Comparison of through-space homonuclear correlations between quadrupolar nuclei in solids

Various two-dimensional (2D) homonuclear correlation experiments have been proposed to observe proximities between identical half-integer spin quadrupolar nuclei in solids. These experiments select either the single- or double-quantum coherences during the indirect evolution period, t₁. We compare here the efficiency and the robustness of the 2D double-quantum to single-quantum (DQ-SQ) and SQ-SQ homonuclear correlations for two half-integer spin quadrupolar isotopes subject to small chemical shift anisotropy (CSA): ¹¹B with a nuclear spin I = 3/2 and ²⁷Al with I = 5/2. Such a comparison is performed using experiments on two model samples: Li₂B₄O₇ for ¹¹B and AlPO₄-14 for ²⁷Al. For both isotopes, the DQ-SQ homonuclear correlations are recommended since they allow probing the proximities between nuclei with close or identical frequencies. In the case of small or moderate isotropic chemical shift differences (e.g. ¹¹B) the [SR2₂¹] or [BR2₂¹] bracketed DQ-SQ recoupling schemes are recommended; whereas it is the BR2₂¹ un-bracketed one otherwise (e.g. ²⁷Al).

Ultrafast Magic Angle Spinning Solid-State NMR Spectroscopy: Advances in Methodology and Applications

Solid-state NMR spectroscopy is one of the most commonly used techniques to study the atomic-resolution structure and dynamics of various chemical, biological, material, and pharmaceutical systems spanning multiple forms, including crystalline, liquid crystalline, fibrous, and amorphous states. Despite the unique advantages of solid-state NMR spectroscopy, its poor spectral resolution and sensitivity have severely limited the scope of this technique. Fortunately, the recent developments in probe technology that mechanically rotate the sample fast (100 kHz and above) to obtain "solution-like" NMR spectra of solids with higher resolution and sensitivity have opened numerous avenues for the development of novel NMR techniques and their applications to study a plethora of solids including globular and membrane-associated proteins, self-assembled protein aggregates such as amyloid fibers, RNA, viral assemblies, polymorphic pharmaceuticals, metal-organic framework, bone materials, and inorganic materials. While the ultrafast-MAS continues to be developed, the minute sample quantity and radio frequency requirements, shorter recycle delays enabling fast data acquisition, the feasibility of employing proton detection, enhancement in proton spectral resolution and polarization transfer efficiency, and high sensitivity per unit sample are some of the remarkable benefits of the ultrafast-MAS technology as demonstrated by the reported studies in the literature. Although the very low sample volume and very high RF power could be limitations for some of the systems, the advantages have spurred solid-state NMR investigation into increasingly complex biological and material systems. As ultrafast-MAS NMR techniques are increasingly used in multidisciplinary research areas, further development of instrumentation, probes, and advanced methods are pursued in parallel to overcome the limitations and challenges for widespread applications. This review article is focused on providing timely comprehensive coverage of the major developments on instrumentation, theory, techniques, applications, limitations, and future scope of ultrafast-MAS technology.

On the use of radio-frequency offsets for improving double-quantum homonuclear dipolar recoupling of half-integer-spin quadrupolar nuclei

Detecting proximities between nuclei is crucial for atomic-scale structure determination with nuclear magnetic resonance (NMR) spectroscopy. Different from spin-1/2 nuclei, the methodology for quadrupolar nuclei is limited for solids due to the complex spin dynamics under simultaneous magic-angle spinning (MAS) and radio-frequency irradiation. Herein, the performances of several homonuclear rotary recoupling (HORROR)-based homonuclear dipolar recoupling sequences are evaluated for ²⁷ Al (spin-5/2). It is shown numerically and experimentally on mesoporous alumina that BR 2 2 1 outperforms the supercycled S₃ sequence and its pure double-quantum (DQ) (bracketed) version, [S₃ ], both in terms of DQ transfer efficiency and bandwidth. This result is surprising since the S₃ sequence is among the best low-power recoupling schemes for spin-1/2. The superiority of BR 2 2 1 is thoroughly explained, and the crucial role of radio-frequency offsets during its spin dynamics is highlighted. The analytical approximation of BR 2 2 1 , derived in an offset-toggling frame, clarifies the interplay between offset and DQ efficiency, namely, the benefits of off-resonance irradiation and the trough in DQ efficiency for BR 2 2 1 when the irradiation is central between two resonances, both for spin-1/2 and half-integer-spin quadrupolar nuclei. Additionally, density matrix propagations show that the BR 2 2 1 sequence, applied to quadrupolar nuclei subject to quadrupolar interaction much larger than radio-frequency frequency field, can create single- and multiple-quantum coherences for near on-resonance irradiation. This significantly perturbs the creation of DQ coherences between central transitions of neighboring quadrupolar nuclei. This effect explains the DQ efficiency trough for near on-resonance irradiation, in the case of both cross-correlation and autocorrelation peaks. Overall, this work aids experimental acquisition of homonuclear dipolar correlation spectra of half-integer-spin quadrupolar nuclei and provides theoretical insights towards improving recoupling schemes at high magnetic field and fast MAS.

