Multiple-quantum cross-polarization and two-dimensional MQMAS NMR of quadrupolar nuclei

Cross-polarization from (1)H to the multiple-quantum coherences of a quadrupolar nucleus is used in combination with the two-dimensional multiple-quantum magic angle spinning (MQMAS) NMR experiment in order to extract high-resolution CPMAS NMR spectra. The technique is demonstrated on (23)Na (S = 3/2), (17)O, (27)Al (both S = 5/2), and (45)Sc (S = 7/2) nuclei, showing the applicability of multiple-quantum cross-polarization to systems with differing spin quantum number, gyromagnetic ratio, and relative nuclide abundance. The utility of this two-dimensional MAS NMR experiment for spectral editing and site-specific measurement of cross-polarization intensities is demonstrated. The possibility of direct cross-polarization to higher order multiple-quantum coherences is also considered and three-, five-, and seven-quantum cross-polarized (45)Sc MAS NMR spectra are presented.     

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.     

Theoretical and experimental assessment of single- and multiple-quantum cross-polarization in solid state NMR

Continuous wave cross-polarization (CP) NMR experiments with magic angle spinning (MAS) are reviewed for the case of isolated spin pairs I-S, with spin quantum numbers I = ½ and S ½ (1/2, 3/2, …). For two spin-1/2 nuclei, the Hartmann-Hahn matching conditions are examined at various sample rotation rates ν_R, especially with regard to off-resonance behaviour. In addition to signal enhancement, the CPMAS experiment can be used for the selective determination of inter-nuclear distances between spin-1/2 nuclei. Theoretical examination of the CP transfers to single-quantum (1Q-CPMAS) and multiple-quantum (MQ-CPMAS) levels of quadrupolar nuclei is presented. Simple analytical formulae describing the Hartmann-Hahn matching under various experimental conditions are verified using computer simulations of the spin density matrix under MAS, and the experimental data. The strategies for the most efficient acquisition of 1Q-CPMAS and MQ-CPMAS spectra are extensively discussed.     

Molecular dynamics of half-integer quadrupolar nuclei studied by QCPMG solid-state NMR experiments on static and rotating samples. Theory and simulations

Simulations of QCPMG NMR type experiments have been used to explore dynamic processes of half-integer quadrupolar nuclei in solids. By setting up a theoretical approach that is well suited for efficient numerical simulations the QCPMG type experiments have been analyzed regarding the effect of the magnitude of the EFG- and CSA-tensors, the spin-quantum number, different dynamical processes and MAS. Compared to the QE experiment the QCPMG experiment offers not only intensity gain by an order of magnitude and changes in overall lineshape as a function of the kinetic rate constant but the lineshape of the individual spin-echo sidebands is also very sensitive towards dynamics. Hereby a visual identification of the dynamics is obtained. In common for all the simulations the spin-echo sidebands are narrow in the slow (k< or =10(2) Hz) and the fast (k> or =10(7) Hz) dynamic regime whereas they are broadened in the intermediate regime 10(3)< or =k< or =10(7) Hz. The maximum intensity of the spin-echo sidebands for two-site jumps is highly dependent on the type of anisotropic interactions involved and the type of QCPMG experiment. Hence, in the fast limit the maximum intensity was 140% of the initial intensity when significant CSA was present or under the QCPMG-MAS experiment compared to 89 or 71% for the static experiment influenced by the quadrupolar interaction only. For 3-, 4-, and 6-site jumps the maximum intensity in the fast limit reached up to 339% of the intensity in the static limit.     

Ergodicity and efficiency of cross-polarization in NMR of static solids

Cross-polarization transfer is employed in virtually every solid-state NMR experiment to enhance magnetization of low-gamma spins. Theory and experiment is used to assess the magnitude of the final quasistationary magnetization amplitude. The many-body density matrix equation is solved for relatively large (up to N=14) spin systems without the spin-temperature assumption for the final spin states. Simulations show that about 13% of the thermodynamic limit is still retained within the proton bath. To test this theoretical prediction, a combination of a reverse cross-polarization experiment and multiple contacts is employed to show that the thermodynamic limit of magnetization cannot be transferred from high- to low-gamma nuclei in a single contact. Multiple contacts, however, fully transfer the maximum magnetization. A simple diffusion on a cone model shows that slow dynamics can affect the build up profile for the transferred magnetization.     

