Amplitude-modulated decoupling in rotating solids: a bimodal Floquet approach

This paper centers on a theoretical study of amplitude-modulated heteronuclear decoupling in solid-state NMR under magic-angle spinning (MAS). A spin system with a single isolated rare spin coupled to a large number of abundant spins is used in the analysis. The phase-alternating decoupling scheme (XiX decoupling) is analyzed using bimodal Floquet theory and the operator-based perturbation method developed by van Vleck. An effective Hamiltonian correct to second order is calculated for the spin system under XiX decoupling. The results of these calculations indicate that under XiX decoupling the main contribution to the residual line width comes from a cross-term between the heteronuclear and the homonuclear dipolar couplings. This is in contrast to continuous-wave decoupling, where the residual line width is dominated by the cross-term between the heteronuclear dipolar coupling and the chemical-shielding tensor of the irradiated spin. For high-power decoupling the method results in very good decoupling provided that certain unfavorable recoupling conditions, imposed by specific ratios of the amplitude modulation frequency and the MAS frequency, are avoided. For low-power decoupling, the method leads to acceptable decoupling when the pulse length corresponds to an integer multiple of a 2pi rotation and the rf-field amplitude is less than a quarter of the MAS frequency. The performance of the XiX scheme is analyzed over a range of values of the rf power, and numerical results that agree well with the most recent experimental observations are presented.     

Insights into homonuclear decoupling from efficient numerical simulation: techniques and examples

A combination of techniques, including rational number synchronisation and pre-diagonalisation of the time-dependent periodic Hamiltonian, are described which allow the efficient simulation of NMR experiments involving both magic-angle spinning (MAS) and RF irradiation, particularly in the important special case of phase-modulated decoupling sequences. Chebyshev and conventional diagonalisation approaches to calculating propagators under MAS are also compared, with Chebyshev methods offering significant advantages in cases where the Hamiltonian is large and time-dependent but not block-diagonal (as is the case for problems involving combined MAS and RF). The ability to simulate extended coupled spin systems efficiently allows 1H spectra under homonuclear decoupling to be calculated directly and compared to experimental results. Reasonable agreement is found for the conditions under which homonuclear decoupling is typically applied for rigid solids (although the increasing deviation of experimental results from the predictions of theory and simulation at higher RF powers is still unexplained). Numerical simulations are used to explore three features of these experiments: the interaction between the magic-angle spinning and RF decoupling, the effects of tilt pulses in acquisition windows and the effects of "phase propagation delays" on tilted axis precession. In each case, the results reveal features that are not readily anticipated by previous analytical studies and shed light on previous empirical observations.     

Low-power XiX decoupling in MAS NMR experiments

Low-power XiX proton decoupling under fast magic-angle spinning is introduced. The method is applicable if the MAS frequency exceeds the proton-proton interactions. For rigid organic solids this is the case for MAS frequencies above approximately 40 kHz. It is shown that the quality of the decoupling as well as the sensitivity to frequency offsets can be improved compared to low-power continuous-wave decoupling. The decoupling efficiency is somewhat reduced compared to optimized high-power decoupling: in a peptide sample investigated at an MAS frequency of 50 kHz a loss of about 10% in signal intensity for CH3 and CH groups, and of about 40% for CH2 groups was observed. Taking into consideration, that the rf amplitude in the low-power XiX was about 15 times lower than in high-power XiX decoupling, such a reduction in line intensity is sometimes tolerable.     

Heteronuclear decoupling under fast MAS by a rotor-synchronized Hahn-echo pulse train

A new heteronuclear decoupling mechanism under fast magic-angle spinning MAS is introduced. It is based on refocusing the coherences responsible for the dephase of low-gamma nuclei ((13)C, (15)N) transverse spin-polarization in the presence of strongly dipolar-coupled protons, and has the advantage that can be implemented by pulsed techniques, with all the benefits resulting from a reduced duty cycle compared with conventional decoupling by continuous rf irradiation. The decoupling efficiency of a simple rotor-synchronized Hahn-echo pulse train is analyzed both theoretically and experimentally. It was found that a substantial improvement in sensitivity and resolution can be achieved in compounds with small (1)H chemical shielding parameters even at moderate sample spinning, and some interesting applications are shown. It is also shown that much faster spinning frequencies, or alternative refocusing sequences, are needed for applications on rigid organic solids, i.e., in systems with larger (1)H chemical shifts.     

