Recoupling of heteronuclear dipolar interactions with rotational-echo double-resonance at high magic-angle spinning frequencies

Heteronuclear dipolar recoupling with rotational-echo double-resonance (REDOR) is investigated in the rapid magic-angle spinning regime, where radiofrequency irradiation occupies a significant fraction of the rotor period (10-60%). We demonstrate, in two model (13)C-(15)N spin systems, [1-(13)C, (15)N] and [2-(13)C, (15)N]glycine, that REDOR DeltaS/S(0) curves acquired at high MAS rates and relatively low recoupling fields are nearly identical to the DeltaS/S(0) curve expected for REDOR with ideal delta-function pulses. The only noticeable effect of the finite pi pulse length on the recoupling is a minor scaling of the dipolar oscillation frequency. Experimental results are explained using both numerical calculations and average Hamiltonian theory, which is used to derive analytical expressions for evolution under REDOR recoupling sequences with different pi pulse phasing schemes. For xy-4 and extensions thereof, finite pulses scale only the dipolar oscillation frequency by a well-defined factor. For other phasing schemes (e.g., xx-4 and xx-4) both the frequency and amplitude of the oscillation are expected to change.     

13C/14N heteronuclear multiple-quantum correlation with rotary resonance and REDOR dipolar recoupling

A two-dimensional (13)C/(14)N heteronuclear multiple quantum correlation (HMQC) experiment using dipolar recoupling under magic-angle spinning (MAS) is described. The experiment is an extension of the recent indirect (13)C detection scheme for measuring (14)N quadrupolar coupling under MAS. The recoupling allows the direct use of the much larger dipolar interaction instead of the small J and residual dipolar couplings for establishing (13)C/(14)N correlations. Two recoupling methods are incorporated into the HMQC sequence, both applying rf only to the observed (13)C spin. The first one uses the REDOR sequence with two pi-pulses per rotor cycle. The second one uses a cw rf field matching the spinning frequency, known as rotary resonance. The effects of CSA, T(2)(') signal loss, MAS frequency and stability and t(1)-noise are compared and discussed.     

C–H dipolar recoupling under very fast magic-angle spinning using virtual pulses

A new solid-state NMR pulse sequence for recoupling ¹³C–¹H dipolar interactions under magic-angle spinning is proposed, which works under a spinning speed of a few to several tens kilohertz. The sequence is composed of two different frequency switched Lee–Goldburg sequences, and the modulation of the spin part of the ¹³C–¹H dipolar interaction is introduced by a virtual pulse sequence consisting of unitary operators connecting the rotating frame and the tilted rotating frame. When the cycle time of the spinning is equal to or twice the cycle time of the sequence, the ¹³C–¹H dipolar interactions can be recoupled. The sequence is insensitive to experimental imperfections such as rf inhomogeneity or frequency offset, and the resulting lineshape can be represented by a simple analytical equation based on the zeroth-order average Hamiltonian. Experimental results for [2-¹³C] -valine·HCl are reported.     

Band-selective recoupling of homonuclear double-quantum dipolar interaction with a generalized composite 0 degrees pulse: application to 13C aliphatic region-selective magnetization transfer in solids

Recoupling of homonuclear double quantum (DQ)-dipolar interactions is a useful technique for the structural analysis of molecules in solids. We have designed a series of elemental 0 degrees pulses for the recoupling sequences with the rf phase rotation about the z-axis, known as CN. The proposed 0 degrees pulses whose total flip angle >/=360 degrees provide spin rotation vectors in the xy-plane. Thus, the residual spin rotation can be canceled by rf phase rotation about the z-axis. An analysis by the coherent averaging theory showed that effective bandwidths of the recoupling sequences are limited not by the reduction in the dipolar scaling factor but by the increase in the residual spin rotation due to offset. A CN sequence with these elemental pulses provides an effective bandwidth of DQ-dipolar recoupling from ca. 0.5nu(R) to 4nu(R) for numerical simulations. Here, nu(R) is the sample spinning frequency. The 0 degrees pulses were applied to band-selective recoupling for the magnetization transfer in uniformly 13C-labeled molecules. Narrow-band recoupling enhances the magnetization transfer between spins within the effective range by decoupling the dipolar interactions between spins one of which is outside the range. The narrow band operation reduces rf field strength, which improves the CH decoupling. Increases in signal intensities by the use of the proposed 0 degrees pulses are experimentally shown for 13C-labeled amino acids.     

