Iterative Lineshape Fitting of MAS NMR Spectra: A Tool to Investigate HomonuclearJCoupling in Isolated Spin Pairs

Possibilities and limitations of iterative lineshape fitting procedures of MAS NMR spectra of isolated homonuclear spin pairs, aiming at determination of magnitudes and orientations of the various interaction tensors, are explored. Requirements regarding experimental MAS NMR spectra as well as simulation and fitting procedures are discussed. Our examples chosen are the isolated³¹P spin pairs in solid Na₄P₂O₇· 10H₂O, (1), and Cd(NO₃)₂· 2PPh₃, (2). In both cases the two³¹P chemical shielding tensors in the molecular unit are related byC₂symmetry, and determination of the orientations of these two tensors in the molecular frame is possible. In addition, aspects of homonuclearJcoupling will be addressed. For 1, both magnitude and sign of²J_iso(³¹P,³¹P) (J_iso= −19.5 ± 2.5 Hz) are obtained; for 2, (J_iso= +139 ± 3 Hz) anisotropy ofJwith an orientation of theJ-coupling tensor collinear, or nearly collinear, with the dipolar coupling tensor can be excluded, while absence or presence of anisotropy ofJwith any other relative orientation of theJ-coupling tensor cannot be determined.     

Unusual "AB" Spectra in High-Resolution Magic-Angle-Spinning NMR-Studies of Solids

Phosphorus-31CP-MAS spectra of Cd(NO₃)₂(PPh₃)₂ have been obtained as a function of spinning frequency. Although the two ³¹P nuclei are crystallographically equivalent and have the same isotropic chemical shifts in the solid state, they exhibit spinning-rate-dependent MAS spectra which have been analyzed to obtain the value of ²J(P, P). At high spinning rates, the spectra are analogous to "A₂" spectra in isotropic solutions, while at slower spinning rates, the spectra are more characteristic of strongly coupled "AB" solution spectra. The AB spectra are unusual in that δ_A = δ_B and J(A, B) is given by the splitting between the alternate peaks in the four-peak multiplet as opposed to the splitting between the outer and adjacent inner lines. This assignment was confirmed by a 2D CP-MAS J-resolved experiment. The unusual spinning-rate-dependent MAS lineshapes result from recoupling of the J interaction between the two crystallographically equivalent nuclei via anisotropic interactions, i.e., weak homonuclear dipolar coupling and differences in the orientation dependence of the chemical-shift tensors. Such spinning-rate-dependent MAS lineshapes are predicted to be a more frequent observation at higher applied magnetic fields.     

The effects of interplay of shielding,dipolar coupling,and indirect coupling tensors in the Tin-119 NMR spectra of solid triorganyl tin fluorides

Tin-119 magic-angle-spinning NMR spectra have been recorded for four solid triorganyl tin fluorides R₃SnF (R = methyl, isobutyl, phenyl, and mesityl). The centerbands give evidence of the polymeric nature of the first three compounds, which have fluorine bridges and pentacoordinate tin. The spinning sidebands show the influence of the interplay of shielding, dipolar coupling, and indirect coupling tensors. The theory of such interplay for AX₂ spin systems with coaxial tensors of axial symmetry is developed. Its application to the spectra discussed here results in values for shielding tensor components and dipolar coupling constants (including the pseudo-dipolar contribution) and thence (in principle) in estimates for the indirect coupling anisotropy ΔJ. The values of ΔJ may be given unambiguously since the absolute sign of the isotropic indirect coupling is known, but X-ray data on Sn-F distances are not yet known sufficiently well to make full use of the NMR results. Data from spinning-sideband analysis of trimesityltin fluoride are also given.     

