Multiple quantum dipolar coupling

Cross-correlated dipolar relaxation can be measured between a variety of nuclei. The measurement requires two central nuclear spins, each of which is directly attached to a remote nuclear spin (Fig. 16.4). The central spin and its attached remote spin must be connected via a large scalar coupling, and the remote spin must be the primary source of dipolar relaxation for the central spin. The two central spins do not need to be scalar coupled, although the necessity to create multiple quantum coherence between them requires them to be close together in a scalar or dipolar coupled network. In practice, the central spins will be heteroatoms (e.g. 13C or 15N in isotopically enriched biomolecules), and the remote spins will be their directly attached protons. 

Selective Residual Dipolar Couplings by 1H Multiple-Quantum NMR Spectroscopy... 

Double-Quantum. (DQ) Proton Spectroscopy. Multiple-quantum (MQ) coherences are routinely used in high-resolution solution-state NMR spectroscopy. The MQ coherences cannot be observed directly and the application of two-dimensional methodology is required. The Double-Quantum (DQ) methodology is particularly useful to derive the information on the spatial proximity of different spins on the basis of the homonuclear dipolar couplings. ... 

Static H Multiple Quantum (MQ) NMR spectroscopy, on the other hand, has shown the ability to more reliably quantitatively characterize elastomer network structure and heterogeneities (14-19). H MQ NMR methods allow for the measurement of absolute residual dipolar couplings (cooperative dynamics without interference from magnetic susceptibility and field gradients which complicate relaxation measurements (13, 14, 20,21). It has previously been shown that the residual dipolar couplings are directly related to the dynamic order parameter, Sb, and the crosslink density (1/N)(P) ... 

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. 

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... 

Multidimensional NMR experiments also provide additional information that is unavailable from onedimensional (ID) spectra even in the limit of high-resolution. For example, 2D 2H exchange experiments, which identify a particular change in molecular orientation between two evolution periods, have already been mentioned above.9 For dipolar-coupled nuclei, the combination of fast MAS with 2D multiple-quantum (MQ) spectroscopy achieves high resolution, while allowing the structural and dynamic information inherent to the dipolar couplings to be accessed. Specifically, using the homonuclear H- H double-... 

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. 

MQCs are not excited uniformly and the efficiency with which the various orders of MQC are excited depends specifically on the parameters of the spin system (dipolar couplings, scalar couplings, quadrupolar couplings, chemical shifts) in the spin system and the choice of the preparation time t. Many researchers have co-added spectra acquired with different preparation times to ensure that all transitions are observed with reasonable intensity. A number of broadband excitation techniques have been developed,13-15 where the value of t in the preparation sequence has been varied either in a pseudo-random or systematic fashion to achieve a more uniform excitation in the multiple quantum domain. An experimental search method has been used to optimise the delays in the preparation period of the MQ excitation sequence16 and Wimperis17 used average Hamiltonian theory to propose... 

On the other hand, vide infra) in the case of developing multiple quantum coherence of coupled groups of protons, one wishes an average Hamiltonian for the homonuclear dipolar interaction, / dt 3fDn(t), which is not zero, but is manipulated such that the density operator develops multiple quantum coherence as time progresses, as outlined in the next section. 

One of the more recent applications of proton NMR in solid polymers has been the use of multiple quantum coherence (MQCOH), which is developed among clusters of dipolar coupled protons vide infra) to infer details of chain dynamics [20], and (which is another way of making the same statement) local dipolar couplings [21]. 

As indicated in Section 6.1.2.2, the appearance of multiple quantum coherence in dipolar coupled spin 2 solids is a direct reflection of the strength of the dipolar couplings present. In the presence of molecular motion, which makes the coordinate space term (1-3 cos time-dependent (1-3 cos dij) (1 - 3 cos 0/.y(t)), then it is the time average of the dipolar Hamilton-... 

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