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 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 sequence is used without π/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 ²⁷Al NMR experiments on the aluminophosphates berlinite, VPI5, AlPO₄-14, and AlPO₄-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 ²⁷Al sites exceeds 10 kHz.     

Two-dimensional one pulse MAS of half-integer quadrupolar nuclei

We show that the two-dimensional one pulse (TOP) representation of magic-angle spinning nuclear magnetic resonance data of half-integer quadrupolar nuclei has significant advantages over the conventional one-dimensional spectrum. The TOP spectrum, which correlates NMR frequency to spinning sideband order, provides a rapid determination of the number of sites as well as the size of the their quadrupolar coupling. Additionally, synchronous acquisition spectra of the central and satellite transition resonances can be separated by different projections of the TOP spectrum, with higher resolution spectra often found in the satellite transitions projection. A previously perceived problem of centerband aliasing in TOP can be eliminated with an algorithm that uses larger subspectral widths and the sideband order dimension to distinguish centerbands from sidebands.     

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.     

Spin-locking mechanism of spin I = 3/2 quadrupolar nuclei undergo magic angle spinning

The spin-locking mechanism of the spin I=3/2 quadrupolar nuclei under magic angle spinning (MAS) has been theoretically and experimentally investigated, and the criterion of adiabatic passage around zero-crossings of the quadrupole splitting was inferred from the time-dependent Shrödinger equation in this article. The theory, numerical simulations, and experiments conducted in this work all indicated that second-order quadrupole interaction and off-resonance play important roles in the spin-locking of the quadrupolar nuclei, and they were responsible for the great loss of the spin-locking signals. The spin-locking for a spin I=3/2 nucleus might be achieved by minimizing the effect of the second-order quadrupole interaction by using a radio frequency (RF) offset. This offset was realized by setting the RF to the opposite position of the isotropic second-order quadrupolar shift of single quantum coherences.     

Spin-locking mechanism of spin I=3/2 quadrupolar nuclei undergo magic angle spinning

The spin-locking mechanism of the spin I=3/2 quadrupolar nuclei under magic angle spinning (MAS) has been theoretically and experimentally investigated, and the criterion of adiabatic passage around zero-crossings of the quadrupole splitting was inferred from the time-dependent Shrödinger equation in this article. The theory, numerical simulations, and experiments conducted in this work all indicated that second-order quadrupole interaction and off-resonance play important roles in the spin-locking of the quadrupolar nuclei, and they were responsible for the great loss of the spin-locking signals. The spin-locking for a spin I=3/2 nucleus might be achieved by minimizing the effect of the second-order quadrupole interaction by using a radio frequency (RF) offset. This offset was realized by setting the RF to the opposite position of the isotropic second-order quadrupolar shift of single quantum coherences.     

Decay of correlations in spin systems

We investigate the decay of initial correlations in a spin system where each spin relaxes independently by an intramolecular mechanism. The equation of motion for the spin density matrix is assumed to be the Redfield equation, which is of the form of a quantum mechanical master equation. Our analysis of this problem is based on the techniques of Shuler, Oppenheim, and coworkers, who have studied the decay of correlations in systems which can be described by classical stochastic master equations. We find that the off-diagonal elements of the reduced spin density matrices approach their equilibrium values faster than the diagonal elements. The Ursell functions, which are a measure of the correlations in the system, decay to their zero equilibrium values faster than the spin density matrix except for the furthest off-diagonal elements. Far off-diagonal matrix elements of the spin density matrix approach equilibrium at the same rate as the Ursell functions, which is the important difference between the quantum mechanical model studied here and the classical models studied earlier.Supported in part by the National Science Foundation.     

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.     

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.     

Multiple-quantum magic-angle spinning NMR with cross-polarization: Spectral editing of high-resolution spectra of quadrupolar nuclei

An experiment is presented that combines the multiple-quantum magic-angle spinning (MQMAS) technique with cross-polarization (CP). As a preliminary test of this new method, we measured and compared the ²⁷Al 3QMAS and ¹⁹F → ²⁷A1 CP 3QMAS spectra of a fluorinated AlPO₄ aluminophosphate. Complete discrimination between the fluorinated and nonfluorinated Al sites was easily achieved, which demonstrates the usefulness of CP MQMAS for spectral editing. Future applications of this experiment will include other spin pairs and heteronuclear correlation NMR spectroscopy.     

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.     

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.     

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.     

Satellite-transition MAS NMR of spin I = 3/2, 5/2, 7/2, and 9/2 nuclei: sensitivity,resolution, and practical implementation