Small 51V chemical shift anisotropy for LaVO4 from MQMAS and MAS NMR spectroscopy

51V MQMAS NMR of the triple-quantum transitions is shown to be particularly useful in the determination of the sign and magnitude of the chemical shift anisotropy (CSA) parameter delta(sigma)(= delta(iso)-delta(zz)) along with the asymmetry parameter (eta(sigma)) for a vanadium environment with a small CSA and a rather strong quadrupole coupling. This is demonstrated for the orthovanadate LaVO(4) for which 51V magic-angle spinning (MAS) NMR of the central and satellite transitions at 14.1T gives precise values for the quadrupole coupling parameters, however, an ambiguous sign for delta(sigma). The CSA parameters are reliably obtained from analysis of the spinning sidebands observed in a 51V triple-quantum MAS experiment. Combining these data with least-squares analysis of the manifold of spinning sidebands in the single-pulse MAS NMR spectrum results in a precise determination of the magnitudes and relative orientation of the 51V quadrupole coupling and CSA tensors for LaVO(4).     

魔角旋转情形下固体的非均匀相互作用

各向异性非均匀相互作用的慢旋转MAS-NMR谱是一系列的旋转边带,这些边带的强度包含了该相互作用张量的全部信息,只要计算和分析少数几条边带就可以得到这些有用的结构信息,本文用不可约球谐张量算符表示非均匀相互作用,采用Bessel函数展开法分析计算非均匀相互作用产生的旋转边带,这种分析计算方法适用于各种非均匀相互作用。以化学位移和四极相互作用为例的实验与理论符合很好。 关键词：     

Filtering of spinning sidebands in 1D MAS NMR spectra

Spinning sidebands (SSBs) in the MAS NMR spectrum of a polycrystalline solid are related to the principal values of the chemical shift or quadrupole coupling tensors. At present, 2D methods are widely used to sort out the SSBs for each isotropic peak. Here a simple and efficient method for separating the SSBs in 1D MAS NMR spectra is described. It is based on finding the optimal spinning rate with a mathematical algorithm and subsequently treating the spectra with filtering functions.     

NMR study of heterogeneity in pyridine-N-oxide...HCl crystal

An origin of narrow ¹H NMR signals in pyridine-N-oxide (PyO)...HCl crystal has been investigated by means of MAS, SPEDAS, NOESY and COSY techniques. Spectra of crystalline samples are compared with those of solid phase obtained from liquid PyO...HCl solutions (in acetonitile/H₂O) after the heterogeneous phase separation. It has been concluded that partially resolved peaks in ¹H NMR spectra of solids are related with heterogeneity of spin system and presence of different H-bond clusters of water molecules. NOESY spectra show no cross-peaks even at very long mixing time (500 ms). This indicates there is no exchange process between spins causing different peaks, and thus the corresponding molecular aggregates are captured in “islands of mobility8 without any channels sufficient for exchange. Appearance of MAS side bands as “pseudo8 cross-peaks in 2D NMR spectra using MAS/COSY technique is reported. In the case of accidental coincidence of spinning frequency (ω _MAS ) with spectral distances between some diagonal signals, intensive non-diagonal peaks are observed at the corresponding cross-positions. A misleading conclusion concerning spin coupling is easy to avoid using various ω _MAS . This work is dedicated to Professor Robert Blinc on the occasion of his 70^th birthday.     

59Co chemical shift anisotropy and quadrupole coupling for K3Co(CN)6 from MQMAS and MAS NMR spectroscopy

59Co triple-quantum (3Q) MAS and single-pulse MAS NMR spectra of K3Co(CN)6 have been obtained at 14.1 T and used in a comparison of these methods for determination of small chemical shift anisotropies for spin I = 7/2 nuclei. From the 3QMAS NMR spectrum a spinning sideband manifold in the isotropic dimension with high resolution is reconstructed from the intensities of all spinning sidebands in the 3QMAS spectrum. The chemical shift anisotropy (CSA) parameters determined from this spectrum are compared with those obtained from MAS NMR spectra of (i) the complete manifold of spinning sidebands for the central and satellite transitions and of (ii) the second-order quadrupolar lineshapes for the centerband and spinning sidebands from the central transition. A good agreement between the three data sets, all of high precision, is obtained for the shift anisotropy (delta(sigma) = delta(iso) - delta(zz)) whereas minor deviations are observed for the CSA asymmetry parameter (eta(sigma)). The temperature dependence of the isotropic 59Co chemical shift has been studied over a temperature range from -28 to +76 degrees C. A linear and positive temperature dependence of 0.97 ppm/degree C is observed.     

