Spin—Lattice Relaxation in Multilevel Systems

Abstract

Spin—lattice relaxation behavior is calculated for the six lines of the high-resolution NMR spectrum of an AX spin system in which the A spin has I = ½ and the X, 32. Intramolecular dipole—dipole interactions, quadrupole relaxation of the spin three-halves nucleus, and chemical shift anisotropies of both spins are considered. For simplicity all of the tensor operators are taken to be axially symmetric about the A—X internuclear vector, and random isotropic reorientation of the molecules is assumed. The latter assumption can be removed in a phenomenological manner. Cross terms in the Redfield relaxation matrix elements lead to asymmetric relaxation. In general, none of the lines relax in exponential fashion, unless the quadrupole relaxation of spin X is rapid. The relevance of these calculations to proton saturation recovery experiments on (CD3O)211B–H is discussed. Small differences observed previously in the relaxation of the proton spectrum of this compound are probably due to instrumental effects.