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.     

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.     

Enhanced triple-quantum excitation in 13C magic-angle spinning NMR

We describe a new method for exciting triple-quantum coherences in 13C-labelled powder samples under MAS. The proposed method combines selective double-quantum excitation with rotational resonance and frequency-selective composite pulses. The spin dynamics of this new method are described theoretically. Numerical calculations of the spin dynamics are compared to experimental results on fully 13C-labelled L-alanine. The observed triple-quantum filtering efficiency is around 10% for the most intense spectral peak. The method is also demonstrated on other fully 13C-labelled compounds, including a uniformly 13C-labelled amino acid.     

Magnetization-recovery experiments for static and MAS-NMR of I=3/2 nuclei

Multifrequency pulsed NMR experiments on quadrupole-perturbed I=3/2 spins in single crystals are shown to be useful for measuring spin-lattice relaxation parameters even for a mixture of quadrupolar plus magnetic relaxation mechanisms. Such measurements can then be related to other MAS-NMR experiments on powders. This strategy is demonstrated by studies of (71)Ga and (69)Ga (both I=3/2) spin-lattice relaxation behavior in a single-crystal (film) sample of gallium nitride, GaN, at various orientations of the axially symmetric nuclear quadrupole coupling tensor. Observation of apparent single-exponential relaxation behavior in I=3/2 saturation-recovery experiments can be misleading when individual contributing rate processes are neglected in the interpretation. The quadrupolar mechanism (dominant in this study) has both a single-quantum process (T(1Q1)) and a double-quantum process (T(1Q2)), whose time constants are not necessarily equal. Magnetic relaxation (in this study most likely arising from hyperfine couplings to unpaired delocalized electron spins in the conduction band) also contributes to a single-quantum process (T(1M)). A strategy of multifrequency irradiation with observation of satellite and/or central transitions, incorporating different initial conditions for the level populations, provides a means of obtaining these three relaxation time constants from single-crystal (71)Ga data alone. The (69)Ga results provide a further check of internal consistency, since magnetic and quadrupolar contributions to its relaxation scale in opposite directions compared to (71)Ga. For both perpendicular and parallel quadrupole coupling tensor symmetry axis orientations small but significant differences between T(1Q1) and T(1Q2) were measured, whereas for a tensor symmetry axis oriented at the magic-angle (54.74 degrees ) the values were essentially equal. Magic-angle spinning introduces a number of complications into the measurement and interpretation of the spin-lattice relaxation. Comparison of (71)Ga and (69)Ga MAS-NMR saturation-recovery curves with both central and satellite transitions completely saturated by a train of 90 degrees pulses incommensurate with the rotor period provides the simplest means of assessing the contribution from magnetic relaxation, and yields results for the quadrupolar mechanism contribution that are consistent with those obtained from the film sample.     

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.     

Calculation of pulsed NMR signal in I = 3/2 quadrupolar spin system

The rf pulse response of I=3/2 spin system experiencing first order quadrupolar splitting is studied using density matrix approach. A general expression is derived in terms of spin populations, quadrupole splitting and duration and amplitude of the rf pulse for calculating the NMR signal arising due to the centre line and satellite resonances for the situation where the impressed rf pulse excites the resonances selectively as well as non-selectively. The necessary 4×4 transformation matrix obtained analytically by diagonalyzing the Hamiltonian are used to get the expression for the centre line response. The satellite signals are obtained in the same way but by using the numerical values of the roots of the related quartics. The widths of the corresponding π/2-pulses are calculated for different initial spin populations. The variations of this pulse-width and the corresponding signal amplitude as a function of satellite splitting are studied.     

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.     

