High-resolution multiple quantum MAS NMR spectroscopy of half-integer quadrupolar nuclei

Alumina: discriminative analysis using 3D correlation of solid-state NMR parameters

Synthetic transition aluminas (χ, κ, θ, γ, δ, η, ρ) exhibit unique adsorptive and catalytic properties leading to numerous practical applications. Generated by thermal transformation of aluminium (oxy)hydroxides, structural differences between them arise from the variability of aluminium coordination numbers and degree of dehydroxylation. Unequivocal identification of these phases using X-ray diffraction has proven to be very difficult. Quadrupolar interactions of 27Al nuclei, highly sensitive to each site symmetry, render advanced 27Al solid-state NMR a unique spectroscopic tool to fingerprint and identify the different phases. In this paper, 27Al NMR spectroscopic data on alumina reported in literature are collected in a comprehensive library. Based on this dataset, a new 3D correlative method of NMR parameters is presented, enabling fingerprinting and identification of such phases. Providing a gold standard from crystalline samples, this approach demonstrates that any sort of crystalline, ill crystallized or amorphous, mixed periodic or aperiodically ordered transition alumina can now be assessed beyond the current limitations of characterisation. Adopting the presented approach as a standard characterisation of alumina samples will readily reveal NMR parameter-structure-property relations suitable to develop new or improved applications of alumina. Methodological guidance is provided to assist consistent implementation of this characterisation throughout the fields involved.

(14)N overtone transition in double rotation solid-state NMR

Solid-state NMR transitions involving outer energy levels of the spin-1 (14)N nucleus are immune, to first order in perturbation theory, to the broadening caused by the nuclear quadrupole interaction. The corresponding overtone spectra, when acquired in conjunction with magic-angle sample spinning, result in lines, which are just a few kHz wide, permitting the direct detection of nitrogen compounds without the need for labeling. Despite the success of this technique, "overtone" resonances are still broadened due to indirect, second order effects arising from the large quadrupolar interaction. Here we demonstrate that another order of magnitude in spectral resolution may be gained by using double rotation. This brings the width of the (14)N solid-state NMR lines much closer to the region commonly associated with high-resolution solid-state NMR spectroscopy of (15)N and demonstrates the improvements in resolution that may be possible through the development of pulsed methodologies to suppress these second order effects.

Understanding multi-quantum NMR through secular approximation

With the development of technology and improved understanding of nuclear spin-spin interactions and their behavior in static/oscillating magnetic fields, NMR spectroscopy has emerged as a powerful tool for characterizing molecular structure in a wide range of systems of chemical, physical and biological relevance. Here in this article, we revisit the important connection between "Secular-Approximation" (a well-known fundamental concept) and NMR spectroscopy. Employing recent experimental results as the background, an alternate interpretation of the secular approximation is presented for describing and understanding the nuances of Multi-Quantum (MQ) NMR spectroscopy of quadrupolar nuclei. Since MQ NMR spectroscopy of quadrupolar nuclei forms the basis of the structural characterization of inorganic solids and clusters, we believe that the analytic theory presented herein would be beneficial both in the understanding and design of MQ NMR experiments. Additionally, the analytic results are corroborated with rigorous numerical simulations and could be employed in the quantitative interpretation of experimental results.

19F-decoupling of half-integer spin quadrupolar nuclei in solid-state NMR: application of frequency-swept decoupling methods

In solid-state NMR studies of minerals and ion conductors, quadrupolar nuclei like (7)Li, (23)Na or (133)Cs are frequently situated in close proximity to fluorine, so that application of (19)F decoupling is beneficial for spectral resolution. Here, we compare the decoupling efficiency of various multi-pulse decoupling sequences by acquiring (19)F-decoupled (23)Na-NMR spectra of cryolite (Na(3)AlF(6)). Whereas the MAS spectrum is only marginally affected by application of (19)F decoupling, the 3Q-filtered (23)Na signal is very sensitive to it, as the de-phasing caused by the dipolar interaction between sodium and fluorine is three-fold magnified. Experimentally, we find that at moderate MAS speeds, the decoupling efficiencies of the frequency-swept decoupling schemes SW(f)-TPPM and SW(f)-SPINAL are significantly better than the conventional TPPM and SPINAL sequences. The frequency-swept sequences are therefore the methods of choice for efficient decoupling of quadrupolar nuclei with half-integer spin from fluorine.