Probing Medium-Range Order in Oxide Glasses at High Pressure

Densification in glassy networks has traditionally been described in terms of short-range structures, such as how atoms are coordinated and how the coordination polyhedron is linked in the second coordination environment. While changes in medium-range structures beyond the second coordination shells may play an important role, experimental verification of the densification beyond short-range structures is among the remaining challenges in the physical sciences. Here, a correlation NMR experiment for prototypical borate glasses under compression up to 9 GPa offers insights into the pressure-induced evolution of proximity among cations on a medium-range scale. Whereas amorphous networks at ambient pressure may favor the formation of medium-range clusters consisting primarily of similar coordination species, such segregation between distinct coordination environments tends to decrease with increasing pressure, promoting a more homogeneous distribution of dissimilar structural units. Together with an increase in the average coordination number, densification of glass accompanies a preferential rearrangement toward a random distribution, which may increase the configurational entropy. The results highlight the direct link between the pressure-induced increase in medium-range disorder and the densification of glasses under extreme compression.

Assessment of new symmetry-based dipolar recoupling schemes for homonuclear magnetization exchange between quadrupolar nuclei in two-dimensional correlation MAS NMR

We provide an extensive experimental and numerical evaluation of MQ-phase (S)M supercycles with M={3,4} of three groups of symmetry-based homonuclear dipolar recoupling rf-pulse sequences, [Formula: see text] , for establishing proximities among half-integer spin quadrupolar nuclei under moderately fast magic-angle-spinning (MAS) conditions in single-quantum-single-quantum (1Q-1Q) correlation NMR experiments. The relative merits of the (S)M schemes for variations in resonance offsets and rf-amplitude errors were assessed by numerically simulated magnetization transfers in spin-3/2 pairs with variable isotropic chemical shifts and quadrupolar coupling constants. Experimental demonstrations of ²³Na (spin-3/2) NMR on Na₂MoO₄·2H₂O and ²⁷Al (spin-5/2) NMR on AlPO-CJ19 [(NH₄)₂Al₄(PO₄)₄HPO₄·H₂O] are presented at 14.1 T and 24 kHz MAS. We recommend using the (SR2₂¹)3 or (SR2₂¹)4 supercycles for samples that exhibit small chemical-shift dispersions (<3 kHz), and any (SRN_N^N/2)3 scheme with N⩾10 for larger spreads of isotropic chemical shifts. However, because the (SRN_N^N/2)3 sequences recouple heteronuclear dipolar interactions, their application to proton-bearing samples requires high-power proton decoupling during the mixing period. Alternatively, the (SR2₄¹)3 and (SR2₄¹)4 schemes may be employed in the absence of proton decoupling, but with poorer compensation to resonance-offsets and rf-amplitude errors.

Improved Magnetization Transfers among Quadrupolar Nuclei in Two-Dimensional Homonuclear Correlation NMR Experiments Applied to Inorganic Network Structures

We demonstrate that supercycles of previously introduced two-fold symmetry dipolar recoupling schemes may be utilized successfully in homonuclear correlation nuclear magnetic resonance (NMR) spectroscopy for probing proximities among half-integer spin quadrupolar nuclei in network materials undergoing magic-angle-spinning (MAS). These (SR221)M, (SR241)M, and (SR281)M recoupling sequences with M=3 and M=4 offer comparably efficient magnetization transfers in single-quantum–single-quantum (1Q–1Q) correlation NMR experiments under moderately fast MAS conditions, as demonstrated at 14.1 T and 24 kHz MAS in the contexts of 11B NMR on a Na2O–CaO–B2O3–SiO2 glass and 27Al NMR on the open framework aluminophosphate AlPO-CJ19 [(NH4)2Al4(PO4)4HPO4·H2O]. Numerically simulated magnetization transfers in spin–3/2 pairs revealed a progressively enhanced tolerance to resonance offsets and rf-amplitude errors of the recoupling pulses along the series (SR221)M< (SR241)M< (SR281)M for increasing differences in chemical shifts between the two nuclei. Nonetheless, for scenarios of a relatively minor chemical-shift dispersions (≲3 kHz), the (SR221)M supercycles perform best both experimentally and in simulations.

