Hyperfine distribution

Collisions between I and closed-shell collision partners (He, Ar, and N2) did not relax the nonequilibrium hyperfine distribution to any measurable degree. But, in accord with the theoretical picture outlined above, hyperfine relaxation was observed for collisions with 02(A). For example, the shift towards equilibrium can be seen in Fig. 9 by comparing traces recorded in the absence and presence of O2. Hyperfine transfer induced by collisions with O2 was examined at the temperatures T = 295, 150, and 10 K. For T > 150 K, I quenching and hyperfine transfer occurred at simUar rates. Hence, both processes were considered in the kinetic model used to extract the rate constants. At the lowest temperature (10 K) quenching was negligible. The hyperfine transfer rate constants were found to be independent of temperature, within the experimental errors. Values oi k F = 2 F = 3) = (2.3 0.5) X 10- and fc(F = 3 -> F = 2) = (1.6 0.5) x 10" cm s... 

A typical set of simulated spectra was obtained by Chappert et al. (1982) and these spectra have been reproduced in fig. 86. They have a few features that deserve separate mention Comparison of the spectra shown in figs. 86a and b shows that some of the resonance lines remain unaffected by the presence of a quadrupole interaction. This pertains primarily to the iimermost and outermost lines. As a consequence these lines will remain sharp in the presence of various types of distributions in the quadrupolar interactions (figs. 86c and d). Some broadening of these lines will occur, however, in the presence of a distribution in the hyperfine field (fig. 86e). These features led Chappert et al. to argue that in the case of Dy Mossbauer spectroscopy it will be possible in general to separate the quadrupolar and magnetic hyperfine distributions even by visual inspection of the spectra. 

G. Le Caer, J.M. Dubois, Evaluation of hyperfine distributions liom overlapped Mossbauer spectra of amorphous alloys. J. Phys. E. Sci. Instrum. 12, 1083-1090 (1979)... 

Crystal can compute a number of properties, such as Mulliken population analysis, electron density, multipoles. X-ray structure factors, electrostatic potential, band structures, Fermi contact densities, hyperfine tensors, DOS, electron momentum distribution, and Compton profiles. 

The ESR spectra of a large variety of sulfonyl radicals have been obtained photolytically in liquid phase over a wide range of temperature. Some selected data are summarized in Table 2. The magnitudes of hyperfine splittings and the observations of line broadening resulting from restricted rotation about the C—S bond have been used successfully in conjunction with INDO SCF MO calculations to elucidate both structure and conformational properties. Thus the spin distribution in these species is typical of (T-radicals with a pyramidal center at sulfur and in accord with the solid-state ESR data. 

The origin of postulate (iii) lies in the electron-nuclear hyperfine interaction. If the energy separation between the T and S states of the radical pair is of the same order of magnitude as then the hyperfine interaction can represent a driving force for T-S mixing and this depends on the nuclear spin state. Only a relatively small preference for one spin-state compared with the other is necessary in the T-S mixing process in order to overcome the Boltzmann polarization (1 in 10 ). The effect is to make n.m.r. spectroscopy a much more sensitive technique in systems displaying CIDNP than in systems where only Boltzmann distributions of nuclear spin states obtain. More detailed consideration of postulate (iii) is deferred until Section II,D. 

Contact shifts give information on the electronic structure of the iron atoms, particularly on the valence distribution and on the magnetic coupling within polymetallic systems. The magnetic coupling scheme, which is considered later, fully accounts for the variety of observed hyperfine shifts and the temperature dependence. Thus, through the analysis of the hyperfine shifts, NMR provides detailed information on the metal site(s) of iron-sulfur proteins, and, thanks to the progress in NMR spectroscopy, also the solution structure 23, 24 ). 

Hyperfine coupling constants provide a direct experimental measure of the distribution of unpaired spin density in paramagnetic molecules and can serve as a critical benchmark for electronic wave functions [1,2], Conversely, given an accurate theoretical model, one can obtain considerable information on the equilibrium stmcture of a free radical from the computed hyperfine coupling constants and from their dependenee on temperature. In this scenario, proper account of vibrational modulation effects is not less important than the use of a high quality electronic wave function. 

In many cases, the actual width of a Mossbauer line has strong contributions from inhomogeneous broadening due to the distribution of unresolved hyperfine splitting in the source or absorber. Often a Gaussian distribution of Lorentzians,... 

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). 

Fig. 4.17 Magnetic hyperfine pattern of a powder sample with randomly distributed internal magnetic field (a), and with (b) an applied magnetic field (0q = 90°), and (c) an applied magnetic field (00 = 0°)...

An interesting study of oxidic spinel ferrites of the type CO cNi5/3 xFeSbi/304 was reported [21], where three different Mbssbauer-active probes Fe, Ni and Sb were employed on the same material. The results have been interpreted in terms of the cation distributions over spinel A- and B-lattice sites, magnetic moments and spin structure, and the magnitude of the supertransferred hyperfine... 

Au-Ni and Cu-Ni-Au alloys Magnetic hyperfine spitting at Au, // and isomer shift as function of composition, model to describe charge density distribution... 

Pietrzyk, P., Piskorz, W., Sojka, Z. et al. (2003) Molecular structure, spin density distribution, and hyperfine coupling constants of the i7l CuNO n adduct in the ZSM-5 zeolite DFT calculations and comparison with EPR data, J. Phys. Chem. B., 107, 6105. 

Table 4 Hyperfine coupling constants obtained from EPR spectra of frozen solution and unpaired electron distribution of phosphaquinoid compounds3...

Early treatments of powder patterns attempted to deal with the spatial distribution of resonant fields by analytical mathematics.9 This approach led to some valuable insights but the algebra is much too complex when non-axial hyperfine matrices are involved. Consider the simplest case a single resonance line without hyperfine structure. The resonant field is given by eqn (4.3). Features in the first derivative spectrum correspond to discontinuities or turning points in the absorption spectrum that arise when dB/dB or dB/dcp are zero ... 

In a similar vein, the observation of multiple hyperfine interactions in the spectra of organic radicals allows for a delineation of the distribution in space and time of the unpaired electron over the atoms of the compound. A helpful simple relation,... 

Formally, this procedure is correct only for spectra that are linear in the frequency, that is, spectra whose line positions are caused by the Zeeman interaction only, and whose linewidths are caused by a distribution in the Zeeman interaction (in g-values) only. Such spectra do exist low-spin heme spectra (e.g., cytochrome c cf. Figure 5.4F) fall in this category. But there are many more spectra that also carry contributions from field-independent interactions such as hyperfine splittings. Our frequency-renormalization procedure will still be applicable, as long as two spectra do not differ too much in frequency. In practice, this means that they should at least be taken at frequencies in the same band. For a counter-example, in Figure 5.6 we plotted the X-band and Q-band spectra of cobalamin (dominated by hyperfine interactions) normalized to a single frequency. To construct difference spectra from these two arrays obviously will generate nonsensical results. 

Nanoparticles of dilute magnetic semiconductors have also been studied by NMR. Here one important question is whether the magnetic ion is incorporated into the NC or resides on the surface. The 113Cd MAS-NMR of NCs of Cd0.991Co0.009S with diameters from 3.5 to 29.5 nm showed peaks shifted by electron hyperfine interactions from next-nearest neighbor Co2+ ions, and by comparison with results from bulk samples that were discussed in Sect. 3.5 it was concluded that Co2+ ions occupied Cd2+ sites and were distributed homogeneously ... 

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