Solid-State Si, Cd, Sn, and P NMR Studies of II-IV-P2 Semiconductors

Solid-state ²⁹Si, ¹¹³Cd, ¹¹⁹Sn, and ³¹P MAS NMR spectra are reported on a series of II-IV-P₂ compounds. In favorable cases (e.g., high degree of crystallinity, low concentration of unpaired electrons), well-defined spectra, with sharp lines for each specific nearest-neighbor configuration, are observed; in such cases, expected J coupling patterns are also seen. High-resolution solid-state NMR studies of this type provide useful information on structure (disorder), doping, and electron-mediated coupling in semiconductor systems.     

Fast magic-angle sample spinning solid-state NMR at 60–100 kHz for natural abundance samples

In spite of tremendous progress made in pulse sequence designs and sophisticated hardware developments, methods to improve sensitivity and resolution in solid-state NMR (ssNMR) are still emerging. The rate at which sample is spun at magic angle determines the extent to which sensitivity and resolution of NMR spectra are improved. To this end, the prime objective of this article is to give a comprehensive theoretical and experimental framework of fast magic angle spinning (MAS) technique. The engineering design of fast MAS rotors based on spinning rate, sample volume, and sensitivity is presented in detail. Besides, the benefits of fast MAS citing the recent progress in methodology, especially for natural abundance samples are also highlighted. The effect of the MAS rate on ¹H resolution, which is a key to the success of the ¹H inverse detection methods, is described by a simple mathematical factor named as the homogeneity factor k. A comparison between various ¹H inverse detection methods is also presented. Moreover, methods to reduce the number of spinning sidebands (SSBs) for the systems with huge anisotropies in combination with ¹H inverse detection at fast MAS are discussed.     

Differential Line Broadening in the Presence of Quadrupolar–CSA Interference

The formalism for calculating the lineshape of a spin 1/2J-coupled to a high-spin nucleus undergoing quadrupolar and chemical shift anisotropy (CSA) relaxations is derived in the case where the tensors of both interactions are noncoincident and nonaxial. The expressions show that the CSA–quadrupolar interference term which is responsible for the asymmetry of lines involves a term depending on tensorial parameters. The effect of this term on the lineshapes is discussed with respect to three cases, namely coincident–axially symmetric, noncoincident–axially symmetric, and general noncoincident quadrupolar and CSA tensors. These cases are considered in the analysis of the lineshape of the¹H-decoupled spectra of the³¹P nucleusJ-coupled to the⁵⁹Co nucleus encountered in the tetrahedral cluster HFeCo₃(CO)₁₁PPh₂H.     

Critical factors in obtaining meaningful fast MAS NMR spectra of non-integral spin quadrupolar nuclei. A review with particular emphasis on27Al MAS NMR of catalysts and minerals

In the last decade, magic angle spinning (MAS) NMR has become an extremely important method for studying the structure of inorganic solids. Advances in NMR technology have greatly aided in understanding the structure of catalysts, minerals, clays, ceramics, glasses, etc. Obtaining meaningful MAS spectra of spin-1/2 nuclei such as²⁹Si and³¹P is relatively straightforward and well understood. In contrast, obtaining meaningful MAS spectra is far from simple with non-integral spin quadrupolar nuclei such as¹¹B (I=3/2),¹⁷O (I=5/2),²³Na (I=3/2),²⁷Al (I=5/2),⁶⁹Ga (I=3/2), and⁷¹Ga (I=3/2)?to name some of the most commonly studied nuclei. Many additional factors have to be considered. This paper will deal with these factors and the utility of very fast MAS for studying non-integral spin quadrupolar nuclei in inorganic solids.     

