Adiabatic decoupling sidebands

An analytical solution is given for amplitudes and phases of adiabatic decoupling sidebands as a function of spin inversion time tau. Since all the adiabatic decoupling phases theta(t, tau) refocus at two periods (2T) of the decoupling pulse, the sidebands are located at n/2T rather than at n/T as observed in other decoupling schemes. The real (R(n)(tau)) and imaginary (I(n)(tau)) amplitudes of the sidebands have symmetry R(n)(tau) = R(-n)(tau) and I(n)(tau) = -I(-n)(tau), forming a mirror image between the counterparts of the sidebands. When frequency sweep changes direction all I(n)(tau) are inverted while all R(n)(tau) remain unchanged, leading to pure absorption sidebands with two accumulations as demonstrated by Kupce and Freeman, and to an exchange of sidebands between counterparts. The sum of the real parts for sidebands n = 1 and 2 is almost a constant near on-resonance decoupling, and it increases substantially for large decoupling offsets. The phase defocusing can be minimized for all decoupling offsets by inserting an initial decoupling period with T(ini) = T/2, eliminating all sidebands located at n/2T (n = +/-1, +/-3, +/-5, ...).     

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.     

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.     

A two-dimensional artifact from asynchronous decoupling

Many heteronuclear NMR experiments employ decoupling to collapse the heteronuclear multiplet, using decoupling schemes with a periodic phase modulation like WALTZ, MLEV, or GARP. Because of the periodic nature of these schemes, cycling sidebands are generated, whose intensity can be strongly reduced by decoupling asynchronously. We show that the most common implementation of asynchronous decoupling on modern spectrometers is such that the cycling sidebands are subjected to a periodic modulation. For multidimensional experiments, this results in ridges that can seriously compromise the quality of the spectrum. Based on our model, the artifact in a 2D [(1)H]-(15)N NOE equilibrium experiment is simulated and it is shown that the artifact can be prevented by using synchronous decoupling.     

A new decoupling method for accurate quantification of polyethylene copolymer composition and triad sequence distribution with 13C NMR

(13)C NMR is a powerful analytical tool for characterizing polyethylene copolymer composition and sequence distribution. Accurate characterization of the composition and sequence distribution is critical for researchers in industry and academia. Some common composite pulse decoupling (CPD) sequences used in polyethylene copolymer (13)C NMR can lead to artifacts such as modulations of the decoupled (13)C NMR signals (decoupling sidebands) resulting in systematic errors in quantitative analysis. A new CPD method was developed, which suppresses decoupling sidebands below the limit of detection (less than 1:40,000 compared to the intensity of the decoupled signal). This new CPD sequence consists of an improved Waltz-16 CPD, implemented as a bilevel method. Compared with other conventional CPD programs this new decoupling method produced the cleanest (13)C NMR spectra for polyethylene copolymer composition and triad sequence distribution analyses.     

Low-power XiX decoupling in MAS NMR experiments

Low-power XiX proton decoupling under fast magic-angle spinning is introduced. The method is applicable if the MAS frequency exceeds the proton-proton interactions. For rigid organic solids this is the case for MAS frequencies above approximately 40 kHz. It is shown that the quality of the decoupling as well as the sensitivity to frequency offsets can be improved compared to low-power continuous-wave decoupling. The decoupling efficiency is somewhat reduced compared to optimized high-power decoupling: in a peptide sample investigated at an MAS frequency of 50 kHz a loss of about 10% in signal intensity for CH3 and CH groups, and of about 40% for CH2 groups was observed. Taking into consideration, that the rf amplitude in the low-power XiX was about 15 times lower than in high-power XiX decoupling, such a reduction in line intensity is sometimes tolerable.     

A two-dimensional experiment that separates decoupling sidebands from the main peaks.

Broadband decoupling techniques generate undesirable cycling sidebands. The new two-dimensional technique described here allows separation of these sidebands from the main peaks by spreading the sideband responses in the indirectly detected dimension (F(1)) according to their frequency separations from the parent peaks, leaving the main resonances at zero frequency in F(1). This trace at zero frequency shows a thousandfold suppression of the residual sidebands, making possible the detection of very weak signals from dilute constituents of the sample. The experimental results can be displayed as one-dimensional "quiet decoupling" spectra without any significant loss of sensitivity. The new technique (DESIRE-decoupling sideband resolved spectroscopy) is simple, robust, and straightforward to implement.     

"BEST" homonuclear adiabatic decoupling for 13C- and 15N-double-labeled proteins.

