High-resolution solid-state NMR spectroscopy of protons with homonuclear dipolar decoupling schemes under magic-angle spinning

High-resolution NMR spectroscopy of ¹H spins in the solid state is normally rendered difficult due to the strong homonuclear ¹H–¹H dipolar couplings. Even under very high-speed magic-angle spinning (MAS) at ca. 60–70 kHz, these couplings are not completely removed. An appropriate radiofrequency pulse scheme is required to average out the homonuclear dipolar interactions in combination with MAS to get high-resolution ¹H NMR spectrum in solid state. Several schemes have been introduced in the recent past with a variety of applications also envisaged. Development of some of these schemes has been made possible with a clear understanding of the underlying spin physics based on bimodal Floquet theory. The utility of these high-resolution pulse schemes in combination with MAS has been demonstrated for spinning speeds of 10–65 kHz in a range of ¹H Larmor frequencies from 300 to 800 MHz.     

Spin-locking and recoupling of homonuclear dipolar interaction between spin-3/2 nuclei under magic-angle sample spinning

Numerical simulations and experiments were used to examine the possibility of employing strong spin-lock fields for recoupling of homonuclear dipolar interactions between spin-3/2 quadrupolar nuclei and to compare it to the rotary-resonance recoupling at weak spin-lock fields. It was shown that strong spin-lock pulses under MAS conditions can lead to recoupling, provided that the electric-field gradient principal axes systems of the coupled nuclei are aligned and that their quadrupolar coupling constants are approximately the same. The phenomenon is based on the fact that strong spin-lock pulses induce adiabatic transfer of magnetization between the central-transition coherence and the triple-quantum coherence with equal periodicity as is the periodicity of the time-dependent dipolar coupling. Because of the synchronous variation of the state of the spin system and of the dipolar interaction, the effect of the latter on the central-transition coherence and on the triple-quantum coherence is not averaged out by sample rotation. The approach is, however, very sensitive to the relative orientation of the electric-field gradient principal axes systems and therefore less robust than the approach based on weak spin-lock pulses that satisfy rotary-resonance condition.     

Compound radiofrequency-driven recoupling pulse sequences for efficient magnetization transfer by homonuclear dipolar interaction under magic-angle spinning conditions

The maximum of the transferred magnetization in rotating powdered solids under the radiofrequency-driven recoupling (RFDR) pulse sequence is enhanced by reducing the orientation dependence of the effective recoupled homonuclear dipolar interaction. The compound RFDR (CRFDR) pulse sequence for this enhancement consists of RFDR pulse units (tau(i)-pi-tau(R)-pi-1171;tau(i)) with different tau(i), where tau(R) is the sample rotation period, tau(i) and 1171;tau(i) (=tau(R) - tau(i)) are delays, and pi is a 180 degrees pulse. The delay tau(i) modifies the zero-quantum spin operators and the sample rotation-angle dependence of the recoupled dipolar Hamiltonian. The CRFDR pulse sequences were optimized for mixing by varying tau(i). Numerical simulation for the two-spin system only with a dipolar interaction and isotropic chemical shifts indicates that the transfer efficiency of CRFDR averaged over the powder is about 70%, which is 30% higher than the efficiency of the RFDR pulse over a broad range of about 1/tau(R) in resonance frequency difference. The CRFDR sequences need about 60% longer mixing times to maximize the transferred magnetizaion in comparison with the original RFDR sequence. Chemical shift anisotropy, the other dipolar interactions, and relaxation generally reduce the enhancement by CRFDR. Experiments for fully (13)C-labeled alanine, however, show that the maximum of the magnetization transferred with CRFDR from the carboxyl to alpha carbon is about 15% greater than that with RFDR. Copyright 2000 Academic Press.     