Separation of isotropic chemical and second-order quadrupolar shifts by multiple-quantum double rotation NMR

Using a two-dimensional multiple-quantum (MQ) double rotation (DOR) experiment the contributions of the chemical shift and quadrupolar interaction to isotropic resonance shifts can be completely separated. Spectra were acquired using a three-pulse triple-quantum z-filtered pulse sequence and subsequently sheared along both the ν₁ and ν₂ dimensions. The application of this method is demonstrated for both crystalline (RbNO₃) and amorphous samples (vitreous B₂O₃). The existence of the two rubidium isotopes (⁸⁵Rb and ⁸⁷Rb) allows comparison of results for two nuclei with different spins (I = 3/2 and 5/2), as well as different dipole and quadrupole moments in a single chemical compound. Being only limited by homogeneous line broadening and sample crystallinity, linewidths of approximately 0.1 and 0.2 ppm can be measured for ⁸⁷Rb in the quadrupolar and chemical shift dimensions, enabling highly accurate determination of the isotropic chemical shift and the quadrupolar product, P_Q. For vitreous B₂O₃, the use of MQDOR allows the chemical shift and electric field gradient distributions to be directly determined—information that is difficult to obtain otherwise due to the presence of second-order quadrupolar broadening.     

Fast amplitude-modulated pulse trains with frequency sweep (SW-FAM) in static NMR of half-integer spin quadrupolar nuclei

In solid-state NMR of quadrupolar nuclei with half-integer spin I, fast amplitude-modulated (FAM) pulse trains have been utilised to enhance the intensity of the central-transition signal, by transferring spin population from the satellite transitions. In this paper, the signal-enhancement performance of the recently introduced SW-FAM pulse train with swept modulation frequency [T. Br?uniger, K. Ramaswamy, P.K. Madhu, Enhancement of the central-transition signal in static and magic-angle-spinning NMR of quadrupolar nuclei by frequency-swept fast amplitude-modulated pulses, Chem. Phys. Lett. 383 (2004) 403-410] is explored in more detail for static spectra. It is shown that by sweeping the modulation frequencies linearly over the pulse pairs (SW1/tau-FAM), the shape of the frequency distribution is improved in comparison to the original pulse scheme (SWtau-FAM). For static spectra of 27Al (I=5/2), better signal-enhancement performance is found for the SW1/tau-FAM sequence, as demonstrated both by experiments and numerical simulations.     

Homogeneous broadenings in 2D solid-state NMR of half-integer quadrupolar nuclei

The question of the homogeneous broadening that occurs in 2D solid-state NMR experiments is examined. This homogeneous broadening is mathematically introduced in a simple way, versus the irreversible decay rates related to the coherences that are involved during t1 and t2. We give the pulse sequences and coherence transfer pathways that are used to measure these decay rates. On AlPO4 berlinite, we have measured the 27Al echo-type relaxation times of the central and satellite transitions on 1Q levels, so that of coherences that are situated on 2Q, 3Q, and 5Q levels. We compare the broadenings that can be deduced from these relaxation times to those directly observed on the isotropic projection of berlinite with multiple-quantum magic-angle spinning (MAS), or satellite-transition MAS. We show that the choice of the high-resolution method, should be done according to the spin value and the corresponding homogeneous broadening.     

Use of SPAM and FAM pulses in high-resolution MAS NMR spectroscopy of quadrupolar nuclei

The merits of SPAM and FAM pulses for enhancing the conversion of triple- to single-quantum coherences in the two-dimensional MQMAS experiment are compared using (87)Rb (spin I=3/2) and (27)Al (I=5/2) NMR of crystalline and amorphous materials. Although SPAM pulses are more easily optimized, our experiments and simulations suggest that FAM pulses yield greater signal intensity in all cases. In conclusion, we argue that, as originally suggested, SPAM and FAM pulses are best implemented in phase-modulated whole-echo MQMAS experiments and that the use of SPAM pulses to record separate echo and antiecho data sets, which are then combined, generally yields lower signal-to-noise ratios.     

Theoretical and experimental study of quadrupolar echoes for half-integer spins in static solid-state NMR

Numerical simulations of powder spectra produced by a two-pulse sequence applied to a quadrupolar nuclei system of half-integer spin number make it possible to propose simple experimental instructions to record static echo spectra with minimum lineshape distortion. Calculations take into account quadrupolar (first and second orders), shielding, scalar and inhomogeneous dipolar interactions as well as the radiofrequency pulse specifications (strength, duration, phase). The suggested instructions have been checked experimentally in different cases: for a large spin number system with Li⁹³NbO₃, when two interactions are present with a ^63/65Cu complex, and in the two-site system of ⁸⁷Rb₂SO₄.     

