Subject quadrupolar

Let us calculate the frequencies of transitions between Zeeman eigenstates s) and r), assuming that the nuclei are only subjected to an isotropic chemical shift and the first- and second-order quadrupolar interaction. As seen in Sect. 2.1, the Hamiltonian that governs the spin system in the frame of the Zeeman interaction (the rotating frame) is... 

A number of isotopically labelled organogermanium compounds have been prepared and subjected to spectroscopic investigation (microwave, infrared and Raman) with a view to obtaining structural information about the compound. More specifically, these studies have sought information on bond strengths, bond lengths, dipole moments, quadrupolar... 

When Be(OH)2 is dissolved in strong alkali (pH > 12) a narrow 9Be NMR signal is observed at ca. 2 ppm (91). This is probably due to the ion [Be(OH)4]2 which, with near tetrahedral symmetry, would be subject to little quadrupolar broadening. 

Both [14N1- and [lsN]-pyrrole have been subjected to extensive analyses in the pursuit of accurate f3C chemical shifts and heteronuclear coupling constants. The resonance due to the a-carbons in [14N]pyrrole is broadened as a consequence of non-zero coupling to, and quadrupolar relaxation by, the 14N nucleus. 

Fig. 3. Energy level diagram for a spin f nucleus showing the effect of the first-order quadrupolar interaction on the Zeeman energy levels. Frequency of the central transition (shown in bold lines) is independent of the quadrupolar interaction to first order, but is subject to second-order quadrupolar effects (see text).

At a quantitative level, near criticality the FL theory overestimates dissociation largely, and WS theory deviates even more. The same is true for all versions of the PMSA. In WS theory the high ionicity is a consequence of the increase of the dielectric constant induced by dipolar pairs. The direct DD contribution of the free energy favors pair formation [221]. One can expect that an account for neutral (2,2) quadruples, as predicted by the MC studies, will improve the performance of DH-based theories, because the coupled mass action equilibria reduce dissociation. Moreover, quadrupolar ionic clusters yield no direct contribution to the dielectric constant, so that the increase of and the diminution of the association constant becomes less pronounced than estimated from the WS approach. Such an effect is suggested from dielectric constant data for electrolyte solutions at low T [138, 139], but these arguments may be subject to debate [215]. We note that according to all evidence from theory and MC simulations, charged triple ions [260], often assumed to explain conductance minima, do not seem to play a major role in the ion distribution. 

The calculations presented here are based on the density operator formalism using the Liouville-von-Neumann equation and the theoretical approach is confined to quadrupolar nuclei subjected to EFG as well as CSA-interactions. Following the approach of Barbara et al.,20 the Hamiltonian for an N-site jump may be written as... 

Ions travelling along the z axis are subjected to the influence of a total electric field made up of a quadrupolar alternative field superposed on a constant field resulting from the application of the potentials upon the rods ... 

In modern FTICR instruments, an ion of mass m and charge q is subjected to an axial homogenous magnetic field B and a quadrupolar electric field E derived from a potential V = Vq(z2 - frll)/2d2. with d1 = (z2 + p /2)/2, where p0 is the polar coordinate in the xy plane. 

An alternative way of investigating diamagnetic metal-ion binding is to observe NMR signals from the diamagnetic metal itself. Na, K and Cs have been the subject of a few studies [9] however, quadrupolar nuclei are inherently insensitive to detection. Further advances using high field NMR instruments can be expected. 

As an example, quadrupole nutation NMR of nuclei with half-integer quadrupolar spin in zeolitic materials can distinguish between nuclei of the same chemical element subjected to different quadrupole interactions, the signals of which overlap in conventional spectra. The situation is favourable for half-integer quadrupolar spins since the m=l/2 <-> m= -1/2 transition for these nuclei is broadened by the quadrupole interaction only in second-order perturbation theory. The technique can be usefully applied for the determination of the local environment of A1 in zeolitic catalysts (28). It allows discrimination between species of similar chemical shift but different quadrupolar coupling constants (see Figure 5). The main difficulty in the interpretation is the complex spectmm that results from a nutation experiment since it can consist of many overlapping powder patterns (29). 

The application of relaxation time measurements to study segmental motion (in polymers) as well as diffusional chain motion is very well documented but is still a subject of study, particularly using the frequency dependence of relaxation times to test the detailed predictions of models (McBriety and Packer 1993). The anisotropy of reorientation can also be studied conveniently, and recent interest in motion of molecules on surfaces (e.g. water on porous silica) has been investigated with great sueeess (Gladden 1993). Since the dipolar interaction is usually both intermolecular and intramolecular, the relaxation of spin- /2 nuclei (e.g. H) in the same molecule as a quadrupolar nucleus (e.g. H) can permit a complete study of reorientation and translation at a microscopic level (Schmidt-Rohr and Spiess 1994). 

Si has a spin 1= >2, which means it is not subject to quadrupolar peak broadening and distortion. Despite its relatively low natural abundance (4.7%), the spectral resolution of Si is high due to its relatively narrow resonance lines. It is, however, subject to the two principal sources of broadening in a spin = nucleus (Chapter 2). These are ... 

Serious complications arise, however, if the spins are subject to strong nuclear electric quadrupolar interactions, which tend to modify the echo amplitudes measured. In such cases, it is still possible to extract dipole-dipole coupling information from spin echo decay spectroscopy, if the 71-pulses are applied entirely selectively to the central l/2>o -l/2> transition [6]. If the resonance frequencies between the coupled nuclei are sufficiently similar to allow for spin-exchange via the flip-flop mechanism, Eq. (5) turns into... 

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