Symmetry-based recoupling of 17O-1H spin pairs in magic-angle spinning NMR

We have performed magic-angle-spinning solid-state NMR experiments in which protons are recoupled to oxygen-17 nuclei by applying a symmetry-based recoupling sequence at the proton Larmor frequency. Two-dimensional quadrupole-dipole correlation spectra are produced, in which the second-order quadrupolar shift of the oxygen-17 central transition is correlated with the recoupled heteronuclear dipole-dipole interaction. These spectra are sensitive to the relative orientation of the electric field gradient at the site of the oxygen-17 nucleus and the O-H internuclear vector. We also demonstrate experiments in which polarization is transferred from protons to oxygen-17, and show that oxygen-17 signals may be selected according to the protonation state of the oxygen site. We discuss the small observed value of the heteronuclear dipolar splitting in the central-transition oxygen-17 spectra.     

Double-quantum dipolar recoupling at high magic-angle spinning rates

A full investigation of the possible homonuclear double-quantum recoupling sequences, based on the RN family of sequences with N < or = 20, is given. Several new RN sequences, R16(6)(5), R18(8)(5), and R18(10)(5), were applied at high magic-angle spinning rates and compared with theory. The R18(10)(5) technique can be used to recouple dipolar couplings at spinning rates up to 39 kHz, and the application of the sequence in an INADEQUATE experiment is shown for a spinning rate of 30 kHz.     

Double-quantum homonuclear NMR correlation spectroscopy of quadrupolar nuclei subjected to magic-angle spinning and high magnetic field

We present a new application of the symmetry-based dipolar recoupling scheme, for exciting directly double-quantum (2Q) coherences between the central transition of homonuclear half-integer quadrupolar nuclei. With respect to previously published 2Q-recoupling methods (M. Eden, D. Zhou, J. Yu, Chem. Phys. Lett. 431 (2006) 397), the sequence is used without π/2 bracketing pulses and with an original super-cycling. This leads to an improved efficiency (a factor of two for spin-5/2) and to a much higher robustness to radio-frequency field inhomogeneity and resonance offset. The 2Q-coherence excitation performances are demonstrated experimentally by ²⁷Al NMR experiments on the aluminophosphates berlinite, VPI5, AlPO₄-14, and AlPO₄-CJ3. The two-dimensional 2Q–1Q correlation experiments incorporating these recoupling sequences allow the observation of 2Q cross-peaks between central transitions, even at high magnetic field where the difference in offset between octahedral and tetrahedral ²⁷Al sites exceeds 10 kHz.     

Time displacement rotational echo double resonance: heteronuclear dipolar recoupling with suppression of homonuclear interaction under fast magic-angle spinning

We have developed a novel variant of REDOR which is applicable to multiple-spin systems without proton decoupling. The pulse sequence is constructed based on a systematic time displacement of the pi pulses of the conventional REDOR sequence. This so-called time displacement REDOR (td-REDOR) is insensitive to the effect of homonuclear dipole-dipole interaction when the higher order effects are negligible. The validity of td-REDOR has been verified experimentally by the P-31{C-13} measurements on glyphosate at a spinning frequency of 25 kHz. The experimental dephasing curve is in favorable agreement with the simulation data without considering the homonuclear dipole-dipole interactions.     

Combining PGSE NMR with homonuclear dipolar decoupling

A new robust approach for combining multiple-pulse homonuclear decoupling and PGSE NMR is introduced for accurately measuring molecular diffusion coefficients in systems with nonvanishing static homonuclear dipolar couplings. Homonuclear decoupling suppresses dipolar dephasing during the gradient pulses but its efficiency and scaling factor for the effective gradient vary across the sample because of the large variation of the frequency offset caused by the gradient. The resulting artifacts are reduced by introducing a slice selection scheme. The method is demonstrated by (19)F PGSE NMR experiments in a lyotropic liquid crystal.     

C–H dipolar recoupling under very fast magic-angle spinning using virtual pulses

A new solid-state NMR pulse sequence for recoupling ¹³C–¹H dipolar interactions under magic-angle spinning is proposed, which works under a spinning speed of a few to several tens kilohertz. The sequence is composed of two different frequency switched Lee–Goldburg sequences, and the modulation of the spin part of the ¹³C–¹H dipolar interaction is introduced by a virtual pulse sequence consisting of unitary operators connecting the rotating frame and the tilted rotating frame. When the cycle time of the spinning is equal to or twice the cycle time of the sequence, the ¹³C–¹H dipolar interactions can be recoupled. The sequence is insensitive to experimental imperfections such as rf inhomogeneity or frequency offset, and the resulting lineshape can be represented by a simple analytical equation based on the zeroth-order average Hamiltonian. Experimental results for [2-¹³C] -valine·HCl are reported.     