MAS NMR spectra of quadrupolar nuclei in disordered solids: the Czjzek model

Structural disorder at the scale of two to three atomic positions around the probe nucleus results in variations of the EFG and thus in a distribution of the quadrupolar interaction. This distribution is at the origin of the lineshape tailing toward high fields which is often observed in the MAS NMR spectra of quadrupolar nuclei in disordered solids. The Czjzek model provides an analytical expression for the joint distribution of the NMR quadrupolar parameters upsilon(Q) and eta from which a lineshape can be predicted. This model is derived from the Central Limit Theorem and the statistical isotropy inherent to disorder. It is thus applicable to a wide range of materials as we have illustrated for 27Al spectra on selected examples of glasses (slag), spinels (alumina), and hydrates (cement aluminum hydrates). In particular, when relevant, the use of the Czjzek model allows a quantitative decomposition of the spectra and an accurate extraction of the second moment of the quadrupolar product. In this respect, it is important to realize that only rotational invariants such as the quadrupolar product can make sense to describe the quadrupolar interaction in disordered solids.     

Triple, quintuple and higher order multiple quantum MAS NMR of quadrupolar nuclei

The optimization of the coherence transfers involved in five, seven and nine-quantum versions of the recently discovered MQMAS technique, is analysed numerically. Data reported in this paper may serve as starting parameters for the experiment set up. An analysis of the intensity and resolution given by each type of experiment is performed, which confirms the need to use very high rf fields for MQ transfers. It follows that five-quantum is achievable rather easily but the use of seven and nine-quantum MAS experiments becomes increasingly difficult due to the demand for high rf power and decreasing sensitivity. The advantages of using the z-filter MQMAS method with respect to a two-pulse sequence are analysed. The method for qualitatively and quantitatively interpret the MQMAS spectra is described. The nature of the spinning side bands along the multiple quantum dimension is explained. It is shown that the rotor synchronization can be conveniently used to eliminate these side bands, but only for 3QMAS experiments. The use of the multiple-quantum method in combination with static samples and VAS, DAS and DOR techniques is finally discussed.     

Spectral editing in solid-state MAS NMR of quadrupolar nuclei using selective satellite inversion

A sensitivity enhancement method based on selective adiabatic inversion of a satellite transition has been employed in a (pi/2)CT-(pi)ST1-(pi/2)CT spectral editing sequence to both enhance and resolve multisite NMR spectra of quadrupolar nuclei. In addition to a total enhancement of 2.5 times for spin 3/2 nuclei, enhancements up to 2.0 times is reported for the edited sites in a mixture of rubidium salts.     

Powder MAS NMR lineshapes of quadrupolar nuclei in the presence of second-order quadrupole interaction

We derive a complete analytical solution for the powder magic angle spinning (MAS) nuclear magnetic resonance (NMR) lineshape in the presence of second-order quadrupole interaction, considering a radiofrequency (rf) pulse of finite width, a finite MAS frequency, and a non-zero asymmetry parameter. I_x is calculated using two approaches. The first applies time-dependent perturbation theory in the presence of the rf pulse and stationary perturbation theory (SPT) in its absence. The second is based on the Magnus expansion of the density matrix in the interaction representation during the pulse and SPT in its absence. We solve the problem in the laboratory frame using the properties of the Fourier transform and spin operators. Diagonalisation is not required. Both approaches agree well with each other under all conditions and also with the transition probability approach for the central transition. The Magnus expansion exists at all times and the effect of the non-secular terms is negligible. We describe an analytical method of averaging I_x over the Euler angles and simulate the ¹¹B MAS NMR lineshapes for crystalline and vitreous B₂O₃. A critical analysis is given of all earlier calculations of the MAS NMR lineshape.     

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.     

Implementing SPAM into STMAS: a net sensitivity improvement in high-resolution NMR of quadrupolar nuclei

Gan and Kwak recently introduced two new tools for high-resolution 2D NMR methods applied to quadrupolar nuclei: double-quantum filtering in STMAS (DQF-STMAS) and the soft-pulse added mixing (SPAM) idea. Double-quantum filtering suppresses all undesired signals in the STMAS method with limited loss in sensitivity. With SPAM, all pathways are added constructively after the second hard-pulse instead of using a single pathway as previously. Here, the sensitivity, advantages and drawbacks of DQF-STMAS are compared to 3QMAS. Additionally, SPAM can be included into DQF-STMAS method, resulting in a net sensitivity gain with respect to 3QMAS of ca. 10-15.     

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.     

Measurement of J-couplings between spin-(1/2) and quadrupolar nuclei by frequency selective solid-state NMR

We report a REDOR-based scheme for the measurement of heteronuclear J-couplings in solid samples with well defined structure, containing spin-12 and quadrupolar nuclei, which can be used with selective RF irradiation to target a specific spin pair, and which provides direct information about the number of coupled spins.     

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.