The pulse sequence

Figure Al.6.22 (a) Sequence of pulses in the canonical echo experiment, (b) Polarization versus time for the pulse sequence in (a), showing an echo at a time delay equal to the delay between the excitation pulses.

Figure Al.6.30. (a) Two pulse sequence used in the Tannor-Rice pump-dump scheme, (b) The Husuni time-frequency distribution corresponding to the two pump sequence in (a), constmcted by taking the overlap of the pulse sequence with a two-parameter family of Gaussians, characterized by different centres in time and carrier frequency, and plotting the overlap as a fiinction of these two parameters. Note that the Husimi distribution allows one to visualize both the time delay and the frequency offset of pump and dump simultaneously (after [52a]).

Advantages. The experiment can be readily carried out with a conventional probe-head, although the fastest spiiming and highest RF powers available are usefid. The pulse sequences are relatively easy to set up (compared to DAS and DOR) and the results are usually quite straightforward to interpret in temis of the number of sites and detemiination of the interactions. 

A measure of the echo attenuation within each pixel of an image created using the pulse sequence of figure Bl.14,9 perhaps by repeating the experiment with different values of and/or 8, gives data from which a true diffusion map can be constructed [37, 38],... 

Figure Bl.15.11. Fomiation of electron spin echoes. (A) Magnetization of spin packets i,j, /rand / during a two-pulse experiment (rotating frame representation). (B) The pulse sequence used to produce a stimulated echo. In addition to this echo, which appears at r after the third pulse, all possible pairs of the tluee pulses produce primary echoes. These occur at times 2x, 2(x+T) and (x+2T).

B2.5.351 after multiphoton excitation via the CF stretching vibration at 1070 cm. More than 17 photons are needed to break the C-I bond, a typical value in IR laser chemistry. Contributions from direct absorption (i) are insignificant, so that the process almost exclusively follows the quasi-resonant mechanism (iii), which can be treated by generalized first-order kinetics. As an example, figure B2.5.15 illustrates the fonnation of I atoms (upper trace) during excitation with the pulse sequence of a mode-coupled CO2 laser (lower trace). In addition to the mtensity, /, the fluence, F, of radiation is a very important parameter in IR laser chemistry (and more generally in nuiltiphoton excitation) ... 

The pulse sequence (stages 2-3) can be repeated hundreds of times to enhance the signal to noise ratio The duration of time for stage 2 is on the order of milliseconds and that for stage 3 is about 1 second... 

The pulse sequence which is used to record CH COSY Involves the H- C polarisation transfer which is the basis of the DEPT sequence and which Increases the sensitivity by a factor of up to four. Consequently, a CH COSY experiment does not require any more sample than a H broadband decoupled C NMR spectrum. The result is a two-dimensional CH correlation, in which the C shift is mapped on to the abscissa and the H shift is mapped on to the ordinate (or vice versa). The C and //shifts of the //and C nuclei which are bonded to one another are read as coordinates of the cross signal as shown in the CH COSY stacked plot (Fig. 2.14b) and the associated contour plots of the a-plnene (Fig. 2.14a and c). To evaluate them, one need only read off the coordinates of the correlation signals. In Fig. 2.14c, for example, the protons with shifts Sh= 1.16 (proton A) and 2.34 (proton B of an AB system) are bonded to the C atom at c = 31.5. Formula 1 shows all of the C//connectivities (C//bonds) of a-pinene which can be read from Fig. 2.14. 

HC HMQC (heteronuclear multiple quantum coherence) and HC HSQC (heteronuclear single quantum coherence) are the acronyms of the pulse sequences used for inverse carbon-proton shift correlations. These sensitive inverse experiments detect one-bond carbon-proton connectivities within some minutes instead of some hours as required for CH COSY as demonstrated by an HC HSQC experiment with a-pinene in Fig. 2.15. 

Next a period of time T (T > T ) is allowed for the entire system to relax to its steady-state configuration. Then the pulse sequence is repeated, with a different value for t. In this way the decay of M is measured by sampling it via the 90° pulse. The sequence is called a 18(f, t, 90° sequence. l/T, is found from a semilogarithmic plot. 

Fig. 2. The pulse sequence for the CP/MAS experiment. The values of the different time parameters depend on the relaxation behaviours and on the mobilities of the nuclei in the compounds investigated. (Reproduced with permission of Ref. I0))...

If the three light pulses of the pulse sequence are only separated in time, and not separated in space (i.e. if the velocity of the atoms is parallel to the laser beams), the interferometer is in a gravimeter or accelerometer configuration. In a uniformly accelerating frame with the atoms, the frequency of the driving... 

