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.     

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.     

Through-space R3-HETCOR experiments between spin-1/2 and half-integer quadrupolar nuclei in solid-state NMR

We present several new methods that allow to obtain through-space 2D HETCOR spectra between spin-1/2 and half-integer quadrupolar nuclei in the solid state. These methods use the rotary-resonance concept to create hetero-nuclear coherences through the dipolar interaction instead of scalar coupling into the HMQC and refocused INEPT experiments for spin n/2 (n>1). In opposite to those based on the cross-polarization transfer to quadrupolar nuclei, the methods are very robust and easy to set-up.     

Symmetry-based recoupling of 17O-1H spin pairs in magic-angle spinning NMR

We have performed magic-angle-spinning solid-state NMR experiments in which protons are recoupled to oxygen-17 nuclei by applying a symmetry-based recoupling sequence at the proton Larmor frequency. Two-dimensional quadrupole-dipole correlation spectra are produced, in which the second-order quadrupolar shift of the oxygen-17 central transition is correlated with the recoupled heteronuclear dipole-dipole interaction. These spectra are sensitive to the relative orientation of the electric field gradient at the site of the oxygen-17 nucleus and the O-H internuclear vector. We also demonstrate experiments in which polarization is transferred from protons to oxygen-17, and show that oxygen-17 signals may be selected according to the protonation state of the oxygen site. We discuss the small observed value of the heteronuclear dipolar splitting in the central-transition oxygen-17 spectra.     

Relaxation-induced dipolar exchange with recoupling-An MAS NMR method for determining heteronuclear distances without irradiating the second spin

A new magic-angle spinning NMR method for distance determination between unlike spins, where one of the two spins in question is not irradiated at all, is introduced. Relaxation-induced dipolar exchange with recoupling (RIDER) experiments can be performed with conventional double-resonance equipment and utilize the familiar π-pulse trains to recouple the heteronuclear dipolar interaction under magic-angle spinning conditions. Longitudinal relaxation of the passive spin during a delay between two recoupling periods results in a dephasing of the heteronuclear coherence and consequently a dephasing of the magnetization detected after the second recoupling period. The information about the dipolar coupling is obtained by recording normalized dephasing curves in a fashion similar to the REDOR experiment. At intermediate mixing times, the dephasing curves also depend on the relaxation properties of the passive spin, i.e., on single- and double-quantum longitudinal relaxation times for the case of I = 1 nuclei, and these relaxation times can be estimated with this new method. To a good approximation, the experiment does not depend on possible quadrupolar interactions of the passive spin, which makes RIDER an attractive method when distances to quadrupolar nuclei are to be determined. The new method is demonstrated experimentally with ¹⁴N and ²H as heteronuclei and observation of ¹³C in natural abundance.     

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.     

Rotary resonance echo double resonance for measuring heteronuclear dipolar coupling under MAS

A rotary resonance echo double resonance (R-REDOR) experiment is described for measuring heteronuclear dipolar coupling under magic-angle spinning. Rotary resonance reintroduces both dipolar coupling and chemical shift anisotropy with an rf field matching the spinning frequency. The resonance effect from chemical shift anisotropy can be refocused with a rotary resonance echo. The R-REDOR experiment thus measures the dephasing of the rotary resonance echo from the heteronuclear dipolar coupling to determine the dipolar coupling constant. The rotary resonance experiment is suitable for measuring dipolar coupling with quadrupolar nuclei because it applies the recoupling rf only to the observed spin-1/2. The rotary resonance scheme has the advantages of a long T2' and susceptible to spinning frequency fluctuation.     

Frequency offset refocused PISEMA-type sequences

The popular PISEMA experiment is highly sensitive to the 1H chemical shift dispersion and the choice of the 1H carrier frequency. This is due to the off-resonance 1H irradiation in the FSLG-CP sequence employed during the dipolar evolution period. In the modified approach described in this work, the interfering frequency offset terms are suppressed. In the new pulse schemes, conventional FSLG-CP is intercalated with 180 degrees pulses applied simultaneously to both frequency channels, and with phases set orthogonal to those of the spin-lock fields. The technique is demonstrated on a nematic liquid-crystalline sample. Extensions to amplitude-modulated FSLG-CP recoupling under MAS are also presented.     

Geometry of kinked protein helices from NMR data

Residual dipolar couplings between spin-1/2 and quadrupolar nuclei are often observed and exploited in the magic-angle spinning (MAS) NMR spectra of spin-1/2 nuclei. These orientation-dependent splittings contain information on the dipolar interaction, which can be translated into structural information. The same type of splittings may also be observed for pairs of quadrupolar nuclei, although information is often difficult to extract from the quadrupolar-broadened lineshapes. Here, the complete theory for describing the dipolar coupling between two quadrupolar nuclei in the frequency domain by Hamiltonian diagonalization is given. The theory is developed under MAS and double-rotation (DOR) conditions, and is valid for any spin quantum numbers, quadrupolar coupling constants, asymmetry parameters, and tensor orientations at both nuclei. All terms in the dipolar Hamiltonian become partially secular and contribute to the NMR spectrum. The theory is validated using experimental 11B and 35/37Cl NMR experiments carried out on powdered B-chlorocatecholborane, where both MAS and DOR are used to help separate effects of the quadrupolar interaction from those of the dipolar interaction. It is shown that the lineshapes are sensitive to the quadrupolar coupling constant of both nuclei and to the J coupling (including its sign). From these experiments, the dipolar coupling constant for a heteronuclear spin pair of quadrupolar nuclei may be obtained as well as the sign of the quadrupolar coupling constant of the perturbing nucleus; these are two parameters that are difficult to obtain experimentally otherwise.     