Two-dimensional MAS NMR correlation protocols involving double-quantum filtering of quadrupolar spin-pairs

Three two-dimensional (2D) NMR homonuclear correlation techniques invoking double-quantum (2Q) filtration of the central transitions of half-integer spins are evaluated numerically and experimentally. They correlate directly detected single-quantum (1Q) coherences in the t(2) domain with either of 1Q, two-spin 2Q or single-spin multiple-quantum coherence-evolutions in the indirect (t(1)) dimension. We employ experimental (23)Na and (27)Al NMR on sodium sulfite and the natural mineral sillimanite (SiAl(2)O(5)), in conjunction with simulated 2D spectra from pairs of dipolar-recoupled spins-3/2 and 5/2 at different external magnetic fields, to compare the correlation strategies from the viewpoints of 2D spectral resolution, signal sensitivity, implementational aspects and their relative merits for establishing internuclear proximities and quadrupolar tensor orientations.

Enhancing MQMAS of low-gamma nuclei by using a high B(1) field balanced probe circuit

A balanced probe circuit is used to generate high B(1) magnetic field for sensitivity enhancement of multiple-quantum magic-angle spinning (MQMAS) experiment applied to low-gamma quadrupolar nuclei. Electrical balancing of the sample coil can cut the peak voltage by a half, therefore improving the power handling when generating a two-fold higher B(1) field. Experimental results, illustrated here with (25)Mg data for two layered double hydroxides, show that the MQMAS efficiency increases more than linearly with the B(1) field strength. The multiplicative enhancements from high B(0) and B(1) fields and an optimized MQMAS pulse sequence provide the critically needed sensitivity for acquiring MQMAS spectra of low-gamma quadrupolar nuclei such as (25)Mg at natural abundance.

Application of shaped adiabatic pulses to MQMAS NMR spectroscopy of spin 3/2 nuclei

Competition between nutation (r.f. driven) and adiabatic (rotor-driven) multi-quantum coherence transfer mechanisms in spin 3/2 systems results in diminished performance of rotation induced adiabatic coherence transfer (RIACT) in isotropic multiple-quantum magic-angle spinning (MQMAS) experiments for small e(2)qQ/h (<2 MHz) and high radio-frequency powers. We present a simple shaped RIACT pulse consisting of a truncated sine wave (spanning 0-0.8pi) that corrects the sensitivity losses, phase twist and relative intensity errors that can arise in MQMAS spectra utilizing constant-amplitude RIACT pulses. The shaped RIACT pulse may enhance the study of metals in biomolecules where quadrupole couplings of S=3/2 nuclei such as (23)Na tend to be small.

Natural abundance 43Ca solid-state NMR characterisation of hydroxyapatite: identification of the two calcium sites

Natural abundance (43)Ca solid-state NMR of hydroxyapatite (Ca(10)(PO(4))(6)(OH)(2)) was performed at three different fields (8.45, 14.1 and 18.8 T). The two crystallographically distinct calcium sites of the apatite structure were spectroscopically resolved at 18.8 T. The (43)Ca NMR interaction parameters (delta(iso), C(Q) and eta(Q)) of each site were determined by multiple magnetic-field simulations. The peaks with delta(iso) = 11.2 +/- 0.8 and - 1.8 +/- 0.8 ppm, both with C(Q) = 2.6 +/- 0.4 MHz, were assigned to the Ca(II) and Ca(I) sites, respectively, on the basis of their relative intensities.

Improved Excitation Schemes for Multiple-Quantum Magic-Angle Spinning for Quadrupolar Nuclei Designed Using Optimal Control Theory

We have investigated the use of optimal control theory for the design of improved multiple-quantum excitation schemes for the popular multiple-quantum magic-angle spinning NMR experiment for quadrupolar nuclei with half-integer quadrupolar spin. The advantage of the new low-power experiments, termed OCFASTER, is demonstrated by sensitivity improvements approaching 50% for 87Rb in RbClO4 and RbNO3 as compared to FASTER and standard strong-pulse excitation schemes.

