Adiabatic inversion

The best and easiest way to implement such an experiment is to use adiabatic inversion pulses, in order to introduce heterogeneity for evolution under 13C-1H scalar or residual dipolar couplings by means of a frequency-swept 180° pulse on 13C that inverts 13C nuclei at different positions in the NMR sample at different times (Figure 13) 40,45 This filter is robust with respect to pulse miscalibration and operates efficiently without the need to cycle the phases of pulses that otherwise is a common feature of non-destructive LPJFs. 

Siegel et al. showed that enhancement of the CT can also be obtained using hyperbolic secant (HS) pulses to invert selectively the STs [74], Unlike the DFS waveform, whose frequency sweep is generated by a constant rf-pulse phase while modulating the amplitude, the HS pulse utilizes both amplitude and phase modulation, yielding an enhancement exceeding that obtained by DFS or RAPT [61, 74, 75]. Most recently, the pulse sequence called wideband uniform-rate smooth truncation (WURST) [76] was introduced to achieve selective adiabatic inversion using a lower power of the rf-field than that required for the HS pulses [77,78]. One of its applications involved more efficient detection of insensitive nuclei, such as 33S [79]. 

The idea of using the linear phase increments to achieve frequency-shifted excitation can be adopted almost to any pulses, such as hard (amplitude fixed) pulses, shaped pulses, and even adiabatic inversion pulses. Unlike any other pulses, the adiabatic pulses have already used non-linear phase increments for tilting the effective RF field slowly compared with the Larmor frequency of the spins in the rotating frame in order to fulfill the adiabatic condition. 

The idea of using phase increment to achieve frequency-shifted excitation can be extended virtually to any sort of RF pulses, including the most complicated adiabatic inversion pulses where a non-linear phase increment has already been applied. Using the phase increment, double or multiple pulses can be constructed with only a single waveform generator in order to excite different regions of a NMR spectrum or to compensate the BSFS, BSPS, as well as BSOS. 

Fig. 11.5 Schematic comparison of (a) sudden and (b) adiabatic inversion of the z-component of the polarization vector. In the sudden case a n-pulse is applied while in the adiabatic case a frequency sweep is shown. The time evolution of the z-polarization as a function of the pulse duration...

Fig. 17.5 Use of an adiabatic inversion pulse in a 13C filter. An almost linear relationship exists between a 13C chemical shift and the corresponding Yh,13C coupling constant (left panel). With an adiabatic 180° pulse on 13C, sweeping from high...

Even if the optimisation of the use of DFS, RAPT or adiabatic inversion pulses is not straightforward for nuclei with low sensitivity, it is nonetheless worth applying one of these methods to improve sensitivity. As long as there is no influence on the CT resonance, these techniques are likely to produce an enhanced CT signal compared to standard spin-echo experiments. Therefore, for Mg (as well as for other insensitive half-integer spin quadrupolar nuclei such as S, K and Ca), it is always advisable to apply some population transfer technique before the excitation of the CT signal. 

The combined use of adiabatic inversion and composite adiabatic pulses can have a dramatic effect on the sensitivity of 1,1-ADEQUATE on a 600-MHz NMR spectrometer as illustrated on spectra of cholesteryl acetate in Figure 7 28... 

Figure 9 13C-detected I PAP INADEQUATE (A) non-refocused (AP) and (B) refocused (IP) INADEQUATE T = 0.S/nJcc, the 90° rectangular pulses are shown as filled rectangles 90° BEBOP and 180° BIBOP pulses are indicated as narrow and wide rectangles, respectively the adiabatic inversion pulse is designated by an inclined arrow. Phase cycling is given in Table 1. From Ref. 32, reproduced by permission of John Wiley and Sons. 

These experiments use 1H decoupling during most parts of the pulse sequence, which increases the lifetime of coherences.31 The purging of the residual AP component of doublets is achieved by a combination of an adiabatic inversion and a low-level pulsed field gradient. 

Figure 13 Pulse sequences of -detected IPAP DEPT-INADEQUATE.The insert is used when in-phase doublets are acquired. The filled and open rectangles represent 90° and 180° rectangular pulses, respectively, applied from the x-axis unless stated otherwise. The dashed rectangles of the DEPT pulse sequence represent rectangular pulses with flip angle 6 = 90° or 45°. The 180° BIBOP pulses are indicated as wide rectangles with a sine wave. The 13C adiabatic inversion pulses are designated by an inclined arrow. The following delays were used t = 0.5/Vch> At = 0.25/VCo A2 = 0.25/ycc. For other parameters see Ref. 31. Reproduced by permission of Elsevier.

Figure 9.9. The adiabatic inversion pulse. An rf frequency sweep during the pulse causes the effective rf field experienced by the spins to trace an arc from the +z-axis to the -z-axis, dragging with it the bulk magnetisation vector.

The presence of zero-quantum coherence during the mixing time can substantially distort NOE intensities. This coherence can not be removed with phasecycling or gradient pulses while preserving z-magnetisation. A z-filter scheme was proposed earlier for the elimination of the coherence. It utilises an adiabatic inversion pulse with linear frequency sweep applied simultaneously with a gradient. Cano et alP demonstrated that a better suppression is achieved with a z-filter cascade that combines several filter elements. The attainable suppression ration is then equal to the multiplication of the ratios for each element. 

W. Kozminski, K. Jackowski, Application of adiabatic inversion pulses for elimination of baseline distortions in Fourier transform NMR. A natural abtmdance 170 NMR spectrum for gaseous acetone, Magn. Reson. Chem. 38 (2000) 459—462. 

Nesbitt, Child and Clarys applied the theory, with this modification, to the (10°0), (12o0) and (110) bands of Ar HF, using the I type doubling of the (110) bands to deperturb the (12 0) band, and thereby obtained the diatomic like potential curves in Fig.3. An adiabatic inversion procedure was then adopted, in the sense that the three potential curves were interpreted as bending vibrational eigenvalues (parametrically dependent on R) of a three term potential surface. 

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