The satellite-transition MAS (STMAS) experiment offers an alternative approach to established methods such as dynamic angle spinning (DAS), double rotation (DOR), and multiple-quantum MAS (MQMAS) for obtaining high-resolution NMR spectra of half-integer quadrupolar nuclei. Unlike the multiple-quantum experiment, STMAS involves two-dimensional correlation of purely single-quantum coherences; satellite transitions in t(1) (or F(1)) and the central transition in t(2) (or F(2)). To date, STMAS has primarily been demonstrated for nuclei with spin quantum numbers I = 3/2 and, to a lesser extent, I > 5/2. However, many chemically relevant nuclei possess I > 3/2, such as (17)O and (27)Al (both I = 5/2), (59)Co (I = 7/2), and (93)Nb (I = 9/2). Here, we discuss the application of STMAS to nuclei with spin quantum numbers from I = 3/2 to 9/2. First, we consider the practical implementation of the STMAS experiment using (87)Rb (I = 3/2) NMR as an example. We then extend the discussion to include nuclei with higher spin quantum numbers, demonstrating (27)Al, (45)Sc (I = 7/2), (59)Co, and (93)Nb STMAS experiments on both crystalline and amorphous samples. We also consider the possibility of experiments involving satellite transitions other than m(I) = +/- 1/2 <--> +/- 3/2 and, using (93)Nb NMR, demonstrate the correlation of all single-quantum satellite transitions up to and including m(I) = +/- 7/2 <--> +/- 9/2. The absolute chemical shift scaling factors in these experiments are discussed, as are the implications for isotropic resolution.     

Short range correlations between nucleons in finite nuclei

The short-range correlation between nucleons in finite nuclei is investigated in high energy protonnucleus and α-nucleus elastic scattering in the framework of Glauber multiple scattering theory without any free parameters. The effects on the p-4He and 4He-12C elastic scattering, and in particular on the proton elastic scattering off hallo-like nuclei, 6,8He, are estimated. Our calculations show that the short-range correlations play an important role in reproducing experimental data and could be also thought of as being possible origin and nature of halo-like phenomena in the nuclear structure. More accurate calculations along this line are needed.     

Quantum logical operations for spin 3/2 quadrupolar nuclei monitored by quantum state tomography

This article presents the realization of many self-reversible quantum logic gates using two-qubit quadrupolar spin 3/2 systems. Such operations are theoretically described using propagation matrices for the RF pulses that include the effect of the quadrupolar evolution during the pulses. Experimental demonstrations are performed using a generalized form of the recently developed method for quantum state tomography in spin 3/2 systems. By doing so, the possibility of controlling relative phases of superimposed pseudo-pure states is demonstrated. In addition, many aspects of the effect of the quadrupolar evolution, occurring during the RF pulses, on the quantum operations performance are discussed. Most of the procedures presented can be easily adapted to describe selective pulses of higher spin systems (>3/2) and for spin 1/2 under J couplings.     

19F-decoupling of half-integer spin quadrupolar nuclei in solid-state NMR: application of frequency-swept decoupling methods

In solid-state NMR studies of minerals and ion conductors, quadrupolar nuclei like ⁷Li, ²³Na or ¹³³Cs are frequently situated in close proximity to fluorine, so that application of ¹⁹F decoupling is beneficial for spectral resolution. Here, we compare the decoupling efficiency of various multi-pulse decoupling sequences by acquiring ¹⁹F-decoupled ²³Na-NMR spectra of cryolite (Na₃AlF₆). Whereas the MAS spectrum is only marginally affected by application of ¹⁹F decoupling, the 3Q-filtered ²³Na signal is very sensitive to it, as the de-phasing caused by the dipolar interaction between sodium and fluorine is three-fold magnified. Experimentally, we find that at moderate MAS speeds, the decoupling efficiencies of the frequency-swept decoupling schemes SW_f-TPPM and SW_f-SPINAL are significantly better than the conventional TPPM and SPINAL sequences. The frequency-swept sequences are therefore the methods of choice for efficient decoupling of quadrupolar nuclei with half-integer spin from fluorine.     

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.     

Precise measurement of magnetic moment of short-lived β-emitting nuclei 12B (Iπ= 1+, T1/2 = 20.18 ms)

The spin polarized β-emitting nuclei 12B (Iπ = 1+, T1/2 = 20.18 ms) were produced by the nuclear reaction 11B(d, p) 12B and by the selection technique of the incident deuteron energy and the 12B recoil angle following the nuclear reaction. The nuclear magnetic moment of the short-lived nuclei 12B was measured by β-NMR with the β-NMR and β-NQR setup established for the first time in China. The nuclear magnetic moment of 12B was determined to be μ = 0.99993 ± 0.00048 nm or g = 0.99993 ± 0.00048 after the precise correction of the Knight shift.     

Stray-field imaging of quadrupolar nuclei of half integer spin in solids

A report is presented on the observation of Hahn echoes from the following quadrupolar nuclei of half integer spin (I) in polycrystalline solids in the large static magnetic field gradient (37.5 T/m) which exists in the fringe field of a superconducting solenoid: ⁷Li, ²³Na, ¹¹B, ⁶⁵Cu (I = 3/2); ²⁷Al (I = 5/2); ⁵¹V, ⁵⁹Co (I = 7/2); and ¹¹⁵In (I = 9/2). ²³Na echo-trains from NaCl (with non-selective excitation) and from Na₂SO₄ (with selective excitation) are compared quantitatively for two different RF pulse sequences: 90_x-(τ-90_y-τ-echo-)_n and 90_x-(τ-90_x-τ-echo-)_n. The signals obtained from RF pulses corresponding to non-selective 90 ° pulses were shown to be quantitative, whereas in the selective case smaller signals were obtained since only the central transition contributed. The loss of signal from this cause can be distinguished from small signals resulting from low density of nuclei by use of the second sequence. A ⁷Li image obtained from LiF in a cylindrical glass-vial is shown.