H-1 NMRD profile and ESR lineshape calculation for an isotropic electron spin system with S=7/2. A generalized modified Solomon-Bloembergen-Morgan theory for nonextreme-narrowing conditions

A generalization of the modified Solomon-Bloembergen-Morgan (MSBM) theory is presented for electron-spin quantum number S = 7/2 taking multiexponential electron-spin relaxation into account. The theoretical approach closely follows P.-O. Westlund [Mol. Phys. 85, 1165-1178 (1995)]. In the nonextreme-narrowing regime for the electron spin system, three correction terms to the traditional MSBM equations arise. They are all derived in closed analytical form to give the generalized equations in a simple and convenient form: MSBM x (1 + correction). The ESR lineshape function for S = 7/2 is also given in closed analytical form. A number of proton T-1 NMRD profiles representing different Gd(III) complexes are investigated, using a spectral density function of the transient ZFS interaction which allows for two relaxation times. For Gd-macromolecular complexes the largest deviation from the traditional MSBM theory may be about 15.2%, but for the parameter sets investigated the corrections were about 2-3%. A computer program is developed which calculates the NMRD profile and the ESR lineshape (X band or Q band) for the set of model parameters. These parameters describe the electron spin system in terms of Delta, (the root-mean-square value of the transient ZFS interaction) and tau(v1), tau(v2), and S-0 (correlation times and an order parameter of the transient ZFS correlation function). For the paramagnetically enhanced nuclear (I = 1/2) spin relaxation, the parameters tau(R) (the reorientational correlation time), q (the number of fast exchanging water molecules in the first hydration shell), and r(1S) (the point spin-dipole distance) are also used. (C) 1996 academic Press, Inc.