Multiple-pulse experiment

Multiple-pulse experiment An experiment in which more than one pulse is applied to the nuclei. 

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). 

In section 3.2 the main principles of ID and 2D NMR experiments are brielly discussed and some typical examples are shown. It is not the aim of this book to give you an introduction into the mechanics of multiple pulse experiments or the gymnastics of spins in such experiments. If you are interested in the physics and the experimental aspects of the various NMR experiments you are referred to Data Acquisition (volume 2) of this series, where these topics are discussed in detail. 

B This pulse sequence, the ID DEFT (Distorsionless Enhancement by Polarization Transfer) experiment, was developed to measure carbon chemical shifts with enhanced sensitivity and to determine at the same time their multiplicities, to differentiate between CH, CH, CH and C. It is a heteronuclear multiple pulse experiment with pulses applied to perturb both carbon and proton spins. Il consists of a preparation, a mixing (used to transfer proton polarization to the directly bound carbons) and a detection period. 

Ziessow, D., Understanding Multiple-Pulse Experiments, Concepts in Magnetic Resonance An Educational Journal, 1990,2 (No 2)... 

The previous discussion shows that the relaxation processes emerge from the quantum dynamics under appropriate circumstances leading to the formation of time-dependent quasiclassical parts in the observable quantities. Let us add that quasiclassical and semiclassical methods have been recently applied to the optical response of quantum systems in several works [65, 66] where the relation to the Liouville formulation of quantum mechanics has been discussed, without however pointing out the existence of Liouvillian resonances as we discussed here above. The connection between the property of chaos and n-time correlation functions or the nth-order response of a system in multiple-pulse experiments has also been discussed [67, 68]. 

The study of nucleic acid bases by NMR has been reported in a number of monographs (/), but very little data is available on the, 3C and, 5N NMR chemical shift tensors in these compounds. The low sensitivity of NMR spectroscopy and the long relaxation times exhibited by many of these compounds have posed the main impediments for these studies. The use of sample doping with free radical relaxation reagents, to reduce the relaxation times facilitating 2D multiple pulse experiment (2, 3), enables one to measure and analyze the principal values of the chemical shift tensors in natural abundance samples. In previous papers from this laboratory we have presented, 5N NMR chemical shift principal values for adenine, guanine, cytosine, thymine and uracil (4, 5). 

We now consider multiple-pulse experiments and two-dimensional (2-D) NMR. Exactly what does the term dimension in NMR mean The familiar proton spectrum is a plot of frequency (in S units) versus intensity (arbitrary units)—obviously 2-D but called a 1-D NMR experiment, the one-dimension referring to the frequency axis. It is important to remember that the frequency axis, with which we are comfortable, is derived from the time axis (the acquisition time) of the FID through the mathematical process of Fourier transformation. Thus, experimentally, the variable of the abscissa of a 1-D experiment is in time units. 

With the advances in experimental solid-state NMR and computational resources (both software and computing power), it is now possible to use both the experimental and computational results (sometimes in a complementary way) to study biologically important macromolecules such as proteins. The quantum-chemical computation (particularly by density functional theory) of NMR parameters in solids has found important application in protein structure determination.30-36 Tesche and Haeberlen37 calculated the proton chemical shift tensor of the methyl groups in dimethyl terephthalate and found the theoretical results were in good agreement with the multiple pulse experiment. 

Using time-dependent perturbation theory and taking full account of the symmetry and commutation relations for the high-order dipolar Hamiltonians, Hohwy et al.61 69 gave a systematic analysis of homonuclear decoupling under sample rotation and proposed a novel approach to the design of multiple-pulse experiments. Based on the theoretical analysis, they proposed a pulse sequence that can average dipolar interaction up to the fifth order. One example of these pulse sequences is shown at the top of Fig. 3. This sequence is sufficiently powerful that it is possible to obtain precise measurement of proton chemical shift anisotropies, as shown in Fig. 3. 

