Quadrupolar asymmetry parameter

In addition, quadrupolar asymmetry parameters (q) were also correlated quantitatively with hydrogen bond geometries [71]. 

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 ... 

Figure 3 Plot of quadrupolar asymmetry parameter of the central anion versus. .. X. . -I angle in halogen-bonded systems. The black diamonds represent the calculated values for Cl in a FsC-l- Cl - I-CF3 model system. The red (gray in the print version) triangles and blue (dark gray in the print version) circles represent the experimental values for Cl and Br, respectively. From Ref. [23], Copyright 2014 American Chemical Society.

Computer simulations of selected spectra observed at 40.7 and 67.8 MHz in the crystalline phases are shown in Figure 7-14. The simulations included the effects of the chemical shift anisotropy (CSA) as well as the quadrupolar interaction. The chemical shifts and quadrupolar parameters of PDFS determined are shown together with those of 0-enriched cyclic tetramer DjEtg as the model compound of PDFS in Table 7-3. These include the quadrupolar coupling constant (Cq), the quadrupolar asymmetry parameter (tiq), the isotropic chemical shift ( i, ), cs = 33 - I833 - Sisol > 8ii - Ko > I822 - Sisol. the chemical shift... 

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))... 

In addition, the asymmetry parameter of the quadrupolar coupling, r], is defined in equation 9... 

A function closely related to QCC is the Li quadrupolar splitting constant (QSC), defined as QSC = (1 -h/7 /3) x( Li), where r is the asymmetry parameter. The Li QSC values can be estimated from the Li and C(para) spin-lattice relaxation times. The QSC values are correlated with the effects of structure, solvent and temperature on association in solution for aryllithium compounds (155, 171, 172). Conclusions can be drawn about the structure of the associated species in cases where no supporting XRD evidence is available. ... 

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) ...

Deuterium nuclei in water molecules have negligible asymmetry parameters and residual anisotropies. After correcting for the paramagnetic impurities present, that affect relaxation rates somewhat (35), one obtains from the experimental data a value of the longitudinal relaxation rate for the water deuterons in the bound state of 650 s 1. This value incorporates the quadrupolar coupling constant (above determined) and the correlation time for bound waters. Using the standard expression for quadrupolar relaxation (29,35) yields a value for t 1.6 ns. 

Fig. 2. Theoretical 2H MAS NMR spectra calculated with quadrupolar coupling constant Cq = 200 kHz, asymmetry parameter r Q = 0.10, rotation frequency = 5.0 kHz (left) and uT = 10.0 kHz (right). The spectra represent (a) ideal RF irradiation conditions with RF field strength i/Rf = 100 kHz and optimum pulse length Tp = 2.25 fis, and (b, c) nonideal RF irradiation conditions with i rf = 25 kHz and tp = 4.25 fjbs. The phase distortion effects are illustrated in (b), while (c) demonstrates the result of performing a first-order phase correction. (Adapted from Kristensen et alP with permission.)...

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... 

Here 7 is the nuclear spin, is the quadrupolar coupling constant, tj is an asymmetry parameter, is the Gd- O distance, and r j is defined by Eq. 12. The difficulty of this technique is that both the quadrupolar coupling constant and the Gd - O distance can only be estimated. However, rotational correlation times obtained from longitudinal 2Q relaxation rates can provide a good comparison for similar Gd(III) complexes. One advantage is that the rotational correlation time is measured directly on the Gd(III) complex. Furthermore, the determined in this way corresponds to the rotation of the Gd(III) - coordinated water oxygen vector which is probably analogous to the rotation of the Gd(III) - coordinated water proton, which, itself determines proton relaxivity. 

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). 

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