High-Speed Magic-Angle SpinningC MAS NMR Spectra of Adamantane: Self-Decoupling of the Heteronuclear Scalar Interaction and Proton Spin Diffusion

We have investigated the carbon line shape of solid adamantane under high-speed magic-angle sample spinning (MAS) acquired without proton decoupling. The CH-group shows a spinning-speed-dependent line broadening while the CH₂-group consists of a spinning-speed-independent sharp component and a spinning-speed-dependent broader part. These phenomena can be explained by self-decoupling of theJ-interaction due to proton spin diffusion. Such a self-decoupling process can be described by a magnetization exchange process between the multiplet lines. Changing the spin-diffusion rate constant by off-resonance irradiation of the protons allows us to observe the full range from slow exchange to coalescence to fast exchange of the carbon spectra. One of the multiplet components in the CH₂-group corresponds to a group spin of the protons of zero and therefore does not couple to the other protons. This gives rise to the sharp central line. The magnetization exchange rate constant between the different multiplet lines can be determined from the spectra and is a measure for the spinning-speed-dependent proton spin-diffusion rate constant. Even at an MAS speed of 30 kHz, proton spin diffusion is still observable despite the relatively weak intermolecular proton dipolar-coupling network in adamantane which results in a static proton line width of only 14 kHz (full width at half height).     

Measurement of the local 1H spin-diffusion coefficient in polymers

Proton spin diffusion is widely used to determine domain sizes in heterogeneous organic solids. For an accurate analysis, spin diffusion coefficients are required. However, in most cases they are not directly measured, but instead derived from model systems. The effects of magic-angle spinning (MAS), mobility, or spin-lock fields on spin-diffusion coefficients have also been difficult to quantify. In this work, direct measurement of local (1)H spin-diffusion coefficients in any rigid polymer is achieved in experiments with heteronuclear dephasing of the (1)H magnetization, a mixing time for (1)H spin diffusion, and (13)C detection after cross-polarization. In the presence of (1)H homonuclear decoupling and (13)C 180 degrees-pulse recoupling, each (13)C spin dephases a significant number (3-20) of protons, depending on the dephasing time. For (13)C and other sufficiently dilute heteronuclei, the dephasing of the protons is described by simple spin-pair REDOR curves. As a result, every (13)C nucleus will "burn" a spherical hole of known diameter and profile into the proton magnetization distribution. (1)H spin diffusion into the hole during the mixing time can be monitored and simulated accurately for every resolved (13)C site, with the spin-diffusion coefficient as the only significant unknown parameter. By varying the dephasing time, holes with diameters of 0.4-0.8 nm can be burned into the proton magnetization profile and thus the dependence of the local spin-diffusion coefficients on the proton density or partial mobility can be explored. The effects of transverse or magic-angle spin-lock fields on spin diffusion can be quantified conveniently by this method. Analytical and numerical fits yield short-range spin-diffusion coefficients of 0.2-0.5 nm(2)/ms on the 0.5-nm scale, which is smaller than the value of 0.8 nm(2)/ms for organic solids previously measured on the 10-nm scale.     

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.     

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.     

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.     

Symmetry-based recoupling of proton chemical shift anisotropies in ultrahigh-field solid-state NMR

A two-dimensional NMR experiment for estimating proton chemical shift anisotropies (CSAs) in solid powders under magic-angle spinning conditions is demonstrated in which 1H CSAs are reintroduced with a symmetry-based recoupling sequence while the individual proton sites are resolved according to their isotropic chemical shifts by magic-angle spinning (MAS) or combined rotation and multiple pulse (CRAMPS) homonuclear decoupling. The experiments where carried out on an ultrahigh-field solid-state NMR instrument (900 MHz 1H frequency) which leads to increased resolution and reliability of the measured 1H CSAs. The experiment is expected to be important for investigating hydrogen bonding in solids.     

Local monitoring of proton spin diffusion in static and rotating samples via spy detection

A method is described for investigating local proton “spin diffusion” by means of a ¹³C spin probe. The procedure does not require spectral resolution of proton resonance lines and can be applied in the laboratory frame of reference as well as in the rotating frame. Experimental results are presented for a static single crystal of ferrocene and for a powder sample under magic-angle spinning. The spin-diffusion rate constant is found to be proportional to the spinning speed in the range from 1 to 8 kHz.     

