The Magic Angle

Although dipolar decoupling removes dipolar interactions, it does not remove CSA, nor does it permit observation of abundant spin species such as protons, since observation and decoupling cannot be done at the same time. Different, more selective means are needed to remove these interactions. 

These rates are sufficient to attenuate or remove linebroadening due to CSA, but are far short of the 20 KHg 

---

Disadvantages. The magic angle must be extremely stable and accurately set. The spiiming speed must show good stability over the duration of the experiment. The probe needs to be accurately tuned and careful correction for irradiation and detection variations with frequency, and baseline effects are necessary. The gain... 

Fig. I. The position of the spinning rotor in the magnetic field in the magic angle method...

Fig. 7. A C-13 relaxation time measurement of solid state wetted cellulose acetate (6% by weight water) using the inversion recovery (IR) method at 50.1 MHz and spinning at 3.2 kHz at the magic angle (54.7 deg) with strong proton decoupling during the aquisition time (136.3 ms), (upper part of the Figure). Tau represents the intervals between the 180 deg (12.2 us) inverting and 90 deg (6.1 us) measuring pulse. 2200 scans were collected and the pulse delay time was 10 s, Cf. Table 3 and Ref.281...

The well-resolved C=0 li peak in the fenchone XPS provides an excellent opportunity to examine PECO from a single, well-characterized initial orbital. As has been previously mentioned, it might be thought that such a localized, spherically symmetric initial orbital would not be sensitive to the molecular enantiomer s handedness, but as can be seen in Fig. 15 (a) the dichroism in the electron yield recorded at the magic angle is sufficiently large to be easily visible by eye as a difference in the intensity of the Icp and rep spectra. 

Figure 15. Circular dichroism of the C=0 C li peak (BE = 292.7 eV) in fenchone at three different photon energies, indicated, (a) Photoelectron spectrum of the carbonyl peak of the (1S,4R) enantiomer, recorded with right (solid line) and left (broken line) circularly polarized radiation at the magic angle, 54.7° to the beam direction, (b) The circular dichroism signal for fenchone for (1R,4A)-fenchone (x) and the (lS,41 )-fenchone (+) plotted as the raw difference / p — /rep of the 54.7° spectra, for example, as in the row above, (c) The asymmetry factor, F, obtained by normalizing the raw difference. In the lower rows, error bars are included, but are often comparable to size of plotting symbol (l/ ,4S)-fenchone (x), (lS,4R)-fenchone (+). Data are taken from Ref. [38],...

Polarization inversion spin exchange at the magic angle... 

Figure 1, Representation of the geometric arrangement for a sample spinning at the magic angle to the magnetic field vector H0. (Reproduced with permission from Ref, 40, Copyright 1982, Royal Society of London,)...

As is well known, this term vanishes when the sample is spun at the magic angle, i.e., when f RL = acos(l/-v/3) = 54.736° (Fig. 2). 

When the rotor is spun at the magic angle, the term containing 0(jSJ L) vanishes, and (18) reduces to... 

This term is independent of the coherence order p. Furthermore, it vanishes for all symmetric transitions (q = 0), and thus can be disregarded when describing the SQ CT coherence or the symmetric MQ coherence. Note, however, that this is not the case for the STs (q 0), which are therefore strongly affected by the first-order quadrupolar interaction, except when the sample is spun at the magic angle. 

In 2006 Wimperis et al. proposed a method called satellite transitions acquired in real time by MAS (STARTMAS) [142, 202], which allows for the real-time acquisition of high-resolution NMR spectra of spin-3/2 nuclei under MAS. This method combines a train of pulses, similar to CPMG [109, 110], with sample rotation at the magic angle to refocus the quadrupolar broadening in a series of echoes, while allowing the isotropic quadrupolar shift and chemical shift to evolve. 

If j Rf is exactly the magic angle and infinite spinning speed is assumed, the first-order anisotropic terms are zero for both single and DQ coherence (33). This does not hold true for finite spinning speed, but a complete averaging of the first-order effect occurs at the exact rotor cycles. Therefore, the x evolution time has to match exactly a multiple of the rotor period. The second-order anisotropy refocusing occurs for... 

---