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.     

Comparison of high-resolution solid-state NMR MQMAS and STMAS methods for half-integer quadrupolar nuclei

Several different amplitude-modulated two-dimensional high-resolution methods, based on MQMAS and STMAS, are compared. They include 3QMAS, 5QMAS, DQ-STMAS, and DQF-STMAS experiments. A new method, called t1-split-STMAS, is also proposed for spin-3/2 nuclei. The comparison is performed in terms of isotropic resolution and spectral-width, efficiency, and sensitivity to magic-angle offset and spinning speed fluctuations.     

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.     

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.     

High-resolution NMR of quadrupolar nuclei using mixed multiple-quantum coherences

A multiple-quantum magic angle spinning (MQMAS) NMR experiment of quadrupolar nuclei is demonstrated, which uses two different multiple quantum coherences in t(1) to refocus the quadrupolar broadening. This experiment has the potential of achieving improved resolution over current techniques.     

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.     

Homogeneous broadenings in 2D solid-state NMR of half-integer quadrupolar nuclei

The question of the homogeneous broadening that occurs in 2D solid-state NMR experiments is examined. This homogeneous broadening is mathematically introduced in a simple way, versus the irreversible decay rates related to the coherences that are involved during t1 and t2. We give the pulse sequences and coherence transfer pathways that are used to measure these decay rates. On AlPO4 berlinite, we have measured the 27Al echo-type relaxation times of the central and satellite transitions on 1Q levels, so that of coherences that are situated on 2Q, 3Q, and 5Q levels. We compare the broadenings that can be deduced from these relaxation times to those directly observed on the isotropic projection of berlinite with multiple-quantum magic-angle spinning (MAS), or satellite-transition MAS. We show that the choice of the high-resolution method, should be done according to the spin value and the corresponding homogeneous broadening.     

Polarization of quadrupolar nuclei

A method of obtaining high polarization and pure spin states of impurity nuclei with a moderately strong quadrupole interaction in solid diamagnetic hosts whose nuclei have spin 1/2, a large g factor (like ¹H and ¹⁹F), and a high degree of polarization is proposed. The method employs cross-relaxation transitions of the impurity nuclei with the host spins (with adiabatic variation of the external magnetic field) and simple radio-frequency pulses that invert the host nuclei or give rise to two-spin resonance of the host and impurity nuclei. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 7, 539–543 (10 October 1998)     

Single- and multiple-quantum cross-polarization in NMR of quadrupolar nuclei in static samples

Cross-polarization from a spin I=1/2 nucleus (e.g., ¹H) to a spin S = 3/2 nucleus (e.g., ²³Na) or a spin S = 5/2 nucleus (e.g., ²⁷A1 or ⁿO) in static powder samples is investigated. The results of conventional (single-quantum), three-quantum, and five-quantum cross-polarization experiments are presented and discussed. Based on a generalization of an existing theory of cross-polarization to quadrupolar nuclei, computer simulations are used to model the intensity and lineshape variations observed in cross-polarized NMR spectra as a function of the radio-frequency field strengths of the two simultaneous spin-locking pulses. These intensity and lineshape variations can also be understood in terms of the spin S = 3/2 or 5/2 nutation rates determined from experimental quadrupolar nutation spectra. The results of this study are intended as a preliminary step towards understanding single- and multiple-quantum cross-polarization to quadrupolar nuclei under MAS conditions and the application of these techniques to the MQMAS NMR experiment.     

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 t₁ period while STs are detected during t₂. 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 t₂, it is possible to over-sample the data and then to process them to suppress the CT–CT correlation resonance.     

Efficient triple-quantum excitation in modified RIACT MQMAS NMR for I=3/2 nuclei

A new approach involving the creation of triple-quantum (TQ) coherences from both TQ and central transitions (CT) is investigated, in order to enhance the efficiency of triple-quantum excitation for I=3/2 nuclei. The RIACT excitation scheme, a soft pi/2 and hard spin-locking pulse, is shown to induce both adiabatic coherence transfer between CT and TQ coherences and TQ nutation. By combining the RIACT scheme with the presaturation of the satellite transitions, a significant improvement in the TQ excitation can be achieved mainly through enhanced CT polarization via the RIACT mechanism, in particular for nuclei with moderate to large quadrupole coupling constants (> or = 2.0 MHz). There also exists a nontrivial contribution from the TQ transition, which depends on the size of the quadrupole interaction.     

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 e²qQ/h (<2 MHz) and high radio-frequency powers. We present a simple shaped RIACT pulse consisting of a truncated sine wave (spanning 0–0.8π) 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 ²³Na tend to be small.     

SCAM-STMAS: satellite-transition MAS NMR of quadrupolar nuclei with self-compensation for magic-angle misset

Several methods are available for the acquisition of high-resolution solid-state NMR spectra of quadrupolar nuclei with half-integer spin quantum number. Satellite-transition MAS (STMAS) offers an approach that employs only conventional MAS hardware and can yield substantial signal enhancements over the widely used multiple-quantum MAS (MQMAS) experiment. However, the presence of the first-order quadrupolar interaction in the satellite transitions imposes the requirement of a high degree of accuracy in the setting of the magic angle on the NMR probehead. The first-order quadrupolar interaction is only fully removed if the sample spinning angle, chi, equals cos(-1)(1/3) exactly and rotor synchronization is performed. The required level of accuracy is difficult to achieve experimentally, particularly when the quadrupolar interaction is large. If the magic angle is not set correctly, the first-order splitting is reintroduced and the spectral resolution is severely compromised. Recently, we have demonstrated a novel STMAS method (SCAM-STMAS) that is self-compensated for angle missets of up to +/-1 degrees via coherence transfer between the two different satellite transitions ST(+)(m(I)=+3/2<-->+1/2) and ST(-)(m(I)=-1/2<-->-3/2) midway through the t(1) period. In this work we describe in more detail the implementation of SCAM-STMAS and demonstrate its wider utility through 23Na (I=3/2), 87 Rb (I=3/2), 27 Al (I=5/2), and 59 Co (I=7/2) NMR. We discuss linewidths in SCAM-STMAS and the limits over which angle-misset compensation is achieved and we demonstrate that SCAM-STMAS is more tolerant of temporary spinning rate fluctuations than STMAS, resulting in less "t(1) noise" in the two-dimensional spectrum. In addition, alternative correlation experiments, for example involving the use of double-quantum coherences, that similarly display self-compensation for angle misset are investigated. The use of SCAM-STMAS is also considered in systems where other high-order interactions, such as third-order quadrupolar effects or second-order quadrupole-CSA cross-terms, are present. Finally, we show that the sensitivity of the experiment can be improved through the use of amplitude-modulated pulses.     

Ensemble of single quadrupolar nuclei in rotating solids: sidebands in NMR spectrum

A novel way is proposed to describe the evolution of nuclear magnetic polarization and the induced NMR spectrum. In this method, the effect of a high-intensity external static magnetic field and the effects of proper Hamiltonian left over interaction components, which commute with the first, are taken into account simultaneously and equivalently. The method suits any concrete NMR problem. This brings forth the really existing details in the registered spectra, evoked by Hamiltonian secular terms, which may be otherwise smoothed due to approximate treatment of the effects of the secular terms. Complete analytical expressions are obtained describing the NMR spectra including the rotational sideband sets of single quadrupolar nuclei in rotating 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.     

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.