Determination of the backbone torsion psi angle by tensor correlation of chemical shift anisotropy and heteronuclear dipole-dipole interaction

We demonstrate that the backbone torsion psi angle of a uniformly labeled residue can be determined accurately by correlating the chemical shift anisotropy of the carbonyl carbon and the 13C-1H heteronuclear dipole-dipole interaction of the alpha carbon. To obtain the highest sensitivity for the psi angle determination, the following conditions are desired: (i) the recoupling pulse sequences for the CSA and the heteronuclear dipolar interactions are gamma encoded, in which the spatial parts of m=2 are selected; (ii) the homonuclear polarization transfer is based on the scalar spin-spin coupling. Experimental data were obtained for [U-13C, 15N]-alanine and N-acetyl-[U-13C, 15N]-d,l-valine under magic-angle spinning at 25kHz. Only three data points are required for the measurements and the dihedral angles determined are in excellent agreement with the diffraction data.     

Supercycled symmetry-based double-quantum dipolar recoupling of quadrupolar spins in MAS NMR: I. Theory

Using average Hamiltonian (AH) theory, we analyze recently introduced homonuclear dipolar recoupling pulse sequences for exciting central-transition double-quantum coherences (2QC) between half-integer spin quadrupolar nuclei undergoing magic-angle-spinning. Several previously observed differences among the recoupling schemes concerning their compensation to resonance offsets and radio-frequency (rf) inhomogeneity may qualitatively be rationalized by an AH analysis up to third perturbation order, despite its omission of first-order quadrupolar interactions. General aspects of the engineering of 2Q-recoupling pulse sequences applicable to half-integer spins are discussed, emphasizing the improvements offered from a diversity of supercycles providing enhanced suppression of undesirable AH cross-terms between resonance offsets and rf amplitude errors.     

Sensitivity enhancement in structural measurements by solid state NMR through pulsed spin locking

Free induction decay (FID) signals in solid state NMR measurements performed with magic angle spinning can often be extended in time by factors on the order of 10 by a simple pulsed spin locking technique. The sensitivity of a structural measurement in which the structural information is contained in the dependence of the integrated FID amplitude on a preceding evolution period can therefore be enhanced substantially by pulsed spin locking in the signal detection period. We demonstrate sensitivity enhancements in a variety of solid state NMR techniques that are applicable to selectively isotopically labeled samples, including 13C-15N rotational echo double resonance (REDOR), 13C-13C dipolar recoupling measurements using the constant-time finite-pulse radio-frequency-driven recoupling (fpRFDR-CT) and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) techniques, and torsion angle measurements using the double quantum chemical shift anisotropy (DQCSA) technique. Further, we demonstrate that the structural information in the solid state NMR data is not distorted by pulsed spin locking in the detection period.     

Selective dephasing of OH and NH proton magnetization based on (1)H chemical-shift anisotropy recoupling

A method for selectively suppressing the signals of OH and NH protons in (1)H combined rotation and multiple-pulse spectroscopy (CRAMPS) and in (1)H-(13)C heteronuclear correlation (HETCOR) solid-state NMR spectra is presented. It permits distinction of overlapping CH and OH/NH proton signals, based on the selective dephasing of the magnetization of OH and NH protons by their relatively large (1)H chemical-shift anisotropies. For NH protons, the (14)N-(1)H dipolar coupling also contributes significantly to this dephasing. The dephasing is achieved by a new combination of heteronuclear recoupling of these anisotropies with (1)H homonuclear dipolar decoupling. Since the 180 degrees pulses traditionally used for heteronuclear dipolar and chemical-shift anisotropy recoupling would result in undesirable homonuclear dephasing of proton magnetization, instead the necessary inversion of the chemical-shift Hamiltonian every half rotation period is achieved by inverting the phases of all the pulses in the HW8 multiple-pulse sequence. In the HETCOR experiments, carefully timed (13)C 180 degrees pulses remove the strong dipolar coupling to the nearby (13)C spin. The suppression of NH and OH peaks is demonstrated on crystalline model compounds. The technique in combination with HETCOR NMR is applied to identify the CONH and NH-CH groups in chitin and to distinguish NH and aromatic proton peaks in a peat humin.     

