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.     

Rotational-resonance distance measurements in multi-spin systems

It is demonstrated that internuclear distances can be evaluated from rotational-resonance (RR) experiments in uniformly (13)C-labelled compounds. The errors in the obtained distances are less than 10% without the need to know any parameters of the spin system except the isotropic chemical shifts of all spins. We describe the multi-spin system with a simple fictitious spin-1/2 model. The influence of the couplings to the passive spins (J and dipolar coupling) is described by an empirical constant offset from the rotational-resonance condition. Using simulated data for a three-spin system, we show that the two-spin model describes the rotational-resonance transfer curves well as long as none of the passive spins is close to a rotational-resonance condition with one of the active spins. The usability of the two-spin model is demonstrated experimentally using a sample of acetylcholine perchlorate with labelling schemes of various levels of complexity. Doubly-, triply-, and fully labelled compounds lead to strongly varying RR polarization-transfer curves but the evaluated distances using the two-spin model are identical within the expected error limits and coincide with the distance from the X-ray structure. Rotational-resonance distance measurements in fully labelled compounds allow, in particular, the measurement of weak couplings in the presence of strong couplings.     

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.     

Selective homonuclear Hartmann–Hahn for 13C→13C polarization transfer in solution state NMR

Polarization transfer has become a commonplace technique for the enhancement of a variety of nuclei in high field nuclear magnetic resonance (NMR). In this paper the homonuclear Hartmann-Hahn method for polarization transfer is revisited and it is shown that a 90% transfer of polarization can be achieved experimentally between a pair of scalar coupled ¹³C nuclei in a sample of isotopically enriched glycine. This may show particular utility in the field of dynamic nuclear polarization (DNP) and could be used as an addendum to already established DNP techniques allowing the favourable enhancement to be ‘stored’ on long-lived nuclei and subsequently transferred to shorter-lived nuclei prior to observation.     

Cross-polarisation method for improvement of 14N NQR signal detectability

This is a study of the cross-polarization effects in the case of 14N quadrupolar spin-system with a long spin-lattice relaxation time. Two important benefits of the cross-polarization technique were demonstrated for PETN: (i) a polarization transfer resulting in increased NQR single shot signal response and (ii) a dynamic reduction in recovery time of the NQR system allowing scan repetition on a much shorter timescale. It was proved that this technique can reduce the optimal waiting time between pulse sequences up to 60 times through a significant reduction of the relaxation time of the quadrupolar spin-system. All experiments were carried out at room temperature using spin-locking multi-pulse sequences and small external magnetic field.     

Probing through bond connectivities with MQMAS NMR

Polarization transfer from quadrupolar (27Al) to spin-1/2 (31P) nuclei via J-coupling is employed to measure two-dimensional 27Al-31P heteronuclear correlation spectra with isotropic resolution. The proposed experiment, MQ-J-HETCOR, uses multiple quantum magic angle spinning (MQMAS) NMR for elimination of the second-order quadrupolar broadening and INEPT, INEPTR, INEPT+ and DEPT sequences for the polarization transfer. The experimental conditions leading to best sensitivity and resolution are detailed using AlPO4-14 as a test sample.     

Enhancing sensitivity of quadrupolar nuclei in solid-state NMR with multiple rotor assisted population transfers

Rotor-assisted population transfer (RAPT) was developed as a method for enhancing MAS NMR sensitivity of quadrupolar nuclei by transferring polarization associated with satellite transitions to the central m=12-->-12 transition. After a single RAPT transfer, there still remains polarization in the satellite transitions that can be transferred to the central transition. This polarization is available without having to wait for the spin system to return to thermal equilibrium. We describe a new RAPT scheme that uses the remaining polarization of the satellites to obtain a further enhancement of the central transition by performing RAPT-enhanced experiments multiple times before waiting for re-equilibration of the spin system. For 27Al (I=5/2) in albite we obtain a multiple RAPT enhancement of 3.02, a 48% increase over single RAPT. For 93Nb (I=9/2) in NaNbO(3) we obtain a multiple RAPT enhancement of 5.76, an 89% increase over single RAPT. We also describe a data processing procedure for obtaining the maximum possible signal-to-noise ratio.     

