Quadrupole-induced shift

As if can be seen in fhese simulations, all MAS spectra are shifted towards low frequencies wifh respecf fo fhe true isotropic chemical shift—an effect known as the second-order quadrupole-induced shift. The centre of gravity ( g) of fhese lineshapes is given by ° ... 

The isotropic shift and the quadrupole induced shift (QIS = Co(p)/Co(l), with Cs defined in Table 2.4) can readily be obtained from the data. Firstly, the 2D spectrum must be referenced correctly. To obtain the correct ppm scale in the FI dimension one must set the spectrometer frequency in the FI dimension to pVo. The shift reference is most readily set at the carrier frequency, i.e. the shift in ppm at the carrier frequency in the multiple quantum dimension Ft is the same as the shift in ppm at the carrier frequency in the single quantum dimension F2. This is valid for data obtained with or without delayed acquisition and processed with or without shearing. The isotropic chemical shift is the same for both the single quantum and the multiple quantum dimensions. The QIS is different in both dimensions, however, and is given by... 

Figure 7.5. MQMAS NMR spectra of A. NaMg(P03)3 and B. NaZn(P03)3, showing the resolution of the three similar Na sites in each compound. The broken line indicates the axis of the quadrupole-induced shift. From Abrahams et al. (2000), by permission of the Royal Society of...

The isotropic shift and the quadrupole-induced shift (QIS) can easily be obtained from the data. The QIS is different in both dimensions, however, and is given by... 

NMR spectra, where the v. axis nearly purely reflects the isotropic chemical shift, and the quadrupolar parameters (second-order quadrupolar broadening and quadrupole-induced shift) are separated along the V axis (Fig. 19D). 

From the beginnings, attempts to model the line shapes of collision-induced absorption spectra were based on the assumption that the various rotational lines of induced spectra, Figs. 3.10 through 3.14, are superpositions of scaled and shifted line profiles, g(C)(v), °f a small number of different, e.g., overlap- and quadrupole-induced, types [313, 404],... 

Because of rapid, quadrupole-induced relaxation, NMR signals frequently are 200 or 300 Hz wide or more. This is not as severe a problem as it may at first appear because vanadium-51 has a large chemical shift range of about 3000 ppm. As illustrated in Figure 2.2, the line widths shown vary from about 130 to 1000 Hz (1.3 to 10.0 ppm with a 400 MHz spectrometer), yet the spectrum is well resolved. The fast relaxation does mean that spectra can be accumulated very rapidly. Only in atypical situations will 20 or 30 accumulations per second lead to problems of... 

Compared with the pronounced solvent-induced chemical shifts observed with ionic and dipolar solutes, the corresponding shifts of nonpolar solutes such as tetrame-thylsilane are rather small cf. Table 6-6. A careful investigation of chemical shifts of unsubstituted aromatic, as well as alternant and nonalternant, unsaturated hydrocarbons in aliphatic and aromatic non-HBD solvents by Abboud et al. has shown that the differential solvent-induced chemical shift range (relative to benzene as reference) is of the order of only —1.4...+1.0 ppm (positive values representing downfield shifts) [405]. The NMR spectra of these aromatic compounds have been shown to be sensitive to solvent dipolarity and polarizability, except in aromatic solvents, for which an additional specific aromatic solvent-induced shift (ASIS see later) has been found. There is no simple relationship between the solvent-induced chemical shifts and the calculated charge distribution of the aromatic solute molecules. This demonstrates the importance of quadrupoles and higher multipoles in solute/solvent interactions involving aromatic solutes [405]. 

A major advantage of MQAS is that it allows separation and measurement of the isotropic chemical shifts and quadrupolar-induced shifts by recording and analysing a single two-dimensional spectrum. Determination of quadrupole parameters and relative site populations are also possible, even for disordered and amorphous materials. In the present section we address these problems. 

Figure 16 2D 3Q/MAS NMR spectrum of l anite measured by the three-pulse sequence with z-filter. No shearing transformation was applied. Labels "A," "CS," and "QiS" describe anisotropic axis, isotropic chemical shift axis and axis of quadrupole-induced isotropic shift, respectively. Three different AlOg structural units are clearly defined.

Subsequently, based on the principles of 2D NMR spectroscopy, distinct sites can be clearly resolved (Fig. 16), and, using mathematical analysis, the isotropic chemical shift and quadrupole-induced isotropic shift can be separated from the anisotropic second-order quadrupolar spHtting. The principle condition for obtaining the required results or separating the anisotropic component of the quadrupolar interaction from isotropic contributions is based on the correct setup of the ratio of t and <2 detection times, during which the 3Q generally p-quantum) and IQ coherences evolve. This ratio must fulfill the following condition [72,73] ... 

The perturbation of the four substates of the excited 7 = 3/2 manifold by induces a typical asymmetry of the resulting magnetically split Mossbauer spectrum as pictured at the bottom of Fig. 4.10 for positive the inner four lines, 2-5, are shifted to lower velocities, whereas the outer two lines, 1 and 6, are shifted to higher velocities by equal amounts. In first order, the line intensities are not affected. For negative the line asymmetry is just inverted, as the quadmpole shift of the nuclear 1/2 and 3/2 states is opposite. Thus, the sign and the size of the EFG component along the field can be easily derived from a magnetic Mossbauer spectrum with first-order quadrupole perturbation. 

For an absolute agreement between the observed and calculated crystal field effects in such dipolar crystal lattices, the zero point vibrations have to be considered, as Bersohn pointed out. Furthermore, we think that the part of the solid state shift is due to the contribution of the quadrupole polarization (antishielding factor). The inner shell electrons of the atom considered experience an induced quadrupole moment under the influence of the external fields. This... 

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