Double-quantum-filtered nuclear magnetic resonance spectroscopy applied to quadrupolar nuclei in solids

Advanced solid-state NMR spectroscopy and its applications in zeolite chemistry

Solid-state NMR spectroscopy (ssNMR) can provide details about the structure, host-guest/guest-guest interactions and dynamic behavior of materials at atomic length scales. A crucial use of ssNMR is for the characterization of zeolite catalysts that are extensively employed in industrial catalytic processes. This review aims to spotlight the recent advancements in ssNMR spectroscopy and its application to zeolite chemistry. We first review the current ssNMR methods and techniques that are relevant to characterize zeolite catalysts, including advanced multinuclear and multidimensional experiments, in situ NMR techniques and hyperpolarization methods. Of these, the methodology development on half-integer quadrupolar nuclei is emphasized, which represent about two-thirds of stable NMR-active nuclei and are widely present in catalytic materials. Subsequently, we introduce the recent progress in understanding zeolite chemistry with the aid of these ssNMR methods and techniques, with a specific focus on the investigation of zeolite framework structures, zeolite crystallization mechanisms, surface active/acidic sites, host-guest/guest-guest interactions, and catalytic reaction mechanisms.

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).

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.

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.

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.

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.

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.

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.

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.

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.

Heteronuclear dipolar recoupling of half-integer quadrupole nuclei under fast magic angle spinning

An experimental method for the heteronuclear dipolar recoupling of half-integer quadrupole nuclei is proposed. The idea is to manipulate the central transition based on the recoupling technique of spin-polarization-inversion rotary resonance. This method allows the extraction of structural parameters under fast magic-angle spinning. Its validity has been examined by the average Hamiltonian theory and numerical simulations. The initial rotational-echo dephasing arising from the dipolar evolution can be approximated by a parabolic function, from which the heteronuclear van Vleck second moment can be estimated. A factor, estimated from two-spin simulations, is required to account for the effects of the quadrupolar coupling and is rather independent of the geometry and the orders of the spin systems. Our method can facilitate the structural characterization of materials containing half-integer quadrupole nuclei under high-resolution condition. Experimental verification has been carried out on two aluminophosphate systems, namely, AlPO(4)-5 and AlPO(4)-11.

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.

Homonuclear dipolar recoupling of half-integer spin quadrupolar nuclei: techniques and applications

We review recent advances in solid state NMR methodology for recovering homonuclear dipolar interactions among half-integer quadrupolar spins undergoing sample rotation. Existing dipolar recoupling techniques are contrasted, based on (i) the form of their associated dipolar Hamiltonian, (ii) the different experimental conditions necessitating their realization and (iii) their roles as components in multi-dimensional NMR correlation spectroscopy. Various types of structural information accessible from such solid state NMR experimentation is reviewed. Promises and limitations of methodologies targeting homonuclear dipolar couplings between half-integer spins under high-resolution conditions are discussed, with particular focus on the demands set for structural investigations of crystalline as well as structurally disordered (amorphous) inorganic network materials.

Spin-locking and recoupling of homonuclear dipolar interaction between spin-3/2 nuclei under magic-angle sample spinning

Numerical simulations and experiments were used to examine the possibility of employing strong spin-lock fields for recoupling of homonuclear dipolar interactions between spin-3/2 quadrupolar nuclei and to compare it to the rotary-resonance recoupling at weak spin-lock fields. It was shown that strong spin-lock pulses under MAS conditions can lead to recoupling, provided that the electric-field gradient principal axes systems of the coupled nuclei are aligned and that their quadrupolar coupling constants are approximately the same. The phenomenon is based on the fact that strong spin-lock pulses induce adiabatic transfer of magnetization between the central-transition coherence and the triple-quantum coherence with equal periodicity as is the periodicity of the time-dependent dipolar coupling. Because of the synchronous variation of the state of the spin system and of the dipolar interaction, the effect of the latter on the central-transition coherence and on the triple-quantum coherence is not averaged out by sample rotation. The approach is, however, very sensitive to the relative orientation of the electric-field gradient principal axes systems and therefore less robust than the approach based on weak spin-lock pulses that satisfy rotary-resonance condition.

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.

Enhancing sensitivity or resolution of homonuclear correlation experiment for half-integer quadrupolar nuclei

We have recently introduced double-quantum homonuclear correlation NMR experiment for half-integer quadrupolar nuclei in solids, which was based on rotary resonance recoupling [J. Chem. Phys. 120 (2004) 2835]. In this contribution we show on two 23Na (I=3/2) containing samples, Na2SO4 and Na2HPO4, that the efficiency of the experiment can be substantially enhanced by adding rotor assisted population transfer (RAPT) and Carr-Purcell-Meiboom-Gill (CPMG) sequences to it. We also present an upgraded two-dimensional experiment, in which double- and six-quantum coherences are correlated during t1 evolution period, yielding a high-resolution isotropic spectrum along an indirectly detected dimension. The sensitivity of the upgraded experiment is, however, greatly reduced compared to the sensitivity of the original experiment, so that its application is feasible only when RAPT and CPMG can be used as well.

Double-quantum homonuclear correlation magic angle sample spinning nuclear magnetic resonance spectroscopy of dipolar-coupled quadrupolar nuclei

A double-quantum homonuclear correlation nuclear magnetic resonance experiment for dipolar-coupled half-integer quadrupolar nuclei in solids is presented. The experiment is based on rotary resonance dipolar recoupling and uses bracketed spin-lock pulses to excite double-quantum coherence and later to convert it to the zero-quantum one. A central-transition-selective pi pulse at the beginning of the t1 evolution period differentiates coherence transfer pathways of double-quantum coherences arising from coupled spins and from a single spin, so that the latter can be efficiently filtered out by phase cycling. The experiment was tested on an aluminophosphate molecular sieve AlPO4-14, a material with a variety of aluminum quadrupolar coupling constants, isotropic chemical shifts and homonuclear distances. In a two-dimensional spectrum aluminum dipolar couplings with internuclear distances between 2.9 and 5.5 A were resolved. Although the experiment requires an application of weak radio-frequency fields, frequency offsets did not affect its performance crucially.