An efficient amplification pulse sequence for measuring chemical shift anisotropy under fast magic-angle spinning

A two-dimensional experiment for measuring chemical shift anisotropy (CSA) under fast magic-angle spinning (MAS) is presented. The chemical shift anisotropy evolution is amplified by a sequence of π-pulses that repetitively interrupt MAS averaging. The amplification generates spinning sideband manifolds in the indirect dimension separated by the isotropic shift along the direct dimension. The basic unit of the pulse sequence is designed based on the magic-angle turning experiment and can be concatenated for larger amplification factors.     

Correlating fast and slow chemical shift spinning sideband patterns in solid-state NMR

An experiment is presented that enables the measurement of small chemical shift anisotropy tensors under fast magic-angle spinning (MAS). The two-dimensional spectra obtained give a fast MAS sideband pattern in the directly observed dimension with the spinning sideband intensities equivalent to the chemical shift anisotropy scaled by a factor of N, or equivalently the sample spinning frequency scaled by 1/N, in the indirectly observed dimension. The scaling factor may be arbitrarily varied by changing the number and timings of the rotor synchronized pi-pulses used. Desirable features of the experiment include a fixed length pulse sequence and efficient sampling of the indirectly observed dimension. In addition, neither quadrature detection in the indirect dimension nor storage periods are required, consequently no signal intensity is discarded by the pulse sequence. The experiment is demonstrated using (31)P NMR of sodium phosphate and (13)C NMR of fumaric acid monoethyl ester for which a scaling factor of N=10.2 was employed.     

Applications of the CSA-amplified PASS experiment

The recently reported CSA-amplified PASS experiment correlates the spinning sidebands at the true spinning frequency omega(r) with the spinning sidebands that would be obtained at the effective spinning frequency omega(r)/N, where N is termed the scaling factor. The experiment is useful for the measurement of small chemical shift anisotropies, for which slow magic-angle spinning frequencies, required to measure several spinning sidebands, can be unstable. We have experimentally evaluated the reliability of this experiment for this application. In particular we have demonstrated that large scaling factors of the order of N=27 may be used, whilst still obtaining accurate chemical shift sideband intensities at the effective spinning frequency from the F(1) projection. Moreover, the sideband intensities are accurately obtained even in the presence of significant pulse imperfections. A second application of the CSA-amplified PASS experiment is the measurement of the chemical shift anisotropy of sites that experience homonuclear dipolar coupling, as may be found in uniformly labelled biological molecules, or for nuclei with a high natural abundance. The effects of homonuclear dipolar coupling on CSA-amplified PASS spectra has been investigated by numerical simulations and are demonstrated using uniformly (13)C enriched l-histidine monohydrochloride monohydrate.     

Chemical shift anisotropy amplification

A new NMR experiment which allows a measurement of the chemical shift anisotropy (CSA) tensor under magic angle spinning (MAS) is described. This correlates a fast MAS spectrum in the omega2 dimension with a sideband pattern in omega1 in which the intensities mimic those for a sample spinning at a fraction of the rate omega r/N, and these sidebands result from an amplification by a factor N of the modulation caused by the CSA. Standard methods can be used to extract the principal tensor components from the omega1 sideband patterns, and the nature of the experiment is such that the use of a large number of t1 increments can be avoided without compromising the resolution of different chemical sites. The new experiment is useful for accurately measuring narrow shift anisotropies.     

Chemical shift anisotropy amplification with high amplification factor and improved sensitivity

An improved version of the recently proposed chemical shift anisotropy amplification experiment is described. The original experiment correlates a fast magic angle spinning spectrum in the omega2 dimension with a sideband pattern in omega1 in which the intensities mimic those for a sample spinning at a fraction of the rate omegar/N. Advantages of the experiment include the use of standard methods to extract the principal tensor components from the omega1 sideband patterns and the small number of t1 increments required. The improved version described here permits large amplification factors N to be obtained without resort to prohibitively long sequences of pi-pulses and allows sensitivity to be maximized by eliminating the need to store the magnetization along the z-axis for t1. Amplification factors up to 32 are demonstrated experimentally.     

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.     

Multiple-rotor-cycle 2D PASS experiments with applications to (207)Pb NMR spectroscopy

Thetwo-dimensional phase-adjusted spinning sidebands (2D PASS) experiment is a useful technique for simplifying magic-angle spinning (MAS) NMR spectra that contain overlapping or complicated spinning sideband manifolds. The pulse sequence separates spinning sidebands by their order in a two-dimensional experiment. The result is an isotropic/anisotropic correlation experiment, in which a sheared projection of the 2D spectrum effectively yields an isotropic spectrum with no sidebands. The original 2D PASS experiment works best at lower MAS speeds (1-5 kHz). At higher spinning speeds (8-12 kHz) the experiment requires higher RF power levels so that the pulses do not overlap. In the case of nuclei such as (207)Pb, a large chemical shift anisotropy often yields too many spinning sidebands to be handled by a reasonable 2D PASS experiment unless higher spinning speeds are used. Performing the experiment at these speeds requires fewer 2D rows and a correspondingly shorter experimental time. Therefore, we have implemented PASS pulse sequences that occupy multiple MAS rotor cycles, thereby avoiding pulse overlap. These multiple-rotor-cycle 2D PASS sequences are intended for use in high-speed MAS situations such as those required by (207)Pb. A version of the multiple-rotor-cycle 2D PASS sequence that uses composite pulses to suppress spectral artifacts is also presented. These sequences are demonstrated on (207)Pb test samples, including lead zirconate, a perovskite-phase compound that is representative of a large class of interesting materials.     