Implementing SPAM into STMAS: a net sensitivity improvement in high-resolution NMR of quadrupolar nuclei

Gan and Kwak recently introduced two new tools for high-resolution 2D NMR methods applied to quadrupolar nuclei: double-quantum filtering in STMAS (DQF-STMAS) and the soft-pulse added mixing (SPAM) idea. Double-quantum filtering suppresses all undesired signals in the STMAS method with limited loss in sensitivity. With SPAM, all pathways are added constructively after the second hard-pulse instead of using a single pathway as previously. Here, the sensitivity, advantages and drawbacks of DQF-STMAS are compared to 3QMAS. Additionally, SPAM can be included into DQF-STMAS method, resulting in a net sensitivity gain with respect to 3QMAS of ca. 10-15.

Improved quantitation in 3QMAS of spin 5/2 nuclei by RF power modulation of FAM-II

High-resolution NMR of quadrupolar I = 5/2 nuclei using triple-quantum magic angle spinning (3QMAS) techniques can provide more accurate quantitative information on sites with small quadrupolar coupling constants by changing the pulse strength in addition to the pulse length in the FAM-II multiple-quantum conversion sequence. These effects are illustrated using (27)Al NMR of yttrium aluminium garnet and andalusite.

Increasing the sensitivity of 2D high-resolution NMR methods applied to quadrupolar nuclei

Gan and Kwak recently proposed a soft-pulse added mixing (SPAM) idea in the classical two-pulse multiple-quantum magic-angle spinning scheme. In the SPAM method, a soft pi/2 pulse is added after the second hard-pulse (conversion pulse) and all coherence orders in between them are constructively used to obtain the signal. We, here, further extend this idea to distributed samples where the signal mainly results from echo pathways and that from anti-echo pathways dies out after a few t1 increments. We show that, with a combination of SPAM and collection of fewer anti-echoes, an enhancement of the signal to noise ratio by a factor of ca. 3 may be obtained over the z-filtered version. This may prove to be useful even for samples with long T2' relaxation times.

Effects of pulse strength, width, and sample spinning speed on the spectral spin diffusion of multiquantum coherences of spin-32 quadrupolar nuclei

The effects of radio-frequency pulse strength, width, and sample spinning speed on the spin-diffusion spectrum of half-integer quadrupolar spins in solids have been studied by theoretical, numerical, and experimental investigations. It is revealed that the line shape of the cross peaks changes nonmonotonically with respect to the change of pulse strength, pulse width, or sample spinning speed. It is also found that the sample spinning speed has much more pronounced influence on the spin diffusion spectral line shape. In many cases of practical importance, the effect of sample spinning must be included in spectral analysis, in contrast to the practice of previous studies. Moreover, this effect can be exploited to further improve the precision in the determination of relative orientation of the electric-field gradient tensors of the exchange partners.

Efficient 5QMAS NMR of spin-5/2 nuclei: use of fast amplitude-modulated radio-frequency pulses and cogwheel phase cycling

We report here an efficient multiple-quantum magic-angle spinning (MQMAS) pulse sequence involving fast amplitude-modulated (FAM) radio-frequency pulses for excitation and conversion of five-quantum (5Q) coherences of spin-5/2 nuclei. The use of a FAM-I type pulse train for the conversion of 5Q into 1Q coherences proves to be easier to implement experimentally than the earlier suggested use of a FAM-II type sequence [J. Magn. Reson. 154 (2002) 280], while delivering at least equal signal enhancement. Results of numerical simulations and experimental 27Al 5QMAS spectra of aluminium acetylacetonate for different excitation and conversion schemes are compared to substantiate these claims. We also demonstrate the feasibility of acquiring 5QMAS spectra of spin-5/2 systems using cogwheel phase cycling [J. Magn. Reson. 155 (2002) 300] to select the desired coherence pathways. A cogwheel phase cycle of only 57 steps is shown to be as effective as the minimum conventional nested 77-step phase cycle.

