Paramagnetic systems

S spin remains in tliennal equilibrium on die time scale of the /-spin relaxation. This situation occurs in paramagnetic systems, where S is an electron spin. The spin-lattice relaxation rate for the / spin is then given by ... 

Hyperfine Interaction (dipolar and scalar) 2,0 Electron relaxation, may be complicated Paramagnetic systems and Impurities [17-191... 

The negative sign in equation (b 1.15.26) implies that, unlike the case for electron spins, states with larger magnetic quantum number have smaller energy for g O. In contrast to the g-value in EPR experiments, g is an inlierent property of the nucleus. NMR resonances are not easily detected in paramagnetic systems because of sensitivity problems and increased linewidths caused by the presence of unpaired electron spins. 

Perspectives on the field of NMR of iron-sulfur proteins are those common to the broader field of NMR of diamagnetic proteins, with a particular need for high technical skills. For some applications, new experiments/protocols tailored for the study of paramagnetic systems such as those described here will probably have to be designed and... 

Figure 2. Plot of relative magnetization, a/Os ns a function of H/T. (a) A paramagnetic system Is characterized by an effective magnetic moment, with a Bohr Magneton number vlO per Ion, and by the absence of hysteresis. Paramagnetic saturation occurs at very high "H/T" == 10 Oe K"l. (b) l.angevln curve for S.P. clusters, (c) Part of a ferromagnetic hysteresis curve.

In contrast, soft magnetic solids and paramagnetic systems with weak anisotropy may be completely polarized by an applied field, that is, the effective field at the Mossbauer nucleus is along the direction of the applied field, whereas the EFG is powder-distributed as in the case of crystallites or molecules. In this case, first-order quadrupole shifts cannot be observed in the magnetic Mossbauer spectra because they are symmetrically smeared out around the unperturbed positions of hyperfine fines, as given by the powder average of EQ mj, d, in (4.51). The result is a symmetric broadening of all hyperfine fines (however, distinct asymmetries arise if the first-order condition is violated). 

The spin-Hamiltonian concept, as proposed by Van Vleck [79], was introduced to EPR spectroscopy by Pryce [50, 74] and others [75, 80, 81]. H. H. Wickmann was the first to simulate paramagnetic Mossbauer spectra [82, 83], and E. Miinck and P. Debmnner published the first computer routine for magnetically split Mossbauer spectra [84] which then became the basis of other simulation packages [85]. Concise introductions to the related modem EPR techniques can be found in the book by Schweiger and Jeschke [86]. Magnetic susceptibility is covered in textbooks on molecular magnetism [87-89]. An introduction to MCD spectroscopy is provided by [90-92]. Various aspects of the analysis of applied-field Mossbauer spectra of paramagnetic systems have been covered by a number of articles and reviews in the past [93-100]. 

However, when it comes to the simulation of NFS spectra fi om a polycrystalline paramagnetic system exposed to a magnetic field, it turns out that this is not a straightforward task, especially if no information is available from conventional Mossbauer studies. Our eyes are much better adjusted to energy-domain spectra and much less to their Fourier transform therefore, a first guess of spin-Hamiltonian and hyperfine-interaction parameters is facilitated by recording conventional Mossbauer spectra. 

The spin state of a paramagnetic system with total spin S wiU lift its (25 + l)-fold degeneracy under the influence of ligand fields (zero-field interaction) and applied fields (Zeeman interaction). The magnetic hyperfine field sensed by the iron nuclei is different for the 25 + 1 spin states in magnitude and direction. Therefore, the absorption pattern of a particular iron nucleus for the incoming synchrotron radiation and consequently, the coherently scattered forward radiation depends on how the electronic states are occupied at a certain temperature. 

Figure 9.5 PHI [25] simulation of the -ASm for an arbitrary system of two s = 7/2 spins with a Mw of 1300 Da. Key as shown, where Para is a paramagnetic system, F is a ferromagnetic interaction between spins...

CP-ENDOR has been introduced by Schweiger and Giinthard104 to reduce the density of ENDOR lines of complicated paramagnetic systems with a large number of interacting nuclei. ENDOR spectra of solutions (liquid or frozen), polycrystalline powders and single crystals can often be simplified remarkably using this technique. 

The phenomenon of asymmetric hfs tensors was first discussed by McConnell134). Later, Kneubiihl135,136) proved the existence of asymmetric g and A tensors in paramagnetic systems with low symmetry. Evaluation of the asymmetry of A using EPR and ENDOR spectroscopy has been treated by several authors132,137 141). Recently, low-symmetry effects in EPR have been covered in a comprehensive review article by Pilbrow and Lowrey142). 

As the essentials of this book are devoted to paramagnetic systems, we shall, for the sake of completeness, conclude this introductory chapter by a related discussion about diamagnetic systems and more precisely about water NMRD in protein solutions. 

The angle Qsin is that between the IN axis and the IS axis. The expression (3cos 0—1)/2 in Eq. (28) is characteristic for the cross-correlated relaxation effects. An analogous and somewhat more general expression for the case of anisotropic susceptibility was given by Bertini et al. (56). The crosscorrelation-driven coherence transfer phenomena between nuclear spins in paramagnetic systems with anisotropic susceptibility were even earlier considered by Desvaux and Cochin (65). 

Fig. 3. Variation of the completely reduced dipole-dipole spectral density (see text) for the model of a low-symmetry complex for S = 3/2. Reprinted from J. Magn. Reson., vol. 59,Westlund, RO. Wennerstrom, H. Nordenskiold, L. Kowalewski, J. Benetis, N., Nuclear Spin-Lattice and Spin-Spin Relaxation in Paramagnetic Systems in the Slow-Motion Regime for Electron Spin. III. Dipole-Dipole and Scalar Spin-Spin Interaction for S = 3/2 and 5/2 , pp. 91-109, Copyright 1984, with permission from Elsevier.

Fig. 12. Experimental and calculated NMRD profiles for GdEDTA in aqueous solution in the presence (upper curve) and absence (lower curve) of bovine serum albumin. Reprinted from J. Magn. Reson. vol. 162, Kruk, D. Kowalewski, J., Nuclear Spin Relaxation in Paramagnetic Systems (S > 1) under Fast Rotation Conditions , pp. 229-240, Copyright 2003, with permission from Elsevier.

Theoretical models for outer-sphere nuclear spin relaxation in paramagnetic systems, including an improved description of the electron spin relaxation, have been developed intensively for the last couple of years. They can be treated as counterparts of the models of inner-sphere PRE, described in the Section V.B and V.C. 

The work on theory of relaxation in paramagnetic systems performed at Stockholm University has been supported by the Swedish Natural Science Research Council, Swedish Research Council and the Wenner-Gren Foundations. We wish to acknowledge the courtesy of the publishers who permitted reproductions of the figures published in their journals. 

This is not all. In fact, the structural and dynamic information at a molecular level that are contained in the NRMD profiles of a paramagnetic system comprise geometrical parameters (distances and angles), which determine the position of protons relative to the paramagnetic site the... 

In the last ten years several novel theories for the analysis of NMRD profiles have been proposed for different paramagnetic systems. These have resulted in novel equations and computer programs for numerical calculations. In this review we tried to summarize the classical theory as well as some recent theoretical treatments, and to show their applicability to different metal ion systems by selecting some experimental profiles which exhibit the most characteristic features. In the last few years, dedicated instruments, called field-cycling relaxometers, have appeared on the market... 

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