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.     

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.     

Sensitivity enhancement of the central-transition signal of half-integer spin quadrupolar nuclei in solid-state NMR: features of multiple fast amplitude-modulated pulse transfer

Sensitivity enhancement of solid-state NMR spectrum of half-integer spin quadrupolar nuclei under both magic-angle spinning (MAS) and static cases has been demonstrated by transferring polarisation associated with satellite transitions to the central m=-1/2-->1/2 transition with suitably modulated radio-frequency pulse schemes. It has been shown that after the application of such enhancement schemes, there still remains polarisation in the satellite transitions that can be transferred to the central transition. This polarisation is available without having to wait for the spin system to return to thermal equilibrium. We demonstrate here the additional sensitivity enhancement obtained by making use of this remaining polarisation with fast amplitude-modulated (FAM) pulse schemes under both MAS and static conditions on a spin-3/2 and a spin-5/2 system. Considerable signal enhancement is obtained with the application of the multiple FAM sequence, denoted as m-FAM. We also report here some of the salient features of these multiple FAM sequences with respect to the nutation frequency of the pulses and the spinning frequency.     

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.     

A practical comparison of MQMAS techniques

A systematic experimental evaluation of several approaches to multiple-quantum MAS NMR was performed for spin-5/2 nuclei using (27)Al NMR of the aluminosilicate andalusite and the porous aluminum phosphate AlPO(4)-14 as model. Experiments were conducted in the fields of 9.4 and 17.6T using magic-angle spinning frequencies up to 30kHz and rf-field strengths of 250 and 120kHz. Numerical SIMPSON optimizations of the NMR parameters were performed alongside the experimental evaluations. Both theory and experiment show that the optimization is most critical for the species in the sample that have the largest quadrupolar coupling constant. For 5QMAS experiments it could be confirmed that the highest available rf-field strength and rotation frequency are favorable for the efficiency of the experiments. For 3QMAS experiments of sites with moderate quadrupolar coupling constants optimum results were obtained at less stringent conditions. The comparison of a FAM II-modification and DFS gave the expected improvement by a factor of about two with respect to a rectangular pulse. No significant difference between these techniques concerning the signal-to-noise ratios was obtained. An actual improvement of the isotropic resolution by a factor of about two was obtained going from 3QMAS to 5QMAS. In addition the resolution of the spectra increases by a factor of about two going from 9.4 to 17.6T.     

Application of fast amplitude-modulated pulse trains for signal enhancement in static and magic-angle-spinning 47,49Ti-NMR spectra

It is demonstrated that the use of fast amplitude-modulated RF pulse trains with constant (FAM-I) and incremented pulse durations (SW-FAM) leads to considerable sensitivity enhancement for the central-transition signal (via spin population transfer from the satellite transitions) for solid-state NMR spectra of titanium, 47Ti (I = [Formula: see text] and 49Ti (I = [Formula: see text]. For the magic-angle spinning spectra of TiO2 and BaTiO3, the intensity of the 49Ti central-transition line was more than doubled compared to simple Hahn-echo acquisition, while for the static case, enhancement factors of 1.6 (TiO2) and 1.8 (BaTiO3) were obtained. No lineshape distortions are observed in either MAS or static spectra of both compounds. Employment of the FAM and SW-FAM sequences should be useful in the routine acquisition of 47,49Ti spectra, as the NMR signal can be detected much faster.     

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.     

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.     

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.     

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.     

Triple-quantum dynamics in multiple-spin systems undergoing magic-angle spinning: application to 13C homonuclear correlation spectroscopy

We analyze the multiple-quantum dynamics governed by a new homonuclear recoupling strategy effecting an average dipolar Hamiltonian comprising three-spin triple-quantum operators (e.g., S(p)+S(q)+S(r)+) under magic-angle spinning conditions. Analytical expressions are presented for polarization transfer processes in systems of three and four coupled spins-1/2 subject to triple-quantum filtration (3QF), and high-order multiple-quantum excitation is investigated numerically in moderately large clusters, comprising up to seven spins. This recoupling approach gives highly efficient excitation of triple-quantum coherences: ideally, up to 67% of the initial polarization may be recovered by 3QF in three-spin systems in polycrystalline powders. Two homonuclear 2D correlation strategies are demonstrated experimentally on powders of uniformly 13C-labeled alanine and tyrosine: the first correlates the single-quantum spectrum in the first dimension with the corresponding 3QF spectrum along the other. The second protocol correlates triple-quantum coherences with their corresponding single-quantum coherences within triplets of coupled spins.     

