Use of Pulsed Field Gradients

Many variants of this scheme are possible and can most readily be devised by considering coherence order diagrams. The requirement for rephasing of a coherence is that 

3 Verify the derivation of Eqs. 11.29 and 11.30 by repeating the algebra in each step. 

7 Use the density matrix treatment to verify the results shown in Fig. 9.2 for application of a 180° pulse to (a) / only, (b) S only, or (c) both / and S. Begin with the equilibrium density matrix, Eq. 11.50, apply a nonselective 90° pulse to obtain p as given in Eq. 11.56, consider the evolution through t, and then treat a, b, and c separately. 

8 Summarize the results of Problem 11.7 in terms of product operators. 

9 Verify that the multiple quantum coherence expressed in the density matrix of Eq. 11.68 does not give rise to observable H magnetization. 

---

One of the fastest growing areas in NMR over the past decade has been the use of pulsed field gradients , or PFG-NMR, for selective ID and 2D experiments. The basic pulsed gradient spin-echo (PGSE) experiment [174] relies on the use of pulsed linear magnetic field gradients (of amplitude g, duration 8 and separation A) that are applied during a spin-echo experiment [184],... 

Artifacts may be roughly categorized into those due to inherent limitations (e.g. pulses cannot excite unlimited bandwidths even if all hardware components work perfectly) and those that result from improper set-up of the experiment or nonideal functioning of the NMR spectrometer system. In this chapter we will mainly focus on the latter two. These artifacts are more likely to appear in multiple-pulse experiments. Quite often, they are avoided by clever programming of the experiments (e.g. interleaved acquisition of data for NOE spectra, use of pulsed-field gradients instead of phase-cycling). 

The use of actively shielded magnetic field gradients has made the use of pulsed field gradients possible. The use of pulsed field gradients reduces experiment time, minimizes artifacts, and allows for further solvent suppression. 

Because of the favorable cross-peak multiplet fine-structure, the HSQC experiment offers superior spectral resolution over the HMQC (heteronuclear multiple quantum coherence) experiment [13, 14], On the other hand, the HMQC experiment works with fewer pulses and is thus less prone to pulse imperfections. The real advantage of the HSQC experiment is for measurements of samples at natural isotopic abundance and without the use of pulsed field gradients, since the HSQC experiment lends itself to purging with a spin-lock pulse. Spin-lock purging in the HMQC experiment... 

A well-established area in the field of NMR is the use of Pulsed Field Gradients, or PFG NMR. It is ironic to consider that so much effort has been expended over so many years to provide a homogenous or stable magnetic field. Today, most modern high field NMR spectrometers are routinely equipped with hardware (coils)... 

As usual, suitable phase cycling and/or use of pulsed field gradients is critical to avoid the detection of undesired coherences. 

In principle, the procedure can be extended to additional dimensions. However, as we pointed out in Section 10.1, a 4D experiment takes 4-5 days of data accumulation, even when phase cycling is minimized by optimum use of pulsed field gradients. Expansion beyond four dimensions with adequate spectral resolution to cover complex multiline spectra would require exorbitant amounts of... 

BIRD-HMQC. The most difficult aspect of implementing the HMQC experiment is the suppression of signals from protons attached to C (the center-band or single quantum coherences) in favor of the protons attached to C (the satellites or double quantum coherences). The use of pulse field gradients (PFG, Section 6-6) is the most effective technique, but relatively few spectrometers are equipped with the hardware required for their generation. Fortunately, there is an effective alternative for the suppression of center bands by means of the BIRD Bilinear Rotation Decoupling) sequence, which is outlined by the vector... 

Recently, the use of pulsed-field gradient (PFG) technology to obtain diffusion coefficients of molecules has been demonstrated as a useful technique for mixture analysis (53). Unlike any other 2D experiment, size-resolved or diffusion-resolved NMR assigns the resonances based on the diffusion coefficient for each proton (or other spin) in the molecule and therefore can be used to distinguish resonances arising from different molecules (63-70) (Fig. 22). A method that involves the use of PFG and TOCSY, called diffusion-encoded spectroscopy (DECODES), simplifies mixture analysis by NMR (71). The combination of PFG and TOCSY decodes the spin systems, allowing individual components in complicated mixtures to be assigned. A typical DECODES spectrum obtained in this manner is shown in Fig. 23. The use of TOCSY aids the calculation of the diffusion coefficient and determination of molecular identity. 

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. 

One of the fastest growing areas in NMR over the past decade has been the use of pulsed field gradients, or... 

In many cases, we find that our sample is concentrated enough to obviate the need to collect more than one scan per tj time increment, yet the minimum phase cycle dictates the collection of at least four scans per h time increment. Fortunately, the use of pulsed field gradients allows the collection of COSY spectra with just one scan per tj time increment through a process called coherence selection. The gradient-selected COSY (gCOSY) experiment often allows us to collect a 2-D ff- ff gCOSY experiment with 256 FlDs (256 tj time increments) in 6 minutes. Another favorable feature of the gCOSY experiment is that it is tolerant of poorly calibrated pulses. 

When collected in a phase-sensitive mode, HMBC cross peaks are found to have a mixed phase character. That is, we cannot phase HMBC cross peaks so that they are purely absorptive. The use of pulsed field gradients for the purpose of coherence selection in the HMBC experiment (gHMBC) renders a nonphase-sensitive 2-D data set. This latter method is generally preferred because phasing of the spectrum is not required. 

The HMQC or HSQC sequences may be transformed into their ID equivalents by simply removing the incremental t time period (Fig. 6.22) so that the experiment becomes just a heteronuclear filter. Only magnetisation that has passed via the X spin will be observed in the final spectrum and again the suppression of all unwanted signals is greatly improved by the use of pulsed field gradients. The selective observation of C-labelled glycine in an aqueous mixture is illustrated in Fig. 6.23. 

---