Characteristic properties of the nuclear magnetic resonance–paramagnetic relaxation enhancement arising from integer and half-integer electron spins

Abstract

The influence of zero field splitting (zfs) interactions on the magnetic field dispersion profile of the nuclear magnetic resonance–paramagnetic relaxation (NMR–PRE) (i.e., the enhancement of nuclear magnetic relaxation rates that is produced by paramagnetic solute species in solution) has been explored systematically for S=1, 3/2, 2, and 5/2 spin systems using recently developed theory. To facilitate comparison of results for different spin values, the theory was expressed in a reduced form with Larmor frequencies in units of ωD (the uniaxial zfs parameter D in rad s−1), and correlation times and spin relaxation times in units of ωD−1. For S=1, the functional form of the profile can be described in terms of five types of qualitative features. Two of these are characteristic of Zeeman-limit [Solomon, Bloembergen, and Morgan (SBM)] theory and result from the magnetic field dependence of the spin energy level splittings. The remaining three have no analog in Zeeman-limit theory and arise from a change in the quantization axis of the electron spin precessional motion which, in the zfs limit, lies along molecule-fixed coordinate axes, and, in the Zeeman limit, lies along the external field direction. The reduced field dispersion profiles for the integer spin systems S=1 and S=2 were found to be very similar to each other, the principal difference being that the midfield positions of the requantization features (types 2, 3, and 4) are shifted for S=2 relative to S=1, the magnitude and sign of the shift depending on the position of the nuclear spin in the molecular coordinate frame. For half-integer spins, the dispersion profiles exhibit, in addition to the five features characteristic of integer spins, a sixth type of feature, which is centered somewhat to low field of ωSτc=1, where τc is the dipolar correlation time. The type-6 feature results from field-dependent level splitting of the mS=±1/2 Kramers doublet. It is present when ωDτc≥1. These theoretical predictions have been examined by means of reinterpretations of the NMR–PRE data for tris-(acetylacetonato)–metal complexes of V(III) (S=1), Cr(III) (S=3/2), Mo(III) (S=3/2), Mn(III) (S=2), and Fe(III) (S=5/2). As predicted, type-6 features are absent for the integer spin complexes, for which the T1 field dispersion profiles are nearly field independent. The experimental profiles were successfully simulated quantitatively by the generalized theory, but not by Zeeman-limit theory. For the half-integer spin systems, the predicted zfs-related type-6 features appear to be present in the profiles, particularly for Mo(acac)3, for which the data deviate significantly from the Zeeman-limit profile in a manner that is explained by the generalized theory.