Heteronuclear spin decoupling in solid-state NMR under magic-angle sample spinning

Achieving high spectral resolution is an important prerequisite for the application of solid-state NMR to biological molecules. Higher spectral resolution allows to resolve a larger number of resonances and leads to higher sensitivity. Among other things, heteronuclear spin decoupling is one of the important factors which determine the resolution of a spectrum. The process of heteronuclear spin decoupling under magic-angle sample spinning is analyzed in detail. Continuous-wave RF irradiation leads only in a zeroth-order approximation to a full decoupling of heteronuclear spin systems in solids under magic-angle spinning (MAS). In a higher-order approximation, a cross-term between the dipolar-coupling tensor and the chemical-shielding tensor is reintroduced, providing a scaled coupling term between the heteronuclear spins. In strongly coupled spin systems this second-order recoupling term is partially averaged out by the proton spin-diffusion process, which leads to exchange-type narrowing of the line by proton spin flips. This process can be described by a spin-diffusion type superoperator, allowing the efficient simulation of strongly coupled spin systems under heteronuclear spin decoupling. Low-power continuous-wave decoupling at fast MAS frequencies offers an alternative to high-power irradiation by reversing the order of the averaging processes. At fast MAS frequencies low-power continuous-wave decoupling leads to significantly narrower lines than high-power continuous-wave decoupling while at the same time reducing the power dissipated in the sample by several orders of magnitude. The best decoupling is achieved by multiple-pulse sequences at high RF fields and under fast MAS. Two such sequences, two-pulse phase-modulated decoupling (TPPM) and X-inverse-X decoupling (XiX), are discussed and their properties analyzed and compared.     

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).     

High-resolution solid-state NMR of anisotropically mobile molecules under very low-power H decoupling and moderate magic-angle spinning

We show that for observing high-resolution heteronuclear NMR spectra of anisotropically mobile systems with order parameters less than 0.25, moderate magic-angle spinning (MAS) rates of 11 kHz combined with ¹H decoupling at 1–2 kHz are sufficient. Broadband decoupling at this low ¹H nutation frequency is achieved by composite pulse sequences such as WALTZ-16. We demonstrate this moderate MAS low-power decoupling technique on hydrated POPC lipid membranes, and show that 1 kHz ¹H decoupling yields spectra with the same resolution and sensitivity as spectra measured under 50 kHz ¹H decoupling when the same acquisition times (50 ms) are used, but the low-power decoupled spectra give higher resolution and sensitivity when longer acquisition times (>150 ms) are used, which are not possible with high-power decoupling. The limits of validity of this approach are explored for a range of spinning rates and molecular mobilities using more rigid membrane systems such as POPC/cholesterol mixed bilayers. Finally, we show ¹⁵N and ¹³C spectra of a uniaxially diffusing membrane peptide assembly, the influenza A M2 transmembrane domain, under 11 kHz MAS and 2 kHz ¹H decoupling. The peptide ¹⁵N and ¹³C intensities at low-power decoupling are 70–80% of the high-power decoupled intensities. Therefore, it is possible to study anisotropically mobile lipids and membrane peptides using liquid-state NMR equipment, relatively large rotors, and moderate MAS frequencies.     

Quantification of homonuclear dipolar coupling networks from magic-angle spinning 1H NMR

Numerical simulations of magic-angle spinning (MAS) spectra of dipolar-coupled nuclear spins have been used to assess different approaches to the quantification of dipolar couplings from ¹H solid-state NMR. Exploiting the translational symmetry of periodic spin systems allows extended networks with ‘realistic’ numbers of spins to be considered. The experimentally accessible parameter is shown to be the root-sum-square of the dipolar couplings to a given spin. The effectiveness of either fitting the resulting spinning sideband spectra to small spin system models, or using analyses based on moment expansions, has been examined. Fitting of the spinning sideband pattern is found to be considerably more robust with respect to experimental noise than frequency domain moment analysis. The influence of the MAS rate and system geometry on robustness of the quantification is analysed and discussed.     

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.     

Experimental aspects of proton NMR spectroscopy in solids using phase-modulated homonuclear dipolar decoupling

In this paper we demonstrate experimentally that the continuously phase-modulated homonuclear decoupling sequence DUMBO-1 is suitable for high-resolution proton NMR spectroscopy of rigid solids. Over a wide range of experimental conditions, we show on the model sample L-alanine as well as on small peptides that proton linewidths of less than 0.5 ppm can be obtained under DUMBO-1 decoupling. In particular the DUMBO-1 sequence yields well resolved proton spectra both at slow and fast MAS. The DUMBO-1 decoupling scheme can in principle be inserted in any multi-nuclear or multi-dimensional solid-state NMR experiment which requires a high-resolution 1H dimension. An example is provided with the 13C-1H MAS-J-HMQC experiment.     