Meakin and Jesson (48) used the Bloch equations in part of their work on the computer simulation of multiple-pulse experiments. They find that this approach is efficient for the effect upon the magnetization vector of any sequence of pulses and delays in weakly coupled spin systems. However, relaxation processes and tightly coupled spin systems cannot be dealt with satisfactorily in this way and require the use of the density matrix. 

M. Hohwy and N. C. Nielsen, Systematic design and evaluation of multiple-pulse experiments in nuclear magnetic resonance spectroscopy using a semi-continuous Baker-Campell-Hausdorff expansion. J. Chem. Phys., 1998, 109, 3780-3791. 

Figure 1. Results from multiple-pulse experiment. Pulsing 1.0 10 molecules of CO over oxygen-precovered platinum (333 K).

Results of series of multiple-pulse experiments over Pt sponge. The values given are the total amounts for the multiple-pulse experiment (accuracy +/-10 %). 

If both the amounts of CO produced in Table 1 are added and compared to the amounts of oxygen and carbon monoxide used, it can be seen, that the amount of oxygen and CO used, corresponds to the amount needed for the CO produced. The amount of CO produced during one multiple pulse experiment should be equal to the number of active sites on the catalyst. If the amount of produced carbon dioxide is compared to the calculated number of platinum surface atoms from the SEM micrographs or B.E.T. measurement, it can be seen that these are in good agreement. 

The vector model, introduced in Chapter 3, is very useful for describing basic NMR experiments but unfortunately is not applicable to coupled spin systems. When it comes to two-dimensional NMR many of the experiments are only of interest in coupled spin systems, so we really must have some way of describing the behaviour of such systems under multiple-pulse experiments. 

The product operator formalism is a complete and rigorous quantum mechanical description of NMR experiments and is well suited to calculating the outcome of modem multiple-pulse experiments. One particularly appealing feature is the fact that the operators have a clear physical meaning and that the effects of pulses and delays can be thought of as geometrical rotations, much in the same way as we did for the vector model in Chapter 3. 

Time-domain spectroscopies entail a major shift in emphasis from traditional spectroscopies, since the experimenter can control, in principle, the duration, shape, and sequence of pulses. One may say that traditional, CW spectroscopy, is passive—the experimenter attempts to study static properties of a particular molecule. Coherent pulse experiments are active in that, given a set of molecular properties (which may in fact be known from various spectroscopies), one tries to arrange for a desired chemical product, or to design a pulse sequence that will probe new molecular properties. The time-dependent quantum mechanics-wavepacket dynamics approach developed here is a natural framework for formulating and interpreting new multiple pulse experiments. Femtosecond experiments yield to a particularly simple interpretation within our approach. 

Multiple Pulse Experiments. In an attempt to improve the modulation frequency by increasing the grating depths, experiments with multiple pulses (two to ten) have been performed. 

An external trigger capability for the digitizer is useful for at least two reasons. One is to be able to sample the magnetization at the correct points in a multiple pulse experiment. (An example would be to sample just the tops of the echoes in a CPMG experiment as described in I.C.2.) The other reason is to allow for synchronization of two digitizers, for example, in quadrature detection. 

It should be noted that very high H homogeneity is necessary only in certain cases. A high resolution spectrum results even if different parts of the sample experience different H s. In a cross coil probe, it is easier to achieve uniform H while having the sample approximate an infinite cylinder with respect to the receiver coil. High H homogeneity is important for multiple pulse experiments, however. 

Multiple pulse experiments were done in the temperature range of 328 to 423 K. Figure 2A shows the result of one of these experiments as measured directly. As it is difficult to see small variations in pulse size, a different representation for the experiments was used, in which the individual pulse responses are integrated. Figure 2B shows the result of such an integration. In these figures the amount of CO ... 

Results of series of multiple-pulse experiments over 291 mg Pt sponge. 

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