Inversion phase cycling

Technically, the inverse experiment used to be very demanding because the excess of protons not coupled to the nucleus of interest (e.g., protons coupled to the almost hundred-fold excess of 12C instead of 13C) needed to be suppressed. Originally, this was achieved by the use of elaborate phase-cycling schemes, but today the coherence pathway selection by gradient pulses facilitates this process. 

Fig. 17. NMR spectrum obtained using a single 90° pulse without H decoupling in pure DPPC bilayers at 50 °C and 1 bar (a) and P NMR spectra obtained using a fully phase-cycled Hahn echo sequence with inversely gated H decoupling in pure DPPC bilayers at 50 °C and 1 bar in the LC phase (b), 1 kbar in the GI phase (c), 1.75 kbar in the interdigitated Gi gel phase (d), 2.5 kbar in the GII gel phase (e), 3.7 kbar in the GUI gel phase (f), and 5.1 kbar in the GX gel phase (g) (after Refs. 4, 18).

Users of any NMR instrument are well aware of the extensive employment of what is known as pulse sequences. The roots of the term go back to the early days of pulsed NMR when multiple, precisely spaced RF excitation pulses had been invented (17,98-110) and employed to overcome instrumental imperfections such as magnetic field inhomogeneity (Hahn echo) or receiver dead time (solid echo), monitor relaxation phenomena (saturationrrecovery, inversion recovery, CPMG), excite and/or isolate specific components of NMR signals (stimulated echo, quadrupole echo), etc. Later on, employment of pulse sequences of increasing complexity, combined with the so-called phase-cycling technique, has revolutionized FT-NMR spectroscopy, a field where hundreds of useful excitation and detection sequences (111,112) are at present routinely used to acquire qualitatively distinct ID, 2D, and 3D NMR... 

The classical Jeener Broekaert sequence (133) is used to determine the dipolar-order relaxation time (in systems of spin 1/2 nuclides) and the Tiq relaxation time (in systems with spin 1 nuclides) of spin 1 nuclides with quadrupolar contributions to 7. Its FFC version is similar to the Inversion Recovery, except that the first 180° pulse is replaced by the sequence 90, — 5 — 45, the detection pulse becomes 45 and a special phase cycle is required. We shall not dwell on the details and purpose of the sequence since they go beyond the scope of this chapter. We wish to underline, however, the fact that sequences of this type require a close coordination of the preparatory sub-sequence with the signal-detection sub-sequence in order to isolate not just a particular magnetization component but a particular relaxation pathway. 

Fig. 1. Pulse sequences for determining spin-lattice relaxation time constants. Thin bars represent tt/2 pulses and thick bars represent tt pulses, (a) The inversion-recovery sequence, (b) the INEPT-enhanced inversion recovery, (c) a two-dimensional proton-detected INEPT-enhanced sequence and (d) the CREPE sequence. T is the waiting period between individual scans. In (b) and (c), A is set to (1 /4) Jm and A is set to (1 /4) Jm to maximize the intensity of IH heteronuclei and to (1/8) Jm to maximize the intensity of IH2 spins. The phase cycling in (c) is as follows 4>i = 8(j/),8(-j/) 3 = -y,y A = 2(x),2(-x) Acq = X, 2 —x), X, —X, 2(x), —x, —x, 2(x), —x, x, 2 —x),x. The one-dimensional version of the proton-detected experiment can be obtained by omitting the f delay. In sequence (d), the phase 4> is chosen as increments of 27r/16 in a series of 16 experiments.

A variety of sequences exist, which differ with respect to the detected interaction ( J, or Jx ) and the mode of detection ( C or H detected, magnitude or phased mode, phase cycling or gradients for coherence selection). In view of the reduced sensitivity of heteronudear experiments with respect to homonuclear COSY experiments and the steadily decreasing sample amounts submitted for NMR experiments, there is no doubt that the inverse ( H) detected, gradient enhanced experiments are currently the best methods to apply. However on older type spectrometers, not equipped for inverse detection the old-fashioned direct C detected experiments are still in use. 

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. 

Figure 5-26 Phase cycling in the inversion recovery experiment.

For the 3Q experiment, the echo pathway 0 +3(ti) -l(/cti)-CP is selected by phase-cycling a series of 24 scans. The phase ( >i of the first pulse is then shifted by 60° for the additional 24 scans, in order to achieve the spin temperature inversion, as it results in a 3x60°= 180° shift of the coherence prior to the CP transfer. The same principle is applied to the selection of the 0 -5(ti) -l(/cti)-CP pathway in the 5QHETCOR experiment. In this case, the phase ( i in a series of 40 scans is shifted by 36° to achieve the spin temperature inversion. It should be noted that the phases applied to the CP pulse on the I channel follow those of the I spin coherence at time kti. This procedure... 

Fig. 5. Various presaturation-based suppression sequences (A) presaturation, (B) ID NOESY, (C) FLIPSY and (D) SCUBA. TTie phase cycling for the ID NOESY and FLIPSY sequences can be found elsewhere. The tt pulse in the SCUBA sequence can be replaced with a composite tt pulse to ensure more complete inversion.

Figure 5.68. Two practical schemes for implementing TOCSY based on (a) the MLEV-17 mixing scheme and (b) the DIPST2 isotropic mixing scheme. The MLEV sequence is bracketed by short, continuous-wave, spin-lock trim pulses (SL) to provide pure-phase data. In scheme (b) this can be achieved by phase-cycling the 90° z-filter pulses that surround the mixing scheme. This demands the independent inversion of each bracketing 90° pulse with coincident receiver inversion, thus (p =x, —X, X, —x (j) = X, X, —X, —X and (j)r = x, —X, —X, X. The S periods allow for the necessary power switching.

The basic components of the INADEQUATE phase cycle comprise doublequantum filtration and fi quadrature detection. The filtration may be achieved as for the DQF-COSY experiment described previously, that is, all pulses involved in the DQ excitation (those prior to ti in this case) are stepped x, y, —X, —y with receiver inversion on each step (an equivalent scheme found in spectrometer pulse sequences is to step the ftnal 90° pulse x, y, —x, —y as the receiver steps in the opposite sense x, —y, —x, y, other possibilities also exist). This simple scheme may not be sufficient to fully suppress singlet contributions, which appear along fi = 0 as axial peaks and are distinct from genuine C-C correlations. Extension with the EXORCYCLE sequence (Section 7.2.2) on the 180° pulse together with CYCLOPS (Section 3.2.5) may improve this. Cleaner suppression could also be achieved by the use of pulsed field gradients, which for sensitivity reasons requires a gradient probe optimised for C observation. 

The HMQC sequence aims to detect only those protons that are bond to a spin- A heteronucleus, or in other words only the satellites of the conventional proton spectrum. In the case of C, this means that only 1 in every 100 proton spins contribute to the 2D spectrum (the other 99 being attached to NMR inactive C) whilst for N with a natural abundance of a mere 0.37%, only 1 in 300 contribute. When the HMQC FID is recorded, all protons will induce a signal in the receiver on each scan and the unwanted resonances, which clearly represent the vast majority, must be removed with a suitable phase cycle if the correlation peaks are to be revealed (the notable exception to this is when pulsed field gradients are employed for signal selection, see Section 6.3.3 below). By inverting the first C pulse on alternate scans, the phase of the C satellites are themselves inverted whereas the C-bound protons remain unaffected (Fig. 6.5). Simultaneous inversion of the receiver will lead to cancellation of the unwanted resonances with corresponding addition of the desired satellites. This two step procedure is the fundamental phase-cycle of the HMQC experiment, as indicated in Fig. 6.3 above. 

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