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.     

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, AlPO₄-5 and AlPO₄-11.     

Dynamics of Spin I=3/2 under Spin-Locking Conditions in an Ordered Environment

We have derived approximate analytic solutions to the master equation describing the evolution of the spin I=3/2 density operator in the presence of a radio-frequency (RF) field and both static and fluctuating quadrupolar interactions. Spectra resulting from Fourier transformation of the evolutions of the on-resonance spin-locked magnetization into the various coherences display two satellite pairs and, in some cases, a central line. The central line is generally trimodal, consisting of a narrow component related to a slowly relaxing mode and two broad components pertaining to two faster relaxing modes. The rates of the fast modes are sensitive to slow molecular motion. Neither the amplitude nor the width of the narrow component is affected by the magnitude of the static coupling, whereas the corresponding features of the broad components depend in a rather complicated manner on the spin-lock field strength and static quadrupolar interaction. Under certain experimental conditions, the dependencies of the amplitudes on the dynamics are seen to vanish and the relaxation rates reduce to relatively simple expressions. One of the promising emerging features is the fact that the evolutions into the selectively detected quadrupolar spin polarization order and the rank-two double-quantum coherence do not exhibit a slowly relaxing mode and are particularly sensitive to slow molecular motion. Furthermore, these coherences can only be excited in the presence of a static coupling and this makes it possible to discern nuclei in anisotropic from those in isotropic environment. The feasibility of the spin-lock pulse sequences with limited RF power and a nonvanishing average electric field gradient has been demonstrated through experiments on sodium in a dense lyotropic DNA liquid crystal.     

Enhancing MQMAS sensitivity using signals from multiple coherence transfer pathways

Multiple-quantum magic-angle spinning experiment removes second-order quadrupolar broadening from the central-transition of half-integer quadrupolar nuclei. This paper presents a novel scheme to enhance the sensitivity of MQMAS using signals from multiple coherence transfer pathways. The enhancement can be obtained in two ways. The first method uses the multiplex phase cycling to acquire MQMAS spectra from various coherence transfer pathways simultaneously. An addition of spectra collected with no extra time enhances the efficiency of the experiment. The second method, soft-pulse-added-mixing, is designed based on a complete alias of coherence transfer pathways. By properly fixing the soft-pulse phase, signals from various coherence transfer pathways can add constructively resulting higher signal intensities. The two methods are demonstrated for sensitivity enhancement with samples of spin-3/2 and 5/2.     

Comparison of several hetero-nuclear dipolar recoupling NMR methods to be used in MAS HMQC/HSQC

We compare several hetero-nuclear dipolar recoupling sequences available for HMQC or HSQC experiments applied to spin-1/2 and quadrupolar nuclei. These sequences, which are applied to a single channel, are based either on the rotary resonance recoupling (R3) irradiation, or on two continuous rotor-synchronized modulations (SFAM1 and SFAM2), or on four symmetry-based sequences (R2(1)1,SR4(1)2,R12(3)5,R20(5)9), or on the REDOR scheme. We analyze systems exhibiting purely hetero-nuclear dipolar interactions as well as systems where homo-nuclear dipolar interactions need to be canceled. A special attention is given to the behavior of these sequences at very fast MAS. It is shown that R3 methods behave poorly due to the narrowness of their rf-matching curves, and that the best methods are SR4(1)2 and SFAM (SFAM1 or SFAM2 if homo-nuclear interactions are not negligible). REDOR can also recouple efficiently hetero-nuclear dipolar interactions, provided the sequence is sent on the non-observed channel and homo-nuclear dipolar interactions are negligible. We anticipate that at ultra-fast spinning speed, SFAM1 and SFAM2 will be the most efficient methods.     

Recoupled polarization transfer heteronuclear 1H-13C multiple-quantum correlation in solids under ultra-fast MAS.

A new approach for high-resolution solid-state heteronuclear multiple-quantum MAS NMR spectroscopy of dipolar-coupled spin-12 nuclei is introduced. The method is a heteronuclear chemical shift correlation technique of abundant spins, like 1H with rare spins, like 13C in natural abundance. High resolution is provided by ultra-fast MAS and high magnetic fields, high sensitivity being ensured by a direct polarization transfer from the abundant protons to 13C. In a rotor-synchronized variant, the method can be used to probe heteronuclear through-space proximities, while the heteronuclear dipolar coupling constant can quantitatively be determined by measuring multiple-quantum spinning-sideband patterns. By means of recoupling, even weak heteronuclear dipolar interactions are accessible. The capabilities of the technique are demonstrated by measurements on crystalline L-tyrosine hydrochloride salt.     