The Monetite Structure Probed by Advanced Solid-State NMR Experimentation at Fast Magic-Angle Spinning

We present a solid-state nuclear magnetic resonance (NMR) spectroscopy study of the local 31P and 1H environments in monetite [CaHPO4; dicalcium phosphate anhydrous (DCPA)], as well as their relative spatial proximities. Each of the three 1H NMR peaks was unambiguously assigned to its respective crystallographically unique H site of monetite, while their pairwise spatial proximities were probed by homonuclear 1H–1H double quantum–single quantum NMR experimentation under fast magic-angle spinning (MAS) of 66 kHz. We also examined the relative 1H–31P proximities among the inequivalent {P1, P2} and {H1, H2, H3} sites in monetite; the corresponding shortest internuclear 1H–31P distances accorded well with those of a previous neutron diffraction study. The NMR results from the monetite phase were also contrasted with those observed from the monetite component present in a pyrophosphate-bearing calcium phosphate cement, demonstrating that while the latter represents a disordered form of monetite, it shares all essential local features of the monetite structure.

Direct Experimental Evidence for Abundant BO4-BO4 Motifs in Borosilicate Glasses From Double-Quantum 11B NMR Spectroscopy

By using double-quantum-single-quantum correlation ¹¹B nuclear magnetic resonance (NMR) experiments and atomistic molecular dynamics (MD) simulations, we resolve the long-standing controversy of whether directly interlinked BO₄-BO₄ groups exist in the technologically ubiquitous class of alkali/alkaline-earth based borosilicate (BS) glasses. Most structural models of Na₂O-B₂O₃-SiO₂ glasses assume the absence of B^[4]-O-B^[4] linkages, whereas they have been suggested to exist in Ca-bearing BS analogs. Our results demonstrate that while B^[4]-O-B^[4] linkages are disfavored relative to their B^[3]-O-B^[3]/B^[4] counterparts, they are nevertheless abundant motifs in Na₂O-B₂O₃-SiO₂ glasses over a large composition space, while the B^[4]-O-B^[4] contents are indeed elevated in Na₂O-CaO-B₂O₃-SiO₂ glasses. We discuss the compositional and structural parameters that control the degree of B^[4]-O-B^[4] bonding.

Medium-Range Structural Organization of Phosphorus-Bearing Borosilicate Glasses Revealed by Advanced Solid-State NMR Experiments and MD Simulations: Consequences of B/Si Substitutions

The short and intermediate range structures of a large series of bioactive borophosphosilicate (BPS) glasses were probed by solid-state nuclear magnetic resonance (NMR) spectroscopy and atomistic molecular dynamics (MD) simulations. Two BPS glass series were designed by gradually substituting SiO₂ by B₂O₃ in the respective phosphosilicate base compositions 24.1Na₂O-23.3CaO-48.6SiO₂-4.0P₂O₅ ("S49") and 24.6Na₂O-26.7CaO-46.1SiO₂-2.6P₂O₅ ("S46"), the latter constituting the "45S5 Bioglass" utilized for bone grafting applications. The BPS glass networks are built by interconnected SiO₄, BO₄, and BO₃ moieties, whereas P exists mainly as orthophosphate anions, except for a minor network-associated portion involving P-O-Si and P-O-B^[4] motifs, whose populations were estimated by heteronuclear ³¹P{¹¹B} NMR experimentation. The high Na⁺/Ca²⁺ contents give fragmented glass networks with large amounts of nonbridging oxygen (NBO) anions. The MD-generated glass models reveal an increasing propensity for NBO accommodation among the network units according to BO₄ < SiO₄ < BO₃ ≪ PO₄. The BO₄/BO₃ intermixing was examined by double-quantum-single-quantum correlation ¹¹B NMR experiments, which evidenced the presence of all three BO₃-BO₃, BO₃-BO₄, and BO₄-BO₄ connectivities, with B^[3]-O-B^[4] bridges dominating. Notwithstanding that B^[4]-O-B^[4] linkages are disfavored, both NMR spectroscopy and MD simulations established their presence in these modifier-rich BPS glasses, along with non-negligible B^[4]-NBO contacts, at odds with the conventional structural view of borosilicate glasses. We discuss the relative propensities for intermixing of the Si/B/P network formers. Despite the absence of pronounced preferences for Si-O-Si bond formation, the glass models manifest subtle subnanometer-sized structural inhomogeneities, where SiO₄ tetrahedra tend to self-associate into small chain/ring motifs embedded in BO₃/BO₄-dominated domains.

