Description of Pulse Sequences

The detection of NMR signals is based on the perturbation of spin systems that obey the laws of quantum mechanics. The effect of a single hard pulse or a selective pulse on an individual spin or the basic understanding of relaxation can be illustrated using a classical approach based on the Bloch equations. However as soon as scalar coupling and coherence transfer processes become part of the pulse sequence this simple approach is invalid and fails. Consequently most pulse experiments and techniques cannot be described satisfactorily using a classical or even semi-classical description and it is necessary to use the density matrix approach to describe the quantum physics of nuclear spins. The density matrix is the basis of the more practicable product operator formalism. 

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In this chapter these interactions and the relaxation of spins are described with respect to their relevance in adsorption layer studies. A detailed account of the foundations of NMR, practical aspects of Fourier transform (FT) NMR methods, and descriptions of pulse sequences, however, can be found in textbooks of liquid or solid state NMR, respectively. 

Books listed in previous chapters by van de Ven,109 Gunther,64 and Brey116 contain good descriptions of many 2D experiments. 150 and More Basic NMR Experiments—A Practical Course by S. Braun, et al.,41 described in Chapter 3, provides excellent summaries of pulse sequences, applications, and product operator descriptions of many 2D and 3D experiments. The Encyclopedia of NMR includes 16 articles specifically devoted to more detailed exposition of most of the commonly used 2D and 3D methods. 

Fig. 7.1.3 [Blii2] NMR-timescale of molecular motion and filter transfer functions of pulse sequences which can be utilized for selecting magnetization according to the timescale of molecular motion. The concept of transfer functions provides an approximative description of the filters. A more detailed description needs to take into account magnetic-field dependences and spectral densities of motion. The transfer functions shown for the saturation recovery and the stimulated-echo filter apply in the fast motion regime.

The mathematical description of the echo intensity as a fiinction of T2 and for a repeated spin-echo measurement has been calculated on the basis that the signal before one measurement cycle is exactly that at the end of the previous cycle. Under steady state conditions of repeated cycles, this must therefore equal the signal at the end of the measurement cycle itself For a spin-echo pulse sequence such as that depicted in Figure B 1.14.1 the echo magnetization is given by [17]... 

Muns ENDOR mvolves observation of the stimulated echo intensity as a fimction of the frequency of an RE Ti-pulse applied between tlie second and third MW pulse. In contrast to the Davies ENDOR experiment, the Mims-ENDOR sequence does not require selective MW pulses. For a detailed description of the polarization transfer in a Mims-type experiment the reader is referred to the literature [43]. Just as with three-pulse ESEEM, blind spots can occur in ENDOR spectra measured using Muns method. To avoid the possibility of missing lines it is therefore essential to repeat the experiment with different values of the pulse spacing Detection of the echo intensity as a fimction of the RE frequency and x yields a real two-dimensional experiment. An FT of the x-domain will yield cross-peaks in the 2D-FT-ENDOR spectrum which correlate different ENDOR transitions belonging to the same nucleus. One advantage of Mims ENDOR over Davies ENDOR is its larger echo intensity because more spins due to the nonselective excitation are involved in the fomiation of the echo. 

The DDIF experiment consists of a stimulated echo pulse sequence [50] and a reference scan to measure and separate the effect of spin-lattice relaxation. The pulse diagrams for these two are shown in Figure 3.7.2. Details of the experiments have been discussed in Ref. [51] and a brief description will be presented here. 

In this chapter, we first present a brief overview of the experimental techniques that we and others have used to study torsional motion in S, and D0 (Section II). These are resonant two-photon ionization (R2PI) for S,-S0 spectroscopy and pulsed-field ionization (commonly known as ZEKE-PFI) for D0-S, spectroscopy. In Section HI, we summarize what is known about sixfold methyl rotor barriers in S0, S, and D0, including a brief description of how the absolute conformational preference can be inferred from spectral intensities. Section IV describes the threefold example of o-cholorotoluene in some detail and summarizes what is known about threefold barriers more generally. The sequence of molecules o-fluorotoluene, o-chlorotoluene, and 2-fluoro-6-chlorotoluene shows the effects of ort/io-fluoro and ortho-chloro substituents on the rotor potential. These are approximately additive in S0, S, and D0. Finally, in Section V, we present our ideas about the underlying causes of these diverse barrier heights and conformational preferences, based on analysis of the optimized geometries and electronic wavefunctions from ab initio calculations. 