Exploring the limits of polarization transfer efficiency in homonuclear three spin systems

The limits of polarization transfer efficiency are explored for systems consisting of three isotropically coupled spins 1/2 in the absence of relaxation. An idealized free evolution and control Hamiltonian is studied, which provides an upper limit of transfer efficiency (in terms of transfer amplitude and transfer time) for realistic homonuclear spin systems with arbitrary Heisenberg-type coupling constants J12, J13, and J23. It is shown that optimal control based pulse sequences have significantly improved transfer efficiencies compared to conventional transfer schemes. An experimental demonstration of optimal polarization transfer is given for the case of the carbon spin system of fully 13C labelled alanine at 62.5 MHz Larmor frequency.     

Analytical polarization and coherence transfer functions for three dipolar coupled spins 12

Analytical polarization and coherence transfer functions are presented for a spin system consisting of three dipolar coupled homonuclear spins 12 under energy matched conditions. Based on these transfer functions, optimal durations of Hartmann-Hahn mixing periods can be determined for arbitrary dipolar coupling constants D(12), D(13), and D(23). In addition, the dependence of the transfer efficiency on the relative size of the dipolar coupling constants is illustrated.     

QUantitative Cross-Polarization at magic-angle spinning frequency of about 20 kHz

We study the QUantitative Cross-Polarization (QU-CP) method proposed by Hou et al. (Chem. Phys. Lett. 421 (2006) 356) under the moderate MAS speed of 23 kHz, re-examining its two building blocks, namely, the CP polarization transfer from (1)H to (13)C, and the thermal equalization of the (13)C magnetizations. We show that the nuclear-integrated cross-polarization (NI-CP) scheme is conveniently used for (1)H-(13)C polarization transfer, because of its simplicity, robustness to rf-mismatch, and compatibility with fast sample spinning. In the mixing part, in addition to dipolar-assisted rotational-resonance (DARR) recoupling, we examine the Phase-Alternated Recoupling Irradiation Schemes (PARIS and PARIS(xy)), and Second-order Hamiltonian among Analogous Nuclei Generated by Hetero-nuclear Assistance Irradiation (SHANGHAI) sequences, and show that SHANGHAI gives the best performances in equalizing the (13)C magnetizations.     

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.     

Homonuclear correlation experiments for quadrupolar nuclei, spinning away from the magic angle

We present a set of homonuclear correlation experiments for half-integer quadrupolar spins in solids. In all these exchange-type experiments, the dipolar interaction is retained during the mixing time by spinning the sample at angles other than the “regular magic angle” (54.7°). The second-order quadrupolar interaction is averaged by different strategies for the different experiments. The multiple-quantum off magic angle spinning (MQOMAS) exchange experiment is essentially a regular MQMAS experiment where the quadrupolar interaction is averaged by combining magic angle spinning with a multiple- to single-quantum correlation scheme. The sample is spun at the magic angle at all times except during the mixing time which is added to establish homonuclear correlation. In the multiple-quantum P₄ magic angle spinning (MQP₄MAS) exchange experiment, the sample is spun at one of the angles at which the fourth-order Legendre polynomial vanishes (P₄ magic angle), the remaining second-order quadrupolar interaction now governed by a second-rank tensor is refocussed by the multiple to single-quantum correlation scheme. In the dynamic angle spinning (DAS) exchange experiment, the second-order quadrupolar interaction is averaged by correlating the evolution from two complementary angles. These experiments are demonstrated and compared, in view of their specific advantages and disadvantages, for ²³Na in the model compound Na₂SO₃.     

Signal enhancement in solid-state NMR of quadrupolar nuclei

Recent progress in the development and application of signal enhancement methods for NMR of quadrupolar nuclei in solids is presented. First, various pulse schemes for manipulating the populations of the satellite transitions in order to increase the signal of the central transition (CT) in stationary and rotating solids are evaluated (e.g., double-frequency sweeps, hyperbolic secant pulses). Second, the utility of the quadrupolar Carr–Purcell–Meiboom–Gill (QCPMG) and WURST-QCPMG pulse sequences for the rapid and efficient acquisition of particularly broad CT powder patterns is discussed. Third, less frequently used experiments involving polarization transfer from abundant nuclear spins (cross-polarization) or from unpaired electrons (dynamic nuclear polarization) are assessed in the context of recent examples. Advantages and disadvantages of particular enhancement schemes are highlighted and an outlook on possible future directions for the signal enhancement of quadrupolar nuclei in solids is offered.     

