Nuclear-spin relaxation in paramagnetic solutions when the electronic zero-field splitting and zeeman interactions are of arbitrary magnitude

Expressions for the dipolar nuclear-spin relaxation rates in paramagnetic salt solutions have been derived under conditions where the electronic zero-field splitting (zfs) and Zeeman interactions are of arbitrary magnitude and when electron-spin relaxation is rapid compared to molecular reorientation. The theory is intended to provide continuity between the limiting analytical expressions previously derived for the Zeeman limit [Solomon-Bloembergen-Morgan (SBM) theory] and the zfs limit (R. Sharp, J Chem. Phys. 93, 6921, 1990). The more general solutions parallel the forms of both of these limiting theories in that they are comprised of sums of terms, each term consisting of a mean-square dipolar coupling energy times a spectral density function at one of the transition frequencies of the coupled I-S spin system. Geometric aspects of the problem are exhibited in simplest form in terms of spherical tensors, and the resulting expressions reduce in a straightforward manner to the Zeeman- and zfs-limit equations. As in the limiting theories, the electronspin relaxation time is treated as a parameter of the theory rather than calculated in detail from the time dependence of the electron-spin Hamiltonian. The theory has been applied to the analysis of magnetic field-dependent proton relaxation data of the ligand methyl protons in solutions of tris(acetylacetonato)Mn(III). The agreement with experiment is much superior to that found for SBM theory.