The paramagnetic linewidth

Observed linewidths of NMR signals in paramagnetic systems vary enormously and the conditions that govern the observed widths are considerably more complex than in diamagnetic systems. Swift (30) reviewed the problem some years ago. Relaxation times of spin-j nuclei are governed by dipolar and hyperfine exchange (Fermi contact) relaxation processes. The dipolar interaction is normally dominant except in some delocalized systems in which considerable unpaired spin density exists on nuclei far removed from the metal ions (e.g. Ti-radicals). Distinction between the two processes can be made by consideration of the different mathematical expressions involved. For dipolar relaxation when o)fx 1 (t = rate constant for rotation of the species containing the coupled pair and to, = nuclear resonance frequency)  

In these equations S is the total electron spin of the paramagnetic ion, r is the electron-nuclear distance, co is the electron resonance frequency, and x i - and x 2 are the rate constants for the reorientation of the coupled magnetic moment vectors. They are related to other rate constants by the expressions  

Tie and Tae are the electron spin relaxation times and % is the rate constant for proton exchange. Thus, if this mechanism is dominant the observed linewidths, Aui[ = (71X2) ], must reflect the r dependence on the electron-nuclear distance. Hyperfine exchange relaxation, however, is given by the expressions  

in cases where contact shifts are observed the squares of the shifts must correlate with (nT2) since equation (20) involves the square of the hyperfine coupling constant A. 

In the present context the former produces a nuclear resonance shift (the pseudocontact shift) whereas the latter only affects the relaxation behaviour. In the absence of chemical exchange and in cases when Tie r the local field experienced by the nucleus is given by  

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The linewidth of the diamagnetic MnOT resonance, fV°, is broadened on the addition of the paramagnetic MnO ", but there is no shift in the signal position, which is proof that we are in the slow-exchange region. The broadened line width is a linear function of added MnOj"... 

The magnetic susceptibility relaxation is usually more important for than for Ti. In fact, this mechanism is often dominant in determining the proton linewidth in paramagnetic proteins at high magnetic fields (3). Gillis and co-workers have recently developed a theory for the related case of proton linewidth in colloidal solutions of so-called superparamagnetic particles (54,55). 

Oxidized Fe2S2 ferredoxins, containing two equivalent iron atoms, with J = 400 cm , show sharper NMR lines with respect to the monomeric iron model provided by oxidized rubredoxin (107-109), due to the decreased Boltzmann population of the paramagnetic excited states. For reduced ferredoxins (Si = 5/2, S2 = 2), with J = 200 cm , the ground state is paramagnetic (S = 1/2) (110). A smaller decrease in linewidth is expected. However, the fast electron relaxation rates of the iron(II) ion cause both ions to relax faster, and the linewidths in the dimer are sharp. 

The first criterion really related to the content of this book is the analysis of T and 72. As the dominant contribution to nuclear relaxation is dipolar in nature, Tfl and linewidths will decrease as we move farther from the paramagnetic center. Even the contact contribution to relaxation often decreases with the number of chemical bonds from the paramagnetic center. A caveat, however, should be given. Spin density transfer causes ligand-centered relaxation. Significant spin density on ax orbital of an sp2 carbon may relax an attached proton more than the paramagnetic center itself, owing to the different distances and to the sixth power dependence on distance. 

The EPR linewidths of Gd(III) complexed with cacodylate buffer and bovine albumin serum have been obtained which were consistent with the action of Gd(III) as a paramagnetic relaxation probe with the same protein [44]. A host of inorganic and organic ligands including amino acids and nucleotides complexed with Gd(III) were studied and two types of peaks were observed (i.e.) narrow symmetric peaks and broad asymmetric peaks [45],... 

The narrow linewidths of liquids allow one to observe weak spin interactions such as the indirect spin-spin (/) coupling and the isotropic chemical shift (7>). In the solid state, however, linewidths are broadened considerably by much stronger interactions, involving mainly the dipole-dipole interaction (typically 10-100 kHz), chemical-shift anisotropy ( 1 kHz), the quadrupole interaction ( 250 kHz) and the effect of paramagnetic impurities. For these reasons the / and <5 interactions are generally not observed in solids.2... 

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