Multi-dimensional spectroscopy

In principle, any scheme of multi-dimensional liquid-state or solid-state spectroscopy can be combined with spatial resolution to mD spectroscopic D imaging. However, measurement times rapidly become excessive, so that meaningful applications are quite rare. 

The principle of 2D-COSY imaging has been demonstrated on the hypocotyl of the castor bean, enabling the formation of images showing the distributions of sucrose. 

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 

This 2D experiment is well suited for imaging, because the indirectly detected spectroscopic dimension requires stepping of the spectroscopic evolution time t from an arbitrary but fixed rotor phase in only 16 steps through one rotor cycle tg. This dimension introduces the information about molecular order into the spectrum. Following t, magnetization is cross-polarized from H to C, and the response is acquired by frequency 

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The next milestone, in the history of NMR [Frel], was the extension of the NMR spectrum to more than one frequency coordinate. It is called multi-dimensional spectroscopy and is a form of nonlinear spectroscopy. The technique was introduced by Jean Jeener in 1971 [Jeel] with two-dimensional (2D) NMR. It was subsequently explored systematically by the research group of Richard Ernst [Em 1 ] who also introduced Fourier imaging [Kuml]. Today such techniques are valuable tools, for instance, in the structure elucidation of biological macromolecules in solution in competition with X-ray analysis of crystallized molecules as well as in solid state NMR of polymers (cf. Fig. 3.2.7) [Sch2]. 

Inomata K, Ohno A, Tochio H, Isogai S, Tenno T, Nakase I, Takeuchi T, Futaki S, Ito Y, Hiroaki H, Shirakawa M (2009) High-resolution multi-dimensional NMR spectroscopy of proteins in human cells. Nature 458 106-109... 

Since the advent of pulsed NMR spectroscopy, a number of advanced two-dimensional techniques have been devised. These methods afford valuable information for the solution of complex structural problems. The technical detail behind multi-dimensional NMR is beyond the scope of this book. 

In experimental impedance spectroscopic studies, however, several factors may complicate the interpretation of the spectra and a few of these complications will briefly be touched upon i) If high conductivities are considered (a > 10-3 S cm-1), then the corresponding relaxation frequencies are well above the measurement range of a conventional impedance set-up (frequencies up to ca. 10 MHz). Hence, processes with high conductivites cannot be separated by conventional impedance spectroscopy. ii) The assumption of a quasi-one-dimensional current flow, which is the basis of the above presented brick layer model, is often violated [203, 211-214]. Some complications due to multi-dimensional potential distributions will be discussed in Sec. 3.2.1. iii) Highly conductive regions perpendicular to the electrodes (e.g. highly... 

In 1971, the idea of 2D NMR spectroscopy was proposed by Jeener and later implemented by Aue, Bartholdi and Ernst, who published their work in 1976.47 The first experiments, carried out mostly in the liquid phase, have unambiguously proved that 2D NMR spectra provide more information about a molecule than ID NMR spectroscopy and are especially useful in determining the structure of molecules that are too complicated to work with using ID NMR. With the progress in the methodology and software improvement, three-dimensional (3D) and four-dimensional (4D) NMR experiments were gradually introduced into the laboratory practice. Such strategy, the so-called multi-dimensional (or ND) NMR spectroscopy, has found a number of spectacular applications in the structure analysis of natural products. 

In the early stage of development of NMR spectroscopy, the applicability of multi-dimensional approach was tested for condensed matter. Today, because of the excellent progress on this field, the "library" of different ND techniques used in SS NMR is pretty rich. On the basic level, these methods can be assigned to two groups homo- (HOMCOR) and heteronuclear correlations (HETCORs). Both correlations employ indirect (through-bond) or direct (through-space) coupling to correlate different spins. 

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