I-STMAS, a new high-resolution solid-state NMR method for half-integer quadrupolar nuclei

In complement to the previously proposed multiple-quantum magic-angle-spinning (MQMAS) and satellite transition MAS (STMAS) sequences, we describe a new two-dimensional high-resolution method, inverse-STMAS (I-STMAS) that allows second-order quadrupolar averaging. Like STMAS, I-STMAS correlates second-order quadrupole dephasing occurring on coherences related to the central transition (CT) and satellite transitions (STs), but does it in a reverse manner: CT evolves during the t(1) period while STs are detected during t(2). Although STMAS and I-STMAS are symmetric, there are some interesting and useful differences between the two methods. For example, we show that during the acquisition time t(2), it is possible to over-sample the data and then to process them to suppress the CT-CT correlation resonance.

Multiple-quantum magic-angle spinning spectroscopy using nonlinear sampling

NMR spectroscopy is a relatively insensitive technique and many biomolecular applications operate near the limits of sensitivity and resolution. A particularly challenging example is detection of the quadrupolar nucleus 17O, due to its low natural abundance, large quadrupole couplings, and low gyromagnetic ratio. Yet the chemical shift of 17O spans almost 1000 ppm in organic molecules and it serves as a potentially unique reporter of hydrogen bonding in peptides, nucleic acids, and water, and as a valuable complement to 13C and 15N NMR. Recent developments including the multiple-quantum magic-angle spinning (MQMAS) experiment have enabled the detection of 17O in biological solids, but very long data acquisitions are required to achieve sufficient sensitivity and resolution. Here, we perform nonlinear sampling in the indirect dimension of MQMAS experiments to substantially reduce the total acquisition time and improve sensitivity and resolution. Nonlinear sampling prevents the use of the discrete Fourier transform; instead, we employ maximum entropy (MaxEnt) reconstruction. Nonlinearly sampled MQMAS spectra are shown to provide high resolution and sensitivity in several systems, including lithium sulfate monohydrate (LiSO(4)-H(2)17O) and L-asparagine monohydrate (H(2)17O). The combination of nonlinear sampling and MaxEnt reconstruction promises to make the application of 17O MQMAS practical in a wider range of biological systems.

Signal enhancement in the triple-quantum magic-angle spinning NMR of spins-3/2 in solids: the FAM-RIACT-FAM sequence

We achieve a significant signal enhancement for the triple-quantum magic-angle spinning NMR of a spin-3/2 system, by using an amplitude-modulated radiofrequency field, followed by a selective 90 degrees pulse and a phase-shifted strong rf field, for the triple-quantum excitation, and an amplitude-modulated radiofrequency field for the conversion of triple-quantum coherence to observable single-quantum coherence. The experiment is demonstrated on the (87)Rb NMR of polycrystalline rubidium nitrate.

A solid-state (17)O nuclear magnetic resonance study of nucleic acid bases

We report a systematic solid-state (17)O NMR study of free nucleic acid bases: thymine (T), uracil (U), cytosine (C), and guanine (G). Site-specifically (17)O-enriched samples were synthesized:[2-(17)O]thymine (1), [4-(17)O]thymine (2), [2-(17)O]uracil (3), [4-(17)O]uracil (4), [2-(17)O]cytosine (5), and [6-(17)O]guanine monohydrate (6). Magic-angle-spinning (MAS) and static (17)O NMR spectra were acquired at 11.75 T for compounds 1-6, from which information about the (17)O chemical shift and electric field gradient tensors was obtained. Extensive quantum chemical calculations were performed at the B3LYP/6-311++G(d,p) level of theory for (17)O NMR properties in various molecular models. The calculated (17)O NMR tensors are highly sensitive to the description of intermolecular hydrogen-bonding interactions at the target oxygen atom. A reasonably good agreement between experimental solid-state (17)O NMR data and B3LYP/6-311++G(d,p) calculations is achievable only in molecular cluster models where a complete hydrogen-bond network is considered. Using this theoretical approach, we also investigated the (17)O NMR tensors in two unusual structures: guanine- and uracil-quartets.

