Quadrupolar nuclear broadening

Fig. 4. Quadrupolar powder patterns (a) Spin NMR powder pattern showing that the central -)<- ) transition is broadened only by dipolar coupling, chemical shift anisotropy, and the second-order quadrupolar interactions, (b) Spin 1 NMR powder pattern for a nucleus in an axially symmetric electric field gradient (see text). The central doublet corresponds to 6 = 90° in Eq. (10). The other features of low intensity correspond to 6 = 0° and 6 = 180°. (c) Theoretical line shape of the ) - -) transition of a quadrupolar nuclear spin in a powder with fast magic-angle spinning for different values of the asymmetry parameter t (IS) ...

The use of NMR spectroscopy to characterize diamagnetic transition metal and posttransition metal complexes has increased tremendously in the past decade (111, 129). Mercury has two NMR-active isotopes, Hg (natural abundance = 13.22%) and (natural abundance = 16.84%). The former is quadrupolar (nuclear spin, / = ), and consequently, much more difficult to observe, due to line broadening. The latter, on the other hand, is one of approximately 20 nuclides in the periodic table with the preferred spin I = i. Its receptivity, a measure of relative signal strength, is five times that of C for comparison, " Cd, the most widely studied of the posttransition nuclei, has a receptivity of only 8 relative to C. Magnetic resonance frequencies are intimately connected with the quantity and dis-... 

The isotope has a nuclear spin quantum number I and so is potentially useful in nmr experiments (receptivity to nmr detection 17 X 10 that of the proton). The resonance was first observed in 1951 but the low natural abundance i>i S(0.75%) and the quadrupolar broadening of many of the signals has so far restricted the amount of chemically significant work appearing on this rcsonance, However, more results are expected now that pulsed fourier-transform techniques have become generally available. 

For quadrupolar nuclei, rapid pulsing can improve the signal-to-noise ratio. They are often most readily measured by vidde-line techniques however, as for example (84) and N (79). Many more wide-line measurements have been made of N, which is quadrupolar, than high-resolution measurements of N, which has spin but is expensive. The broadening increases with the nuclear quadrupole moment, which is small for (2.8 x 10 ), Li (4.6 x 10 ), and (—4 x 10 ), and fairly small, between 10 and 10 , for Be, B, N, S, C1, and C1 (the units are e x 10 cm, where e is the electronic charge) (20, 70). The broadening increases with asymmetry of the nuclear environment thus, the line width increases a thousand-fold from the relatively sharp line... 

Paramagnetic broadening, due to unpaired electrons, is usually much greater than quadrupolar broadening, and the nuclear resonance... 

In their 31P 1H nuclear magnetic resonance (NMR) spectra, the 1,4,2-diphosphastibolide salts display an AX spin system (<5 = 278 ppm, Ox = 309 ppm,. /ax = 55 Hz) with the low field signal considerably broadened, which suggests that it originates from the phosphorus atom adjacent to the quadrupolar antimony center < 1997JOM291, 2001JOM61>. 

It is useful to emphasise from the outset that alternative techniques for investigating solid samples, other than NMR spectroscopy of the quadrupolar halogen nuclei, tend to be considered first this is likely due to the (perceived) difficulty of the technique and may be related to the issues of sensitivity and line broadening mentioned above. However, the information gained is often complementary, and hence solid state nuclear magnetic resonance (SS NMR) spectroscopy is primarily used when it can provide unique insight unavailable with other techniques. 

The important nuclear spin interaction in the context of probing molecular reorientation is provided by the quadrupolar interaction (Q) or the chemical shift anisotropy (CSA), and we assume that the spin system is prepared by, for example, isotopic labeling in such a way that only a single interaction is relevant. The ubiquitous presence of dipolar broadening is assumed to be small. For most NMR experiments it suffices to consider the secular part of the... 

In addition to the interactions which broaden the sohd-state NMR resonances of spin-1/2 nuclei, the electric quadrupole interaction considerably decreases the resolution of the spectra of quadrupolar nuclei (spin />l/2). These nuclei have a non-spherically symmetrical distribution of nuclear charge and possess an electric quadrupole moment, which interacts strongly with any electric field gradient, created by the surrounding electron cloud, at the site of the nucleus. In the tensorial Cartesian form the quadrupolar Hamiltonian is... 

The quadrupolar moments of nuclei with I > 1/2 may interact with electric field gradients in their environments. Depending on the symmetry of the nuclear environment, these interactions can lead to considerable line broadening due to both first- and second-order terms (for a detailed discussion see ref. 17). While both first-and second-order terms each contain angular (relative to the direction of B0) terms only the former contains 3 cos2 0 - 1, like the dipolar interaction term. 

Quadrupole effects are due to the interaction of the nuclear quadrupole moment (caused by a non-spherical distribution of charge on the nucleus) with the electric field gradient at the nucleus. Quadrupole effects cause peak broadening, displacement of the peak from the isotropic (true) chemical shift, and distortion of the peak shape. These effects decrease in magnitude with the square of the Bq field strength, and spectra of quadrupolar nuclides are usually recorded at the highest field available. 

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