27Al-27Al double-quantum single-quantum MAS NMR: Applications to the structural characterization of microporous materials

In this paper, we review and illustrate applications, reported in the literature or used in our group, of ²⁷Al-²⁷Al double-quantum single-quantum (DQ-SQ) MAS NMR experiments for the structural characterization of Al-containing microporous solids, namely zeolites, aluminophosphates and metal-organic frameworks. Information regarding the periodic frameworks or the localization of the various aluminum species in the materials are obtained from the analysis of the two-dimensional NMR spectra, which allows getting local structural details sometimes inaccessible from other characterization technique. An application of ²⁷Al-²⁷Al of the DQ-SQ experiment for the detection of aluminum pairing in zeolite is shown.

Proton Environments in Biomimetic Calcium Phosphates Formed from Mesoporous Bioactive CaO-SiO2-P2O5 Glasses in Vitro: Insights from Solid-State NMR

When exposed to body fluids, mesoporous bioactive glasses (MBGs) of the CaO-SiO₂-P₂O₅ system develop a bone-bonding surface layer that initially consists of amorphous calcium phosphate (ACP), which transforms into hydroxy-carbonate apatite (HCA) with a very similar composition as bone/dentin mineral. Information from various ¹H-based solid-state nuclear magnetic resonance (NMR) experiments was combined to elucidate the evolution of the proton speciations both at the MBG surface and within each ACP/HCA constituent of the biomimetic phosphate layer formed when each of three MBGs with distinct Ca, Si, and P contents was immersed in a simulated body fluid (SBF) for variable periods between 15 min and 30 days. Directly excited magic-angle-spinning (MAS) ¹H NMR spectra mainly reflect the MBG component, whose surface is rich in water and silanol (SiOH) moieties. Double-quantum-single-quantum correlation ¹H NMR experimentation at fast MAS revealed their interatomic proximities. The comparatively minor H species of each ACP and HCA component were probed selectively by heteronuclear ¹H-³¹P NMR experimentation. The initially prevailing ACP phase comprises H₂O and "nonapatitic" HPO₄^2-/PO₄^3- groups, whereas for prolonged MBG soaking over days, a well-progressed ACP → HCA transformation was evidenced by a dominating O¹H resonance from HCA. We show that ¹H-detected ¹H → ³¹P cross-polarization NMR is markedly more sensitive than utilizing powder X-ray diffraction or ³¹P NMR for detecting the onset of HCA formation, notably so for P-bearing (M)BGs. In relation to the long-standing controversy as to whether bone mineral comprises ACP and/or forms via an ACP precursor, we discuss a recently accepted structural core-shell picture of both synthetic and biological HCA, highlighting the close relationship between the disordered surface layer and ACP.

Low-power broadband homonuclear dipolar recoupling in MAS NMR by two-fold symmetry pulse schemes for magnetization transfers and double-quantum excitation

