Homonuclear Two-dimensional Experiments

The importance of solution-state NMR today owes much to the extension of the experiment to a second (and higher) dimension [1]. Two-dimensional (2D) NMR spectroscopy is also of much significance in solid-state NMR. In attempting to classify the many important different 2D solid-state NMR experiments which have been proposed to date, we make, in this article, a distinction between homonuclear (i. e., those involving only one kind of nucleus) and heteronuclear experiments. 

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NOESY NMR spectroscopy is a homonuclear two-dimensional experiment that identifies proton nuclei that are close to each other in space. If one has already identified proton resonances in one-dimensional NMR spectroscopy or by other methods, it is then possible to determine three dimensional structure through NOESY. For instance, it is possible to determine how large molecules such as proteins fold themselves in three-dimensional space using the NOESY technique. The solution structures thus determined can be compared with solid-state information on the same protein obtained from X-ray crystallographic studies. The pulse sequence for a simple NOESY experiment is shown in Figure 3.23 as adapted from Figure 8.12 of reference 19. 

Selecting the C-bound protons before performing a homonuclear two-dimensional experiment enables to measure small heteronuclear coupling constants [16]. Such an experiment with a sample of natural isotopic abundance was first published by Otting and Wuthrich in 1990, where the half-filter element with spin-lock purge pulse was used to select the C-bound protons in a small protein in aqueous solution [6]. Later applications illustrated the usefulness of the same half-filter element with smaller molecules [17, 18]. 

The basic heteronuclear experiments are easy to combine with the two-dimensional homonuclear experiments to produce three- or four-dimensional edited spectra. In this terminology editing means selection of the protons that are attached to the heteronucleus. The main purpose of these experiments is to reduce the signal overlap of the homonuclear two-dimensional experiments. 

Although the first NMR spectra of deuterated proteins were published already in 1968, the deuteration was mainly employed for the purpose of simplifying one-dimensional proton spectra.53,54 Later in the 1980s, LeMaster and co-workers employed random fractional deuteration for the assignment of thioredoxin using homonuclear two-dimensional spectroscopy.55 However, it was realized that deuteration significantly improves the spectral quality of homonuclear multidimensional NMR experiments. 

Under the idealized zero-quantum coupling topologies (see Section V.B), the transfer of magnetization between two spins 1 /2 that are part of an arbitrary coupling network is identical in both directions (see Section VI). This symmetry with respect to the direction of the transfer is related to the symmetry of homonuclear, two-dimensional Hartmann-Hahn spectra with respect to the diagonal (Griesinger et al., 1987a). In Hartmann-Hahn experiments, the properties of the multiple-pulse sequence can induce additional symmetry constraints (Ernst et al., 1991). 

Selective excitation of a resolved resonance followed by homonuclear or heteronuclear Hartmann-Hahn transfer can also be advantageous in the preparation period of two-dimensional experiments. For example, two-dimensional COSY, NOESY, TOCSY, and two-dimensional /-resolved subspectra of individual spin systems can be acquired based on this principle (Homans, 1990 Sklenaf and Feigon, 1990 Nuzillard and Massiot, 1991 Gardner and Coleman, 1994). In selective two-dimensional experiments like soft COSY (Briischweiler et al., 1987 Cavanagh et al., 1987),... 

Broadband Hartmann-Hahn transfer can also be of assistance in alternative approaches to determine coupling constants that do not rely on E.COSY-type multiplets that are separated by large one-bond couplings. The homonuclear two-dimensional PICSY (pure in-phase correlation spectroscopy) experiment (Vincent et al., 1992, 1993), which is based on selective Hartmann-Hahn transfer using doubly selective irradiation, can... 

For such an experiment to work, we have to be able to distinguish the different domains during the evolution and the detection period of the two-dimensional experiment. Since proton spectral resolution in typical solids is very poor, we have to use homonuclear dipolar-decoupling methods to narrow the lines sufficiently to obtain spectral resolution. The 2D spin-diffusion CRAMPS spectrum was first recorded by Caravatti et al. [68] for blends of polystyrene (PS) and polyvinyl methyl-ether (PVME). There are other methods to generate an initial nonequilibrium polarization based on differences in linewidth or relaxation times. The reader is referred to the excellent book of Schmidt-Rohr and Spiess [67] for an overview. 

As in solution state NMR, the extension of experiments into two or more dimensions is the path used to gain the resolution required to measure multiple, large anisotropic interactions (dipolar coupling, CSA) that are accessible in solids. Experiments that focus on homonuclear multi-dimensional experiments include /-mediated correlation and dipolar-mediated H 2D double quantum... 

The principle purpose of correlation experiments is to establish a one-to-one mapping from the signal to its source i.e. to the particular atomic nucleus in the molecule. This assignment task involves identification of the members in the coupling network, referred to as the spin system. In addition, correlation experiments, as such or with modifications, are suitable for measurements of scalar and dipolar couplings. Correlation in the two dimensions is the most natural dimensionality because the spin-spin interactions are pair wise. Three-dimensional or experiments of higher dimensionality are constructed from concatenated two-dimensional experiments. Homonuclear three-dimensional experiments, such as TOCSY-NOESY, are not considered here because in many cases the multidimensional heteronuclear experiments are superior. 

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