Multiple-Rotor-Cycle QPASS Pulse Sequences: Separation of Quadrupolar Spinning Sidebands with an Application to La NMR

The quadrupolar phase-adjusted spinning sidebands (QPASS) pulse sequence has been recently demonstrated as a useful method for obtaining quadrupolar parameters with magic-angle spinning NMR. The sequence separates spinning sidebands by order in a two-dimensional experiment. A sheared projection of the 2D spectrum effectively yields the infinite spinning rate second-order quadrupolar powder pattern, which can be analyzed to determine quadrupolar coupling constants and asymmetry parameters. The RF power and spinning speed requirements of the original QPASS sequence make it an experimentally demanding technique. A new version of the sequence is demonstrated here and is shown to alleviate many problems associated with the original sequence. New solutions to the determining equations, based on the use of multiple rotor cycles in the QPASS sequence, lead to longer delays between the nine π pulses, provide less chance of pulse overlap, and allow for use of weaker RF field strengths that excite only the central quadrupolar transition. A three-rotor-cycle version of the new experiment is demonstrated on the ¹³⁹La nucleus.     

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.     

High resolution heteronuclear correlation NMR spectroscopy between quadrupolar nuclei and protons in the solid state

A high resolution two-dimensional solid state NMR experiment is presented that correlates half-integer quadrupolar spins with protons. In this experiment the quadrupolar nuclei evolve during t1 under a split-t1, FAM-enhanced MQMAS pulse scheme. After each t1 period ending at the MQMAS echo position, single quantum magnetization is transferred, via a cross polarization process in the mixing time, from the quadrupolar nuclei to the protons. High-resolution proton signals are then detected in the t2 time domain during wPMLG5* homonuclear decoupling. The experiment has been demonstrated on a powder sample of sodium citrate and 23Na-1H 2D correlation spectra have been obtained. From the HETCOR spectra and the regular MQMAS spectrum, the three crystallographically inequivalent Na+ sites in the asymmetric unit were assigned. This MQMAS-wPMLG HETCOR pulse sequence can be used for spectral editing of half-integer quadrupolar nuclei coupled to protons.     

Optimization of offset frequency in the SORC pulse sequence using feedback.

The low signal-to-noise ratio (SNR) of nuclear quadrupolar resonance measurements has motivated research on signal enhancement methods, including multipulse sequences that facilitate signal averaging, the development of interlaced pulse sequences, and super-Q coils. More recently, it has been shown that feedback can be used to automatically optimize pulse sequence parameters, maximizing the SNR. This paper extends this work by using feedback to optimize the offset frequency in the strong off-resonant comb pulse sequence. Analysis and results are presented for a sample of sodium nitrite at both liquid nitrogen and room temperatures.     

Noise Reduction in Quadrupolar Echo Spectra at Short Echo Times

The phase cycling scheme Exorcycle embedded into the quadrupolar echo pulse sequence is presented as a tool for reducing ringing effects in broad quadrupolar spectra.     

Site-selective QPASS for the isolation of large quadrupolar coupling environments

Spectral editing of high spinning rate quadrupolar powder patterns observed using the QPASS experiment was achieved through the coupling of QPASS with the selective pi/2-RAPT enhancement sequence. The resulting pi/2-RAPT-QPASS sequence yields spectra that are dominated by the powder patterns form sites with large quadrupolar couplings thus reducing the overlap of patterns from multiple sites of different symmetry in a material. The 93Nb isotropic chemical shifts and quadrupolar coupling parameters were determined for the two niobium crystallographic sites in the layered KCa2Nb3O10. The asymmetric surface site in the structure was selectively enhanced and easily fit to second-order quadrupolar powder pattern with this method.     

Simultaneous Acquisition of Quadrupolar Order and Double-QuantumNa Signals

Na⁺with both residual quadrupolar coupling and biexponential relaxation contributes to the signal acquired from DQF-4, while only Na⁺with residual quadrupolar coupling contributes to the signal acquired with the Jeener–Broekaert sequence. Since RF phases and flip angles for DQF-4 and Jeener-Broekaert sequences are identical, these different types of signals can be generated simultaneously. A phase-cycling scheme is developed to differentiate the signals corresponding to residual quadrupolar coupling and biexponential relaxation after the signals are acquired by use of the same RF sequences. This technique can maximize the attainable information from Na⁺in biological tissues in a given acquisition time.     

