Multiple-quantum approach

The other approach relies on self compensation of relaxation contributions. This proach has been named TROSY for transverse relaxation optimized spectroscopy [18]. It works very well for amide NH s, aromatic CH s, however, not for aliphatic CH pairs where the multiple-quantum approach works best [17]. 

An interesting new approach has been made possible by multiple quantum 27A1 MAS (MQMAS) NMR investigations of zeolites. Due to its nuclear electric quad-rupole moment, 27A1 exhibits broad lineshapes in distorted structural environments. 

Figure 5. Qualitative electronic state (miniband) band diagrams envisaged for 8Ag,(2-p)X,pY-SOD as a new material for a chemistry approach to a resonance tunneling quantum dot transistor and a heterojunction multiple quantum dot laser array.

SateUite Transition MAS (SATRAS or STMAS), developed by Gan in 2000 [25], is an alternative approach to MQMAS for the acquisihon of high-resolution NMR spectra of quadrupolar nuclei. The principal advantage of SATRAS over MQMAS is that it is not dependent upon an efficient transfer of multiple-quantum coherences. like MQMAS, SATRAS is a 2D experiment performed under MAS conditions. The technique involves exciting the sateUite transitions in the spin manifold of quadmpolar nuclei using short radio frequency (rf) pulses. The second-order... 

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. 

It has been pointed out that the central ( 2, transition does not experience any first-order quadrupole interaction. The absence of first-order broadening effects is a general property of symmetric (m, - m) transitions. There are cases where this can be a distinct advantage, the most direct instance being for integer spin nuclei (e.g. D and both 1=1) where there is no ( /2, — /2) transition. The main problem is to excite and detect such higher-order transitions, for which there are two separate approaches. The sample may either be irradiated and detected at the multiple quantum frequency (called overtone spectroscopy) or the MQ transition can be excited and a 2D sequence used to detect the effect on the observable magnetisation. 

Ashbrook et al. proposed an alternative route for combining CP with MQMAS [85,86]. In this method, S-spin multiple-quantum (MQ) coherences are created directly by CP from the I spin and then correlated with SQ coherences in a two-dimensional MQMAS experiment. This seems the simplest and most direct method of using CP to excite MQ coherences at the beginning of an MQMAS experiment. It should be noted that although the theoretical possibihty of performing MQCP had been mentioned before by a number of authors, and experimentally demonstrated on a single crystal [75], Ashbrook et al. [85,86] were the first to show that it is experimentally viable on powdered samples under MAS conditions. This more efficient and direct approach was also demonstrated by Lim and Grey[87] and by Rovnyak et al. [88]. 

The inverse detection heteronuclear multiple quantum coherence (HMQC) experiment is another approach to two-dimensional NMR techniques, which consists of a transfer of chemical shift and coupling information from relatively insensitive nuclei such as and some metals, to more sensitive nuclei such as H. The advantage of this method is a substantial increase in the sensitivity obtained, due to the greater natural abundance of H (Kingery et al., 2001). 

A. Pines, D. J. Ruben, S. Vega, and M. Mehring, New approach to high-resolution proton NMR in solids deuterium spin decoupling by multiple-quantum transitions, Phys. Rev. Lett. 36, 110-113 (1976). 

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. 

Chapter 6 introduces the product operator formalism for analysing NMR experiments. This approach is quantum mechanical, in contrast to the semi-classical approach taken by the vector model. We will see that the formalism is well adapted to describing pulsed NMR experiments, and that despite its quantum mechanical rigour it retains a relatively intuitive approach. Using product operators we can describe important phenomena such as the evolution of couplings during spin echoes, coherence transfer and the generation of multiple quantum coherences. 

In NMR spectroscopy we tend not to use this approach of thinking about energy levels and the transitions between them. Rather, we use different rules for working out the appearance of multiplets and so on. However, it is useful, especially for understanding more complex experiments, to think about how the familiar NMR spectra we see are related to energy levels. To start with we will look at the energy levels of just one spin and them move on quickly to look at two and three coupled spins. In such spin systems, as they are known, we will see that in principle there are other transitions, called multiple quantum transitions, which can take place. Such transitions are not observed in simple NMR spectra, but we can detect them indirectly using two-dimensional experiments there are, as we shall see, important applications of such multiple quantum transitions. 

The product operator approach comes into its own when coupled spin systems are considered such systems cannot be treated by the vector model. However, product operators provide a clean and simple description of the important phenomena of coherence transfer and multiple quantum coherence. 

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