Multiple quantum experiments

An adequate basis set may be obtained from Bowden et al.73 which was developed for multiple-quantum experiments. In this formalism, the irreducible spin operators Tqn,n=0,..., 21 q= — n, n, of rank n and order q form an orthogonal basis set. The orthonormal operators, 7, derived from these form a complete basis set. These are defined as... 

Multiple Quantum Experiments in Dipolar Coupled Systems 160... 

Multiple quantum experiments in dipolar coupled systems Although single quantum coherence is the only magnetisation that can be directly observed, for a collection of N strongly dipolar coupled spins, it is possible to induce multiple quantum coherences. A number of pulse sequences have been developed for this purpose (Gleason 1993), for which one of the most common generators is... 

The HMQC/GHMQC experiments are quite useful and were treated in an early review by Martin and Crouch [71]. Relative to the single quantum variant of the experiment discussed below, the effective Fj resolution of the multiple quantum experiment suffers due to homonuclear coupling modulation during the evolution period, which leads to broadened responses being observed in the Fj dimension. The difference in the effective resolution of the HMQC vs. HSQC experiments was noted in a review on applications of inverse-detection in alkaloid chemistry by Martin and Crouch [70] and has since been treated in more detail by Reynolds and others [117—119]. On this basis, the HSQC/GHSQC experiments discussed in the following section should be preferentially used on a routine basis in the opinion of the authors. 

Normally, the experimentally observed longitudinal and transverse relaxations involve zero- and single-quantum processes Am = i — y = 0 or 1). The other time-dependent density matrix elements p (t) with A i > 1 are classified as multiple-quantum coherences. Although these coherences are not directly observable, it is possible to measure every element of the relaxation density matrix by employing specially designed NMR methods. These coherences are very important for multiple-quantum experiments [13] and quantum computation NMR applications, as it will be described later. 

Generating such a connectivity map for a solid requires additionally a resolution-enhancement technique, such as MAS. Such techniques, as discussed previously, suppress precisely the spin-spin interactions that the connectivity map is meant to reveal. Therefore, to combine multiple-quantum experiments with MAS, a pulse sequence which counteracts the averaging effect of MAS, thereby restoring the dipole coupling, must be implemented during excitation and reconversion of the 2-quantum coherence. A variety of such dipolar recoupling sequences currently exist, of varying levels of performance and complexity. 

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