Floquet-van Vleck analysis of heteronuclear spin decoupling in solids: the effect of spinning and decoupling sidebands on the spectrum

We investigate the effect of magic angle spinning on heteronuclear spin decoupling in solids. We use an analytical Floquet-van Vleck formalism to derive expressions for the powder-averaged signal as a function of time. These expressions show that the spectrum consists of a centerband at the isotropic frequency of the observed spin, omega(0), and rotational decoupling sidebands at omega(0)+/-omega(1)+/-momega(r), where omega(1) is the decoupling field strength and omega(r) is the rotation frequency. Rotary resonance occurs when the rotational decoupling sidebands overlap with the centerband. Away from the rotary resonance conditions, the intensity of the centerband as a function of omega(r)/omega(1) is simply related to the total intensity of the rotational decoupling sidebands. Notably, in the absence of offset terms it is shown that as omega(1) decreases, the centerband intensity can decrease without any associated broadening. Furthermore, the centerband width is shown to be independent of spinning speed, to second order for the effects we consider. The effects of I spin chemical shift anisotropy and homonuclear dipolar couplings are also investigated. The analytical results are compared to simulations and experiments.     

Q-shear transformation for MQMAS and STMAS NMR spectra

The multiple-quantum magic-angle spinning (MQMAS) and satellite-transition magic-angle spinning (STMAS) experiments refocus second-order quadrupolar broadening of half-integer quadrupolar spins in the form of two-dimensional experiments. Isotropic shearing is usually applied along the indirect dimension of the 2D spectra such that an isotropic projection free of anisotropic quadrupolar broadening can be obtained. An alternative shear transformation by a factor equal to the coherence level (quantum number) selected during the evolution period is proposed. Such a transformation eliminates chemical shift along the indirect dimension leaving only the second-order quadrupolar-induced shift and anisotropic broadening, and is expected to be particularly useful for disordered systems. This transformation, dubbed Q-shearing, can help avoid aliasing problems due to large chemical shift ranges and spinning sidebands. It can also be used as an intermediate step to the isotropic representation for expanding the spectral window of rotor-synchronized experiments.     

Heating of samples induced by fast magic-angle spinning

Intense sample heating through high-speed magic-angle spinning (MAS; up to 58 K temperature difference) is demonstrated. The role of probehead and spinner design, as well as that of the temperature of the bearing air on the heating of a rotating sample, is examined. MAS-induced heating can affect the accurate determination of the isotropic value of the chemical shift as well as the principal values, asymmetry and anisotropy parameters of the chemical shift tensor. In some cases, a very large temperature gradient (12 K) within the fast rotating sample was found, which may limit the resolution of high-speed 1H MAS nuclear magnetic resonance (NMR) spectra.     

An approximate method of sideband intensity calculation in magic angle spinning NMR

A theory of sideband intensity is derived by expanding into a Taylor series the free induction decay observed under magic angle spinning (MAS). According to this procedure, the free induction decay signal is completely represented by a basis of irreducible tensors from rank zero to rank infinity. After averaging over all orientations, only the zero-order irreducible tensors contribute to the sideband intensities. Symmetry properties of the sidebands can be seen clearly in this expansion and an approximate formula up to ninth order is obtained by truncating the series. Sideband intensities can be calculated rapidly with this formula. The results agree satisfactorily with the exact sideband intensities obtained by numerical simulation if the ratio of the anisotropy to the spinning speed, ω₀δ/ω_r, is smaller than 3. The relationship of the sideband intensities with the moments of a MAS spectrum shows that the proposed method is an alternative to moment analysis when the spinning speed is not very slow. Anisotropic information about the chemical shift anisotropy interaction therefore can be extracted efficiently from experimental spectra by this approximate method.     

Analytical solutions to several magic-angle spinning NMR experiments

Using the Anderson–Weiss (AW) formalism, analytical expressions of the NMR signal are obtained for the following magic-angle spinning (MAS) experiments: total suppression of sidebands (TOSS); phase adjusted spinning sidebands (PASS); rotational-echo double-resonance (REDOR); rotor-encoded REDOR (REREDOR); cross-polarization magic-angle spinning (CPMAS); exchange induced sidebands (EIS); one-dimensional exchange spectroscopy by sideband alternation (ODESSA); time-reverse ODESSA (trODESSA); centerband-only detection of exchange (CODEX). In order to test the validity of the AW approach, the Gaussian powder approximation is compared with exact powder calculations. A quantitative study of the effect of molecular dynamics on the efficiency of the TOSS and REDOR pulse sequences is then presented.     