31P and 13C chemical shielding tensors in the phosphoenolpyruvate moiety from rotary resonance recoupling 13C and 31P MAS and single crystal 31P NMR

A ³¹P and ¹³C NMR study of powder and single crystal samples of two phosphoenolpyruvate (PEP) compounds, the tris-ammonium salt monohydrate (NH₄)₃(PEP)·H₂O (1), and the mono-ammonium-salt (NH₄)(H₂PEP) (2) is presented. The P chemical shielding tensors in 1 are measured by ³¹P single crystal NMR on four minuscule samples and assigned without ambiguity by exploiting the orientation-dependent ³¹P-³¹p dipolar splittings of the resonance lines. The orientation of the ³¹P chemical shielding tensor is discussed in terms of the C_2v — and C₃-type distortions of the phosphate PO₄-coordination sphere. From ¹³C MAS NMR experiments with ³¹P rotary resonance recoupling on polycrystalline powder samples the orientations of the ³¹P chemical shielding tensors in 1 and 2 are obtained, for 1 in very good agreement with the ³¹P single crystal NMR results. Only some of the orientational parameters of the three ¹³C chemical shielding tensors in the PEP moiety of 1 could be derived from ¹³C MAS NMR experiments with ³¹P rotary resonance recoupling.     

Technical aspects of fast magic-angle turning NMR for dilute spin-1/2 nuclei with broad spectra

For obtaining sideband-free spectra of high-Z spin-1/2 nuclei with large (>1000 ppm) chemical-shift anisotropies and broad isotropic-shift dispersion, we recently identified Gan's modified five-pulse magic-angle turning (MAT) experiment as the best available broadband pulse sequence, and adapted it to fast magic-angle spinning. Here, we discuss technical aspects such as pulse timings that compensate for off-resonance effects and are suitable for large CSAs over a range of 1.8γB₁; methods to minimize the duration of z-periods by cyclic decrementation; shearing without digitization artifacts, by sharing between channels (points); and maximizing the sensitivity by echo-matched full-Gaussian filtering. The method is demonstrated on a model sample of mixed amino acids and its large bandwidth is highlighted by comparison with the multiple-π-pulse PASS technique. Applications to various tellurides are shown; these include GeTe, Sb₂Te₃ and Ag_0.53Pb₁₈Sb_1.2Te₂₀, with spectra spanning up to 190 kHz, at 22 kHz MAS. We have also determined the ¹²⁵Te chemical shift anisotropies from the intensities of the spinning sidebands resolved by isotropic-shift separation.     

Magic Angle-Oriented Sample Spinning (MAOSS): A New Approach toward Biomembrane Studies

The application of magic angle sample spinning (MAS) NMR to uniformly aligned biomembrane samples is demonstrated as a new general approach toward structural studies of membrane proteins, peptides, and lipids. The spectral linewidth from a multilamellar lipid dispersion is dominated, in the case of protons, by the dipolar coupling. For low-γ or dilute spins, however, the chemical shift anisotropy dominates the spectral linewidth, which is reduced by the two-dimensional order in a uniformly aligned lipid membrane. The remaining line broadening, which is due to orientational defects (“mosaic spread”) can be easily removed at low spinning speeds. This orientational order in the sample also allows the anisotropic intermolecular motions of membrane components (such as rotational diffusion, τ_c= 10⁻¹⁰s) for averaging dipolar interactions to be utilized, e.g., by placing the membrane normal parallel to the rotor axis. The dramatic resolution improvement for protons which are achieved in a lipid sample at only 220 Hz spinning speed in a 9.4 T field is slightly better than any data published to date using ultra-high fields (up to 17.6 T) and high-speed spinning (14 kHz). Additionally, the analysis of spinning sidebands provides valuable orientational information. We present the first¹H,³¹P, and¹³C MAS spectra of uniformly aligned dimyristoylphosphatidylcholine (DMPC) bilayers. Also,¹H resolution enhancement for the aromatic region of the M13 coat protein reconstituted into DMPC bilayers is presented. This new method combines the high resolution usually achieved by MAS with the advantages of orientational constraints obtained by working with macroscopically oriented samples. We describe the general potential and possible perspectives of this technique.     

