1H NMRD Profile and ESR Lineshape Calculation for an Isotropic Electron Spin System withS= 7/2. A Generalized Modified Solomon–Bloembergen–Morgan Theory for Nonextreme-Narrowing Conditions
✍ Scribed by Erik Strandberg; Per-Olof Westlund
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 310 KB
- Volume
- 122
- Category
- Article
- ISSN
- 1064-1858
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✦ Synopsis
A generalization of the modified Solomon-Bloembergen-Morportant MRI contrast agents. Many studies in the literature gan (MSBM) theory is presented for electron-spin quantum numare aimed at finding new, and perhaps more efficient, Gd ber S Å 7 2 taking multiexponential electron-spin relaxation into contrast agents. In order to do this, one wishes to relate the account. The theoretical approach closely follows P.-O. Westlund water proton T 1 NMR-dispersion (D) profiles to microscopic [Mol. Phys. 85, 1165Phys. 85, -1178Phys. 85, (1995))]. In the nonextreme-narrowing parameters of theoretical models, which describe local strucregime for the electron spin system, three correction terms to the ture and dynamics of the electron spin system of the paratraditional MSBM equations arise. They are all derived in closed magnetic complex. This requires a theoretical description analytical form to give the generalized equations in a simple and which is extended to high-spin systems and nonextremeconvenient form: MSBM 1 (1 / correction). The ESR lineshape narrowing conditions. Furthermore, we also need to describe function for S Å 7 2 is also given in closed analytical form. A number of proton T 1 NMRD profiles representing different Gd(III) com-in more detail the coupling between the electron spin system plexes are investigated, using a spectral density function of the and the thermal bath. Therefore we include a derivation transient ZFS interaction which allows for two relaxation times. of the Gd(III) ESR lineshape function together with the For Gd-macromolecular complexes the largest deviation from the generalized MSBM theory, to give a more adequate theoretitraditional MSBM theory may be about 15.2%, but for the paramecal description of electron-spin relaxation processes.
ter sets investigated the corrections were about 2-3%. A computer
The relation between the measured paramagnetically enprogram is developed which calculates the NMRD profile and the hanced nuclear spin-lattice relaxation rates T 1 and the spec-ESR lineshape (X band or Q band) for the set of model parameters.
tral density K 1 (v I ) of the paramagnetic nuclear-spin relax-These parameters describe the electron spin system in terms of D t ation theory is (the root-mean-square value of the transient ZFS interaction) and t v1 , t v2 , and S 0 (correlation times and an order parameter of the transient ZFS correlation function). For the paramagnetically
2 ) spin relaxation, the parameters t R (the reorientational correlation time), q (the number of fast exchanging water molecules in the first hydration shell), and r IS (the point where the fast exchange condition is assumed. We will also spin-dipole distance) are also used.