Multiple-quantum magic-angle spinning NMR with cross-polarization: Spectral editing of high-resolution spectra of quadrupolar nuclei

An experiment is presented that combines the multiple-quantum magic-angle spinning (MQMAS) technique with cross-polarization (CP). As a preliminary test of this new method, we measured and compared the ²⁷Al 3QMAS and ¹⁹F → ²⁷A1 CP 3QMAS spectra of a fluorinated AlPO₄ aluminophosphate. Complete discrimination between the fluorinated and nonfluorinated Al sites was easily achieved, which demonstrates the usefulness of CP MQMAS for spectral editing. Future applications of this experiment will include other spin pairs and heteronuclear correlation NMR spectroscopy.     

MAS NMR spectra of quadrupolar nuclei in disordered solids: the Czjzek model

Structural disorder at the scale of two to three atomic positions around the probe nucleus results in variations of the EFG and thus in a distribution of the quadrupolar interaction. This distribution is at the origin of the lineshape tailing toward high fields which is often observed in the MAS NMR spectra of quadrupolar nuclei in disordered solids. The Czjzek model provides an analytical expression for the joint distribution of the NMR quadrupolar parameters upsilon(Q) and eta from which a lineshape can be predicted. This model is derived from the Central Limit Theorem and the statistical isotropy inherent to disorder. It is thus applicable to a wide range of materials as we have illustrated for 27Al spectra on selected examples of glasses (slag), spinels (alumina), and hydrates (cement aluminum hydrates). In particular, when relevant, the use of the Czjzek model allows a quantitative decomposition of the spectra and an accurate extraction of the second moment of the quadrupolar product. In this respect, it is important to realize that only rotational invariants such as the quadrupolar product can make sense to describe the quadrupolar interaction in disordered solids.     

Spectral editing in solid-state MAS NMR of quadrupolar nuclei using selective satellite inversion

A sensitivity enhancement method based on selective adiabatic inversion of a satellite transition has been employed in a (pi/2)CT-(pi)ST1-(pi/2)CT spectral editing sequence to both enhance and resolve multisite NMR spectra of quadrupolar nuclei. In addition to a total enhancement of 2.5 times for spin 3/2 nuclei, enhancements up to 2.0 times is reported for the edited sites in a mixture of rubidium salts.     

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.     

Use of SPAM and FAM pulses in high-resolution MAS NMR spectroscopy of quadrupolar nuclei

The merits of SPAM and FAM pulses for enhancing the conversion of triple- to single-quantum coherences in the two-dimensional MQMAS experiment are compared using (87)Rb (spin I=3/2) and (27)Al (I=5/2) NMR of crystalline and amorphous materials. Although SPAM pulses are more easily optimized, our experiments and simulations suggest that FAM pulses yield greater signal intensity in all cases. In conclusion, we argue that, as originally suggested, SPAM and FAM pulses are best implemented in phase-modulated whole-echo MQMAS experiments and that the use of SPAM pulses to record separate echo and antiecho data sets, which are then combined, generally yields lower signal-to-noise ratios.     

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.     

Rotor-synchronized acquisition of quadrupolar satellite-transition NMR spectra: practical aspects and double-quantum filtration

The very broad resonances of quadrupolar (spin I > 1/2) nuclei are resolved by magic angle spinning (MAS) into a large number of spinning sidebands, each of which often remains anisotropically broadened. The quadrupolar interaction can be removed to a first-order approximation if the MAS NMR spectrum is acquired in a rotor-synchronized fashion, aliasing the spinning sidebands onto a centreband and thereby increasing the signal-to-noise ratio in the resulting, possibly second-order broadened, spectrum. We discuss the practical aspects of this rotor-synchronization in the direct (t(2)) time domain, demonstrating that the audiofrequency filters in the receiver section of the spectrometer have a significant impact on the precise timings needed in the experiment. We also introduce a novel double-quantum filtered rotor-synchronized experiment for half-integer spin quadrupolar (spin I = 3/2, 5/2, etc.) nuclei that makes use of central-transition-selective inversion pulses to both excite and reconvert double-quantum coherences and yields a simplified spectrum containing only the ST(1) (m(I) = +/-1/2 <--> +/-3/2) satellite-transition lineshapes. For spin I = 5/2 nuclei, such as (17)O and (27)Al, this spectrum may exhibit a significant resolution increase over the conventional central-transition spectrum.     

Powder MAS NMR lineshapes of quadrupolar nuclei in the presence of second-order quadrupole interaction

We derive a complete analytical solution for the powder magic angle spinning (MAS) nuclear magnetic resonance (NMR) lineshape in the presence of second-order quadrupole interaction, considering a radiofrequency (rf) pulse of finite width, a finite MAS frequency, and a non-zero asymmetry parameter. I_x is calculated using two approaches. The first applies time-dependent perturbation theory in the presence of the rf pulse and stationary perturbation theory (SPT) in its absence. The second is based on the Magnus expansion of the density matrix in the interaction representation during the pulse and SPT in its absence. We solve the problem in the laboratory frame using the properties of the Fourier transform and spin operators. Diagonalisation is not required. Both approaches agree well with each other under all conditions and also with the transition probability approach for the central transition. The Magnus expansion exists at all times and the effect of the non-secular terms is negligible. We describe an analytical method of averaging I_x over the Euler angles and simulate the ¹¹B MAS NMR lineshapes for crystalline and vitreous B₂O₃. A critical analysis is given of all earlier calculations of the MAS NMR lineshape.     

