Homonuclear dipolar-coupled spins

Having demonstrated the achievement of high-resolution sohd state NMR capability, the authors describe experiments that combine the high-resolution aspect of MAS NMR with methods that retain the structure and/or dynamic information inherent in the anisotropic interactions. Rotational-echo double resonance (REDOR) allows the determination of D between isolated heteronuclear spin pairs. D is related simply and without approximation to intemuclear separation. Hence, REDOR makes possible the unambiguous direct determination of intemuclear distance between the labeled spin pair, independent of pair orientation, i. e., in amorphous and /or microaystaUine solids, and extends our abihty to quantitatively explore complex materials. It is also possible to extract intemuclear distance from homonuclear dipolar coupled spin pairs, and these experiments are also reviewed. 

As demonstrated by Griffin, Levitt, and coworkers in the late 1980s [21, 93], it is also possible to recouple homonuclear dipolar couplings through interference between isotropic chemical shifts and the rotor revolution. This phenomenon, called rotational resonance, occurs when the spinning frequency is adjusted to a submultiple of the isotropic chemical shift difference, i.e., ncor = ct> so o) °. To understand this experiment, the dipolar coupling Hamiltonian in (10) is transformed... 

Fig. 10.22. Diagram showing the cross-polarization from protons, H, to a heteronucleus, X, such as carbons. Heteronuclear dipolar coupling enables the transfer of magnetization from H to X, such as protons to carbons. Homonuclear dipolar coupling between the abundant protons enables the redistribution of proton spin energy through spin diffusion.

Fig. 11.2 Solid-state 13C NMR spectra of a powder sample of U-13C-15N-glycine illustrating the broad NMR resonances in the static sample (a) and the effects of magic-angle spinning at 5 kHz (b) and 10 kHz (c). Both the chemicalshielding tensors and the homonuclear dipolar coupling...

Radio-frequency driven recoupling (RFDR) [58] uses rotor-synchronized 180°-pulses to prevent the averaging of the homonuclear dipolar coupling by the MAS rotation. A single 180°-pulse is placed in the middle of each rotor period (Fig. 11.6a), often using an XY-8 phase cycle [66]. The efficiency of the recoupling depends on the isotropic chemical-shift difference of the two spins and the size and relative orientation of their CSA tensors. 

One of the important advantages of NMR spectroscopy is that it makes possible calculation of the H- H distances in dihydrogen-bonded complexes formed in solution. As we have shown above, the formation of dihydrogen bonds is accompanied by the appearance of H- H contacts that are shorter than a sum of the van der Waals radii of H (< 2.4 A). Snch short H- -H contacts are connected directly with the spin-lattice (Ti) NMR relaxation of target nnclei [32]. The contacts between two nuclei cause strong homonuclear dipolar coupling, DCh-h. which is written as... 

The simplest technique that enables phosphorus-phosphorus correlations for complex multi-component system and elucidation of structural constraints is the PDSD sequence.48 This experiment is relatively easy to set up however, the distances between spins cannot be established with satisfactory precision. One common way of determining distance type information using spin-7i NMR is based on the acquisition of the DQ filtered spectra as a function of the DQ mixing time.49 The recently introduced DQ homonuclear recoupling sequences based on C and/or R symmetry developed by Levitt and co-workers allows very precise analysis of intemuclear distances.50 The accuracy of distances obtained from these DQ experiments depends on the effective suppression of contributions to the spin Hamiltonian other than the required homonuclear dipolar coupling terms. 

At the center of the echo all resonance offsets from interactions linear in the spin quantum number are canceled as long as these interactions operate for the full duration ofTE. Linear spin interactions include chemical shifts, heteronu-clear dipolar couplings, field inhomogeneity, field gradients, and transmitter frequency offsets but do not include quadru-polar and homonuclear dipolar couplings. There will however be a net phase evolution induced by an interaction to the extent its duration or intensity is not balanced with respect to the two halves of TE (that is, the balance with respect to amount of phase evolution on either side of the 180° pulse). 

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. ... 

Both the heteronuclear and the homonuclear dipolar coupling depend on the orientation of the inter-nuclear vector and the inverse cube of the distance, and often give rise to broad lines in powders. However the characteristic lineshape has features, particularly singularities. For an isolated pair of spin- /2 nuclei a pair of strong singularities... 

The factor of /a arises from the fact that the spin spends an equal amount of time along each of the Cartesian directions. It is clear from this expression that the sequence successfully removes the homonuclear dipolar coupling. However, it is important to realise that such manipulation by pulses has the effect of scaling other operators and not completely removing them. The most important is I, its average value for the above sequence being... 

---