Multi-quantum coherence

Multi-quantum transitions can only be observed indirectly by a modulation of the detected signal with the phase of the multi-quantum coherence. This modulation is achieved in an experiment by variation of an evolution time prior to detection. Repetitive detection of the signal for different evolution times provides the information about the evolution of the multi-quantum coherence. The indirect detection of spectroscopic information based on phase or amplitude modulation of the detected signal is the principle of multi-dimensional NMR spectroscopy [Eml]. Thus multi-quantum NMR is a special form of 2D NMR. Also, NMR imaging can be viewed as a special form of multi-dimensional NMR spectroscopy, where the frequency axes have been coded by the use of magnetic field gradients to provide spatial information. 

Chemical parameters Molecular 0.1-1 nm Chemical shift Indirect coupling Chemical shift anisotropy Anisotropy of the dipole-dipole interaction Multi-quantum coherences... 

Basic sequence for preparation of multi-quantum coherences... 

Fig. 7.3.4 Pulse sequences for 2D spectroscopic 2D imaging, (a) COSY spectroscopy [Ziel]. The spectroscopic imaging sequence is preceded by a water suppression sequence of three selective pulses, (b) Heteronuclear multi-quantum coherence-transfer spectroscopy [Zij2]. The hatched gradients are for selection of coherence transfer pathways.

Efficient suppression of water signals is a side benefit of heteronuclear coherence transfer schemes. The heteronuclear multi-quantum coherence (HMQC) method (Fig. 7.3.4(b)) is a broad-band version of the HYCAT experiment of proton detected C imaging (cf. Fig. 7.2.30(a)) [Knii4]. The initial 90° pulse on is used for slice selection. For a heteronuclear AX system, single-quantum proton magnetization is transferred into heteronuclear zero- and double-quantum magnetization by a 90° C pulse after... 

Formally, multi-quantum coherences of order p are described by irreducible tensor operators Tqp (cf. Table 3.1.2 for coupled spins [Eml]. The coherence order is described by p = mf-mi (cf. Fig. 2.2.11), where m and /n, are the final and initial magnetic quantum numbers of a transition. For double-quantum coherence, for example, p = 2. The total spin coherence q corresponds to the maximum order possible. In this case, p = q so that maximum coherence order is described by T,. 

In NMR, multi-quantum coherences can be excited by just two pulses [Eml, Muni] but for rigid samples multi-pulse sequences are more efficient (cf. Fig. 7.2.26) [Bau2, Muni]. Because the receiver coil in the NMR experiment corresponds to a magnetic dipolar detector, only dipolar single-quantum coherence can be detected directly and not multi-polar multi-quantum coherences. However, the latter can be detected indirectly by methods of 2D NMR spectroscopy [Eml]. 

Fig. 8.4.1 General scheme for excitation and indirect detection of multi-quantum signals. The evolution operators for generation and reconversion of multi-quantum coherences are denoted by Up and Umi respectively. The space-encoding field gradient is applied during the evolution period t to modulate the precession phases of the multi-quantum coherences.

Fig. 8.4.2 Proton multi-quantum spectra (bottom) of an adamantane phantom (top) without (a) and with (b) application of a static gradient of 48 mT/m. Evolution time and phase of the preparation pulse sequence were incremented in 32 steps of 0.1 p,s and 2 r/32, respectively. Only even-order multi-quantum coherences were detected. The signals from orders 8 through 14 are also displayed on an expanded scale. The multi-quantum spectra demonstrate the increase in the spatial resolution of the two cylinders with increasing coherence order p. Adapted from [Garl] with permission from the American Physical Society.

Branca et alP reported a detailed and understandable analysis of the evolution of various coherence orders in a Correlated 2D spectroscopy revamped by asymmetric z-gradient echo detection (CRAZED) like pulse sequence, used to select a signal from intermolecular multi quantum coherences (iMQCs). Because the signal to-noise-ratio of iMQC is much lower than the signal from conventional single quantum coherence (SQC), an optimization of experimental parameters is a necessity when measurements are made with iMQC. For this purpose a phase cycle is shown that not only allows a simpler selection of a particular quantum coherence order, but also removes receiver artifacts. 

Experimental and Theoretical Aspects. - Self-diffusion is one of the most fundamental motions of particles in liquids. NMR provides a convenient and noninvasive means of accurately measuring the self-diffusion coefficient of molecules in solution. Lin et al. gave the theoretical expressions of diffusion rates of multi-quantum coherences. 

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