“BEST” Homonuclear Adiabatic Decoupling for C- and N-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 f_1rms 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.     

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.     

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, ...).     

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.     

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.     

Effect of Sweep Direction on Sidebands in Adiabatic Decoupling

The appearance of sidebands in adiabatic decoupling can be substantially reduced simply by matching the sweep rate and direction of adiabatic pulses with the evolution of differentJcouplings. Alternatively, a matched adiabatic defocusing pulse is applied just before the decoupling is turned on, providing an efficient means for complete suppression of sidebands.     

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.     

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.     

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.     

Stark effect and generalized Bloch-Siegert shift in a strongly driven two-level system

A superconducting qubit was driven in an ultrastrong fashion by an oscillatory microwave field, which was created by coupling via the nonlinear Josephson energy. The observed Stark shifts of the "atomic" levels are so pronounced that corrections even beyond the lowest-order Bloch-Siegert shift are needed to properly explain the measurements. The quasienergies of the dressed two-level system were probed by resonant absorption via a cavity, and the results are in agreement with a calculation based on the Floquet approach.     

Efficiency of heteronuclear broadband decoupling and homonuclear J cross polarization analyzed on two time scales

Decoupling sequences can be evaluated, as shown in Waugh's theory, with a J scaling factor on a long time scale. The efficiency of low-power decoupling, however, must be determined by cycling sidebands, as well as by the J scaling factor, when the sampling is not synchronized with the decoupling cycle. We introduced, therefore, another scaling factor which characterizes the decoupling on a short time scale. It is also shown that these scaling factors are useful for evaluating the efficiency of homonuclear J cross polarization. We clarified criteria of the factors suitable for various J coupling constants and chemical-shift ranges. Typical decoupling sequences were analyzed using the two scaling factors.     

A Vector Model of Adiabatic Decoupling

A vector model of adiabatic decoupling is enunciated for an IS-coupled system of two spin- heteronuclei in the high-power limit of ideal adiabatic pulses. The observed S-spin magnetization evolves according to a time-dependent coupling that scales as thezcomponent of an I-spin vector which evolves due to the applied decoupling irradiation. Simple analytical expressions are derived both on and off resonance for the reduced coupling during an ideal sech/tanh inversion pulse and for the resulting signal when either in-phase or antiphase magnetization is present at the start of decoupling. The resulting model allows one to readily envision decoupling experiments, make accurate estimates of sideband intensity, and assess the relative performance of different decoupling schemes. The utility of the model is further demonstrated by applying it to several recently proposed methods for reducing sidebands. In the limit of ideal adiabatic pulses, the predictions of the vector model are almost identical to those of quantum mechanics. At the lower RF power levels used in practical adiabatic decoupling applications, where the pulses are no longer perfectly adiabatic, phase cycles are employed to achieve performance that approximates the ideal limits derived here, so the vector model is more generally applicable, as well. These limits establish standards for future determination of the most efficient parameters for practical applications of broadband adiabatic decoupling in a single transient.     

Frequency shifts in parametrically enhanced low-field MR detection

A high-amplitude, high-frequency readout field has previously been proposed for use with low-field MR. Because the resulting modulation sidebands are at higher frequencies than the low-field steady precession, improved detection sensitivity results. However, if the ac readout field is inhomogeneous, it will necessarily have transverse components resulting in frequency shifts and broadening of the MR signal. Numerical solutions of Bloch's equations are compared to the Bloch-Siegert result to assess the size of the frequency shifts. A formula is derived by the average Hamiltonian method and provides an excellent fit to the numerically obtained shifts.     

Solid-state F NMR investigation of poly(vinylidene fluoride) with high-power proton decoupling

The use of high-power proton decoupling has enabled highly-resolved spectra of fluorine polymers to be recorded, as is exemplified herein for semicrystalline poly(vinylidene fluoride) (PVDF). By means of high MAS speeds (up to 17 kHz), the spinning sidebands are removed from the whole of the relevant chemical shift range. For spectra of the crystalline regions of the polymer, the high-power decoupling is necessary, though its effect is not large. Various relaxation techniques have been used to examine the semicrystallinity and the polymorphism of PVDF, with special pulse sequences used to discriminate between the various domains. Different chemical shifts have been observed for the signals of the amorphous and crystalline phases. Those of the more immobile parts cover a substantial range.     

Floquet engineering in topological crystalline insulator

There is a peculiar type of insulator, which is protected by the crystal symmetry known as topological crystalline insulator (TCI). In off-resonant cases, Floquet theory is an another way to study conventional Rabi oscillations. By using Floquet theory, the various type of Dirac fermionic systems and phases can be distinguished. In this article, it is shown that Floquet frequency can be used as a tool to distinguish different phases of TCI. The study of Bloch-Siegert shift has been performed and shown its variation in different phases of TCI. The collapse-revival spectra have also been studied in the perspective of Floquet theory and shown how quantum and classical Floquet oscillations are related to each other. The verification of the Floquet theory is justified by using numerical simulation.     

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.     

A concise expression for the all-order Bloch-Siegert shift

We derive a simple formula which is found to describe the Bloch-Siegert shift with good accuracy over almost the whole range of field strengths.     

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.     

Heteronuclear decoupling by multiple rotating frame technique

The paper describes the multiple rotating frame technique for designing modulated rf fields, that perform broadband heteronuclear decoupling in solution NMR spectroscopy. The decoupling method presented here is understood by performing a sequence of coordinate transformations, each of which demodulates a component of the rf field to a static component, that progressively averages the chemical shift and the dipolar interaction. We show that by increasing the number of modulations in the decoupling field, the ratio of dispersion in the chemical shift to the strength of the static component of the rf field is successively reduced in the progressive frames. The known decoupling methods like continuous wave decoupling, TPPM, etc., can be viewed as special cases of this method and their performance improves by adding additional modulations in the decoupling field. The technique is also expected to find use in design of broadband excitation, inversion and mixing sequences and broadband experiments in solid state NMR.