Molecular dynamics as studied by static-powder and magic-angle spinning 2H NMR

The 2H NMR magic-angle spinning (MAS) technique is compared to the static-powder quadrupole echo (QE) and Jeener-Brockaert (JB) pulse sequences for a quantitative investigation of molecular dynamics in solids. The linewidth of individual spinning sidebands of the one-dimensional MAS spectra are observed to be characteristic of the correlation time from approximately 10(-2) to approximately 10(-8) s so that the dynamic range is increased by approximately three orders of magnitude when compared to the QE experiment. As a consequence, MAS 2H NMR is found to be more sensitive to the presence of an inhomogeneous distribution of correlation times than the QE and JB experiments which rely upon lineshape distortions due to anisotropic T2 and T1Q relaxation, respectively. All these results are demonstrated experimentally and numerically using the two-site flip motion of dimethyl sulfone and of the nitrobenzene guest in the alpha-p-tert-butylcalix[4]arene-nitrobenzene inclusion compound.     

Analytical solutions to several magic-angle spinning NMR experiments

Using the Anderson–Weiss (AW) formalism, analytical expressions of the NMR signal are obtained for the following magic-angle spinning (MAS) experiments: total suppression of sidebands (TOSS); phase adjusted spinning sidebands (PASS); rotational-echo double-resonance (REDOR); rotor-encoded REDOR (REREDOR); cross-polarization magic-angle spinning (CPMAS); exchange induced sidebands (EIS); one-dimensional exchange spectroscopy by sideband alternation (ODESSA); time-reverse ODESSA (trODESSA); centerband-only detection of exchange (CODEX). In order to test the validity of the AW approach, the Gaussian powder approximation is compared with exact powder calculations. A quantitative study of the effect of molecular dynamics on the efficiency of the TOSS and REDOR pulse sequences is then presented.     

Enhanced triple-quantum excitation in 13C magic-angle spinning NMR

We describe a new method for exciting triple-quantum coherences in 13C-labelled powder samples under MAS. The proposed method combines selective double-quantum excitation with rotational resonance and frequency-selective composite pulses. The spin dynamics of this new method are described theoretically. Numerical calculations of the spin dynamics are compared to experimental results on fully 13C-labelled L-alanine. The observed triple-quantum filtering efficiency is around 10% for the most intense spectral peak. The method is also demonstrated on other fully 13C-labelled compounds, including a uniformly 13C-labelled amino acid.     

Heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance under ultra-high magic-angle spinning

We compare in this communication several heteronuclear dipolar decoupling sequences in solid-state nuclear magnetic resonance experiments under a magic-angle spinning frequency of 60 kHz. The decoupling radiofrequency field amplitudes considered are 190 and 10 kHz. No substantial difference was found among the sequences considered here in performance barring the difference in the optimisation protocol of the various schemes, an aspect that favours the use of swept-frequency two pulse phase modulation (SW(f)-TPPM).     

NMR in rotating magnetic fields: magic-angle field spinning

Magic-angle sample spinning is one of the cornerstones in high-resolution NMR of solid and semisolid materials. The technique enhances spectral resolution by averaging away rank 2 anisotropic spin interactions, thereby producing isotropic-like spectra with resolved chemical shifts and scalar couplings. In principle, it should be possible to induce similar effects in a static sample if the direction of the magnetic field is varied (e.g., magic-angle rotation of the B0 field). Here we will review some recent experimental results that show progress toward this goal. Also, we will explore some alternative approaches that may enable the recovery of spectral resolution in cases where the field is rotating off the magic angle. Such a possibility could help mitigate the technical problems that render difficult the practical implementation of this method at moderately strong magnetic fields.     