Signal enhancement in 5QMAS spectra of spin-5/2 quadrupolar nuclei

5QMAS experiments on spin-5/2 systems display a low sensitivity compared with their 3QMAS counterparts. Nevertheless, the superior resolution of 5QMAS over 3QMAS makes these experiments a favorable choice for many materials. We report an enhancement scheme for the 5QMAS experiment, using an improved five-quantum excitation pulse scheme combined with a FAM-II conversion pulse. The results are verified experimentally on a polycrystalline sample of gamma-(27)Al(2)O(3), showing an enhancement factor of 2.4 over the simple two-pulse (CW) 5QMAS scheme. Numerical computations of the efficiency parameter epsilon support these results.

Procedures for labeling the high-resolution axis of two-dimensional MQ-MAS NMR spectra of half-integer quadrupole spins

The increasing development and application of the multiple-quantum MAS NMR for half-integer quadrupole spins has led to various RF pulse sequences for improving the excitation of multiple-quantum coherences and their conversion to single-quantum coherences. As a result, several conventions for labeling the Fl dimension of a 2D MQ-MAS spectrum appear in the literature. The corresponding relations for extracting the isotropic chemical shift, the quadrupole coupling constant, and the asymmetry parameter from experimental data are not always provided. We analyze these various conventions systematically and propose a new one, similar to that introduced by J.-P. Amoureux and C. Fernandez (2000, Solid State NMR 10, 339-343). These various conventions are illustrated with 27Al (I = 5/2) nuclei in aluminum acetylacetonate Al(CH3COCHCOCH3)3. Another experimental problem often met, the aliasing of peaks in the 2D spectrum, is analyzed and illustrated with 27Al (I = 5/2) in NH4Y zeolite and 23Na (I = 3/2) in sodium pyrophosphate Na4P2O7.

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.

Two-dimensional (17)O multiple quantum magic-angle spinning NMR of organic solids

We report two-dimensional (2D) (17)O multiple-quantum magic-angle spinning (MQMAS) NMR spectra for four (17)O-labeled organic compounds: [(17)O(2)]-D-alanine (1), potassium hydrogen [(17)O(4)]dibenzoate (2), [(17)O(4)]-D,L-glutamic acid.HCl (3) and [2,4-(17)O(2)]uracil (4). The high spectral resolution observed in the 2D (17)O MQMAS NMR spectra allows extraction of precise (17)O NMR parameters for all crystallographically distinct oxygen sites. We demonstrate that rotor synchronization is important in obtaining high-quality (17)O MQMAS spectra for organic compounds. Several issues related to the potential of (17)O MQMAS NMR for large biomolecular systems are also discussed.

Investigation of sodium cations in dehydrated zeolites LSX, X, and Y by 23Na off-resonance RIACT triple-quantum and high-speed MAS NMR spectroscopy

We investigated by two-dimensional 23Na ORIACT MQMAS NMR and one-dimensional 23Na high-speed MAS NMR spectroscopy a homologous series of dehydrated zeolites with faujasite structure. The framework silicon to aluminum ratios varied between 1.06 and 2.60. In the case of zeolites Y (nSi/nAl = 2.60), we studied materials with sodium exchange degrees between 0 and 95%. The recently introduced ORIACT method (Caldarelli, S.; Ziarelli, F. J. Am. Chem. Soc. 2000, 122, 12015) significantly improved the resolution of the MQMAS spectra, in comparison with earlier studies. It was thus possible to extract meaningful quadrupole parameters by MQMAS NMR, which were used as a starting point for the simulation of 1D MAS NMR spectra to obtain more accurate values of the NMR parameters and site occupancy. We were able to show by this approach that in zeolite NaLSX the SI positions in the hexagonal prisms are occupied by sodium cations. For the homologous series of zeolites Y, it was found that sodium cations located at SII positions are the easiest to be substituted by ammonium ions through the exchange process.

Enhanced sensitivity in RIACT/MQ-MAS NMR experiments using rotor assisted population transfer

The rotor assisted population transfer (RAPT) sequence is used to enhance the sensitivity of the RIACT(II) experiment for spin-3/2 quadrupolar nuclei. A detailed theoretical analysis of the polarizations that contribute to different types of MQ-MAS experiments is provided. In particular, two polarization pathways are distinguished for the creation of triple-quantum coherence. The existence of these pathways is experimentally demonstrated by comparing the sensitivities of different sequences with and without RAPT preparation.

