Quadrupolar Relaxation of Spin 3 in the Intermediate ω0τcRegime

Abstract

The equations for the quadrupolar relaxation of spin 3 were derived for the Redfield limit where the molecular reorientation rate is much faster than the size of the quadrupolar interaction. In the extreme narrowing regime (ω0τc⪡ 1), the results converge to the analytical expressions for the relaxation rates available in the literature. For slower motions, both longitudinal (spin–lattice) and transverse (spin–spin) relaxations are described by a superposition of three exponentials, where both the rates themselves and their relative weights are functions of ω0τc. Numerical calculations of the relevant relaxation parameters in the intermediate ω0τcregime are presented. Spin–lattice relaxation is described to very good approximation by a single exponential for all values of ω0τc, with the weight of the dominant decay mode exceeding 0.97 for the entire range. The predictions of these simulations were found to be in good agreement with experimentally measured relaxation rates of the10B resonances in the sodium salt of Na2B12H12S, mercaptoundecahydro-closo-dodecaborane (sodium borocaptate or BSH) dissolved in glycerol, determined at ω0= 53.73 MHz, between temperatures of 268 and 323 K. The fit to the experimental results yielded a value of 1.25 MHz for the average10B quadrupolar coupling constant in this molecule.