Theoretical and experimental study of quadrupolar echoes in solid state NMR

Multi-quantum echoes in GdAl2 zero-field high-resolution NMR

In this paper we present a series of high-resolution zero-field NMR spectra of the polycrystalline intermetallic compound GdAl(2). The spectra were obtained with the sample at 4.2K in the ordered magnetic state and in the absence of an external static magnetic field. Using a sequence composed of two RF pulses, we obtained up to five multi-quantum echoes for the (27)Al nuclei, which were used to construct the zero-field NMR spectra. The spectra obtained from the FID observed after the second pulse and the even echoes exhibited higher resolution than the odd ones. In order to explain such behavior, we propose a model in which there are two regions inside the sample with different inhomogeneous spectral-line broadenings. Moreover, with the enhanced resolution from the FID signal, we were able to determine quadrupolar couplings with great precision directly from the respective spectra. These results were compared with those obtained from the quadrupolar oscillations of the echo signals, and showed good agreement. Similar data were also obtained from (155)Gd and (157)Gd nuclei.

Probing quadrupolar nuclei by solid-state NMR spectroscopy: recent advances

Solid-state nuclear magnetic resonance (NMR) of quadrupolar nuclei has recently undergone remarkable development of capabilities for obtaining structural and dynamic information at the molecular level. This review summarizes the key achievements attained during the last couple of decades in solid-state NMR of both integer spin and half-integer spin quadrupolar nuclei. We provide a concise description of the first- and second-order quadrupolar interactions, and their effect on the static and magic angle spinning (MAS) spectra. Methods are explained for efficient excitation of single- and multiple-quantum coherences, and acquisition of spectra under low- and high-resolution conditions. Most of all, we present a coherent, comparative description of the high-resolution methods for half-integer quadrupolar nuclei, including double rotation (DOR), dynamic angle spinning (DAS), multiple-quantum magic angle spinning (MQMAS), and satellite transition magic angle spinning (STMAS). Also highlighted are methods for processing and analysis of the spectra. Finally, we review methods for probing the heteronuclear and homonuclear correlations between the quadrupolar nuclei and their quadrupolar or spin-1/2 neighbors.

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.

A solid-state 53Cr NMR study of chromate and dichromate salts

Solid-state (53)Cr NMR spectra of a series of chromate (CrO4(2-)) and dichromate (Cr2O7(2-)) salts have been examined by employing the stepped-frequency quadrupolar Carr-Purcell Meiboom-Gill (QCPMG) experiment and high applied magnetic field strengths, 11.75 and 18.8 T. Cr-53 nuclear quadrupolar coupling constants, CQ(53Cr), ranging from 1.23 to 5.01 MHz for the Cr(4(2-) salts and 7.25 to 8.14 MHz for the Cr2O7(2-) salts have been measured. For the dichromate salts, this corresponds to central transition 53Cr NMR lineshapes of 200-250 kHz at 18.8 T. The use of hyperbolic secant (HS) pulses in combination with the Hahn-echo (HE) or QCPMG experiment results in significant sensitivity enhancements when acquiring 53Cr NMR spectra of magic-angle spinning (MAS) samples, provided the MAS rate is fast with respect to the second-order quadrupolar interaction. For the CrO4(2-) and Cr2O7(2-) salts, the anisotropic chromium magnetic shielding interaction is generally negligible compared to the second-order 53Cr nuclear quadrupolar interaction. No simple correlation between the structure of the CrO4(2-) and Cr2O7(2-) anions and the observed CQ(53Cr) values has been found.

Investigation of structure and dynamics in the sodium metallocenes CpNa and CpNa·THF via solid-state NMR, X-ray diffraction and computational modelling

Solid-state (23) Na NMR spectra of two organometallic complexes, cyclopentadienylsodium (CpNa) and the tetrahydrofuran (THF) solvate of CpNa (CpNa·THF), are presented. Analytical simulations of experimental spectra and calculated (23) Na electric-field gradient (EFG) tensors confirm that both complexes are present in microcrystalline samples of CpNa recrystallized from THF. For the solvate, (23) Na NMR experiments at 9.4 T and 11.7 T elucidate sodium chemical shielding (CS) tensor parameters, and establish that the EFG and CS tensor frames are non-coincident. Single-crystal X-ray diffraction (XRD) experiments are used to determine the crystal structure of CpNa·THF: Cmca (a = 9.3242(15) Å, b = 20.611(3) Å, c = 9.8236(14) Å, α = β = γ = 90° , V = 1887.9(5)Å(3) , Z = 8). For CpNa, (23) Na NMR data acquired at multiple field strengths establish sodium CS tensor parameters more precisely than in previous reports. Variable-temperature (VT) powder XRD (pXRD) experiments determine the temperature dependence of the CpNa unit cell parameters. The combination of (23) Na quadrupolar NMR parameters, pXRD data and calculations of (23) Na EFG tensors is used to examine various models of dynamic motion in the solid state. It is proposed that the sodium atom in CpNa undergoes an anisotropic, temperature-dependent, low frequency motion within the ab crystallographic plane, in contrast with previous models.