Two-dimensional one pulse MAS of half-integer quadrupolar nuclei

We show that the two-dimensional one pulse (TOP) representation of magic-angle spinning nuclear magnetic resonance data of half-integer quadrupolar nuclei has significant advantages over the conventional one-dimensional spectrum. The TOP spectrum, which correlates NMR frequency to spinning sideband order, provides a rapid determination of the number of sites as well as the size of the their quadrupolar coupling. Additionally, synchronous acquisition spectra of the central and satellite transition resonances can be separated by different projections of the TOP spectrum, with higher resolution spectra often found in the satellite transitions projection. A previously perceived problem of centerband aliasing in TOP can be eliminated with an algorithm that uses larger subspectral widths and the sideband order dimension to distinguish centerbands from sidebands.     

Multiplex MQMAS NMR of quadrupolar nuclei

A multiplex phase cycling method (N. Ivchenko et al., J. Magn. Reson. 160 (2003) 52-58) has been used to record two-dimensional MQMAS spectra with a very short phase cycling. A straightforward procedure has been developed to easily process the data. Combining this Multiplex approach and the new Soft-Pulse-Adding-Mixing (SPAM) method considerably increases the signal-to-noise ratio of the conventional MQMAS experiment. The Multiplex acquisition procedure is much simpler than the echo/anti-echo method recently proposed, and has been applied with success to record (87)Rb spectra of RbNO(3) and (27)Al 3Q and 5Q MQMAS NMR of microporous aluminophosphate AlPO(4)-14.     

Correlation NMR spectroscopy involving quadrupolar nuclei

We review the recent developments proposed for integer or half-integer quadrupolar nuclei, focussing on the methods to observe them under high-resolution and to analyze their through-space and through-bond connectivities.     

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.     

New opportunities for double rotation NMR of half-integer quadrupolar nuclei

A combined approach is presented which expands the applicability of double rotation (DOR) by overcoming its most prominent disadvantages: spinning stability and sensitivity. A new design using air-bearings for the inner rotor and a computer-assisted start-up procedure allows DOR operation over in principle unlimited time at outer rotor speeds of up to 2000Hz. Sensitivity enhancement of the DOR experiment is achieved by applying amplitude-modulated adiabatic pulses such as the double frequency sweep (DFS) before pulse excitation. Repeating the DFS enhancement and signal readout several times without allowing for spin-lattice relaxation leads to sensitivity enhancements of a factor 3 for (27)Al in various minerals. As a result, it becomes possible to study low sensitivity quadrupolar nuclei and various long duration 2D measurements can be performed routinely. Spinning is adequate to suppress residual homonuclear dipolar couplings in the spectral dimension of typical quadrupolar spin systems. In 2D-exchange spectroscopy, however, homonuclear correlation can still be established through dipolar-quadrupolar cross-terms.     

Signal enhancement in solid-state NMR of quadrupolar nuclei

Recent progress in the development and application of signal enhancement methods for NMR of quadrupolar nuclei in solids is presented. First, various pulse schemes for manipulating the populations of the satellite transitions in order to increase the signal of the central transition (CT) in stationary and rotating solids are evaluated (e.g., double-frequency sweeps, hyperbolic secant pulses). Second, the utility of the quadrupolar Carr–Purcell–Meiboom–Gill (QCPMG) and WURST-QCPMG pulse sequences for the rapid and efficient acquisition of particularly broad CT powder patterns is discussed. Third, less frequently used experiments involving polarization transfer from abundant nuclear spins (cross-polarization) or from unpaired electrons (dynamic nuclear polarization) are assessed in the context of recent examples. Advantages and disadvantages of particular enhancement schemes are highlighted and an outlook on possible future directions for the signal enhancement of quadrupolar nuclei in solids is offered.     

Critical factors in obtaining meaningful fast MAS NMR spectra of non-integral spin quadrupolar nuclei. A review with particular emphasis on27Al MAS NMR of catalysts and minerals

In the last decade, magic angle spinning (MAS) NMR has become an extremely important method for studying the structure of inorganic solids. Advances in NMR technology have greatly aided in understanding the structure of catalysts, minerals, clays, ceramics, glasses, etc. Obtaining meaningful MAS spectra of spin-1/2 nuclei such as²⁹Si and³¹P is relatively straightforward and well understood. In contrast, obtaining meaningful MAS spectra is far from simple with non-integral spin quadrupolar nuclei such as¹¹B (I=3/2),¹⁷O (I=5/2),²³Na (I=3/2),²⁷Al (I=5/2),⁶⁹Ga (I=3/2), and⁷¹Ga (I=3/2)?to name some of the most commonly studied nuclei. Many additional factors have to be considered. This paper will deal with these factors and the utility of very fast MAS for studying non-integral spin quadrupolar nuclei in inorganic solids.     

Multiple-quantum cross-polarization and two-dimensional MQMAS NMR of quadrupolar nuclei

Cross-polarization from (1)H to the multiple-quantum coherences of a quadrupolar nucleus is used in combination with the two-dimensional multiple-quantum magic angle spinning (MQMAS) NMR experiment in order to extract high-resolution CPMAS NMR spectra. The technique is demonstrated on (23)Na (S = 3/2), (17)O, (27)Al (both S = 5/2), and (45)Sc (S = 7/2) nuclei, showing the applicability of multiple-quantum cross-polarization to systems with differing spin quantum number, gyromagnetic ratio, and relative nuclide abundance. The utility of this two-dimensional MAS NMR experiment for spectral editing and site-specific measurement of cross-polarization intensities is demonstrated. The possibility of direct cross-polarization to higher order multiple-quantum coherences is also considered and three-, five-, and seven-quantum cross-polarized (45)Sc MAS NMR spectra are presented.