The cyclic irradiation sidebands appearing in homonuclear adiabatic decoupling are calculated in detail, which reveals the origin of the antisymmetric sidebands. The sidebands can be inverted by inserting an initial decoupling with a different period, but the same f1rms as the main decoupling that is required for Bloch-Siegert shift compensation. The sidebands can be eliminated in a broad decoupling range by adding spectra of opposite sidebands. Based on this scheme, an offset-independent double-adiabatic decoupling, named Bloch-Siegert Shift Eliminated and Cyclic Sideband Trimmed Double-Adiabatic Decoupling, or "BEST" decoupling for short, is constructed, which not only compensates the Bloch-Siegert shift as shown earlier by Zhang and Gorenstein (1998) but also eliminates residual sidebands effectively.     

Influence of the surface anisotropy on the r.f. collapse effect

The influence of magnetic surface anisotropy on the fast relaxation of the hyperfine field forced by an r.f. field in invar (r.f. collapse effect) has been studied using the Mössbauer technique. The Mössbauer measurements were performed as a function of sample thickness (2.5–12 μm) and intensity (1–9 Oe) of the 50 MHz r.f. field applied. Due to the very high sensitivity of the r.f. collapse effect to the anisotropy field it was possible to detect the influence of “spin pinning” on the r.f. collapse effect. It is shown that a decrease of the sample thickness causes a decrease of the r.f. collapse effect at a given r.f. field frequency and intensity which is connected with the increase of the anisotropy field due to surface anisotropy. The dependence of the r.f. sidebands effect, which accompanies the r.f. collapse effect, on the sample thickness is discussed. The r.f. sidebands effect increases with decreasing sample thickness, which is in good agreement with the magnetostriction model of sidebands formation.     

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.     

Amplitude-modulated decoupling in rotating solids: a bimodal Floquet approach

This paper centers on a theoretical study of amplitude-modulated heteronuclear decoupling in solid-state NMR under magic-angle spinning (MAS). A spin system with a single isolated rare spin coupled to a large number of abundant spins is used in the analysis. The phase-alternating decoupling scheme (XiX decoupling) is analyzed using bimodal Floquet theory and the operator-based perturbation method developed by van Vleck. An effective Hamiltonian correct to second order is calculated for the spin system under XiX decoupling. The results of these calculations indicate that under XiX decoupling the main contribution to the residual line width comes from a cross-term between the heteronuclear and the homonuclear dipolar couplings. This is in contrast to continuous-wave decoupling, where the residual line width is dominated by the cross-term between the heteronuclear dipolar coupling and the chemical-shielding tensor of the irradiated spin. For high-power decoupling the method results in very good decoupling provided that certain unfavorable recoupling conditions, imposed by specific ratios of the amplitude modulation frequency and the MAS frequency, are avoided. For low-power decoupling, the method leads to acceptable decoupling when the pulse length corresponds to an integer multiple of a 2pi rotation and the rf-field amplitude is less than a quarter of the MAS frequency. The performance of the XiX scheme is analyzed over a range of values of the rf power, and numerical results that agree well with the most recent experimental observations are presented.     

Correlation of fast and slow chemical shift spinning sideband patterns under fast magic-angle spinning

A new two-dimensional solid-state NMR experiment, which correlates slow and fast chemical shift anisotropy sideband patterns is proposed. The experiment, dubbed ROSES, is performed under fast magic-angle spinning and leads to an isotropic spectrum in the directly detected omega(2) dimension. In the evolution dimension omega(1), the isotropic chemical shift is reduced by a factor S, and spinning sidebands are observed spaced by a scaled effective spinning speed omega(R)/S. These spinning sidebands patterns are not identical to those observed with standard slow magic-angle spinning experiments. Chemical shift anisotropy parameters can be accurately extracted with standard methods from these spinning sideband patterns. The experiment is demonstrated with carbon-13 experiments on powdered samples of a dipeptide and a cyclic undecapeptide, cyclosporin-A.     