Investigation of the effect of a variety of pulse errors on spin I=1 quadrupolar alignment echo spectroscopy

We report on an analysis of a well known three-pulse sequence for generating and detecting spin I=1 quadrupolar order when various pulse errors are taken into account. In the situation of a single quadrupolar frequency, such as the case found in a single crystal, we studied the potential leakage of single and/or double quantum coherence when a pulse flip error, finite pulse width effect, RF transient or a resonance offset is present. Our analysis demonstrates that the four-step phase cycling scheme studied is robust in suppressing unwanted double and single quantum coherence as well as Zeeman order that arise from the experimental artifacts, allowing for an unbiased measurement of the quadrupolar alignment relaxation time, T(1Q). This work also reports on distortions in quadrupolar alignment echo spectra in the presence of experimental artifacts in the situation of a powdered sample, by simulation. Using our simulation tool, it is demonstrated that the spectral distortions associated with the pulse artifacts may be minimized, to some extent, by optimally choosing the time between the first two pulses. We highlight experimental results acquired on perdeuterated hexamethylbenzene and polyethylene that demonstrate the efficacy of the phase cycling scheme for suppressing unwanted quantum coherence when measuring T(1Q). It is suggested that one employ two separate pulse sequences when measuring T(1Q) to properly analyze the short time behavior of quadrupolar alignment relaxation data.     

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.     

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.     

Probing the validity of average Hamiltonian theory for spin I=1, 3/2 and 5/2 nuclei by analyzing a simple two-pulse sequence

In this work, we investigate the accuracy of controlling spin I=1, 3/2 and 5/2 spin systems by average Hamiltonian theory. By way of example, we consider a simple two-pulse echo sequence and compare this perturbation scheme to a numerical solution of the Von Neumann equation. For the different values of I, we examine this precision as a function of the quadrupolar coupling as well as various experimental parameters such as the pulse spacing and pulse width. Experiments and simulations on I=3/2 and I=5/2 spin systems are presented that highlight a spectral artifact introduced due to finite pulse widths as predicted by average Hamiltonian theory. The control of these spin systems by this perturbation scheme is considered by investigating a phase cycling scheme that suppresses these artifacts to zeroth-order of the Magnus expansion.     

Residual 2H quadrupolar couplings in weakly aligned carbohydrates.

We report a novel two-dimensional NMR pulse scheme for the 1H-detected observation of 2H in isotopically 13C, 2H-enriched carbohydrates. This scheme is used for the indirect observation of residual quadrupolar couplings in 13C, 2H-enriched methyl-beta-D-glucopyranoside weakly aligned in a dilute lyotropic liquid-crystalline medium comprising 20% (w/v) dihexanoyl-phosphatidylcholine/dimyristoyl-phosphatidylcholine (1:3 mol/mol) in D2O. The observed residual quadrupolar couplings are substantially larger than residual dipolar one-bond 13C-1H couplings under the same experimental conditions. These quadrupolar couplings are thus a useful alternative to dipolar couplings for the structural analysis of small molecules that align very weakly in dilute liquid-crystalline media. Moreover, since the quadrupolar coupling constant is very uniform throughout endocyclic deuterons of the carbohydrate, these data suggest that adoption of a single average value of this parameter in 2H relaxation studies on the glycan moieties of glycoproteins and glycopeptides is a valid assumption.     

Solomon echoes for spin 7/2 by soft pulse excitation

Solomon echoes are calculated for spin 7/2 in solids taking into account the first-order quadrupolar interaction while the pulses are on. The computation is performed using the algebraic computer program ‘MAPLE’. Fifteen echoes are predicted and the amplitude of each echo is calculated. Each satellite transition produces five echoes whereas no echo is detected for the central transition. Among these echoes, six are ‘forbidden’ which are a result of the refocusing of exclusively multiple quantum coherences which are developed during the first pulse. These echoes cannot be predicted by a calculation based upon ‘hard’ pulse excitation. The results are valid for any ratio of the quadrupolar coupling to the frequency of the RF field (ω_Q/ω₁).     