Improved quantitation in 3QMAS of spin 5/2 nuclei by RF power modulation of FAM-II

High-resolution NMR of quadrupolar I = 5/2 nuclei using triple-quantum magic angle spinning (3QMAS) techniques can provide more accurate quantitative information on sites with small quadrupolar coupling constants by changing the pulse strength in addition to the pulse length in the FAM-II multiple-quantum conversion sequence. These effects are illustrated using (27)Al NMR of yttrium aluminium garnet and andalusite.     

Recoupling of heteronuclear dipolar interactions with rotational-echo double-resonance at high magic-angle spinning frequencies

Heteronuclear dipolar recoupling with rotational-echo double-resonance (REDOR) is investigated in the rapid magic-angle spinning regime, where radiofrequency irradiation occupies a significant fraction of the rotor period (10-60%). We demonstrate, in two model (13)C-(15)N spin systems, [1-(13)C, (15)N] and [2-(13)C, (15)N]glycine, that REDOR DeltaS/S(0) curves acquired at high MAS rates and relatively low recoupling fields are nearly identical to the DeltaS/S(0) curve expected for REDOR with ideal delta-function pulses. The only noticeable effect of the finite pi pulse length on the recoupling is a minor scaling of the dipolar oscillation frequency. Experimental results are explained using both numerical calculations and average Hamiltonian theory, which is used to derive analytical expressions for evolution under REDOR recoupling sequences with different pi pulse phasing schemes. For xy-4 and extensions thereof, finite pulses scale only the dipolar oscillation frequency by a well-defined factor. For other phasing schemes (e.g., xx-4 and xx-4) both the frequency and amplitude of the oscillation are expected to change.     

NMR relaxation in multipolar AX systems under spin locking conditions

A relaxation matrix has been calculated for a multipolar AX spin system under the on-resonance spin-locking condition. Auto- and cross-correlation terms between dipolar, quadrupolar, and CSA interactions are considered. It is shown that the spin-lock leads to many relaxation pathways being blocked, resulting in a considerably simplified relaxation network. The presence of spectral densities at zero frequency, associated with locked nuclei, allows efficient relaxation also in the absence of fast molecular motions.     

Determination of NMR interaction parameters from double rotation NMR

It is shown that the anisotropic NMR parameters for half-integer quadrupolar nuclei can be determined using double rotation (DOR) NMR at a single magnetic field with comparable accuracy to multi-field static and MAS experiments. The (17)O nuclei in isotopically enriched l-alanine and OPPh(3) are used as illustrations. The anisotropic NMR parameters are obtained from spectral simulation of the DOR spinning sideband intensities using a computer program written with the GAMMA spin-simulation libraries. Contributions due to the quadrupolar interaction, chemical shift anisotropy, dipolar coupling and J coupling are included in the simulations. In l-alanine the oxygen chemical shift span is 455 +/- 20 ppm and 350 +/- 20 ppm for the O1 and O2 sites, respectively, and the Euler angles are determined to an accuracy of +/- 5-10 degrees . For cases where effects due to heteronuclear J and dipolar coupling are observed, it is possible to determine the angle between the internuclear vector and the principal axis of the electric field gradient (EFG). Thus, the orientation of the major components of both the EFG and chemical shift tensors (i.e., V(33) and delta(33)) in the molecular frame may be obtained from the relative intensity of the split DOR peaks. For OPPh(3) the principal axis of the (17)O EFG is found to be close to the O-P bond, and the (17)O-(31)P one-bond J coupling ((1)J(OP)=161 +/- 2 Hz) is determined to a much higher accuracy than previously.     

Selective dephasing of OH and NH proton magnetization based on (1)H chemical-shift anisotropy recoupling

A method for selectively suppressing the signals of OH and NH protons in (1)H combined rotation and multiple-pulse spectroscopy (CRAMPS) and in (1)H-(13)C heteronuclear correlation (HETCOR) solid-state NMR spectra is presented. It permits distinction of overlapping CH and OH/NH proton signals, based on the selective dephasing of the magnetization of OH and NH protons by their relatively large (1)H chemical-shift anisotropies. For NH protons, the (14)N-(1)H dipolar coupling also contributes significantly to this dephasing. The dephasing is achieved by a new combination of heteronuclear recoupling of these anisotropies with (1)H homonuclear dipolar decoupling. Since the 180 degrees pulses traditionally used for heteronuclear dipolar and chemical-shift anisotropy recoupling would result in undesirable homonuclear dephasing of proton magnetization, instead the necessary inversion of the chemical-shift Hamiltonian every half rotation period is achieved by inverting the phases of all the pulses in the HW8 multiple-pulse sequence. In the HETCOR experiments, carefully timed (13)C 180 degrees pulses remove the strong dipolar coupling to the nearby (13)C spin. The suppression of NH and OH peaks is demonstrated on crystalline model compounds. The technique in combination with HETCOR NMR is applied to identify the CONH and NH-CH groups in chitin and to distinguish NH and aromatic proton peaks in a peat humin.