A DIELECTRIC THEORY OF SPIN-LATTICE RELAXATION FOR NUCLEI WITH ELECTRIC QUADRUPOLE-MOMENTS

The spin-lattice relaxation time for nuclei possessing electric quadru pole moments is determined mainly by the electric quadrupolar interact ions between the nucleus and its environment. Here we give a microscop ic formulation of the nuclear quadrupolar relaxation problem for a nuc leus of a monatomic solute dissolved in molecular fluids. Our formulat ion is based on classical statistical mechanics and the interaction si te model representation of the intermolecular potential. We assume tha t the fluctuating field gradient felt by the nucleus is caused mainly by the charge distribution of the surrounding solvent molecules, modul ated by the Sternheimer (anti)shielding factor of the nucleus. In the extreme narrowing condition, the problem reduces to the determination of a time integral of the field gradient time correlation function G(t ) on the nucleus position. By separation of G(t) into a static contrib ution G(t = 0) and a normalized time correlation function, we seek mic roscopic expressions for both G(t = 0) and its correlation time tau(Q) . Within certain approximations we express tau(Q) in terms of the wave vector-dependent polarization charge correlation time tau(mu)(k), and G(t = 0) in terms of the pure solvent charge structure factor S-mu(k) and an analytical function of the solute cavity radius a. Taking as in put tau(mu)(k) from molecular dynamics simulations of the pure solvent and S-mu(k) from the extended reference interaction-site model (XRISM ) calculation, we apply the theory to the spin lattice relaxation rate of seven quadrupolar nuclei in acetonitrile solution. The solutes con sidered cover a wide range of size, charge, and nuclear spin quantum n umber. With reasonable choices of the solute cavity radii, the theory successfully reproduces the experimentally measured 1/T-1 for these so lutes. Using molecular dynamics simulation, we also investigate the ef fects on 1/T-1 of neglecting the solute mobility. Our simulated data s uggest that the solute mobility can reasonably be neglected for spin r elaxation of heavy quadrupolar nuclei such as Kr and Xe. Finally, the dielectric continuum limit of our theory is discussed and compared wit h the related theory developed by Hynes and Wolynes. (C) 1998 American Institute of Physics.