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.     

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.     

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.     

Heteronuclear local field NMR spectroscopy under fast magic-angle sample spinning conditions

The acquisition of bidimensional heteronuclear nuclear magnetic resonance local field spectra under moderately fast magic-angle spinning (MAS) conditions is discussed. It is shown both experimentally and with the aid of numerical simulations on multispin systems that when sufficiently fast MAS rates are employed, quantitative dipolar sideband patterns from directly bonded spin pairs can be acquired in the absence of ¹H–¹H multiple-pulse homonuclear decoupling even for “real” organic solids. The MAS speeds involved are well within the range of commercially available systems (10–14 kHz) and provide sidebands with sufficient intensity to enable a reliable quantification of heteronuclear dipolar couplings from methine groups. Simulations and experiments show that useful information can be extracted in this manner even from more tightly coupled –CH₂– moieties, although the agreement with the patterns simulated solely on the basis of heteronuclear interactions is not in this case as satisfactory as for methines. Preliminary applications of this simple approach to the analysis of molecular motions in solids are presented; characteristics and potential extensions of the method are also discussed.     

Heteronuclear decoupling interference during symmetry-based homonuclear recoupling in solid-state NMR

We examine the influence of continuous-wave heteronuclear decoupling on symmetry-based double-quantum homonuclear dipolar recoupling, using experimental measurements, numerical simulations, and average Hamiltonian theory. There are two distinct regimes in which the heteronuclear interference effects are minimized. The first regime utilizes a moderate homonuclear recoupling field and a strong heteronuclear decoupling field; the second regime utilizes a strong homonuclear recoupling field and a weak or absent heteronuclear decoupling field. The second regime is experimentally accessible at moderate or high magic-angle-spinning frequencies and is particularly relevant for many realistic applications of solid-state NMR recoupling experiments to organic or biological materials.     

A solid-state N magic-angle spinning NMR study of some amino acids

Experimental strategies for the acquisition of high-quality 14N magic-angle spinning (MAS) NMR spectra of the simple amino acids, which exhibit 14N quadrupole coupling constants (C(Q)) on the order of 1.2 MHz, are devised. These are the first useful 14N MAS spectra reported for nitrogen compounds having a C(Q)(14N) value in excess of 1 MHz. The complete manifolds of spinning sidebands (ssbs), i.e., about 300 ssbs for a spinning frequency of 6.0 kHz, have been observed in the 14N MAS NMR spectra of a series of amino acids. In their crystal structure these amino acids all exhibit the zwitterionic form and thus the 14N MAS NMR spectra represent those of a rotating -NH(3)(+) group and not of an amino (-NH(2)) group. Computer simulations combined with fitting of simulated to the experimental ssb intensities result in the determination of precise values for the 14N quadrupole coupling (C(Q)) and its associated asymmetry parameter (eta(Q)) for the nitrogen sites in these molecules. For some of the amino acids the 14N MAS NMR spectra exhibit overlap between the manifolds of ssbs from two different nitrogen sites in accordance with their crystal structures. Computer analysis of these spectra results in two different sets of (C(Q), eta(Q)) values which mainly differ in the magnitudes for eta(Q).     

Improvement of homonuclear dipolar decoupling sequences in solid-state nuclear magnetic resonance utilising radiofrequency imperfections

The often annoying imperfections in the phases and pulses of typical radiofrequency multiple-pulse irradiation schemes for homonuclear dipolar decoupling are revisited and analysed here. The analysis is with respect to one such multiple-pulse sequence, namely, the windowed phase-modulated Lee-Goldburg sequence. The error terms in the Hamiltonian due to pulse imperfections may lead to effective rotation of the spins around the z-axis giving rise to image free and high-resolution 1H spectra. Certain precautions to be taken with regard to scale factor estimation are also detailed. The analysis also points out the range of off-set values where the best homonuclear dipolar decoupling performance of a particular pulse scheme may be obtained.     

Interference of homonuclear decoupling and exchange in the solid-state NMR of perfluorocyclohexane

We observe an interference between RF irradiation used for homonuclear decoupling of 19F and conformational exchange in the 13C spectrum of perfluorocyclohexane. We show that these effects can be readily reproduced in simulation, and characterise their dependence on the various NMR and experimental parameters. Their application to observing exchange rates on the kHz timescale is evaluated with respect to T(1rho) measurements and the connections between the two approaches established. The implications for experiments that use homonuclear decoupling of 1H to resolve 1J(CH)couplings in the solid-state are also evaluated in detail.     

