Quantitative Multiple-Quantum Magic-Angle-Spinning NMR Spectroscopy of Quadrupolar Nuclei in Solids

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.

The influence of the radiofrequency excitation and conversion pulses on the lineshapes and intensities of the triple-quantum MAS NMR spectra of I = 3/2 nuclei

A rigorous examination of the various multiple-quantum magic angle spinning sequences is carried out with reference to sensitivity enhancement in the isotropic dimension and the lineshapes of the corresponding MAS peaks in the anisotropic dimension. An echo efficiency parameter is defined here, which is shown to be an indicator of the performance aspects of the various sequences. This can be used in the design of further new experiments in this field. A consequence of such a systematic analysis has been the combination of a spin-lock pulse for excitation of multiple-quantum coherences and an amplitude-modulated pulse for their conversion to observable single-quantum coherences. This approach has resulted in an improved performance over other sequences with respect to both the anisotropic lineshapes and the isotropic intensities.

Very fast MAS and MQMAS NMR studies of the spectroscopically challenging minerals kyanite and andalusite on 400, 500, and 800 MHz spectrometers

The well-characterized minerals kyanite and andalusite have long presented great challenges in using solid state 27Al NMR to determine the isotropic chemical shift deltaCS, quadrupole coupling constant e2qQ/h, and asymmetry parameter eta for each of the inequivalent aluminum sites in these minerals. Indeed, these minerals have frequently been used to test advances in instrumentation. Recent advances in magnet technology (up to 18.8 T = 800 MHz 1H) and in MAS probe technology (spinning up to 35 kHz and considerably stronger rf) and refinements of the two-dimensional, multiple quantum magic angle spinning (MQMAS) technique suggested that these developments could be profitably used to study kyanite and andalusite by solid state 27Al NMR. The benefit of being able to study kyanite both by MAS and MQMAS techniques on 400, 500, and 800 MHz spectrometers is demonstrated. The two octahedral aluminum sites with the largest (and nearly equal) e2qQ/h values give overlapping 1D MAS or 2D 3QMAS signals at all three field strengths. Nevertheless, quantitatively accurate 3Q signal intensities at 9.4 T for all four octahedral aluminum sites (with e2qQ/h values up to 10 MHz) allow more detailed analysis. Even if the 3Q signal intensities are not quantitative, their isotropic shifts provide an approach (if accurate e2qQ/h and eta values are available) other than deconvolution of the MAS spectrum for calculating deltaCS values. For andalusite, 34 kHz MAS on the 800 MHz spectrometer significantly narrows the extremely broad signal for the octahedral aluminum, and only slight difficulties are encountered in quantitating the relative amounts of AlO5 and AlO6 present. Even with e2qQ/h = 15.3 MHz, the octahedral aluminum in andalusite gives a signal in a MQMAS experiment, albeit of reduced intensity. As appropriate, we discuss some of the benefits and limitations of these advances in instrumentation and of different experimental approaches for studying non-integral spin quadrupolar nuclei in solids.

Multiple-quantum MAS NMR spectroscopy of spin-3/2 quadrupolar spin systems using shaped pulses

An investigation of the effect of shaping the pulses in multiple-quantum magic-angle nuclear magnetic resonance experiments was carried out on polycrystalline samples containing spin-32 quadrupolar nuclear spins. Both theoretical analysis and numerical simulations show that there exist types of shaped pulses that are more advantageous than the usual rectangular pulses in exciting multiple-quantum coherences and converting these into single-quantum coherences or zero-quantum coherences (in z-filtering cases). The sensitivities can be enhanced without loss of resolution or increasing the RF offset dependences. Moreover, properly shaped pulses can moderate the requirements on the RF power and sample spinning speeds. Especially important for application purposes is the finding that lattice site quantification can also be improved by the use of certain shaped pulses.

