Paramagnetically induced nuclear magnetic resonance relaxation in solutions containing S⩾1 ions: A molecular-frame theoretical and physical model (original) (raw)
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The Journal of Chemical Physics, 1993
Effects due to the nonuniaxial part of the zero field splitting (ZFS) tensor on NMR relaxation enhancements produced by paramagnetic species in solution (the NMR PRE) has been studied theoretically and experimentally in the ZFS limit, i.e., in the limit where the ZFS energy is large compared to the Zeeman energy. In the ZFS limit, the precessional motion of the electron spin is quantized with respect to molecule-fixed coordinate axes. The uniaxial part of the ZFS tensor induces precessional motion in the transverse (x,y) components of the electron spin vector S, and x,y anisotropy in the ZFS tensor (i.e., a nonzero ZFS parameter E) induces precessional motion in the z component of S. The NMR-PRE phenomenon is particularly sensitive to the motion of S, and hence also to ZFS anisotropy in the xy plane. Mathematical expressions have been derived which describe the motion of the spin vector evolving under the influence of a general rhombic ZFS Hamiltonian and the influence of this motion on the NMR PRE in the ZFS limit. It is shown that oscillations in S, occur at the transition frequencies of the S spin system; the frequencies and amplitudes of the precessional components of S, can be calculated by diagonalizing the general ZFS Hamiltonian. These motions and their consequences with respect to the behavior of the NMR PRE are described in detail for the S=2 spin system. A parametrization of NMR-PRE data is proposed which gives a clear criterion for the conditions under which rhombic parts of the ZFS tensor significantly affect the relaxation enhancements produced by an S=2 spin system. This criterion is of considerable practical importance for the analysis of NMR-PRE data, since it defines conditions under which data may be analyzed without the need for independent experimental information concerning the magnitude of the ZFS tensor.
Journal of Magnetic Resonance, 1999
A generalization of the modified Solomon-Bloembergen-Morgan (MSBM) equations has been derived in order to describe paramagnetic relaxation enhancement (PRE) of paramagnetic complexes characterized by both a transient (⌬ t ZFS) and a static (⌬ s ZFS) zero-field splitting (ZFS) interaction. The new theory includes the effects of static ZFS, hyperfine coupling, and angular dependence and is presented for the case of electron spin quantum number S ؍ 5 2 , for example, Mn(II) and Fe(III) complexes. The model gives the difference from MSBM theory in terms of a correction term ␦ which is given in closed analytical form. The theory may be important in analyzing the PRE of proton spinlattice relaxation dispersion measurements (NMRD profiles) of low-symmetry aqua-metal complexes which are likely to be formed upon transition metal ions associated with charged molecular surfaces of biomacromolecules. The theory has been implemented with a computer program which calculates solvent water proton T 1 NMRD profiles using both MSBM and the new theory.
Journal of Magnetic Resonance, 2001
Proton spin-lattice relaxation rate constants have been measured as a function of magnetic field strength for water, waterglycerol solution, cyclohexane, methanol, benzene, acetone, acetonitrile, and dimethyl sulfoxide. The magnetic relaxation dispersion is well approximated by a Lorentzian shape. The origin of the relaxation dispersion is identified with the paramagnetic contribution from molecular oxygen. In the small molecule cases studied here, the effective correlation time for the electron-nuclear coupling may include contributions from both translational diffusion and the electron T 1 . The electron T 1 for molecular oxygen dissolved in several solvents was found to be approximately 7.5 ps and nearly independent of solvent or viscosity.
International Journal of Molecular Sciences, 2003
The known solvent dependence of 1 J(C c ,H f ) and 2 J(C 1 ,H f ) couplings in acetaldehyde is studied from a theoretical viewpoint based on the density functional theory approach where the dielectric solvent effect is taken into account with the polarizable continuum model. The four terms of scalar couplings, Fermi contact, paramagnetic spin orbital, diamagnetic spin orbital and spin dipolar, are calculated but the solvent effect analysis is restricted to the first term since for both couplings it is by far the dominant contribution. Experimental trends of ∆ 1 J(C c ,H f ) and ∆ 2 J(C 1 ,H f ) Vs ε (the solvent dielectric constant) are correctly reproduced although they are somewhat underestimated. Specific interactions between solute and solvent molecules are studied for dimethylsulfoxide, DMSO, solutions considering two different one-to-one molecular complexes between acetaldehyde and DMSO. They are determined by interactions of type C=O---HC and S=O---HC, and the effects of such interactions on 1 J(C c ,H f ) and 2 J(C 1 ,H f ) couplings are analyzed. Even though only in a semiquantitative way, it is shown that the effect of such interactions on the solvent effects, of ∆ 1 J(C c ,H f ) and ∆ 2 J(C 1 ,H f ), tend to improve the agreement between calculated and experimental values. These results seem to indicate that a continuum dielectric model has not enough flexibility for describing quantitatively solvent Int. J. Mol. Sci. 2003, 4 94 effects on spin-spin couplings. Apparently, even for relatively weak hydrogen bonding, the contribution from "direct" interactions is of the same order of magnitude as the "dielectric" effect.
Nuclear magnetic resonance and spin relaxation in biological systems
Magnetic Resonance Imaging, 2005
Proton nuclear spin-lattice relaxation in biological systems is generally distinguished from that in inorganic systems such as rocks by the presence of locally disordered macromolecular environments. Rapid exchange of readily observed labile small molecules among differently oriented macromolecular sites generally nearly averages the spectral anisotropies in the small molecule resonances. The biological tissue is generally distinguished from the inorganic matrix by the presence of a significant population of protons in the solid components that are well connected by dipolar spin couplings. Magnetic coupling between the solid and the liquid components generally dominates the magnetic field dependence of the spin-lattice relaxation rates observed in the small molecule components which is generally described by a power law in the Larmor frequency. Recent theory involving a modification of the spin-phonon class of relaxation mechanism provides a quantitative understanding of these data in terms of the dynamics of the chain molecules generally present in the solid spin systems, folded proteins for example.