Solid-State 23Na NMR Study of Sodium Lariat Ether Receptors Exhibiting Cation−π Interactions

Noncovalent cation-pi interactions are important in a variety of supramolecular and biochemical systems. We present a 23Na solid-state nuclear magnetic resonance (SSNMR) study of two sodium lariat ether complexes, 1 and 2, in which a sodium cation interacts with an indolyl group that models the side chain of tryptophan. Sodium-23 SSNMR spectra of magic-angle spinning (MAS) and stationary powdered samples have been acquired at three magnetic field strengths (9.4, 11.75, 21.1 T) and analyzed to provide key information on the sodium electric field gradient and chemical shift (CS) tensors which are representative of the cation-pi binding environment. Triple-quantum MAS NMR spectra acquired at 21.1 T clearly reveal two crystallographically distinct sites in both 1 and 2. The quadrupolar coupling constants, CQ(23Na), range from 2.92 +/- 0.05 MHz for site A of 1 to 3.33 +/- 0.05 MHz for site B of 2; these values are somewhat larger than those reported previously by Wong et al. (Wong, A.; Whitehead, R. D.; Gan, Z.; Wu, G. J. Phys. Chem. A 2004, 108, 10551) for NaBPh4, but very similar to the values obtained for sodium metallocenes by Willans and Schurko (Willans, M. J.; Schurko, R. W. J. Phys. Chem. B 2003, 107, 5144). We conclude from the 21.1 T data that the spans of the sodium CS tensors are less than 20 ppm for 1 and 2 and that the largest components of the EFG and CS tensors are non-coincident. Quantum chemical calculations of the NMR parameters substantiate the experimental findings and provide additional insight into the dependence of CQ(23Na) on the proximity of the indole ring to Na+. Taken together, this work has provided novel information on the NMR interaction tensors characteristic of a sodium cation interacting with a biologically important arene.

A Solid-State 39K and 13C NMR Study of Polymeric Potassium Metallocenes

The quadrupolar Carr-Purcell Meiboom-Gill (QCPMG) and double frequency sweep (DFS)/QCPMG pulse sequences are applied in order to acquire the first solid-state 39K NMR spectra of organometallic complexes, the polymeric main group metallocenes cyclopentadienyl potassium (CpK) and pentamethylcyclopentadienyl potassium (Cp*K). Piecewise QCPMG NMR techniques are used to acquire a high S/N 39K spectrum of the broad central transition of Cp*K, which is ca. 200 kHz in breadth. Analytical and numerical simulations indicate that there is a significant quadrupolar interaction present at both potassium nuclei (C(Q)(39K) = 2.55(6)/2.67(8) MHz and 4.69(8) MHz for CpK (static/MAS) and Cp*K, respectively). Experimental quadrupolar asymmetry parameters suggest that both structures are bent about the potassium atoms (eta(Q)(39K) = 0.28(3)/0.29(3) for CpK (static/MAS) and eta(Q)(39K) = 0.30(3) for Cp*K). Variable-temperature (VT) 39K NMR experiments on CpK elucidate temperature-dependent changes in quadrupolar parameters which can be rationalized in terms of alterations of bond distances and angles with temperature. 13C CP/MAS NMR experiments are conducted upon both samples to quantify the carbon chemical shielding anisotropy (CSA) at the Cp' ring carbon atoms. Ab initio carbon CSA and 39K electric-field gradient (EFG) and CSA calculations are conducted and discussed for the CpK complex, in order to correlate the experimental NMR parameters with molecular structure in CpK and Cp*K. 39K DFS/QCPMG and 13C CP/MAS experiments prove invaluable for probing molecular structure, temperature-dependent structural changes, and the presence of impurities in these systems.

Combined 17O NMR and 11B-31P double resonance NMR studies of sodium borophosphate glasses

17O enriched sodium borophosphate glasses were prepared from isotopically enriched NaPO3 and H3BO3. These glasses have been studied by 17O, 11B and 31P NMR including 17O and 11B multiple quantum magic angle sample spinning (MQMAS), 11B-31P heteronuclear correlation (HETCOR) NMR and 11B{31P} rotational echo double resonance (REDOR). For comparison, the crystalline borophosphates BPO4 and Na5B2P3O13 were included in the investigations. The latter compound shows three sharp 31P resonances at -0.2, -2 and -8 ppm and two BO4 sites that can only be resolved by MQMAS. The 17O NMR spectra were recorded using both the static echo method at medium magnetic field (9.4 T) as well as MAS and MQMAS methods at high field (17.6 T). In total, five oxygen sites were identified in these borophosphate glasses: P-O-P, Na...O-P, P-O-B, B-O-B, Na...O-B. However, these five sites are not present simultaneously in any of the glasses. The 17O MQMAS spectra prove that P-O-B links play a major role in borophosphate glasses. These results are confirmed by the complementary 11B MAS spectra that show the presence of asymmetric and symmetric trigonal groups BO3a and BO3s and two tetrahedral BO4 units. 11B{31P} REDOR NMR is used to give independent information to assign the 11B lines to structural units present in the glasses. These REDOR measurements reveal that B-O-P bonds are present for each borate unit, including the BO3 groups. Particularly, a structural proposal for the two different BO4 resonances is given in terms of a different number of bonded phosphate tetrahedra. The 31P MAS spectra are usually broad and not well resolved. It is shown by 11B-31P HETCOR NMR that a possible structural assignment of a 31P signal at about -20 ppm to Q2 units as in binary sodium phosphate glasses is wrong and that the phosphate tetrahedron belonging to this resonance must be connected to borate groups.

