REDOR dipolar couplings

Rotational-echo double-resonance (REDOR)(75,79) is a new solid-state NMR technique which is sensitive to through-space carbon-nitrogen interactions between selectively 13C and 15N-enriched sites separated by up to 5A (20-22). The parameter directly measured in a REDOR experiment is the heteronuclear dipolar coupling constant DCN, which is in itself proportional to the inverse third power of the intemuclear distance, rCN. It is this dependence on (icn)3 which accounts both for REDOR s ability to accurately measure short distances and its insensitivity to longer-range interactions. As a technique which can probe, in detail, intermolecular interactions over a distance range of 5A, REDOR is well suited to studying the distribution of small selectively-labeled molecules in polymer delivery systems. 

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.

In the following, we will discuss heteronuclear polarization-transfer techniques in four different contexts. They can be used as a polarization-transfer method to increase the sensitivity of a nucleus and to shorten the recycle delay of an experiment as it is widely used in 1H-13C or 1H-15N cross polarization. Heteronuclear polarization-transfer methods can also be used as the correlation mechanism in a multi-dimensional NMR experiment where, for example, the chemical shifts of two different spins are correlated. The third application is in measuring dipolar coupling constants in order to obtain distance information between selected nuclei as is often done in the REDOR experiment. Finally, heteronuclear polarization transfer also plays a role in measuring dihedral angles by generating heteronuclear double-quantum coherences. 

Fig. 11.8 (a) REDOR pulse sequence for the determination of dipolar couplings between 13C and 15N. Initially 13C polarization is generated by cross polarization from the protons. During the following evolution period n pulses are used to prevent the averaging of the heteronuclear dipolar... 

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. 11.15 Diagram showing the relative proximity of the two ligands Glp and S3P, which form a stable ternary complex with the enzyme EPSP synthase. The distance constraints were obtained from both homonuclear and heteronuclear dipolar couplings obtained using the REDOR and DRAMA pulse sequence, together with a model showing a...

An example of a spin-1/2 and spin-1 pair, i.e. C and in enriched DL-[2- H,3- C] alanine was later studied by the REDOR technique , proving the applicability of the method in these cases as well. Another spin-1/2 and spin-1 pair of interest in the present context is C- Li. In Figure 4, the dipolar coupling between Li and C is given as a function of the carbon-lithium distance. It is clear from this graph that distances up to ca 4 A can be measured by this method and successful applications of the REDOR technique for the measurement of C-Li distances have been reported (see Section II.D). 

As mentioned in Sections I.B.2.b and II.A, the dipolar coupling between Li- C may complicate solid state NMR spectra of organolithium compounds and its elimination is often desirable. On the other hand, dipolar coupling constants are related to atomic distances and their determination can yield important structural information. It is therefore of general interest that the REDOR technique, briefly described in Section I.B.2.b, provides a means to determine these parameters. 

EIGURE 24. REDOR transform of the decay of the peak at 119 ppm clearly indicating two overlapping signals of different dipolar couplings. Reprinted in part with permission from Reference. Copyright 1997 American Chemical Society... 

Key Words Heteronuclear dipolar couplings, REDOR spectroscopy, Structure, Second moments. Constant time, SIMPSON... 

Thus, from a parabolic fit to the REDOR evolution data, the second moment can be evaluated. As mentioned in Section 1, this analysis has to be restricted to the initial part of the evolution curves AS/Sq <0.3, as exemplified in Figure 2. However, the first order approximation entails a systematic imderestimation of M2, as shovm by Bertmer and Eckert. Numerous variations of the original REDOR pulse sequence have been established to adapt the technique to specific needs. To accoimt for pulse imperfections and other experimental errors, Chan and Eckert introduced compensated REDOR. In this approach, an /-channel 7r-pulse in the centre of the pulse sequence cancels the reintroduction of the 7-S dipolar couplings hence the echo amplitudes are solely attenuated by the... 

Irrespective of the specific version of REDOR, as long as ti-pulses every half rotor period constitute the pulse trains, the fast REDOR dephasing in the presence of very strong dipolar couplings entails severe problems in the data analysis. If the rotation frequency is limited by the NMR... 

In the CT-VPP-REDOR experiment (cf. Figure 3), the positions of the 7t-pulses on the /-channel which are applied at Tr/2 in conventional REDOR are changed stepwise over the complete rotor period, leading to but a partial reintroduction of the heteronuclear dipolar coupling. The resulting AS/So curve depends on the pulse position fpp according to... 

Figure 8 Samples used for the validation of the various CT-REDOR approaches. (A) and (B) second coordination sphere of Al in Al(P03)3 (A) and B in BPO4 (B) as examples for an S-/e and S-/4 multiple-spin system with strong dipolar coupling (C) doubly labelled glycine (in a 9 1 mixture unlabelled/labelled glycine) as an example for an isolated two-spin system.

As shown in the preceding two sections, the constant time version of REDOR, CT-REDOR, may be applied as an expedient alternative to the existing REDOR versions in the presence of strong heteronuclear dipolar couplings. In these cases, only few data points are available for the data analysis, which especially in the case of multiple-spin systems renders an evaluation of the second moments impossible. The efficiency of the dipolar recoupling may be intentionally reduced either via a dislocation of the dephasing Ti-pulses from the centre of the rotor period or via an application of non-Ti-dephasing pulses. A variation of the pulse position fpp... 

CT-VPP-REDOR) or the pulse duration fp (CT-VPD-REDOR) then produces CT-REDOR curves, from which the second moment may be evaluated with distinctively superior accuracy as compared to the values obtained from a parabolic fit to the conventional REDOR data. When restricting the experiment to short dipolar evolution times, the two-spin approximation may be applied for the data analysis, which proves to be especially attractive for amorphous solids, for which the exact spin geometry is unknovm. The data presented on the model compoimds illustrate the various facets of CT-REDOR NMR spectroscopy. First application examples, namely, the evaluation of the heteronuclear Li-Ti dipolar couplings within the garnet structure of Li5La3Nb20i2, the determi-nation of the intemuclear B- P distance in frustrated Lewis pairs, the analysis of Na- F dipolar interaction in fluormica or Na- P... 

---