Multi-dimensional correlation spectra

Equation (4.2.11) describes the response to three delta pulses separated by ti =oi — 02 >0, t2 = 02 — 03 > 0, and t3 = 03 > 0. Writing the multi-pulse response as a function of the pulse separations is the custom in multi-dimensional Fourier NMR [Eml ]. Figure 4.2.3 illustrates the two time conventions used for the nonlinear impulse response and in multi-dimensional NMR spectroscopy for n = 3. Fourier transformation of 3 over the pulse separations r, produces the multi-dimensional correlation spectra of pulsed Fourier NMR. Foinier transformation over the time delays <7, produces the nonlinear transfer junctions known from system theory or the nonlinear susceptibilities of optical spectroscopy. The nonlinear susceptibilities and the multi-dimensional impulse-response functions can also be measured with multi-resonance CW excitation, and with stochastic excitation piul]. 

During a period of evolution in which multiple-quantum states are present, the magnetization acquires a modulation due to the nutation frequency of the MQCs. Thus, signals which are due to single sites during other evolution periods will have the same spectral frequency in a multiple-quantum domain as those signals which had passed through the same MQC. This can therefore easily be read in a multi-dimensional spectrum as a correlation between these nuclear sites. In addition, a multiple-quantum domain as part of a multi-dimensional spectrum removes the auto-correlation peaks on... 

Despite the extremely wide use of multi-dimensional NMR techniques for conformational studies of biological macromolecules, at present, only a small part of the information contained in the NMR spectrum can be used for structure determination [118,119]. The reason is that there are no well-established correlations between NMR chemical shifts and the structural parameters [118] and only a few useful correlations besides Karplus relations [120,121] for nuclear spin-spin coupling constants. As a consequence, a great deal of important information about the system is not available without turning to quantum chemical approaches for the theoretical interpretation. 

HSQC rather than HMQC-based transfer schemes have recently in particular been employed in various indirectly detected two- and three-dimensional 111/X/Y correlation experiments involving multi-step coherence-transfer in either direction.38 40 43 44 The application of PFG s appears to be essential to obtain a sufficiently clean spectrum that is free of artefacts, and in many cases the pulse sequence shows only a satisfactory performance if composite pulses, with a larger excitation bandwidth than normal ones, are employed.21,38,39,43 The pulse schemes yield generally phase-sensitive spectra with pure absorptive lines and do not suffer from splitting or broadening of the cross peaks as a consequence of the undesired evolution... 

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