy in the ZFS tensor (i.e., a nonzero ZFS parameter E) induces precessional motion in the z component of S. The NMR-PRE phenomenon is particularly sensitive to the motion of Sz and hence also to ZFS anisotropy in the xy plane. Mathematical expressions have been derived which describe the motion of the spin vector evolving under the influence of a general rhombic ZFS Hamiltonian and the influence of this motion on the NMR PRE in the ZFS limit. It is shown that oscillations in Sz occur at the transition frequencies of the S spin system; the frequencies and amplitudes of the precessional components of Sz can be calculated by diagonalizing the general ZFS Hamiltonian. These motions and their consequences with respect to the behavior of the NMR PRE are described in detail for the S=2 spin system. A parametrization of NMR-PRE data is proposed which gives a clear criterion for the conditions under which rhombic parts of the ZFS tensor significantly affect the relaxation enhancements produced by an S=2 spin system. This criterion is of considerable practical importance for the analysis of NMR-PRE data, since it defines conditions under which data may be analyzed without the need for independent experimental information concerning the magnitude of the ZFS tensor.