One- and two-dimensional 13C-1H/15N- 1H dipolar correlation experiments under fast magic-angle spinning for determining the peptide dihedral angle phi

A recently proposed 13C-1H recoupling sequence operative under fast magic-angle spinning (MAS) [K. Takegoshi, T. Terao, Solid State Nucl. Magn. Reson. 13 (1999) 203-212.] is applied to observe 13C-1H and 15N-1H dipolar powder patterns in the IH-15N- 3C- H system of a peptide bond. Both patterns are correlated by 15N-to-13C cross polarization to observe one- or two-dimensional (1D or 2D) correlation spectra, which can be simulated by using a simple analytical expression to determine the H-N-C-H dihedral angle. The 1D and 2D experiments were applied to N-acetyl[1,2-13C,15N] DL-valine, and the peptide q angle was determined with high precision by the 2D experiment to be +/- 155.0 degrees +/- 1.2 degrees. The positive one is in good agreement with the X-ray value of 154 degrees +/- 5 degrees. The 1D experiment provided the value of phi = +/- 156.0 degrees +/- 0.8 degrees.     

Recoupling of heteronuclear dipolar interactions with rotational-echo double-resonance at high magic-angle spinning frequencies

Heteronuclear dipolar recoupling with rotational-echo double-resonance (REDOR) is investigated in the rapid magic-angle spinning regime, where radiofrequency irradiation occupies a significant fraction of the rotor period (10-60%). We demonstrate, in two model (13)C-(15)N spin systems, [1-(13)C, (15)N] and [2-(13)C, (15)N]glycine, that REDOR DeltaS/S(0) curves acquired at high MAS rates and relatively low recoupling fields are nearly identical to the DeltaS/S(0) curve expected for REDOR with ideal delta-function pulses. The only noticeable effect of the finite pi pulse length on the recoupling is a minor scaling of the dipolar oscillation frequency. Experimental results are explained using both numerical calculations and average Hamiltonian theory, which is used to derive analytical expressions for evolution under REDOR recoupling sequences with different pi pulse phasing schemes. For xy-4 and extensions thereof, finite pulses scale only the dipolar oscillation frequency by a well-defined factor. For other phasing schemes (e.g., xx-4 and xx-4) both the frequency and amplitude of the oscillation are expected to change.     

Recoupling of residual dipolar couplings in single-domain polymer-stabilized liquid crystals undergoing magic-angle spinning

Measurement of dipolar couplings, chemical shift anisotropies, and quadrupole couplings in oriented media such as liquid crystals are of great importance for extraction of structural parameters in biological macromolecules. Here, we introduce a new technique, SAD-REDOR, that consists of recoupling heteronuclear dipolar couplings in molecules dissolved in a single-domain liquid crystal or other oriented medium through the combined use of magic-angle spinning and rotor-synchronized radiofrequency pulses. This application of the REDOR pulse sequence to oriented media offers several advantages such as selectivity over the type of coupling recovered and tunable scaling of the interaction. The effectiveness of the technique is demonstrated both theoretically and experimentally, using the recently developed polyacrylamide-stabilized Pf1 phage medium and 15N-labeled benzamide as the aligned molecule.     

Biomolecular solid state NMR with magic-angle spinning at 25K

A magic-angle spinning (MAS) probe has been constructed which allows the sample to be cooled with helium, while the MAS bearing and drive gases are nitrogen. The sample can be cooled to 25 K using roughly 3 L/h of liquid helium, while the 4-mm diameter rotor spins at 6.7 kHz with good stability (±5 Hz) for many hours. Proton decoupling fields up to at least 130 kHz can be applied. This helium-cooled MAS probe enables a variety of one-dimensional and two-dimensional NMR experiments on biomolecular solids and other materials at low temperatures, with signal-to-noise proportional to 1/T. We show examples of low-temperature ¹³C NMR data for two biomolecular samples, namely the peptide Aβ_14–23 in the form of amyloid fibrils and the protein HP35 in frozen glycerol/water solution. Issues related to temperature calibration, spin–lattice relaxation at low temperatures, paramagnetic doping of frozen solutions, and ¹³C MAS NMR linewidths are discussed.