Q-shear transformation for MQMAS and STMAS NMR spectra

The multiple-quantum magic-angle spinning (MQMAS) and satellite-transition magic-angle spinning (STMAS) experiments refocus second-order quadrupolar broadening of half-integer quadrupolar spins in the form of two-dimensional experiments. Isotropic shearing is usually applied along the indirect dimension of the 2D spectra such that an isotropic projection free of anisotropic quadrupolar broadening can be obtained. An alternative shear transformation by a factor equal to the coherence level (quantum number) selected during the evolution period is proposed. Such a transformation eliminates chemical shift along the indirect dimension leaving only the second-order quadrupolar-induced shift and anisotropic broadening, and is expected to be particularly useful for disordered systems. This transformation, dubbed Q-shearing, can help avoid aliasing problems due to large chemical shift ranges and spinning sidebands. It can also be used as an intermediate step to the isotropic representation for expanding the spectral window of rotor-synchronized experiments.     

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.     

Spin-locking mechanism of spin I = 3/2 quadrupolar nuclei undergo magic angle spinning

The spin-locking mechanism of the spin I=3/2 quadrupolar nuclei under magic angle spinning (MAS) has been theoretically and experimentally investigated, and the criterion of adiabatic passage around zero-crossings of the quadrupole splitting was inferred from the time-dependent Shrödinger equation in this article. The theory, numerical simulations, and experiments conducted in this work all indicated that second-order quadrupole interaction and off-resonance play important roles in the spin-locking of the quadrupolar nuclei, and they were responsible for the great loss of the spin-locking signals. The spin-locking for a spin I=3/2 nucleus might be achieved by minimizing the effect of the second-order quadrupole interaction by using a radio frequency (RF) offset. This offset was realized by setting the RF to the opposite position of the isotropic second-order quadrupolar shift of single quantum coherences.     

Efficient double-quantum excitation in rotational resonance NMR

We present a new technique for double-quantum excitation in magic-angle-spinning solid-state NMR. The method involves (i) preparation of nonequilibrium longitudinal magnetization; (ii) mechanical excitation of zero-quantum coherence by spinning the sample at rotational resonance, and (iii) phase-coherent conversion of the zero-quantum coherence into double-quantum coherence by frequency-selective spin inversion. The double-quantum coherence is converted into observable magnetization by reversing the excitation process, followed by a pi/2 pulse. The method is technically simple, does not require strong RF fields, and is feasible at high spinning frequencies. In [(13)C(2),(15)N]-glycine, with an internuclear (13)C-(13)C distance of 0.153 nm, we achieve a double-quantum filtering efficiency of approximately 56%. In [11, 20-(13)C(2)]-all-E-retinal, with an internuclear (13)C-(13)C distance of 0.296 nm, we obtain approximately 45% double-quantum filtering efficiency.     

Satellite-transition MAS NMR of spin I = 3/2, 5/2, 7/2, and 9/2 nuclei: sensitivity,resolution, and practical implementation

The satellite-transition MAS (STMAS) experiment offers an alternative approach to established methods such as dynamic angle spinning (DAS), double rotation (DOR), and multiple-quantum MAS (MQMAS) for obtaining high-resolution NMR spectra of half-integer quadrupolar nuclei. Unlike the multiple-quantum experiment, STMAS involves two-dimensional correlation of purely single-quantum coherences; satellite transitions in t(1) (or F(1)) and the central transition in t(2) (or F(2)). To date, STMAS has primarily been demonstrated for nuclei with spin quantum numbers I = 3/2 and, to a lesser extent, I > 5/2. However, many chemically relevant nuclei possess I > 3/2, such as (17)O and (27)Al (both I = 5/2), (59)Co (I = 7/2), and (93)Nb (I = 9/2). Here, we discuss the application of STMAS to nuclei with spin quantum numbers from I = 3/2 to 9/2. First, we consider the practical implementation of the STMAS experiment using (87)Rb (I = 3/2) NMR as an example. We then extend the discussion to include nuclei with higher spin quantum numbers, demonstrating (27)Al, (45)Sc (I = 7/2), (59)Co, and (93)Nb STMAS experiments on both crystalline and amorphous samples. We also consider the possibility of experiments involving satellite transitions other than m(I) = +/- 1/2 <--> +/- 3/2 and, using (93)Nb NMR, demonstrate the correlation of all single-quantum satellite transitions up to and including m(I) = +/- 7/2 <--> +/- 9/2. The absolute chemical shift scaling factors in these experiments are discussed, as are the implications for isotropic resolution.     