Solid-state 17O NMR study of the electric-field-gradient and chemical shielding tensors in polycrystalline γ-glycine

We report the first experimental determination of the carboxylate oxygen electric-field-gradient (EFG) and chemical shielding (CS) tensors in polycrystalline γ-glycine. Analysis of magic-angle spinning (MAS) and stationary ¹⁷O NMR spectra of [¹⁷O]-γ-glycine obtained at 9.4, 14.1, 16.4, and 18.8 T yields the magnitudes of the ¹⁷O EFG and CS tensors and the relative orientations between the two tensors. Extensive quantum chemical calculations at both the restricted Hartree–Fock and density functional levels have been performed to present the absolute tensor orientations in term of the molecular frame. We have demonstrated that ¹⁷O NMR tensor information could be unambiguously derived by the multiple field analyses of stationary ¹⁷O NMR spectra.     

Quantification of homonuclear dipolar coupling networks from magic-angle spinning 1H NMR

Numerical simulations of magic-angle spinning (MAS) spectra of dipolar-coupled nuclear spins have been used to assess different approaches to the quantification of dipolar couplings from ¹H solid-state NMR. Exploiting the translational symmetry of periodic spin systems allows extended networks with ‘realistic’ numbers of spins to be considered. The experimentally accessible parameter is shown to be the root-sum-square of the dipolar couplings to a given spin. The effectiveness of either fitting the resulting spinning sideband spectra to small spin system models, or using analyses based on moment expansions, has been examined. Fitting of the spinning sideband pattern is found to be considerably more robust with respect to experimental noise than frequency domain moment analysis. The influence of the MAS rate and system geometry on robustness of the quantification is analysed and discussed.     

Direct Determination of Motional Correlation Times by 1D MAS and 2D Exchange NMR Techniques

One- and two-dimensional static and magic-angle spinning (MAS) exchange NMR experiments for quantifying slow (τ_c> 1 ms) molecular reorientation dynamics are analyzed, emphasizing the extent to which motional correlation times can be extracteddirectlyfrom the experimental data. The static two-dimensional (2D) exchange NMR experiment provides geometric information, as well as exchange time scales via straightforward and model-free application of Legendre-type orientational autocorrelation functions, particularly for axially symmetric interaction tensors, as often encountered in solid-state²H and¹³C NMR. Under conditions of MAS, increased sensitivity yields higher signal-to-noise spectra, with concomitant improvement in the precision and speed of correlation time measurements, although at the expense of reduced angular (geometric) resolution. For random jump motions, one-dimensional (1D)exchange-inducedsidebands (EIS)¹³C NMR and the recently developed ODESSA and time-reverse ODESSA experiments complement the static and MAS two-dimensional exchange NMR experiments by providing faster means of obtaining motional correlation times. For each of these experiments, the correlation time of a dynamic process may be obtained from a simple exponential fit to the integrated peak intensities measured as a function of mixing time. This is demonstrated on polycrystalline dimethylsulfone, where the reorientation rates from EIS, ODESSA, time-reverse ODESSA, and 2D exchange are shown to be equivalent and consistent with literature values. In the analysis, the advantages and limitations of the different methods are compared and discussed.     

MOMENT EXPANSIONS OF PROTON DIPOLAR SPINNING-SIDEBAND INTENSITIES IN A 1H MAS NMR SPECTRUM

对于包含分子和分子基团绕至少一个轴高速运动的固体体系，本文推导出其质子核磁共振谱的偶极魔角旋转边带强度的理论计算表达式，建立了用其静态粉末谱的矩的展开的计算方法，计算出旋转边带强度按三十阶矩展开的系数，它可以处理包含高达十五阶边带的谱.