Analysis of the anisotropic dimension in the RIACT (II) multiple quantum MAS NMR experiment for I = 3/2 nuclei

Numerical simulations of the anisotropic dimension of the Rotation-Induced Adiabatic Coherence Transfer (RIACT) MQ experiment have been performed as a function of the asymmetry parameter, eta, for different spacings between the triple quantum (3Q) excitation and 3Q to single quantum (1Q) reconversion pulses. Large distortions of the spectra are observed, in comparison to the spectra obtained with 1D MAS NMR methods. The method is very sensitive to the relative orientation of the quadrupolar tensor and rotor axis, and signal can only be obtained from a maximum of 60% of the powder. The intensity varies with the spacing between the two pulses, t1, reaching a minimum of 30% when t1 is either a multiple of a full rotor period (n tau(r)) or for (n + 1/2) rotor periods, for pulse lengths (tau1SL) of a quarter of a rotor period. The maximum of 60% is obtained when t1 = n tau(r) - tau1SL. Experimental spectra were acquired for anhydrous Na2HPO4. Good fits were obtained between the experimental and simulated spectra, even for the non-rotor synchronized experiment, by choosing fixed values of t1. The simulations allowed the quadrupole coupling constants and asymmetry parameters to be extracted from the experimental data.

Efficient Time Propagation Technique for MAS NMR Simulation: Application to Quadrupolar Nuclei

The quantum mechanical Floquet theory is investigated in order to derive an efficient way of performing numerical calculations of the dynamics of nuclear spin systems in MAS NMR experiments. Here, we take advantage of time domain integration of the quantum evolution over one period as proposed by Eden et al. (1). But a full investigation of the propagator U(t, t0), and especially its dependence with respect to t and t0 within a formalized approach, leads to further simplifications and to a substantial reduction in computation time when performing powder averaging for any complex sequence. Such an approximation is suitable for quadrupolar nuclei (I > 1/2) and can be applied to the simulation of the RIACT (rotational induced adiabatic coherence transfer) phenomenon that occurs under special experimental conditions in spin locking experiments (2-4). The present method is also compared to the usual infinite dimensional Floquet space approach (5, 6), which is shown to be rather inefficient. As far as we know, it has never been reported for quadrupolar nuclei with I >/= 3/2 in spin locking experiments. The method can also be easily extended to other areas of spectroscopy. Copyright 1998 Academic Press.

The effect of RF power and spinning speed on MQMAS NMR

It is known that the patterns of spinning sidebands observed in the multiple-quantum dimension of MQMAS spectra are often significantly wider than expected from the anisotropies of relevant interactions. It has been recently shown by others that these sidebands are generated due to the rotor-driven reorientations that the quadrupole tensors of the crystallites undergo during the evolution period between the multiple- and single-quantum conversion processes. We present an experimental and theoretical study of the effects of the spinning speed nuR and RF field strength nuRF on the development of these sideband patterns. The theoretical analysis relies upon numerical simulations and includes propagation of the density matrix during the entire MQMAS experiment. The possibility of additional rotational encoding during the RF pulses is discussed. Both the theoretical and experimental results show the benefits of using the highest available nuR and nuRF. Copyright 1998 Academic Press.

Triple, quintuple and higher order multiple quantum MAS NMR of quadrupolar nuclei

The optimization of the coherence transfers involved in five, seven and nine-quantum versions of the recently discovered MQMAS technique, is analysed numerically. Data reported in this paper may serve as starting parameters for the experiment set up. An analysis of the intensity and resolution given by each type of experiment is performed, which confirms the need to use very high rf fields for MQ transfers. It follows that five-quantum is achievable rather easily but the use of seven and nine-quantum MAS experiments becomes increasingly difficult due to the demand for high rf power and decreasing sensitivity. The advantages of using the z-filter MQMAS method with respect to a two-pulse sequence are analysed. The method for qualitatively and quantitatively interpret the MQMAS spectra is described. The nature of the spinning side bands along the multiple quantum dimension is explained. It is shown that the rotor synchronization can be conveniently used to eliminate these side bands, but only for 3QMAS experiments. The use of the multiple-quantum method in combination with static samples and VAS, DAS and DOR techniques is finally discussed.