Recoupling of Chemical Shift Anisotropy

Under MAS at frequency cor = 2nvr, the high-field Hamiltonian of a spin-1/2 system takes the following form in the rotating frame  

T%0 are irreducible tensor operators of rank X. The Hamiltonian of a static powder sample can be easily derived from the MAS Hamiltonian by setting a r = 0  

ROCS A makes use of the CN n sequences [82, 159] to generate a static CSA powder pattern under MAS condition. The average Hamiltonian for a CNvn sequence is [159] 

All the symbols carry their usual meanings. If we want to create an average Hamiltonian similar to the static one, we just need to keep the terms associated with 720 Furthermore, the scaling factors of those terms should be identical. With the pulse sequence of Cn]n [160, 161], the symmetry allowed terms are 

We want to derive a specific subcycle for Cn such that the scaling factors are identical for m equal to 1 and 2. In general, we have y m = / m ) and therefore the conditions /Xm = y m are equivalent to the conditions that / are real numbers. In particular, if we have a mirror symmetry of 

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Chan and Tycko ° have introduced a novel solid state NMR experiment that combines ROCS A (recoupling of chemical shift anisotropy) and C- H dipolar dephasing. Designed for uniformly labeled samples, this technique is shown to correlate the carbonyl shielding and the dipolar tensors, thereby pro-... 

These angles were determined in turn from distances between backbone carbonyl spins, measured with the DQ filtered dipolar recoupling with a windowless sequence experiment, and by determination of the mutual orientation of chemical shift anisotropy tensors of carbonyl spins on adjacent peptide planes, obtained from the DQ CP MAS spectrum. It was found that peptides composed of periodic sequences of leucines and lysines were bound along the length of the peptide sequence and displayed a tight a-helical secondary structure on the gold nanoparticles. 

Fig. 2 Experimental analysis of the chemical shift anisotropy of high-silica ZSM-5 zeolite, (a) 29Si MAS NMR and (b) extracted CSA lineshapes from a two-dimensional CSA recoupling sequence dashed lines are simulated lineshapes. Adapted with permission from [79]. Copyright 2008 American Chemical Society...

Owing to the orientation dependence that it imparts to the NMR frequency, the chemical-shift anisotropy (CSA) has proven useful not only in studies of slow dynamics but also for characterizing segmental orientation distributions and fast segmental reorientations. While static powder patterns provide this CSA information in the most accessible form, site resolution by MAS is indispensable in all but the simplest unlabeled systems. The two requirements can be combined in two-dimensional (2D) separation experiments. Recently, a robust sequence, termed separation of undistorted powder-patterns by effortless recoupling (SUPER), was introduced that makes CSA measurements under standard MAS conditions routine.28 It enables identification of functional groups and measurements of orientation distributions, segmental dynamics, and conformations. 

Fig. 4. (a) The pulse sequence that recouples under MAS any interaction which is linear in Iz the observed spin, i.e. chemical shift anisotropy and heteronuclear dipolar coupling between a pair of spins IS. (b) Reference pulse sequence. The sequences shown are appropriate for recoupling chemical shift anisotropy. If the interaction to be recoupled is heteronuclear dipolar coupling, the sequence in (a) is applied to the dipolar coupling partner S, while (a) is applied to the observed spin I. In the reference experiment, sequence (b) only is applied to I. 

Fig. 37. CODEX exchange intensities of the carbonyl 13C signal of / -poly(ethyl methacrylate) as a function of 13C chemical shift anisotropy recoupling time N Tr for various temperatures below the glass-transition temperature.64 Each curve can be simulated by assuming a 180° flips of the side group and small-angle liberations of the main chain. Simulations of the expected CODEX curves for these motions are shown on the figure.

Selection of alkyl-carbon and suppression of aromatic-carbon NMR signals has been achieved by exploiting the symmetry-based systematic difference in their chemical shift anisotropies. It was shown that simple three-or five-pulse CSA-recoupling sequences cleanly suppress the signals of all... 

Table 4-3 lists various recoupling techniques, which have been applied to liquid crystals. The methods are eompared in terms of heteronuclear dipolar scaling factor, y-encoding property, sensitivity to frequency offsets and chemical shift anisotropy of S (rare) and I (abundant) spins, tolerance to rf inhomogeneity, accomplishment of active homonuclear proton decoupling, length of rf cycle time (which limits the maximum spectral width in dipolar dimension), and requirement of rotor... 

Formally, when the exchange intensity Hgure 13(b) is plotted as 1 - (tmix NtR)/ it is identical to an orientation autocorrelation function of the process. In the case of CODEX, the recoupling (encoding) time NIr determines the angular sensitivity ((S is the anisotropy parameter of the chemical shift tensor), and the exact mathematics is somewhat involved due to the MAS. In case of static stimulated-echo experiments mentioned above, one obtains essentially analogous, but a mathematically even simpler signal function, that is, the sine-sine correlation function of P2,... 

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