NMR evidence for the coexistence of order-disorder and displacive components in barium titanate

A quadrupole coupling induced 47Ti and 49Ti satellite background which transforms into well-defined satellite lines below T(c) in the ferroelectric phase has been observed in the cubic phase of an ultrapure BaTiO3 single crystal. The results demonstrate the coexistence of a displacive and order-disorder component in the phase transition mechanism and tetragonal breaking of the cubic symmetry due to biased Ti motion between off-center sites in the paraelectric phase above T(c).

Procedures for labeling the high-resolution axis of two-dimensional MQ-MAS NMR spectra of half-integer quadrupole spins

The increasing development and application of the multiple-quantum MAS NMR for half-integer quadrupole spins has led to various RF pulse sequences for improving the excitation of multiple-quantum coherences and their conversion to single-quantum coherences. As a result, several conventions for labeling the Fl dimension of a 2D MQ-MAS spectrum appear in the literature. The corresponding relations for extracting the isotropic chemical shift, the quadrupole coupling constant, and the asymmetry parameter from experimental data are not always provided. We analyze these various conventions systematically and propose a new one, similar to that introduced by J.-P. Amoureux and C. Fernandez (2000, Solid State NMR 10, 339-343). These various conventions are illustrated with 27Al (I = 5/2) nuclei in aluminum acetylacetonate Al(CH3COCHCOCH3)3. Another experimental problem often met, the aliasing of peaks in the 2D spectrum, is analyzed and illustrated with 27Al (I = 5/2) in NH4Y zeolite and 23Na (I = 3/2) in sodium pyrophosphate Na4P2O7.

Determination of quadrupole parameters with a composite pulse for spurious signal suppression

Spurious signals such as the piezoelectric signal from a ferroelectric crystal or the ringing signal from the NMR probe head tuned for low gyromagnetic ratio nuclei are often observed in pulsed NMR. Both signals are cancelled using the Hahn echo sequence with appropriate phase cyclings. The present paper applies a composite-pulse sequence to cancel the ringing signal. The main advantage of this sequence over the Hahn echo sequence is in the simplicity of optimizing the line intensity: the optimization of only one pulse duration for this sequence but of two pulse durations and the interpulse delay for the Hahn echo sequence. We are interested in half-integer quadrupole spins (I = 3/2, 5/2, 7/2, and 9/2), which means that we must consider the first-order quadrupole interaction during the pulses. For simplicity, we deal mainly with spin I = 3/2 nuclei. Since the central-line intensity depends on the ratio of the quadrupole coupling constant (QCC) to the amplitude of the RF pulse, we can determine the QCC from a featureless lineshape by fitting the variation of the experimental central-line intensity for increasing pulse duration with theoretical results. Contrary to the one-pulse sequence where the central-line intensity is proportional to the pulse duration if the latter is short, there is no such condition with the composite-pulse sequence. In other words, this sequence does not allow us to quantify the relative spin populations in powders. The size of the sample must be much smaller than that of the RF coil in order for the RF magnetic field to become homogeneous for the sample. We used (87)Rb (I = 3/2) in an aqueous solution of RbCl and in RbNb2O5F powder, (131)Xe (I = 3/2) of xenon gas physisorbed in Na-Y zeolite, and (23)Na (I = 3/2) in two well-known powders (NaNO3 and NaNO2) to support our theoretical result.

From crystalline to glassy gallium fluoride materials: an NMR study of 69Ga and 71Ga quadrupolar nuclei

Owing to the implementation of acquisition techniques specific for nuclei with very large quadrupolar interaction (full shifted echo and variable offset cumulative spectra (VOCS)), NMR spectra of 69Ga and 71Ga are obtained in crystallised (PbGaF5, Pb3Ga2F12, Pb9Ga2F24 and CsZnGaF6) and glassy (PbF2-ZnF2-GaF3) gallium fluorides. Simulations of both static (full echo or VOCS) and 15 kHz MAS spectra allow to obtain consistent determinations of isotropic chemical shifts and very large quadrupolar parameters (nu(Q) up to 14 MHz). In the crystalline compounds whose structures are unknown, the number and the local symmetry of the different gallium sites are tentatively worked out. For the glassy systems, a continuous Czjzek's distribution of the NMR quadrupolar parameters accounts for the particular shape of the NMR spectrum.