In the first part of this contribution the general principle of multiple frequency selective excitation is explained, followed by a short presentation of correspondingly updated selective ID and 2D pulse sequences and by a few applications and results for demonstration. The contribution concludes with a critical discussion of advantages and limitations for this kind of experiments and the perspectives for further developments. Readers interested in a more detailed description and in experimental details such as spectrometer settings are referred to the corresponding publications [2-6]. 

The use of spin-lock pulses for water suppression is illustrated with the NOESY and ROESY pulse sequences (fig. 5). Using the Cartesian product operator description [9], the effect of the NOESY pulse sequence of fig. 5(A) is readily illustrated ... 

Give an exact description of instrumentation—magnetic field strength, Continuous Wave (CW) or Fourier Transformed (FT), pulse sequence, decoupling, etc. 

Temporal variation of magnetic field gradients along the X, Y, and Z axes a so-called pulse sequence for image acquisition is applied for MRI measurements. Several procedures have been developed for an effective determination of the spatial distribution of the spins. A detailed description of MRI pulse sequences is available in explanations by Callaghan,37 Blumich,38 and Kimmich.39... 

We did a credible job of interpretation of ipsenol using H NMR in Chapter 3, but we can do a better job using correlation methods, quicker and with less ambiguity. Caryophyllene oxide, lactose, and VGSE are, however, too complex to fully analyze using onedimensional H and 13C NMR alone. Before turning our attention to the description of specific experiments and their interpretation, we will first take a closer look at pulse sequences and Fourier transformation. 

Shaped pulses are created from text files that have a line-by-line description of the amplitude and phase of each of the component rectangular pulses. These files are created by software that calculates from a mathematical shape and a frequency shift (to create the phase ramp). There are hundreds of shapes available, with names like Wurst , Sneeze , Iburp , and so on, specialized for all sorts of applications (inversion, excitation, broadband, selective, decoupling, peak suppression, band selective, etc.). The software sets the maximum RF power level of the shape at the top of the curve, so that the area under the curve will correspond to the approximately correct pulse rotation desired (90°, 180°, etc.). When an experiment is started, this list is loaded into the memory of the waveform generator (Varian) or amplitude setting unit (Bruker), and when a shaped pulse is called for in the pulse sequence, the amplitudes and phases are set in real time as the individual rectangular pulses are executed. 

NMR pulse sequence without getting tied up in the details of pulse phases and a mountain of sine and cosine terms only the essential elements of the sample net magnetization will be described at each point. Finally, the formal Hamiltonian description of solution-state NMR will be described and applied to explain two related phenomena strong coupling ( leaning of multiplets) and TOCSY mixing (the isotropic mixing sequence). 

The original GAMMA paper contains an excellent description of what is required of a simulation package that implements a reasonably complete model of the quantum mechanical evolution of a spin system under the influence of a pulse sequence. For anyone seriously interested in the implementation details required for NMR simulation consultation of that paper is highly recommended. Here an overview is provided for completeness. 

Use a coherence pathway or vector description to show that the pulse sequence in Fig. 12.7 leads to a signal at the end of the evolution period that shows no modulation from spin coupling. 

Since the first description of the Hartmann-Hahn transfer in liquids, spectroscopists have been fascinated by this technique. Many theoretical and practical aspects have been thoroughly investigated by several groups. With the development of robust multiple-pulse sequences, homonuclear and heteronuclear Hartmann-Hahn transfer has become one of the most useful experimental building blocks in high-resolution NMR. 

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