We provide an experimental, numerical, and high-order average Hamiltonian evaluation of an open-ended series of homonuclear dipolar recoupling sequences, SR [Formula: see text] with p=1,2,3,…. While operating at a very low radio-frequency (rf) power, corresponding to a nutation frequency of 1/2 of the magic-angle spinning (MAS) rate (ωnut=ωr/2), these recursively generated double-quantum (2Q) dipolar recoupling schemes offer a progressively improved compensation to resonance offsets and rf inhomogeneity for increasing pulse-sequence order p. The excellent recoupling robustness to these experimental obstacles, as well as to CSA, is demonstrated for 2Q filtering (2QF) experiments and for driving magnetization transfers in 2D NMR correlation spectroscopy, where the sequences may provide either double or zero quantum dipolar Hamiltonians during mixing. Experimental and numerical demonstrations, which mostly target conditions of "ultra-fast" MAS (≳50kHz) and high magnetic fields, are provided for recoupling of (13)C across a wide range of isotropic and anisotropic chemical shifts, as well as dipolar coupling constants, encompassing [2,3-(13)C2]alanine, [1,3-(13)C2]alanine, diammonium [1,4-(13)C2]fumarate, and [U-(13)C]tyrosine. When compared at equal power levels, a superior performance is observed for the SR [Formula: see text] sequences with p⩾3 relative to existing and well-established 2Q recoupling techniques. At ultra-fast MAS, proton decoupling is redundant during the homonuclear dipolar recoupling of dilute spins in organic solids, which renders the family of SR [Formula: see text] schemes the first efficient 2Q recoupling option for general applications, such as 2Q-1Q correlation NMR and high-order multiple-quantum excitation, under truly low-power rf conditions.

A 3D experiment that provides isotropic homonuclear correlations of half-integer quadrupolar nuclei

Two 3D experiments, capable of producing enhanced resolution two-spin double-quantum (DQ) homonuclear correlations for half-integer quadrupolar nuclei, are described. The first uses a split-t1 MQMAS sequence followed by a sandwiched oR(3) symmetry-based dipolar recoupling sequence to directly excite DQ coherences. In this case an isotropic single-quantum (SQ) coherence starts the homonuclear DQ excitation. In the second experiment a single strong pulse is used to create triple quantum (TQ) coherence followed by a further single pulse conversion to zero-order before a non-sandwiched oR(3) DQ sequence. The first experiment is demonstrated using (87)Rb in RbNO3, with three Rb sites in a ∼5ppm range, and the second to (11)B in caesium triborate, CsB3O5, with two three-coordinated sites separated by ∼2ppm and one four-coordinated boron site. In both cases, all sites are clearly resolved and their connections observed. The second experiment has higher sensitivity and a good signal to noise is obtained in a reasonable time despite the long T1 relaxation time of (11)B in this material.

Central-transition double-quantum sideband NMR spectroscopy of half-integer quadrupolar nuclei: estimating internuclear distances and probing clusters within multi-spin networks

Clusters within quadrupolar spin networks are probed and internuclear distances between quadrupolar nuclei are estimated by central-transition double-quantum sideband NMR spectroscopy.

Multiple-quantum spin counting in magic-angle-spinning NMR via low-power symmetry-based dipolar recoupling

By using a symmetry-based R2(8)(1)R2(8)(-1) double-quantum (2Q) dipolar recoupling sequence, we demonstrate high-order multiple-quantum coherence (MQC) excitation at fast magic-angle spinning (MAS) frequencies up to 34 kHz. This scheme combines several attractive features, such as a relatively high dipolar scaling factor, good compensation to rf-errors, isotropic and anisotropic chemical shifts, as well as an ultra-low radio-frequency (rf) power requirement. The latter translates into nutation frequencies below 30 kHz for MAS rates up to 60 kHz, thereby permitting rf application for very long excitation periods without risk of damaging the NMR probehead or sample, while the compensation to chemical shifts improves as the MAS rate increases. (31)P MQC spin counting is demonstrated on powders of calcium hydroxyapatite (Ca5(PO4)3OH) and anhydrous sodium diphosphate (Na4P2O7), from which all even coherence orders up to 30 and 14 were detected, respectively, over the respective MAS ranges of 15-24 kHz and 20-34 kHz. The amplitude distributions among the (31)P MQC orders depend on the precise nutation frequency during recoupling, despite that the highest detected order was relatively insensitive to this parameter. An observed gradual transition from a Gaussian to exponential functionality of the MQC amplitude-profile is discussed in relation to the prevailing approach to derive spin-cluster sizes by fitting the MQC amplitude-distribution to a Gaussian decay, where minor systematic deviations between the model and experimental data are frequently reported.