Population and coherence transfer induced by double frequency sweeps in half-integer quadrupolar spin systems

We have recently shown that the sensitivity of single- and multiple-quantum NMR experiments of half-integer (N/2) quadrupolar nuclei can be increased significantly by introducing so-called double frequency sweeps (DFS) in various pulse schemes. These sweeps consist of two sidebands generated by an amplitude modulation of the RF carrier. Using a time-dependent amplitude modulation the sidebands can be swept through a certain frequency range. Inspired by the work of Vega and Naor (J. Chem. Phys. 75, 75 (1981)), this is used to manipulate +/-(m - 1) <--> +/-m (3/2 < or = m < or = N/2) satellite transitions in half-integer spin systems simultaneously. For (23)Na (I = 3/2) and (27)Al (I = 5/2) spins in single crystals it proved possible to transfer the populations of the outer +/-m spin levels to the inner +/-1/2 spin levels. A detailed analysis shows that the efficiency of this process is a function of the adiabaticity with which the various spin transitions are passed during the sweep. In powders these sweep parameters have to be optimized to satisfy the appropriate conditions for a maximum of spins in the powder distribution. The effects of sweep rate, sweep range, and RF field strength are investigated both numerically and experimentally. Using a DFS as a preparation period leads to significantly enhanced central transition powder spectra under both static and MAS conditions, compared to single pulse excitation. DFSs prove to be very efficient tools not only for population transfer, but also for coherence transfer. This can be exploited for the multiple- to single-quantum transfer in MQMAS experiments. It is demonstrated, theoretically and experimentally, that DFSs are capable of transferring both quintuple-quantum and triple-quantum coherence into single-quantum coherence in I = 5/2 spin systems. This leads to a significant enhancement in signal-to-noise ratio and strongly reduces the RF power requirement compared to pulsed MQMAS experiments, thus extending their applicability. This is demonstrated by (27)Al 3QMAS experiments on 9Al(2)O(3). 2B(2)O(3) and the mineral andalusite. In the latter compound, Al experiences a quadrupolar-coupling constant of 15.3 MHz in one of the sites. Finally a 5QMAS spectrum on 9Al(2)O(3). 2B(2)O(3) demonstrates the sensitivity enhancement of this experiment using a double frequency sweep.

On the conversion of triple- to single-quantum coherences in MQMAS NMR

A systematic experimental and numerical evaluation of several basic approaches to multiple-quantum magic angle spinning (MQMAS) NMR is presented for spin-32 nuclei. The approaches use identical MQ excitation, via a single RF pulse of high power, and three types of methods for conversion to observable coherence: (a) nutation by strong continuous wave pulse; (b) rotation-induced adiabatic coherence transfer (RIACT), and (c) fast amplitude modulation (FAM-1). The optimization strategies and maximum achievable MQMAS efficiencies of (87)Rb in RbNO(3) and LiRbSO(4) are investigated using several coherence transfer schemes under a wide range of experimental parameters. These parameters include the strength of the RF magnetic field nu(RF), the sample rotation speed nu(R), the length of the conversion period, and the modulation frequency in FAM-1. The data provide new insights into the spin dynamics involved in these techniques and the experimental guidelines for achieving the best sensitivity. The RF requirements for maximum efficiency of conversion depend on the method to be used. In general, FAM-1 performs better than the nutation and RIACT methods in terms of efficiency and off-resonance behavior, especially when nu(RF) is small compared to the quadrupole frequency nu(Q). The experiments performed using nutation, RIACT, and FAM-1 methods yield similar resolution in the isotropic dimension, regardless of nu(RF).