One-dimensional homonuclear polarization transfer. Studies of parameters which affect intensities in the SPI NMR technique

A study is presented of the effects of strong scalar coupling and of the angle of the nonselective observing pulse, as well as of the effects of selective pulses, in one-dimensional selective population inversion (SPI) experiments of homonuclear spin systems. Density matrix computer simulations, which also take into account relaxation effects, of {A}-B SPI experiments, and for comparison also of {A}-X, reproduce different aspects of the experimental spectra. An insight is therefore offered into the parameters which affect intensities in the SPI one-dimensional NMR technique for homonuclear polarization transfer.     

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.     

Selective Homonuclear Polarization Transfer in the Tilted Rotating Frame under Magic Angle Spinning in Solids

An application of the R2TR method (1995,Chem. Phys. Lett.232,424) to selective homonuclear polarization transfer under magic angle spinning is proposed. It is shown that, for a spinning speed fast enough to remove the maximum homonuclear dipolar coupling constant ω_Dinvolved, the flip-flop and flop-flop mechanisms are suitable for recoupling the spins with a chemical shift difference larger than ω_Dand a difference comparable to or smaller than ω_D, respectively. It is also shown that, for fast polarization transfer, the off-resonance frequencies should be much higher than the RF intensity in the flip-flop condition, while for the flop-flop condition, the off-resonance frequencies should be much lower than the RF intensity. Some one- and two-dimensional experiments are proposed by utilizing the capability of the R2TR method to abruptly switch on and off the recoupling condition, and are demonstrated for triply¹³C-enriched -alanine. The mixing time required for population transfer was found to be ca. 0.5 ms for the methine and methyl¹³C spins separated by 1.5 Å and ca. 5 ms for the methyl and the carboxyl carbons separated by 2.5 Å. The experimental results and theoretical simulations show that selective polarization transfer is achieved when the difference in the isotropic chemical shifts between the relevant pair of spins and a neighboring spin is more than 1000 Hz.     

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.     

Three-dimensional through-bond homonuclear-heteronuclear correlation experiments for quadrupolar nuclei in solid-state NMR applied to (27)Al-O-(31)P-O-(27)Al networks

We present here the first 3D homonuclear/heteronuclear correlation experiment applied to quadrupolar nuclei and making use of the sole scalar J-coupling. This experiment, based on the 2D-Homonuclear-Heteronuclear Single Quantum Correlation (H-HSQC) experiment, uses a relayed transfer from the (27)Al central transition to neighbouring (31)P spins and to the central transition of a second (27)Al. It confirms the correlation map characterizing the two (27)Al and the (31)P NMR signatures of (27)Al-O-(31)P-O-(27)Al chemically bonded molecular motifs.     

Efficient Time Propagation Technique for MAS NMR Simulation: Application to Quadrupolar Nuclei

The quantum mechanical Floquet theory is investigated in order to derive an efficient way of performing numerical calculations of the dynamics of nuclear spin systems in MAS NMR experiments. Here, we take advantage of time domain integration of the quantum evolution over one period as proposed by Edenet al.(1). But a full investigation of the propagatorU(t,t₀), and especially its dependence with respect totandt₀within a formalized approach, leads to further simplifications and to a substantial reduction in computation time when performing powder averaging for any complex sequence. Such an approximation is suitable for quadrupolar nuclei (I> 1/2) and can be applied to the simulation of the RIACT (rotational induced adiabatic coherence transfer) phenomenon that occurs under special experimental conditions in spin locking experiments (2–4). The present method is also compared to the usual infinite dimensional Floquet space approach (5, 6), which is shown to be rather inefficient. As far as we know, it has never been reported for quadrupolar nuclei withI≥ 3/2 in spin locking experiments. The method can also be easily extended to other areas of spectroscopy.