Quadrupolar coupling electric field gradient

If the spin-quantum number, Ik, of a spin k is larger than 1/2, we have an additional term in the Hamiltonian, the quadmpolar coupling, hPk. The quadmpolar Hamiltonian arises from the interaction between the electric-field gradient and the nuclear spin. The first-order quadrupolar Hamiltonian is given by ... 

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. 

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) ...

In the presence of a quadrupolar coupling, the NMR line of a deu-teron is split into a symmetric doublet. With an axial electric field gradient (e.f.g.), the doublet spacing in frequency units is given by ... 

Classically, the electric field gradient at a nucleus is produced by the arrangement of charges (i.e., other nuclei and electrons) about that nucleus 66). If the nucleus is quad-rupolar, as in the case of 27A1, then the interaction of its nuclear quadrupole moment, eQ, with the largest component of the EFG tensor, V33, is defined as the quadrupolar coupling constant, CQ ... 

Carr-Purcell-Meiboom-Gill nuclear quadrupolar coupling constant receptivity relative to aH electric field gradient nuclear spin quantum number magic-angle spinning... 

In case of a deuterated sample (spin 1 case), the spectra are usually dominated by the quadrupolar interaction, that is, the coupling of the nuclear quadrupole moment with the electric field gradient of the C-2H bond. For deuterons in C-2H bonds this can lead to a splitting of about 250 kHz. As in the case of dipolar interaction, a Pake spectrum is obtained for a powder sample. The z-principal axis of the quadrupolar interaction is oriented along the bond axis which makes deuteron NMR particularly useful for studies of segmental orientations and molecular dynamics (reorientation) [1],... 

Quantum mechanical calculations of 33S nuclear quadrupole coupling constants are not an easy matter (not only for the 33S nucleus, but for all quadrupolar nuclei). Indeed, the electric field gradient is a typical core property, and it is difficult to find wave functions correctly describing the electronic distribution in close proximity to the nucleus. Moreover, in the case of 33S, the real importance of the Sternheimer shielding contribution has not been completely assessed, and in any case the Sternheimer effect is difficult to calculate. 

Another special case occurs if the nucleus is at a site of cubic point symmetry (actually tetrahedral symmetry or higher will do). If this condition holds, the electric field gradient must by symmetry disappear, and the quadrupole coupling vanishes. Common examples are tetrahedral ions such as SO -, MoO -, TcOj, and simple salts, such as NaCl, in which the ions reside in sites of cubic symmetry. Unfortunately, this situation almost never occurs for the quadrupolar nuclei, such as l70, l4N, and 35C1, that one might wish to study in organic compounds. The only possible exceptions are symmetrically tetrasubstituted ammonium salts. 

A lower resonance half-high band width for 1-hydrosilatrane 638 + 68 Hz as compared to 2211 103 Hz in 1-methylsilatrane shows that a stronger Si<-N interaction in the former leads to a smaller electric fields gradient and/or a smaller distortion towards the planar nitrogen results in a marked increase in the quadrupolar coupling constant. 

Nuclei with spin quantum number I > can possess electric quadrupole moments. The nuclear quadrupole is directly coupled to the nuclear spin and the electrostatic interaction dominates the nuclear spin relaxation. The quadrupolar interaction is simply the first non-vanishing term in the Taylor expansion of the electrostatic interaction between the charge distribution of the nucleus and that of its surrounding. It can be expressed as a direct product between the nuclear quadrupole tensor and the electric field gradient (EFG) at the nucleus [6]. 

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