Rotor dipolar

Figure 2. Pulse sequence for 13C-serve REDOR NMR. This sequence differs from the original REDOR pulse sequence (ref. 18) in that n pulses alternate between 13C and 15N r.f channels. On alternate scans of the REDOR experiment, the 15N iz pulses are either applied or omitted. This figure illustrates that the REDOR pulse sequence with four rotor periods of 13C-15N dipolar-coupling evolution (Nc = 4) NC can be increased (in increments of two) by adding rotor periods and pairs of 13C and 15N n pulses between the end of the cross-polarization preparation and the start of data acquisition.

The REDOR experiment has formed the basis for a large number of ideal pulse type recoupling experiments, and later finite pulse variants, for heteronuclear dipolar recoupling. These include experiments such as frequency selective REDOR (FS-REDOR) [80], TEDOR (Transferred Echo DOuble Resonance) [25], and 3D variants of TEDOR [81, 82], which have found important applications, e.g., for measurement of intemuclear 13C-15N distances in biological solids. We should also mention that rotor-encoded variants of TEDOR, such as REPT, HDOR [83], and REREDOR [84], have been proposed for 1H13C dipolar recoupling under high-speed MAS conditions. 

The basic RFDR element consists of two 7i-pulses each centered in the middle of each rotor period in two consecutive rotor periods leading to a cyclic rf field. In the toggling frame of ideal (i.e., infinitely strong) 7i-pulses, the Hamiltonian of the chemical shift terms and the homonuclear dipolar coupling interaction is split up into three commuting parts ... 

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... 

The homonuclear dipolar recoupling technique of radio frequency-driven recoupling (RFDR) involves a hard n pulse per rotor period and its recoupling mechanism is based on the modulation of chemical shift difference [35-37]. When the delta-pulse approximation is relaxed so that the pulse width of the 7t pulse is about one-third of the rotor period, the so-called finite-pulse RFDR (fpRFDR) could selectively reintroduce the homonuclear dipole-dipole interaction under fast MAS conditions [38], Because the recoupling mechanism of fpRFDR does not require the presence of chemical shift difference, it can be applied to study samples with a singly labeled site. For the study of amyloid fibrils, the technique of fpRFDR is usually applied in a constant-time framework (see below). 

The novelty of (9) is that the net homonuclear dipolar dephasing can be controlled by a systematic variation of the number of the Ho, Hi, and Hi blocks. This technique has the acronym of PITHIRDS-CT [55] and has the virtues that the effect of T2 is identical for all data points and that the rf field of all the pulses is only 1.67 times the spinning frequency. The only experimental concern is that very stable spinning or active rotor synchronization may be required for the implementation of PITHIRDS-CT. 

Fig. 21 HMQC pulse sequences for (a) 14N-13C and (b) 14N- H correlations under rotor-synchronized MAS. In (b), dipolar recoupling is usually applied during time intervals Texc and Trec. (c) Coherence transfer pathways for the observation of SQ (solid lines) and DQ (dashed lines) in the 14N dimension...

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. 

Rotational-echo double resonance (REDOR), originally introduced by Gullion and Schaefer [102], is a method to recouple heteronuclear spin pairs. The sequence relies on a train of rotor-synchronized n pulses applied to the I spin to interrupt the spatial averaging of the heteronuclear dipolar coupling under MAS to give a nonvanishing dipolar Hamiltonian over a full rotor cycle (Fig. 11.8). Typically, REDOR data are collected by col-... 

Fig. 11.16 The pulse sequence used to monitor the evolution of carboncarbon double-quantum coherence over a single rotor period in the presence of the proton-carbon heteronuclear dipolar coupling (a). The evolution of the double-quantum coherence between the Cl 4 and Cl 5 carbons in the retinal of bacteriorhodopsin in the ground state (b). The observed evolution is consistent with a C14-C15 torsion angle of 164° (reproduced with permission from Ref. [172]).

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