Heteronuclear spin decoupling in solid-state NMR under magic-angle sample spinning

Achieving high spectral resolution is an important prerequisite for the application of solid-state NMR to biological molecules. Higher spectral resolution allows to resolve a larger number of resonances and leads to higher sensitivity. Among other things, heteronuclear spin decoupling is one of the important factors which determine the resolution of a spectrum. The process of heteronuclear spin decoupling under magic-angle sample spinning is analyzed in detail. Continuous-wave RF irradiation leads only in a zeroth-order approximation to a full decoupling of heteronuclear spin systems in solids under magic-angle spinning (MAS). In a higher-order approximation, a cross-term between the dipolar-coupling tensor and the chemical-shielding tensor is reintroduced, providing a scaled coupling term between the heteronuclear spins. In strongly coupled spin systems this second-order recoupling term is partially averaged out by the proton spin-diffusion process, which leads to exchange-type narrowing of the line by proton spin flips. This process can be described by a spin-diffusion type superoperator, allowing the efficient simulation of strongly coupled spin systems under heteronuclear spin decoupling. Low-power continuous-wave decoupling at fast MAS frequencies offers an alternative to high-power irradiation by reversing the order of the averaging processes. At fast MAS frequencies low-power continuous-wave decoupling leads to significantly narrower lines than high-power continuous-wave decoupling while at the same time reducing the power dissipated in the sample by several orders of magnitude. The best decoupling is achieved by multiple-pulse sequences at high RF fields and under fast MAS. Two such sequences, two-pulse phase-modulated decoupling (TPPM) and X-inverse-X decoupling (XiX), are discussed and their properties analyzed and compared.     

Synchronized adiabatic decoupling

A new decoupling scheme termed "synchronized adiabatic decoupling" is developed for use in the indirectly detected dimension. After each increment, the decoupling sequence is replaced by another one with different period T or different initial period T(ini) so that sampling always occurs at the end of a complete decoupling period. The effects of J coupling are therefore completely averaged out for all data points. As a result, all decoupling sidebands disappear and the center band increases correspondingly. Since the synchronized adiabatic decoupling does not require conventional editing techniques to cancel the sidebands, it is useful in high-field gradient-enhanced multidimensional experiments with only a single scan per increment.     

Sodium-23 MAS NMR study on nuclear quadrupole interaction in NA(1-x)Ag(x)NO2.

Ag-impurity effects on the first- and second-order quadrupole interaction (QI) at ²³Na site in an isomorphic mixed system, Na_1−xAg_xNO₂ (x=0, 0.0084, 0.026, 0.079, 0.094, 0.16), have been investigated by employing ²³Na (I=3/2) magic angle spinning nuclear magnetic resonance (MAS NMR) technique. The central transition (CT) and satellite transition (ST) are simultaneously observed with this system. From the spectral analysis, the quadrupole parameter and its distribution width are obtained as a function of Ag concentration. From the intensity loss of CT MAS centerband and of the envelope function of ST MAS sidebands due to impurities, the range of their influence on the second- and first-order QI is estimated. The estimated ranges contain the second and first neighbouring Na sites from the resonating ²³Na nucleus for the first- and second-order QI, respectively.     

Insights into homonuclear decoupling from efficient numerical simulation: techniques and examples

A combination of techniques, including rational number synchronisation and pre-diagonalisation of the time-dependent periodic Hamiltonian, are described which allow the efficient simulation of NMR experiments involving both magic-angle spinning (MAS) and RF irradiation, particularly in the important special case of phase-modulated decoupling sequences. Chebyshev and conventional diagonalisation approaches to calculating propagators under MAS are also compared, with Chebyshev methods offering significant advantages in cases where the Hamiltonian is large and time-dependent but not block-diagonal (as is the case for problems involving combined MAS and RF). The ability to simulate extended coupled spin systems efficiently allows 1H spectra under homonuclear decoupling to be calculated directly and compared to experimental results. Reasonable agreement is found for the conditions under which homonuclear decoupling is typically applied for rigid solids (although the increasing deviation of experimental results from the predictions of theory and simulation at higher RF powers is still unexplained). Numerical simulations are used to explore three features of these experiments: the interaction between the magic-angle spinning and RF decoupling, the effects of tilt pulses in acquisition windows and the effects of "phase propagation delays" on tilted axis precession. In each case, the results reveal features that are not readily anticipated by previous analytical studies and shed light on previous empirical observations.     

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.     

Suppression of artifacts induced by homonuclear decoupling in amino-acid-type edited methyl 1H-13C correlation experiments

A detailed theoretical and experimental analysis of the artifacts induced by homonuclear band-selective decoupling during CT frequency labeling is presented. The effects are discussed in the context of an amino-acid-type editing filter implemented in (1)H-(13)C CT-HSQC experiments of methyl groups in proteins. It is shown that both Bloch-Siegert shifts and modulation sidebands are efficiently suppressed by using additional off-resonance decoupling as proposed by Zhang and Gorenstein [J. Magn. Reson. 132 (1998) 81], and appropriate adjustment of a set of pulse sequence parameters. The theoretical predictions are confirmed by experiments performed on (13)C-labeled protein samples, yielding artifact-free amino-acid-type edited methyl spectra.