To what extent does the centerband and each spinning sideband contain contributions from different crystallites of the powder sample?

It is shown that due to the destructive interference of the magnetization paths of crystallites taking place during the rotor period at slow spinning regime, the contribution of different crystallites to the centerband and to each spinning sideband is strongly weighted. For this, a separated-local-field experiment is used to tag the crystallites contributing to a given spinning sideband at different spinning speeds. The orientation dependence of spinning sidebands is also responsible for different lineshapes of the centerband and of each spinning sidebands observed under conditions of off-magic angle spinning.     

Heteronuclear local field NMR spectroscopy under fast magic-angle sample spinning conditions

The acquisition of bidimensional heteronuclear nuclear magnetic resonance local field spectra under moderately fast magic-angle spinning (MAS) conditions is discussed. It is shown both experimentally and with the aid of numerical simulations on multispin systems that when sufficiently fast MAS rates are employed, quantitative dipolar sideband patterns from directly bonded spin pairs can be acquired in the absence of ¹H–¹H multiple-pulse homonuclear decoupling even for “real” organic solids. The MAS speeds involved are well within the range of commercially available systems (10–14 kHz) and provide sidebands with sufficient intensity to enable a reliable quantification of heteronuclear dipolar couplings from methine groups. Simulations and experiments show that useful information can be extracted in this manner even from more tightly coupled –CH₂– moieties, although the agreement with the patterns simulated solely on the basis of heteronuclear interactions is not in this case as satisfactory as for methines. Preliminary applications of this simple approach to the analysis of molecular motions in solids are presented; characteristics and potential extensions of the method are also discussed.     

A new sensitive isotropic-anisotropic separation experiment-SPEED MAS

A new sensitive 2D isotropic-anisotropic separation experiment that utilizes stroboscopic phase encoding in the evolution dimension (SPEED) under magic angle sample spinning is presented. This 2D experiment consists of a train of 2N - 1 pi pulses that are applied over 2N rotor periods. The pi pulse train effectively reduces the apparent spinning speed in the evolution dimension by a factor of 1 / (2N) from the mechanical spinning speed. Thus, problems commonly associated with magic angle turning such as stable slow spinning, different matching and TPPM proton decoupling conditions are avoided. Data replication similar to the five pi replicated magic angle turning (FIREMAT) and pseudo 2D sideband suppression (P2DSS) experiments transfers resolution from the acquisition dimension to the evolution dimension. Hence, large spectral windows with good digital resolution are obtained with a few evolution increments. Here, slow spinning sideband patterns are extracted from the replicated 2D dataset with TIGER processing. Nevertheless, 2D Fourier transformation is also applicable. The extracted sideband patterns are identical to magic angle turning sideband pattern allowing for easy extraction of principal shift components. Accurate (13)C principal shift components are obtained for 3-methylglutaric acid using SPEED and FIREMAT experiments to validate the method. Furthermore, SPEED spectra for calcium acetate and alpha santonin are reported to show the wide applicability of this new experiment.     

Shift Anisotropy Tensors in Amorphous Natural-Abundance Solids: High-Resolution <Superscript>29</Superscript>Si Chemical Shift Anisotropy Distributions under Very Slow Sample Rotation

The magic-angle turning technique is applied to amorphous natural-abundance silicate materials and high-resolution silicon-29 correlations between the isotropic and anisotropic chemical shifts are obtained. Very narrow tilted spinning sideband patterns are resolved in the two-dimensional spectra whose line width corresponds to the natural line width of the silicon nuclei. Various numerical approaches are implemented to extract the distribution of the chemical shift anisotropy tensors in these materials and their results are compared. Authors' address: Dimitris Sakellariou, Laboratoire Claude Fréjacques, Service de Chimie Moléculaire, Commissariat à l'Energie Atomique Saclay, 91191 Gif-sur-Yvette cedex, France     

Two-dimensional chemical shift/heteronuclear dipolar coupling spectra obtained with polarization inversion spin exchange at the magic angle and magic-angle sample spinning (PISEMAMAS)

High-resolution two-dimensional ¹⁵N chemical shift/¹H-¹⁵N dipolar coupling polarization inversion spin exchange at the magic angle (PISEMA) spectra of a polycrystalline sample of ¹⁵N-acetylvaline were obtained with and without magic-angle sample spinning. These spectra demonstrate the advantages of the PISEMA experiment over conventional approaches to separated local-field spectroscopy, especially the high resolution in the dipolar dimension where the spinning sidebands have uniformly narrow linewidths.     

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).     

Using chemical shift anisotropy to resolve isotropic signals in solid-state NMR

A key problem in solid-state NMR is resolving overlapping isotropic signals. We present here a two-dimensional method which can enable sites with the same isotropic chemical shift to be distinguished according to their chemical shift anisotropy and asymmetry. The method involves correlating sideband spectra at different effective spinning rates using CSA-amplification pulse sequences. The resulting two-dimensional correlation pattern allows very accurate determination of the chemical shift principal values in addition to the recovery of parameters for two overlapping patterns which allows the resolution of overlapping signals.