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A generalization of the modified SBM theory is developed in closed analytical form. The theory is applied to describe the paramagnetically enhanced water proton spin–lattice relaxation rates of the aqueous-systems containing a gadolinium(S=7/2) complex(MS-325) in the presence or absence of human serum albumin (HSA). MS-325 binds to HSA: in the absence of the protein the reorientational time, τR, is short, but when HSA is added τR becomes much longer. In this way, the effect of reorientational motion, static (Δs), and transient (Δt) zero-field splitting (ZFS) interactions on both the water proton relaxivity and the Gd ESR lineshapes are investigated.

Two dynamic models of electron spin relaxation are presented, characterized by transient and static ZFS-interactions. X-, Q-, and W-bands ESR spectra of MS-325+HSA are analyzed in order to describe the effect on the electron spin system upon binding to a macromolecule. A computer program based on this theory is developed which calculates solvent water proton T1 NMRD profiles and the corresponding X-, Q-, U-, and W-bands ESR lineshapes.

A complete description of the T1-NMRD profiles and the ESR lineshape of Gd(III) complexes (S = 7/2) was presented using second-order perturbation theory (GSBM) by Zhou et al. [J. Magn. Reson. 167 (2004) 147]. This report compares the GSBM with the stochastic Liouville approach (SLA) to determine the validity of the closed analytical expressions of NMRD and the ESR lineshape functions. Both approaches give the same results at high fields while a very small divergence is observed for X- and W-band ESR lineshapes when the magnitude of the perturbation term times the correlation time approaches the limit of the perturbation regime, ΔZFSτf ≈ 0.1. There was a clear discrepancy between the theoretical GSBM X-band spectrum and the recorded ESR spectrum of the Gd(III) MS-325 + HSA complex. This is probably due to a slow-motion effect caused by a slow modulation of the ZFS interaction. The characteristic correlation time of this slow modulation is in the range of 150 ps, which therefore cannot be due to the reorientational motion of the whole MS-325 + HSA complex.

X-band ESR spectra of Gd-aqua complex in various weight concentration of glycerol have been recorded at four temperatures. The interpretation of the ESR linewidth is preformed using both the stochastic Liouville approach (SLA) and a perturbation theory. The SLA uses a one dynamic model of the zero-field splitting whereas the perturbation approach uses a two dynamic model. Both models can reproduce the variation of the linewidth with respect to viscosity. In the SLA model, both the zero-field splitting (ZFS) interaction and the correlation time vary with the glycerol content. In the two dynamic perturbation model, only the correlation times are viscosity dependent. The two models give different NMRD profiles.

Water proton T1-NMRD profiles of the Gd(H2O)83+ complex have been recorded at three temperatures and at four concentrations of glycerol. The analysis is performed using both the generalized Solomon–Bloembergen–Morgan (GSBM) theory [J. Magn. Reson. 167(2004), 147–160], and the stochastic Liouville approach (SLA). The GSBM approach uses a two processes dynamic model of the zero-field splitting (ZFS) correlation function whereas SLA uses a single process model. Both models reproduce the proton T1-NMRD profiles well. However, the model parameters extracted from the two analyses, yield different ESR X-band spectra which moreover do not reproduce the experimental ESR spectra. It is shown that the analyses of the proton T1-NMRD profiles recorded for a solution Gd(H2O)83+ ions are relatively insensitive to the slow modulation part of dynamic model of the ZFS interaction correlation function. The description of the electron spin system results in a very small static ZFS, while recent ESR lineshape analysis indicates that the contribution from the static ZFS is important. Analysis of proton T1-NMRD profiles of Gd(H2O)83+ complex do result in a description of the electron spin system but these microscopic parameters are uncertain unless they also are tested in a ESR-lineshape analysis.