Estimating internuclear distances between half-integer quadrupolar nuclei by central-transition double-quantum sideband NMR spectroscopy

We demonstrate the estimation of homonuclear dipolar couplings, and thereby internuclear distances, between half-integer spin quadrupolar nuclei by central-transition (CT) double-quantum (2Q) sideband nuclear magnetic resonance (NMR) spectroscopy. It is shown that the rotor-encoded sideband amplitudes from CT 2Q coherences in the indirect dimension of the two-dimensional NMR spectrum are sensitive probes of the magnitude of the homonuclear dipolar coupling, but are significantly less affected by other NMR parameters such as the magnitudes and orientations of the electric field gradient tensors. Experimental results of employing the [Formula: see text] recoupling sequence to the 11B spin pair of bis(catecholato)diboron resulted in an estimation of the internuclear B–B distance as (169.6 ± 3) pm, i.e., with a relative uncertainty of ±2%, and in excellent agreement with the distance of 167.8 pm determined by single-crystal X-ray diffraction.

Probing quadrupolar nuclei by solid-state NMR spectroscopy: recent advances

Solid-state nuclear magnetic resonance (NMR) of quadrupolar nuclei has recently undergone remarkable development of capabilities for obtaining structural and dynamic information at the molecular level. This review summarizes the key achievements attained during the last couple of decades in solid-state NMR of both integer spin and half-integer spin quadrupolar nuclei. We provide a concise description of the first- and second-order quadrupolar interactions, and their effect on the static and magic angle spinning (MAS) spectra. Methods are explained for efficient excitation of single- and multiple-quantum coherences, and acquisition of spectra under low- and high-resolution conditions. Most of all, we present a coherent, comparative description of the high-resolution methods for half-integer quadrupolar nuclei, including double rotation (DOR), dynamic angle spinning (DAS), multiple-quantum magic angle spinning (MQMAS), and satellite transition magic angle spinning (STMAS). Also highlighted are methods for processing and analysis of the spectra. Finally, we review methods for probing the heteronuclear and homonuclear correlations between the quadrupolar nuclei and their quadrupolar or spin-1/2 neighbors.

Recent technique developments and applications of solid state NMR in characterising inorganic materials

A broad overview is given of some key recent developments in solid state NMR techniques that have driven enhanced applications to inorganic materials science. Reference is made to advances in hardware, pulse sequences and associated computational methods (e.g. first principles calculations, spectral simulation), along with their combination to provide more information about solid phases. The resulting methodology has allowed more nuclei to be observed and more structural information to be extracted. Cross referencing between experimental parameters and their calculation from the structure has given an added dimension to NMR as a characterisation probe of materials. Emphasis is placed on the progress made in the last decade especially from those nuclei that were little studied previously. The general points about technique development and the increased range of nuclei observed are illustrated through some specific exemplars from inorganic materials science.

Two-dimensional MAS NMR correlation protocols involving double-quantum filtering of quadrupolar spin-pairs

Three two-dimensional (2D) NMR homonuclear correlation techniques invoking double-quantum (2Q) filtration of the central transitions of half-integer spins are evaluated numerically and experimentally. They correlate directly detected single-quantum (1Q) coherences in the t(2) domain with either of 1Q, two-spin 2Q or single-spin multiple-quantum coherence-evolutions in the indirect (t(1)) dimension. We employ experimental (23)Na and (27)Al NMR on sodium sulfite and the natural mineral sillimanite (SiAl(2)O(5)), in conjunction with simulated 2D spectra from pairs of dipolar-recoupled spins-3/2 and 5/2 at different external magnetic fields, to compare the correlation strategies from the viewpoints of 2D spectral resolution, signal sensitivity, implementational aspects and their relative merits for establishing internuclear proximities and quadrupolar tensor orientations.

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 R2(2)(1) 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 R2(2)(1) sequence is used without pi/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 (27)Al NMR experiments on the aluminophosphates berlinite, VPI5, AlPO(4)-14, and AlPO(4)-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 (27)Al sites exceeds 10 kHz.

Supercycled symmetry-based double-quantum dipolar recoupling of quadrupolar spins in MAS NMR: I. Theory

Using average Hamiltonian (AH) theory, we analyze recently introduced homonuclear dipolar recoupling pulse sequences for exciting central-transition double-quantum coherences (2QC) between half-integer spin quadrupolar nuclei undergoing magic-angle-spinning. Several previously observed differences among the recoupling schemes concerning their compensation to resonance offsets and radio-frequency (rf) inhomogeneity may qualitatively be rationalized by an AH analysis up to third perturbation order, despite its omission of first-order quadrupolar interactions. General aspects of the engineering of 2Q-recoupling pulse sequences applicable to half-integer spins are discussed, emphasizing the improvements offered from a diversity of supercycles providing enhanced suppression of undesirable AH cross-terms between resonance offsets and rf amplitude errors.