A solid-state 14N magic-angle spinning NMR study of some amino acids

Experimental strategies for the acquisition of high-quality 14N magic-angle spinning (MAS) NMR spectra of the simple amino acids, which exhibit 14N quadrupole coupling constants (C(Q)) on the order of 1.2 MHz, are devised. These are the first useful 14N MAS spectra reported for nitrogen compounds having a C(Q)(14N) value in excess of 1 MHz. The complete manifolds of spinning sidebands (ssbs), i.e., about 300 ssbs for a spinning frequency of 6.0 kHz, have been observed in the 14N MAS NMR spectra of a series of amino acids. In their crystal structure these amino acids all exhibit the zwitterionic form and thus the 14N MAS NMR spectra represent those of a rotating -NH(3)(+) group and not of an amino (-NH(2)) group. Computer simulations combined with fitting of simulated to the experimental ssb intensities result in the determination of precise values for the 14N quadrupole coupling (C(Q)) and its associated asymmetry parameter (eta(Q)) for the nitrogen sites in these molecules. For some of the amino acids the 14N MAS NMR spectra exhibit overlap between the manifolds of ssbs from two different nitrogen sites in accordance with their crystal structures. Computer analysis of these spectra results in two different sets of (C(Q), eta(Q)) values which mainly differ in the magnitudes for eta(Q).     

Efficient heteronuclear dipolar decoupling in solid-state NMR using frequency-swept SPINAL sequences

Aiming to improve heteronuclear spin decoupling efficiency in NMR spectroscopy of solids and liquid crystals, we have modified the original Small Phase Incremental ALteration (SPINAL) sequence by incorporating a frequency sweep into it. For the resulting sequence, termed SW_f-SPINAL, the decoupling performance of a large number of sweep variants was explored by both numerical simulations and NMR experiments. It is found that introducing a frequency sweep generally increases both the ‘on-resonance’ decoupling performance and the robustness towards parameter offsets compared to the original SPINAL sequence. This validates the concept of extending the range of efficient decoupling by introducing frequency sweeps, which was recently suggested in the context of the frequency-swept SW_f-TPPM method. The sequence found to be best performing among the SW_f-SPINAL variants consists of fully swept 16 pulse pairs and is designated (32)-SPINAL-32. Its good decoupling performance for rigid spin systems is confirmed by numerical simulations and also experimentally, by evaluating the CH₂ resonance of a powder sample of l-tyrosine under MAS. For moderate MAS frequencies, the new sequence matches the decoupling achieved with SW_f-TPPM, and outperforms all other tested sequences, including TPPM and SPINAL-64. (32)-SPINAL-32 also shows excellent decoupling characteristics for liquid crystalline systems, as exemplified by experiments on the 5CB liquid crystal.     

Solid-state NMR spectroscopy under periodic modulation by fast magic-angle sample spinning and pulses: a review

Fast magic-angle spinning (MAS) holds promise for new approaches to pulsed high-resolution NMR in solids where homogeneous interactions dominate. Prerequisite for developing new pulse methods is the understanding of signal encoding by spin interactions under MAS conditions and of interferences between MAS and pulses. This review discusses corresponding strategies and techniques in a coherent way with particular concentration on homonuclear decoupling techniques for line-narrowing in solids.     

Triple-quantum dynamics in multiple-spin systems undergoing magic-angle spinning: application to 13C homonuclear correlation spectroscopy

We analyze the multiple-quantum dynamics governed by a new homonuclear recoupling strategy effecting an average dipolar Hamiltonian comprising three-spin triple-quantum operators (e.g., S(p)+S(q)+S(r)+) under magic-angle spinning conditions. Analytical expressions are presented for polarization transfer processes in systems of three and four coupled spins-1/2 subject to triple-quantum filtration (3QF), and high-order multiple-quantum excitation is investigated numerically in moderately large clusters, comprising up to seven spins. This recoupling approach gives highly efficient excitation of triple-quantum coherences: ideally, up to 67% of the initial polarization may be recovered by 3QF in three-spin systems in polycrystalline powders. Two homonuclear 2D correlation strategies are demonstrated experimentally on powders of uniformly 13C-labeled alanine and tyrosine: the first correlates the single-quantum spectrum in the first dimension with the corresponding 3QF spectrum along the other. The second protocol correlates triple-quantum coherences with their corresponding single-quantum coherences within triplets of coupled spins.     

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.