Quadrupolar interaction asymmetry parameter

FIGURE 2. Calculated powder patterns for spin-1 (a) and spin-3/2 (b) nuclei with a dominating quadrupolar interaction (QUASAR simulation) tj is the asymmetry parameter of the quadmpolar interaction (equation (9))... 

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) ...

Correlations between 2H quadrupole interaction parameters and hydrogen bond geometry have also been considered for situations other than 0-H---0 hydrogen bonds. For example, solid state 2H NMR spectra of 2H labelled amino acids, peptides and polypeptides were measured over a wide temperature range [74]. From spectral simulations based on dynamic 2H NMR theory, parameters such as the 2H quadrupolar coupling constant and asymmetry parameter were determined, and relationships between these NMR parameters and the hydrogen... 

The NMR lineshape of solids is determined by the quadrupolar interaction, which can be described by two parameters the quadrupole frequency, o Q, and the asymmetry parameter, t/ (19,20). The parameter q)q is determined by the electric quadrupole moment of the deuteron and the zz component of the electric field gradient at the deuteron site. For deuterons bonded to carbon atoms, the asymmetry parameter is approximately zero and the z axis is along the C—D bond. In this case, the dependence of the resonance frequency, m, from the orientation of the molecule with respect to the magnetic field applied is given by a relation similar to Eq. (18) (19). 

Under anisotropic conditions, NMR lineshapes for a quadrupolar nucleus are dominated by chemical shielding and (first and second order) quadrupolar interactions. Dipolar interaction is usually a minor contribution only. First-order quadrupole interaction lifts the degeneracy of the allowed 21 (i.e. seven in the case of V / = V2) Zeeman transitions as shown in Figure 3.7, giving rise to seven equidistant lines, viz. a central line (mj = + V2 -V2. unaffected by quadrupole interaction) and six satellite lines. The overall breadth of the spectrum is determined by the size of the nuclear quadrupole coupling constant Cq the deviations from axial symmetry and hence the shape of the spectral envelope are governed by the asymmetry parameter. Static solid-state NMR thus provides additional parameters, in particular the quadrupole coupling constant, which correlates with the electronic situation in a vanadium compound. [ 1 The central component reflects the anisotropy of the chemical shift. 

Fig. 16. Schematic of the occupation probabilities in phase II of TCTMB and DCTMB. From left to right molecules under study, three well potential, averaged quadrupolar interaction and asymmetry parameters measured from powders spectra, occupations probabilities calculated from single-crystal experiments.

The nuclear electric quadrupole interaction (QI) results from the coupling between Q and the EFG at the nuclear site. The EFG is a symmetric tensor quantity of zero trace and may be described by five independent parameters. When in its principal axis system (PAS), the off-diagonal matrix elements equal zero, and two parameters can fully describe the diagonal elements. The diagonal elements of a tensor in its PAS (Pn, P22/ and 1 33 in this case) are called the principal components. In practice, the SSNMR spectrum is usually described by the nuclear quadrupolar coupling constant, Cq, and quadrupolar asymmetry parameter, rj which are related to the principal components of the EFG tensor as follows ... 

Continuing the theme of comprehensive studies, Woessner [23] recently carried out another major investigation of clay structure. The main improvement here is the use of high-speed MAS. Some of the spectra were collected at 9 kHz, which was significantly faster than for most spectra of clays published to that point. Several of the conclusions reached are in agreement with previous structural studies. One additional parameter that was extracted was the SOQE (second-order quadrupole effect), which is simply the isotropic part of the second-order quadrupolar interaction. The QCC (quadrupolar coupling constant) and T] (asymmetry parameter) are defined in this paper as follows... 

To understand why so-called magic-angle spinning (MAS) is so successful as a means of line narrowing, it is first necessary to recognise that the CSA, dipolar, and first-order quadrupolar interaction all have basically the same orientational dependence for an axially symmetric tensor (this is always the case for the dipolar interaction, and corresponds to a CSA or first-order quadrupolar interaction with a zero asymmetry parameter), the orientationally dependent part of the frequency of a particular crystalHte can be expressed in the form... 

In quadrupolar nuclei, the situation differs notably the quadrupolar interaction only affects spins with I>% and is created by electric field gradient resulting from the asymmetry of charge distribution around the nucleus of interest. The quadrupolar interaction is characterized by the nuclear quadrupolar coupling constant Cq (from 0 in symmetrical environments to tens or hundreds of MHz) and an asymmetry parameter T]q. NMR spectra are usually recorded when Cq Vl the Larmor frequency of the quadrupolar spin. In such a case, the NMR spectrum can easily be simulated First, the first-order quadrupolar Hamiltonian, which is the quadrupolar interaction Hamiltonian truncated by the Larmor frequency, has to be taken into account. The first-order quadrupolar interaction (or the zeroth-order term in perturbation theory) is an inhomogeneous interaction and is modulated by MAS and does not affect symmetrical transition —m +m. Therefore, in half-integer spins, the single-quantum central transition (CT, i.e., —1/2 +1/2) is not affected by the first-order quadrupolar inter-... 

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