Efficient spin-spin scalar coupling mediated C-13 homonuclear polarization transfer in biological solids without proton decoupling

We demonstrate that an efficient C′↔C polarization transfer based on J-coupling can be realized under fast magic-angle spinning (MAS) condition without ¹H decoupling. Experimental results are presented for model crystalline compounds as well as a non-crystalline 17-residue polypeptide MB(i+4)EK. Measurements on MB(i+4)EK demonstrate that 53% of the initial C′ polarization was transferred to the cross peaks at 7.05 T under 25 kHz MAS spinning.     

Resolution enhancement using a new multiple-pulse decoupling sequence for quadrupolar nuclei

A new decoupling composite pulse sequence is proposed to remove the broadening on spin S=1/2 magic-angle spinning (MAS) spectra arising from the scalar coupling with a quadrupolar nucleus I. It is illustrated on the (31)P spectrum of an aluminophosphate, AlPO(4)-14, which is broadened by the presence of (27)Al/(31)P scalar couplings. The multiple-pulse (MP) sequence has the advantage over the continuous wave (CW) irradiation to efficiently annul the scalar dephasing without reintroducing the dipolar interaction. The MP decoupling sequence is first described in a rotor-synchronised version (RS-MP) where one parameter only needs to be adjusted. It clearly avoids the dipolar recoupling in order to achieve a better resolution than using the CW sequence. In a second improved version, the MP sequence is experimentally studied in the vicinity of the perfect rotor-synchronised conditions. The linewidth at half maximum (FWHM) of 65 Hz using (27)Al CW decoupling decreases to 48 Hz with RS-MP decoupling and to 30 Hz with rotor-asynchronised MP (RA-MP) decoupling. The main phenomena are explained using both experimental results and numerical simulations.     

13C/14N heteronuclear multiple-quantum correlation with rotary resonance and REDOR dipolar recoupling

A two-dimensional (13)C/(14)N heteronuclear multiple quantum correlation (HMQC) experiment using dipolar recoupling under magic-angle spinning (MAS) is described. The experiment is an extension of the recent indirect (13)C detection scheme for measuring (14)N quadrupolar coupling under MAS. The recoupling allows the direct use of the much larger dipolar interaction instead of the small J and residual dipolar couplings for establishing (13)C/(14)N correlations. Two recoupling methods are incorporated into the HMQC sequence, both applying rf only to the observed (13)C spin. The first one uses the REDOR sequence with two pi-pulses per rotor cycle. The second one uses a cw rf field matching the spinning frequency, known as rotary resonance. The effects of CSA, T(2)(') signal loss, MAS frequency and stability and t(1)-noise are compared and discussed.     

Fast magic-angle spinning proton NMR studies of polymers at surfaces and interfaces

Solid-state proton NMR with fast magic-angle sample spinning has been used to study the structure and dynamics of polymers and the water interface in porous glass composites. The composites were prepared by photopolymerization of poly(ethyl acrylate) and other acrylate formulations in a high surface-area rigid glass matrix with 40-A interconnected pores. High resolution solid-state proton spectra were obtained for polymer films and composites with 15 kHz magic-angle sample spinning at temperatures above the polymer glass transition temperature. The solid-state proton spectra can be detected with high sensitivity and used to determine the composition of polymer and water filling the pores. These results and spin diffusion studies using 1H-29Si 2D heteronuclear correlation and wideline separation NMR show that the polymer fills the central 30 A of the pore, and that the remaining volume is filled with surface hydroxyl groups and water.     

Solid-state 27Al NMR studies of aluminophosphate molecular sieves. Enhanced resolution by quadrupole nutation and double-rotation.

Solid-state 27Al NMR spectra of several aluminophosphate molecular sieves have been recorded with conventional magic-angle spinning (MAS), double-rotation (DOR) and quadrupole nutation with fast MAS. Enhanced resolution was obtained in the quadrupole nutation experiment at certain radiofrequency pulse strengths. This extra resolution can be comparable to that attainable using DOR, and does not introduce spinning sidebands.     

F/Si distance determination in fluoride-containing octadecasil by Hartmann–Hahn cross-polarization under fast magic-angle spinning

¹⁹F/²⁹Si Hartmann–Hahn continuous wave cross-polarization (CP) has been applied under fast magic-angle spinning (MAS) to a powder sample of octadecasil. Strong oscillations occur during CP on a sideband matching condition between the isolated ²⁹Si–¹⁹F spin pairs formed by the silicons in the D4R units and the fluoride anions. The magnitude of the dipolar coupling constant was deduced directly from the line-splitting between the intense singularities of the Pake-like patterns obtained by Fourier transformation of the oscillatory polarization transfer. The corresponding Si–F internuclear distance, r=2.62±0.05 Å, is found to be in very good agreement with the X-ray crystal structure and the value of 2.69±0.04 Å recently reported from rotational echo double resonance (REDOR) and transferred echo double resonance (TEDOR) nuclear magnetic resonance (NMR) experiments. Furthermore, the CP technique is still reliable under fast MAS where both REDOR and TEDOR sequences suffer from severe artefacts due to finite pulse lengths. In octadecasil, a spinning frequency of 14 kHz is shown to be necessary for an effective suppression of ¹⁹F–¹⁹F spin diffusion. The influences of experimental missettings and radiofrequency (RF) field inhomogeneity are taken into account.     

