Hyperfine pattern

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°)...

T] 0.74 (OSP2). It can be seen that the asymmetric hyperfine pattern - in the case of 7 0 (OsOa), which allows the determination of the sign of - becomes more symmetric with increasing asymmetry parameter 77. For rj = 1, the spectra become completely symmetric and the sign of no longer influences the shape of the spectra. 

An additional application of SYNEOS to simulate the magnetic hyperfine pattern in time spectra is provided by the low-spin ferri-heme (Ee, S = 1/2) complex... 

Once a hyperfine pattern has been recognized, the line position information can be summarized by the spin Hamiltonian parameters, g and at. These parameters can be extracted from spectra by a linear least-squares fit of experimental line positions to eqn (2.3). However, for high-spin nuclei and/or large couplings, one soon finds that the lines are not evenly spaced as predicted by eqn (2.3) and second-order corrections must be made. Solving the spin Hamiltonian, eqn (2.1), to second order in perturbation theory, eqn (2.3) becomes 4... 

Figure 3.3 Stick spectrum showing hyperfine pattern for coupling to three equivalent 59Co nuclei (1=1/2) computed to (a) first-order and (b) second-order in perturbation theory. (Adapted from ref. 7.) (c) Isotropic ESR spectrum of [PhCCo3(CO)9r in THF solution at 40°C.

Chemical bonds can have covalent character, and EPR spectroscopy is an excellent tool to study covalency An unpaired electron can be delocalized over several atoms of a molecular structure, and so its spin S can interact with the nuclear spins /, of all these atoms. These interactions are independent and thus afford additive hyperfine patterns. An unpaired electron on a Cu2+ ion (S = 1/2) experiences an / = 3/2 from the copper nucleus resulting in a fourfold split of the EPR resonance. If the Cu is coordinated by a... 

FIGURE 5.1 Isotropic hyperfine pattern for 51VIV in S-band. The spectrum is from V0S04 in aqueous solution. Use of the low frequency enhances the second-order effect of unequal splitting between the eight hyperfine lines. 

FIGURE 5.8 Complex hyperfine patterns due to axes noncolinearity in a low-symmetry prosthetic group. The X-band spectrum is from 65Cu(II)-bicarbonate in human serum transferrin (a,b) experimental spectrum (c,e) simulation assuming axial symmetry (d, f) simulation assuming triclinic symmetry with the A-axes rotated with respect to the g-axes over 15° about the gz-axis and then 60° about the new y -axis. Traces b, e, and f are 5x blow-ups of traces a, c, d, respectively (Hagen 2006). (Reproduced by permisson of The Royal Society of Chemistry.)... 

Qualitatively, all proposals indicate a linear dependence on ml (linewidth over a hyperfine pattern increases from low to high field or vice versa cf. Figure 9.4) plus a quadratic dependence on m, (outermost lines more broadened than inner lines). Multiple potential complications are associated with the lump parameters A, B, C, notably, their frequency dependence (Froncisz and Hyde 1980), partial correlation with g-strain (Hagen 1981), and low-symmetry effects (Hagen 1982a). The bottom line quantitative description of these types of spectra has been for quite some time, and still is, awaiting maturation. 

FIGURE 9.4 Effect of stress on a hyperfine pattern. The four-line parallel hyperfine pattern of the elongated CuOs octahedron in 63Cu(H20)6 is shown in the presence (dotted line) and absence (solid line) of an external hydrostatic stress. (Modified from Hagen 1982a.)... 

The CIDNP method is an indirect method since the hyperfine pattern of a paramagnetic intermediate is derived from the unusual NMR intensities of a diamagnetic product derived from it. This method also has limitations and potential sources of misassignments. Similar to the EPR technique, the CIDNP method only documents the unpaired spin additional evidence for the nature of the paramagnetic intermediate, particularly for the presence of the charge, is derived typically on the basis of mechanistic considerations and from supporting secondary experiments. 

Nevertheless, just that kind of accidental hyperfine equivalence may occur in the case of TME (5) (see below), which shows a nine-line pattern " suggestive of eight equivalent hydrogens. Neither planar nor twisted TME can have eight tmly equivalent hydrogens, so the hyperfine pattern is due to some cause other than molecular symmetry. 

As mentioned for the relationship between the PE spectrum of a parent molecule and the electronic spectrum of its radical cation, any close correspondence between the electronic spectra of anions and cations or their hyperfine coupling patterns holds only for alternant hydrocarbons. The anions and cations of nonalternant hydrocarbons (e.g., azulene) have significantly different hyperfine patterns. Azulene radical anion has major hyperfine splitting constants (hfcs) on carbons 6, and 4,8 (flH = 0-91 mT, H-6 ah = 0-65 mT, H-4,8 ah = 0-38 mT, H-2) in contrast, the radical cation has major hfcs on carbons 1 and 3 (ah = 1.065 mT, H-1,3 Ah = 0.152 mT, H-2 ah = 0.415 mT, H-5,7 ah = 0.112 mT, H-6). °°... 

The divergent hyperfine patterns of the two ions can be ascribed to their 6ti aromatic substructures, cyclopentadienide anion, and cycloheptatrienylium cation, respectively. 

The structures of the ions rest on CIDNP spectra delineating their hyperfine patterns,ab initio calculations - ESR and ENDOR data for 16 +, and TR-ESR results for 15 +. Ab initio calculations (B3LYP/6-31G //UMP2/6-31G ) reproduce positive and negative hyperfine coupling constants satisfactorily. Each radical cation is related uniquely to the geometry of one of the precursors (Fig. 6.13). 

The discussion of the hyperfine tensor has indicated clearly that the analysis of the hyperfine pattern has been very valuable in developing an understanding of the adsorbed oxygen ion. On balance, in the oxide systems it would seem preferable to use the term superoxide rather than peroxide or peroxy for 02. Overall, the picture is largely consistent with an ionic model for 02 on surfaces. 

The multiplet hyperfine pattern of ESR lines in organic radicals is most frequently due to electron-proton interactions, but other nuclei with nonzero spin may also cause hyperfine structure. Weak satellite lines arising from interactions between the unpaired electron and C13 nuclei are sometimes observed C13 has and the analysis is straightforward. Nitrogen-containing radicals may show hyperfine splittings due to N14, which has 7 1. The possible Mj values are 1, 0, and -1, so that an electron... 

Fig. 8.14 Calculation of the ESR hyperfine pattern (solid lines) of die CH CHg radical in solution.

Usually, an organic radical will have more than one magnetic nucleus. In such instances, the EPR spectrum can display rich hyperfine structure, which is useful both for identifying the species and for extracting information about the electronic structure of the radical. The origin of such hyperfine patterns is straightforward, but is most easily understood in terms of concrete examples. 

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