SIMPSON: a general simulation program for solid-state NMR spectroscopy

A computer program for fast and accurate numerical simulation of solid-state NMR experiments is described. The program is designed to emulate a NMR spectrometer by letting the user specify high-level NMR concepts such as spin systems, nuclear spin interactions, RF irradiation, free precession, phase cycling, coherence-order filtering, and implicit/explicit acquisition. These elements are implemented using the Tcl scripting language to ensure a minimum of programming overhead and direct interpretation without the need for compilation, while maintaining the flexibility of a full-featured programming language. Basically, there are no intrinsic limitations to the number of spins, types of interactions, sample conditions (static or spinning, powders, uniaxially oriented molecules, single crystals, or solutions), and the complexity or number of spectral dimensions for the pulse sequence. The applicability ranges from simple 1D experiments to advanced multiple-pulse and multiple-dimensional experiments, series of simulations, parameter scans, complex data manipulation/visualization, and iterative fitting of simulated to experimental spectra. A major effort has been devoted to optimizing the computation speed using state-of-the-art algorithms for the time-consuming parts of the calculations implemented in the core of the program using the C programming language. Modification and maintenance of the program are facilitated by releasing the program as open source software (General Public License) currently at http://nmr.imsb.au.dk. The general features of the program are demonstrated by numerical simulations of various aspects for REDOR, rotational resonance, DRAMA, DRAWS, HORROR, C7, TEDOR, POST-C7, CW decoupling, TPPM, F-SLG, SLF, SEMA-CP, PISEMA, RFDR, QCPMG-MAS, and MQ-MAS experiments.

Characterization of a new hexasodium diphosphopentamolybdate hydrate, Na6[P2Mo5O23]x7H2O, by 23Na MQMAS NMR spectroscopy and X-ray powder diffraction

A novel hexasodium disphosphopentamolybdate hydrate, Na6[P2Mo5O23]x7H2O, has been identified using X-ray powder diffraction, 1H, 23Na, and 31P magic-angle spinning (MAS) NMR, and 23Na multiple-quantum (MQ) MAS NMR. Powder XRD reveals that the hydrate belongs to the triclinic spacegroup P1 with cell dimensions a = 10.090(3) A, b = 15.448(5) A, c = 8.460(4) A, alpha = 101.45(6) degrees, beta = 104.09(2) degrees, gamma = 90.71(5) degrees, and Z = 2. The number of water molecules of crystallization has been determined on the basis of a quantitative evaluation of the 1H MAS NMR spectrum, the crystallographic unit cell volume, and a hydrogen content analysis. The 23Na MQMAS NMR spectra of Na6[P2Mo5O23]x7H2O, obtained at three different magnetic fields, clearly resolve resonances from six different sodium sites and allow a determination of the second-order quadrupolar effect parameters and isotropic chemical shifts for the individual resonances. These data are used to determine the quadrupole coupling parameters (CQ and eta Q) from simulations of the complex line shapes of the central transitions, observed in 23Na MAS NMR spectra at the three magnetic fields. This analysis illustrates the advantages of combining MQMAS and MAS NMR at moderate and high magnetic fields for a precise determination of quadrupole coupling parameters and isotropic chemical shifts for multiple sodium sites in inorganic systems. 31P MAS NMR demonstrates the presence of two distinct P sites in the asymmetric unit of Na6[P2Mo5O23].7H2O while the 31P chemical shielding anisotropy parameters, determined for this hydrate and for Na6[P2Mo5O23]x13H2O, show that these two hydrates can easily be distinguished using 31P MAS NMR.

Pure absorption-mode spectra using a modulated RF mixing period in MQMAS experiments

Different approaches to obtain pure absorption-mode lineshapes in MQMAS experiments employing a train of 180 degrees phase-alternating pulses for the multiple-quantum to single-quantum mixing period are investigated. Four pulse sequences, which achieve this by using either the shifted-echo approach or the hypercomplex approach with symmetric coherence transfer pathways, are presented and their improved lineshape- and sensitivity-performance is experimentally demonstrated by (87)Rb MQMAS of RbNO(3). Compared to the original modulated-rf mixing sequence, sensitivity enhancements by factors up to 1.3 are obtained with the sequences described here.

Multiple-quantum cross polarization in quadrupolar spin systems during magic-angle spinning

We describe the concept of multiple-quantum cross polarization (CP) between an I = 32 and an I = 12 spin during magic-angle spinning. Experimental and theoretical results for (23)Na-(1)H pairs are presented that elucidate the transfer mechanism and the beneficial effect of adiabatic amplitude modulations of the CP field. The multiple-quantum CP approach is shown to be beneficial for improving the sensitivity of CP-MQMAS experiments and for detecting dipolar correlations.