Rotor-encoded heteronuclear MQ MAS NMR spectroscopy of half-integer quadrupolar and spin I=1/2 nuclei

A new two-dimensional heteronuclear multiple-quantum magic-angle spinning (MQ MAS) experiment is presented which combines high resolution for the half-integer quadrupolar nucleus with information about the dipolar coupling between the quadrupolar nucleus and a spin I=1/2 nucleus. Homonuclear MQ coherence is initially created for the half-integer quadrupolar nucleus by a single pulse as in a standard MQ MAS experiment. REDOR recoupling of the heteronuclear dipolar coupling then allows the creation of a heteronuclear multiple-quantum coherence comprising multiple- and single-quantum coherence of the quadrupolar and spin I=1/2 nucleus, respectively, which evolves during t1. Provided that the t1 increment is not rotor synchronized, rotor-encoded spinning-sideband patterns are observed in the indirect dimension. Simulated spectra for an isolated IS spin pair show that these patterns depend on the recoupling time, the magnitude of the dipolar coupling, the quadrupolar parameters, as well as the relative orientation of the quadrupolar and dipolar principal axes systems. Spectra are presented for Na2HPO4, with the heteronuclear 23Na-1HMQ MAS experiments beginning with the excitation of 23Na (spin I=3/2) three-quantum coherence. Coherence counting experiments demonstrate that four- and two-quantum coherences evolve during t1. The heteronuclear spinning-sideband patterns observed for the three-spin H-Na-H system associated with the Na(2) site are analyzed. For an IS2 system, simulated spectra show that, considering the free parameters, the spinning-sideband patterns are particularly sensitive to only, first, the angle between the two IS internuclear vectors and, second, the two heteronuclear dipolar couplings. It is demonstrated that the proton localization around the Na(2) site according to the literature crystal structure of Na2HPO4 is erroneous. Instead, the experimental data is consistent with two alternative different structural arrangements, whereby either there is a deviation of 10 degrees from linearity for the case of two identical Na-H distances, or there is a linear arrangement, but the two Na-H distances are different. Furthermore, the question of the origin of spinning-sidebands in the (homonuclear) MQ MAS experiment is revisited. It is shown that the asymmetric experimental MQ sideband pattern observed for the low-C(Q) Na(2) site in Na(2)HPO4 can only be explained by considering the 23Na chemical shift anisotropy.     

Heteronuclear dipolar recoupling of half-integer quadrupole nuclei under fast magic angle spinning

An experimental method for the heteronuclear dipolar recoupling of half-integer quadrupole nuclei is proposed. The idea is to manipulate the central transition based on the recoupling technique of spin-polarization-inversion rotary resonance. This method allows the extraction of structural parameters under fast magic-angle spinning. Its validity has been examined by the average Hamiltonian theory and numerical simulations. The initial rotational-echo dephasing arising from the dipolar evolution can be approximated by a parabolic function, from which the heteronuclear van Vleck second moment can be estimated. A factor, estimated from two-spin simulations, is required to account for the effects of the quadrupolar coupling and is rather independent of the geometry and the orders of the spin systems. Our method can facilitate the structural characterization of materials containing half-integer quadrupole nuclei under high-resolution condition. Experimental verification has been carried out on two aluminophosphate systems, namely, AlPO₄-5 and AlPO₄-11.     

Heating of samples induced by fast magic-angle spinning

Intense sample heating through high-speed magic-angle spinning (MAS; up to 58 K temperature difference) is demonstrated. The role of probehead and spinner design, as well as that of the temperature of the bearing air on the heating of a rotating sample, is examined. MAS-induced heating can affect the accurate determination of the isotropic value of the chemical shift as well as the principal values, asymmetry and anisotropy parameters of the chemical shift tensor. In some cases, a very large temperature gradient (12 K) within the fast rotating sample was found, which may limit the resolution of high-speed 1H MAS nuclear magnetic resonance (NMR) spectra.