Separation of quadrupolar and magnetic contributions to spin-lattice relaxation in the case of a single isotope

We present a NMR pulse double-irradiation method which allows one to separate magnetic from quadrupolar contributions in the spin–lattice relaxation. The pulse sequence fully saturates one transition while another is observed. In the presence of a Δm = 2 quadrupolar contribution, the intensity of the observed line is altered compared to a standard spin-echo experiment. We calculated analytically this intensity change for spins I = 1, , , thus providing a quantitative analysis of the experimental results. Since the pulse sequence we used takes care of the absorbed radiofrequency power, no problems due to heating arise. The method is especially suited when only one NMR sensitive isotope is available. Different cross-checks were performed to prove the reliability of the results obtained. The applicability of this method is demonstrated by a study of the plane oxygen ¹⁷O (I = ) in the high-temperature superconductor YBa₂Cu₄O₈: the ¹⁷O spin–lattice relaxation rate consists of magnetic as well as quadrupolar contributions.     

Frequency-selective quadrupolar MRI contrast

A method for the selective detection of quadrupolar nuclei located in anisotropic environments is presented. The image contrast can be tuned to the degree of anisotropy in the sample by using frequency-swept pulsed. These methods are particularly useful in the field of sodium-MRI, where sodium signals from locally-ordered environments provide diagnostic information. In solid-state MRI, these methods could be useful for probing structural defects within the sample. We demonstrate here one-dimensional images, in which the pixel contrast indicates the presence or absence of quadrupolar coupling within a certain frequency range.     

High-field QCPMG NMR of strontium nuclei in natural minerals

The only stable NMR-active isotope of strontium, (87)Sr, is a spin-9/2 quadrupolar nucleus that has a low gyromagnetic ratio, a low natural abundance, and a large nuclear electric quadrupole moment. In this work, we utilize the quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) pulse sequence and a 21.14 T NMR spectrometer at the Pacific Northwest National Laboratory to characterize the strontium sites in the natural minerals strontianite (SrCO(3)) and celestine (SrSO(4)). QCPMG at 21.14 T was found to provide sensitivity enhancements of roughly two orders of magnitude over Hahn-echo experiments at an 11.74 T magnetic field. We extracted the quadrupolar parameters for the strontium nuclei through iterative simulations of the experimental spectra with the SIMPSON program by Bak, Rasmussen, and Nielsen. The data show that the quadrupolar parameters of (87)Sr appear to be highly sensitive to the symmetry of the strontium coordination environment and can thus provide information about the strontium binding environment in complex systems.     

A model for the dynamics of spins 3/2 in biological media: signal loss during radiofrequency excitation in triple-quantum-filtered sodium MRI

We have derived the differential equations that describe the dynamics of spin-3/2 nuclei in the presence of radiofrequency (RF) fields and both static and fluctuating quadrupolar interactions. The formalism presented was used to predict the sodium triple-quantum-filtered (TQ-filtered) signal loss in a whole-body scanner, where the widths of the hard 90 degrees RF pulses are on the same order of magnitude as the transverse relaxation times. A small piece of bovine nasal cartilage, known for exhibiting residual quadrupolar splittings, was used to test the theory. The sample was modeled as consisting of small domains, each characterized by a static quadrupolar interaction constant, with an overall Gaussian distribution across the sample. An increase of about 15% in the TQ-filtered signal strength, as the 90 degrees RF pulse width was decreased from 500 to 100 micros, was predicted and demonstrated experimentally for this particular sample.     

Resolution enhancement using a new multiple-pulse decoupling sequence for quadrupolar nuclei

A new decoupling composite pulse sequence is proposed to remove the broadening on spin S=1/2 magic-angle spinning (MAS) spectra arising from the scalar coupling with a quadrupolar nucleus I. It is illustrated on the (31)P spectrum of an aluminophosphate, AlPO(4)-14, which is broadened by the presence of (27)Al/(31)P scalar couplings. The multiple-pulse (MP) sequence has the advantage over the continuous wave (CW) irradiation to efficiently annul the scalar dephasing without reintroducing the dipolar interaction. The MP decoupling sequence is first described in a rotor-synchronised version (RS-MP) where one parameter only needs to be adjusted. It clearly avoids the dipolar recoupling in order to achieve a better resolution than using the CW sequence. In a second improved version, the MP sequence is experimentally studied in the vicinity of the perfect rotor-synchronised conditions. The linewidth at half maximum (FWHM) of 65 Hz using (27)Al CW decoupling decreases to 48 Hz with RS-MP decoupling and to 30 Hz with rotor-asynchronised MP (RA-MP) decoupling. The main phenomena are explained using both experimental results and numerical simulations.     

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.     

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.