Methylene spectral editing in solid-state 13C NMR by three-spin coherence selection

A robust new solid-state nuclear magnetic resonance (NMR) method for selecting CH2 signals in magic-angle spinning (MAS) 13C NMR spectra is presented. Heteronuclear dipolar evolution for a duration of 0.043 ms, under MREV-8 homonuclear proton decoupling, converts 13C magnetization of CH2 groups into two- and three-spin coherences. The CH2 selection in the SIJ (C H H) spin system is based on the three-spin coherence S(x)I(z)J(z), which is distinguished from 13C magnetization (S(x)) by a 1H 0 degrees/90 degrees pulse consisting of two 45 degrees pulses. The two-spin coherences of the type S(y)I(z) are removed by a 13C 90 degrees x-pulse. The three-spin coherence is reconverted into magnetization during the remainder of the rotation period, still under MREV-8 decoupling. The required elimination of 13C chemical-shift precession is achieved by a prefocusing 180 degrees pulse bracketed by two rotation periods. The selection of the desired three-spin coherence has an efficiency of 13% theoretically and of 8% experimentally relative to the standard CP/MAS spectrum. However, long-range couplings also produce some three-spin coherences of methine (CH) carbons. Therefore, the length of the 13C pulse flipping the two-spin coherences is increased by 12% to slightly invert the CH signals arising from two-spin coherences and thus cancel the signal from long-range three-spin coherences. The signal intensity in this cleaner spectrum is 6% relative to the regular CP/TOSS spectrum. The only residual signal is from methyl groups, which are suppressed at least sixfold relative to the CH2 peaks. The experiment is demonstrated on cholesteryl acetate and applied to two humic acids.     

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.     

Sensitivity enhancement of NMR spectra of half-integer spin quadrupolar nuclei in solids using hyperbolic secant pulses

The experimental factors influencing the enhancements achievable for the central NMR transition, m(I)=1/2-->m(I)=-1/2, of spin-3/2 and spin-5/2 nuclei in the solid state using hyperbolic secant, HS, pulses for population transfer are investigated. In the case of powder samples spinning at the magic angle, it is found that the spinning frequency, the bandwidth and the frequency offset of the HS pulse play a crucial role in determining the maximum enhancements. Specifically, the bandwidth must be set to the spinning frequency for maximum signal enhancements. The (87)Rb NMR enhancement obtained for RbClO(4) using HS pulses was relatively insensitive to the magic angle spinning frequency; however, in the case of Al(acac)(3), the (27)Al enhancement increased with MAS frequency. In order to obtain an adiabatic HS sweep, one should optimize the rf field for a given pulse duration or optimize the pulse duration for a given rf field.     

Both experimental and theoretical investigations of solid-state 17O NMR for L-valine and L-isoleucine

We have presented an experimental investigation of the carboxyl oxygen NMR parameters for four distinct sites in l-valine and l-isoleucine. The carboxyl (17)O quadrupolar coupling constant, C(Q), and isotropic chemical shift, delta(iso), for these compounds are obtained by analyzing two-dimensional (17)O multiple-quantum magic-angle spinning (MQMAS) and/or 1D MAS spectra. The values of C(Q) and delta(iso) found to be in the range of 7.00-7.85 MHz, and 264-314 ppm, respectively. Extensive quantum chemical calculations at the density functional levels have been performed for a full cluster of l-valine molecules and a few theoretical models. The calculated results indicated that there was a correlation between the (17)O NMR parameters and C-O bond lengths, which was helpful for the spectral assignment. They also demonstrated that the torsion angle of l-valine plays an important role in determining the magnitudes of (17)O NMR parameters.     

Analytical solutions to several magic-angle spinning NMR experiments

Using the Anderson–Weiss (AW) formalism, analytical expressions of the NMR signal are obtained for the following magic-angle spinning (MAS) experiments: total suppression of sidebands (TOSS); phase adjusted spinning sidebands (PASS); rotational-echo double-resonance (REDOR); rotor-encoded REDOR (REREDOR); cross-polarization magic-angle spinning (CPMAS); exchange induced sidebands (EIS); one-dimensional exchange spectroscopy by sideband alternation (ODESSA); time-reverse ODESSA (trODESSA); centerband-only detection of exchange (CODEX). In order to test the validity of the AW approach, the Gaussian powder approximation is compared with exact powder calculations. A quantitative study of the effect of molecular dynamics on the efficiency of the TOSS and REDOR pulse sequences is then presented.     

Strategies for extracting NMR parameters from 23Na MAS, DOR and MQMAS spectra. A case study for Na4P2O7

The 23Na magic-angle spinning (MAS), double rotation (DOR) and multiple-quantum magic-angle spinning (MQMAS) NMR spectra of anhydrous sodium pyrophosphate, Na4P2O7, measured at five different Larmor frequencies (nuL) ranging from 105.8 MHz (corresponding to 400 MHz 1H frequency) to 211.6 MHz (800 MHz) are analysed and the complete set of NMR parameters (C(qcc), etaQ and delta(iso)) of the four crystallographically inequivalent sodium sites were determined with high accuracy. Different approaches of spectra evaluation are discussed and their results are compared. The most reliable results are obtained from a combined evaluation of five DOR and three MQMAS spectra but also from two DOR and one MAS spectra or even from a single MQMAS spectrum all data can be derived. It is shown that Na4P2O7 may serve as a useful reference material for experimental set-up and reliability tests of the various NMR experiments.     

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.     

Solid-state NMR spectroscopy under periodic modulation by fast magic-angle sample spinning and pulses: a review

Fast magic-angle spinning (MAS) holds promise for new approaches to pulsed high-resolution NMR in solids where homogeneous interactions dominate. Prerequisite for developing new pulse methods is the understanding of signal encoding by spin interactions under MAS conditions and of interferences between MAS and pulses. This review discusses corresponding strategies and techniques in a coherent way with particular concentration on homonuclear decoupling techniques for line-narrowing in solids.     

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.