Double-quantum homonuclear correlations of spin I=5/2 nuclei

The challenges associated with acquiring double-quantum homonuclear Nuclear Magnetic Resonance correlation spectra of half-integer quadrupolar nuclei are described. In these experiments the radio-frequency irradiation amplitude is necessarily weak in order to selectively excite the central transition. In this limit only one out of the 25 double-quantum coherences possible for two coupled spin I=5/2 nuclei is excited. An investigation of all the 25 two spins double quantum transitions reveals interesting effects such as a compensation of the first-order quadrupolar interaction between the two single quantum transitions involved in the double quantum coherence. In this paper a full numerical study of a hypothetical two spin I=5/2 system is used to show what happens when the RF amplitude during recoupling is increased. In principle this is advantageous, since the required double quantum coherence should build up faster, but in practice it also induces adiabatic passage transfer of population and coherence which impedes any build up. Finally an optimized rotary resonance recoupling (oR(3)) sequence is introduced in order to decrease these transfers. This sequence consists of a spin locking irradiation whose amplitude is reduced four times during one rotor period, and allows higher RF powers to be used during recoupling. The sequence is used to measure (27)Al DQ dipolar correlation spectra of Y(3)Al(5)O(12) (YAG) and gamma alumina (γAl(2)O(3)). The results prove that aluminium vacancies in gamma alumina mainly occur in the tetrahedral sites.     

CP/MAS of quadrupolar S = 3/2 nuclei.

The spin dynamics of Hartmann-Hahn cross-polarization from I = 1/2 to quadrupolar S = 3/2 nuclei is investigated. A density-matrix model applicable to cases where the quadrupole frequency vQ is much larger than the rf amplitude v1S of the S spins, predicts the time development of the spin state of an isolated I, S spin pair in static situations and in three distinct cases of magic-angle-spinning speed vR. These cases are characterized as slow, intermediate, and fast, depending on the magnitude of the parameter alpha = v1S2/vQvR relative to the intermediate value of 0.4. The model predictions are supported by numerical simulations. The polarization transfer from I to S is efficient in the limits of slow and fast sample spinning. When alpha < 1, the Hartmann-Hahn condition is shifted over once or twice vR. When the spinning rate is intermediate, poor spin-locking of the quadrupolar spins prevents the accumulation of a cross-polarization signal and, in addition, depletes the spin-locked I magnetization. Experimental CP/MAS data obtained in NaOH show that the concepts developed for isolated spin pairs are also applicable to cross-polarization in a strongly coupled multi-spin system.     

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.     

Selecting ordered environments in NMR of spin 3/2 nuclei via frequency-sweep pulses

We demonstrate that frequency-swept pulses can be used for the selective and enhanced detection of quadrupolar nuclei located in anisotropic environments. The primary driving force for this technique development is the field of sodium-MRI, where sodium signals from locally ordered environments are known to be diagnostic of cartilage defects. We demonstrate here simple one-dimensional images of model systems, in which the signals from free sodium ions are suppressed, while ordered sodium is detected via the narrow central transition signal.     

(3He, 2n) excitation functions for some light nuclei

Excitation functions have been measured for the reaction ⁹Be(³He, 2n)¹⁰C over the range $\text{E(}{}^3\text{He}\text{) = 10–41}\text{MeV}$ and for the reaction ²⁷Al(³He, 2n)²⁸P over the range $\text{E(}{}^3\text{He}\text{) = 14–41}$ MeV by detecting β-delayed γ-rays. An excitation function has also been measured for the reaction ²⁴Mg(³He, 2n)²⁵Si over the range $\text{E(}{}^3\text{He}\text{) = 21–43}\text{MeV}$ by detecting β-delayed protons.     

Solid-state single and triple-quantum 93Nb MAS NMR studies of ferroelectric Pb(Mg1/3Nb2/3)O3 and a related pyrochlore

Pb(Mg1/3Nb2/3)O3 (PMN), a well-known relaxor ferroelectric material, and a related pyrochlore phase have been studied by single- and triple-quantum 93Nb MAS NMR spectroscopy. The assignment of the NMR resonances has been attempted.