Multiple quantum spectra

Phase cycling is widely employed in multipulse NMR experiments. It is also required in quadrature detection. Phase cycling is used to prevent the introduction of constant voltage generated by the electronics into the signal of the sample, to suppress artifact peaks, to correct pulse imperfections, and to select particular responses in 2D or multiple-quantum spectra. 

Oil and 0)2, and (b) 2D shift-correlation spectra, involving either coherent transfer of magnetization [e.g., COSY (Aue et al, 1976), hetero-COSY (Maudsley and Ernst, 1977), relayed COSY (Eich et al, 1982), TOCSY (Braunschweiler and Ernst, 1983), 2D multiple-quantum spectra (Braun-schweiler et al, 1983), etc.] or incoherent transfer of magnedzation (Kumar et al, 1980 Machura and Ernst, 1980 Bothner-By et al, 1984) [e.g., 2D crossrelaxation experiments, such as NOESY, ROESY, 2D chemical-exchange spectroscopy (EXSY) (Jeener et al, 1979 Meier and Ernst, 1979), and 2D spin-diffusion spectroscopy (Caravatti et al, 1985) ]. 

The excitation and detection of multiple quantum transitions in systems of coupled spins offers, among other advantages, an increase in resolution over single quantum n.m.r. since the number of lines decreases as the order of the transition increases. This paper reviews the motivation for detecting multiple quantum transitions by a Fourier transform experiment and describes an experimental approach to high resolution multiple quantum spectra in dipolar systems along with results on some protonated liquid crystal systems. A simple operator formalism for the essential features of the time development is presented and some applications in progress are discussed. 

Applications in progress include the configurational analysis of both ring and chain regions of liquid crystals, the study of relaxation effects in multiple quantum spectra... 

For a system of coupled 7=1/2 nuclei, the transition frequencies in the multiple quantum spectra are determined by the dipolar coupling constants, the scalar coupling constants and the chemical shifts of the nuclei. In theory, the spectra of order N— 1 and N—2 contain sufficient transitions to measure all of the dipolar coupling constants and chemical shifts in an 7V-spin system. For additional accuracy and confidence, the A— 3 quantum spectrum can also be analysed to provide redundancy and more reliable estimates of the Dy. 

Fig. 12. Multiple quantum spectra of 4-chlorotoluene (3a) aligned in liquid crystalline solution obtained as projections from the 3D spectrum acquired using the pulse sequence in Fig. 11. (Reproduced with permission from ref. 43.)...

Field et al.62 developed a general procedure to estimate the Saupe order parameters for spin systems aligned in liquid crystal media by iteratively fitting the experimental and simulated spectral widths of the high-order multiple quantum spectra. 

While the early broadline and relaxation studies of fluoropolymers were very informative, particularly with regard to mobility at the molecular level, modern high-resolution techniques for both F and C are now being applied and show considerable potential for an expansion in the areas of applicability. The more sophisticated pulse sequences (e.g., for multi-dimensional and multiple-quantum spectra) have scarcely been used to date, with a few notable exceptions. The unusually favourable properties of the F nucleus offer the prospect of more detailed studies than are feasible with polymeric systems... 

Chapter 2 considers how we can understand the form of the NMR spectrum in terms of the underlying nuclear spin energy levels. Although this approach is more complex than the familiar successive splitting method for constructing multiplets it does help us understand how to think about multi-plets in terms of active and passive spins. This approach also makes it possible to understand the form of multiple quantum spectra, which will be useful to us later on in the course. The chapter closes with a discussion of strongly coupled spectra and how they can be analysed. 

In a two spin system the double- and zero-quantum spectra are not especially interesting, but we will see in a three-spin system that the situation is rather different. We will also see later on that in two-dimensional spectra we can exploit to our advantage the special properties of these multiple-quantum spectra. 

Kg. 58. Multiple-quantum spectra of a 36mer RNA with correlations from the sugar protons into the bases. The enhancement of signal to noise using the multiple quantum (blue) approach as opposed to the conventional single quantum approach (red) is clearly put into evidence in... 

FIGURE 65.9 Multiple quantum spectra I(k) versus k obtained with the single quantum propagator ... 

Multiple-quantum spectra have a greatly reduced number of lines because the number of different multiple-quantum transitions of order m (e.g., m spins flipping simultaneously) is reduced as the order increases. For a system consisting of n spins there is only one multiple-quantum transition of order m=n. Thus compared to the intractably complex 1-quantum spectrum of an n-spin system, the n-quantum spectrum of the same system consists of only one single line. In most investigations, the most simple and best resolved but nontrivial n- 1-quantum spectra are analyzed. Figure 4 shows as an example the 1-quantum and the 5-quantum spectra of a 6-spin system, naphthaquinone in a nematic solvent [81]. 

Multiple-quantum spectra of a given order can be detected selectively in a two-dimensional experiment using conventional phase-cycling [25] or field-gradient selec-... 

The evolution period may be followed by a mixing period which consists of applying a single nonselective pulse (as in homonuclear shift correlated spectra or homonuclear multiple-quantum spectra) or by a number of nucleus-selective pulses (as in heteronuclear shift correlated spectra). 

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