Figure 2.4 (A) Pulse sequence for the gated spin-echo (GASPE) or attached proton test (APT) experiment. (B) Effect of the pulse sequence on the C magnetization vectors of a CH group.

Figure 2.9 Pulse sequence for the INEPT experiment. (B) Effect of pulses on H magnetization. Application of the pulse sequence shown results in population inversion of one of the two proton vectors of the CH doublet and therefore causes an intensification of the corresponding C lines.

The INEPT experiment can be modified to allow the antiphase magnetization to be precessed for a further time period so that it comes into phase before data acquisition. The pulse sequence for the refocused INEPT experiment (Pegg et al., 1981b) is shown in Fig. 2.13. Another delay, A. is introduced and 180° pulses applied at the center of this delay simultaneously to both the H and the C nuclei. Decoupling during data acquisition allows the carbons to be recorded as singlets. The value of Z), is adjusted to enable the desired type of carbon atoms to be recorded. Thus, with D, set at V4J, the CH carbons are recorded at VsJ, the CH2 carbons are recorded and at VeJ, all protonated carbons are recorded. With D3 at %J, the CH and CH ( carbons appear out of phase from the CH2 carbons. 

The pulse sequence used in the reverse DEPT experiment is shown in Fig. 2.16. Presaturation of the protons removes all H magnetization and pumps up the C population difference due to nOe. Broad-band decoupling of the C nuclei may be carried out. The final spectrum obtained is a one-dimensional H-NMR plot that contains only the H signals to which polarization has been transferred—for instance, from the enriched C nucleus. 

The basic INEPT spectrum cannot be recorded with broad-band proton decoupling, since the components of multiplets have antiphase disposition. With an appropriate increase in delay time, the antiphase components of the multiplets appear in phase. In the refocussed INEPT experiment, a suitable refocusing delay is therefore introduced that allows the C spin multiplet components to get back into phase. The pulse sequences and the resulting spectra of podophyllotoxin (Problem 2.21) from the two experiments are given below ... 

In the one-dimensional NMR experiments discussed earlier, the FID was recorded immediately after the pulse, and the only time domain involved (ij) was the one in which the FID was obtained. If, however, the signal is not recorded immediately after the pulse but a certain time interval (time interval (the evolution period) the nuclei can be made to interact with each other in various ways, depending on the pulse sequences applied. Introduction of this second dimension in NMR spectroscopy, triggered byjeener s original experiment, has resulted in tremendous advances in NMR spectroscopy and in the development of a multitude of powerful NMR techniques for structure elucidation of complex organic molecules. 

A number of parameters have to be chosen when recording 2D NMR spectra (a) the pulse sequence to be used, which depends on the experiment required to be conducted, (b) the pulse lengths and the delays in the pulse sequence, (c) the spectral widths SW, and SW2 to be used for Fj and Fi, (d) the number of data points or time increments that define t, and t-i, (e) the number of transients for each value of t, (f) the relaxation delay between each set of pulses that allows an equilibrium state to be reached, and (g) the number of preparatory dummy transients (DS) per FID required for the establishment of the steady state for each FID. Table 3.1 summarizes some important acquisition parameters for 2D NMR experiments. 

The choice of the pulse sequence to use is of fundamental importance. We must decide carefully what information is required, and choose the right experiment to provide it. Although hundreds of 2D pulse sequences are now available for various experiments, only some have proven themselves to be of general utility. Only such proven techniques should be chosen to solve structural problems. 

In the case of the t domain, since it is only the number N of data points that determines the resolution, and not the time involved in the pulse sequence with various delays, it is advisable to acquire only half the theoretical number of FIDs and to obtain the required digital resolution by zero-filling. Thus the resolution in the Fi domain will be given by R = 2SWi/A i that in the F2 domain is given by / = 1/AQ = 2SW2/A2. 

Figure 5.7 (A) Pulse sequence for gated decoupled /-resolved spectroscopy. It involves decoupling only during the first half of the evolution period

Many variations of this experiment are known. Some of the pulse sequences used for recording heteronuclear 2D/resolved spectra are shown in Fig. 5.8. In a modified gated decoupler sequence (Fig. 5.8b), the decoupler is off during the first half of the evolution period and is svdtched on during the second half. Any C resonances that are folded over in the F, domain may be removed by employing the fold-over corrected gated decoupler sequence (FOCSY) (Fig. 5.8c) or the refocused fold-over corrected decoupler sequence (RE-FOCSY) (Fig. 5.8d). 

The pulse sequence used in homonuclear 2D y-resolved spectroscopy is shown in Fig. 5.18. Let us consider a proton, A, coupled to another proton, X. The 90° pulse bends the magnetization of proton A to the y -axis. During the first half of the evolution period, the two vectors (faster... 

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