Quadrupolar interaction nucleus

Figure 5. Energy level diagram for a spin 5/2 nucleus showing the effect of the first-order quadrupolar interaction on the Zeeman energy levels. The (m V2 m = -V2) transition (shown in bold) is independent of the quadrupolar interaction to...

The strength of the quadrupolar interaction is proportional to the quadrupole moment Q of a nucleus and the electric field gradient (EFG) [21-23]. The size of Q depends on the effective shape of the ellipsoid of nuclear charge distribution, and a non-zero value indicates that it is not spherically symmetric (Fig. 1). 

Fig. 1 (a) Schematic representation of the spherical and non-spherical charge distribution in a nucleus. The value of electric quadrupole moment Q for the quadrupolar nucleus depends on the isotope under consideration, (b) The quadrupolar interaction arises from the interaction of Q with surrounding electric field gradient (EFG)... 

Two additional interactions experienced by the nucleus in the solid state are spin-spin couplings to other nuclei, and quadrupolar interactions, which involve nuclei of spin greater than 1/2. Spin-spin (Hx), or J, coupling,... 

Numerous X-ray investigations have unravelled the solid state structure of contact and solvent-separated ion pairs. It was therefore considered to be of interest to evaluate also the potential of solid state NMR as a tool for the investigation of this structural problem. In addition to the study of chemical shifts discussed above (Section II.B), the quadrupole coupling constant of the nuclide Li, x( Li), was expected to be an ideal sensor for the bonding situation around the lithium cation because, due to its dependence on the electric field gradient, the quadrupolar interaction for this spin-3/2 nucleus is strongly influenced by local symmetry, as exemplified in Section II.C.3. This is also shown with some model calculations in Section ILF. 

When the electric field gradient at the nucleus exerted by the electrons is nonzero, the nuclear levels will be split. The eigenvalues of the quadrupolar interaction Hamiltonian are given by... 

This contribution, through the electric field gradient at the Np nucleus gives information about quadrupolar interaction and is useful in identifying non-equivalent sites of magnet-... 

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) ...

Solid State 170 NMR Spectral Analysis. The 170 nucleus has a 5/2 spin and so has a quadrupolar moment. This means that static and MAS 170 NMR spectrum contains information about quadrupolar interactions and the chemical shift. In order to obtain the quadrupolar coupling constant and chemical shift separately, we have carried out spectral analysis with theoretical calculation taking into account quadrupolar interactions and chemical shift interactions. 

Several reviews on xenon NMR spectroscopy have appeared [1, 2], therefore in this introduction only the most important aspects will be discussed. The xenon atom has two isotopes which are suited for NMR studies, the 129Xe and 131Xe isotopes. For most studies 129Xe is more convenient than 131Xe, while the former nucleus with spin I=V2 does not have an electrical quadrupole moment. In some cases, however, the quadrupolar interaction can provide additional (spectral and relaxation) information. Flere we will only consider the 129Xe isotope. 

The predominant interaction for a 2H spin system is the quadrupolar interaction, which couples the electric quadrupole moment of the 2H nucleus to its electronic surrounding. This interaction is a second-rank tensor Hq which lies approximately along the C-2H bond in organic molecules. Thus, in practice, 2H nuclei may be considered to be isolated. It shows that the 2H NMR formalism is similar to that of an isolated proton pair [8] ... 

Fig. 6. Energy level splitting due to the Zeeman interaction and the quadrupolar interaction for a spin-1 nucleus. The scale has been exaggerated for clarity.

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