Heteronuclear dipolar recoupling in liquid crystals and solids by PISEMA-type pulse sequences

A pulse sequence is described for the recoupling of heteronuclear dipolar interactions under MAS. The method is similar to the PISEMA experiment, but employs a well-defined amplitude modulation of one of the two radio-frequency fields. The technique is used for measurements of 1H-13C dipolar couplings in unoriented solid and liquid-crystalline samples.     

Compound radiofrequency-driven recoupling pulse sequences for efficient magnetization transfer by homonuclear dipolar interaction under magic-angle spinning conditions

The maximum of the transferred magnetization in rotating powdered solids under the radiofrequency-driven recoupling (RFDR) pulse sequence is enhanced by reducing the orientation dependence of the effective recoupled homonuclear dipolar interaction. The compound RFDR (CRFDR) pulse sequence for this enhancement consists of RFDR pulse units (tau(i)-pi-tau(R)-pi-1171;tau(i)) with different tau(i), where tau(R) is the sample rotation period, tau(i) and 1171;tau(i) (=tau(R) - tau(i)) are delays, and pi is a 180 degrees pulse. The delay tau(i) modifies the zero-quantum spin operators and the sample rotation-angle dependence of the recoupled dipolar Hamiltonian. The CRFDR pulse sequences were optimized for mixing by varying tau(i). Numerical simulation for the two-spin system only with a dipolar interaction and isotropic chemical shifts indicates that the transfer efficiency of CRFDR averaged over the powder is about 70%, which is 30% higher than the efficiency of the RFDR pulse over a broad range of about 1/tau(R) in resonance frequency difference. The CRFDR sequences need about 60% longer mixing times to maximize the transferred magnetizaion in comparison with the original RFDR sequence. Chemical shift anisotropy, the other dipolar interactions, and relaxation generally reduce the enhancement by CRFDR. Experiments for fully (13)C-labeled alanine, however, show that the maximum of the magnetization transferred with CRFDR from the carboxyl to alpha carbon is about 15% greater than that with RFDR. Copyright 2000 Academic Press.     

The application of MAS recoupling methods in the intermediate motional regime

We present investigations concerning the effect of molecular motions on the experimental timescale upon the recoupling of anisotropic interactions under magic-angle spinning conditions. An approach for the efficient simulation of spin dynamics occurring during complex pulse sequences, based on a linearization of the general solution of the stochastic Liouville-von Neumann equation, was developed. Using (13)C CSA recoupling of the methyl carbon in dimethylsulfon as a sample interaction, we observed a characteristic signal decay under recoupling upon entering the intermediate motional regime, which can be well described by an apparent transverse relaxation time, T(2)(rcpl). This quantity does not depend on the spinning frequency to a first approximation. Specific recoupling experiments, namely the measurement of tensor parameters by spinning sideband analysis, and the determination of rate constants with the CODEX experiment, are discussed with respect to possibilities and limits of their application in the intermediate motional regime. Important conclusions are drawn with regards to the limited applicability of popular recoupling methods like REDOR to samples exhibiting intermediate mobility.     

Complete Dipolar Decoupling ofC and Its Use in Two-Dimensional Double-Quantum Solid-State NMR for Determining Polymer Conformations

A multiple-pulse technique for complete dipolar decoupling of directly bonded¹³C-labeled sites is described. It achieves significant spectral simplifications in a recently introduced two-dimensional double-quantum solid-state NMR experiment for determining torsion angles. Both homonuclear and heteronuclear dipolar couplings are removed by combining a¹³C multiple-pulse sequence with continuous-wave irradiation on the protons. The¹³C sequence has a fundamental 10-pulse cycle which is a significantly modified magic-sandwich-echo sequence. The crucial heteronuclear decoupling is achieved by breaking the 360° “inner” pulses in the magic sandwich into 90° pulses and spacing them by¹H 360° pulse lengths. Spectral artifacts typical of multiple-pulse sequences are eliminated by phase shifts between cycles. In contrast to many other multiple-pulse decoupling sequences, the long window in the cycle is the dwell time and can be longer than the inverse dipolar coupling, which makes the sequence practical for direct detection even with long pulse ring-down times. A modification of the sequence to scale the chemical shift and increase the effective spectral width is also presented. The 1D and double-quantum 2D experiments are demonstrated on polyethylene with 4%¹³C–¹³C spin pairs. The potential of this approach for distinguishing segmental conformations is illustrated by spectral simulations of the two-dimensional ridge patterns that correlate double-quantum and single-quantum chemical-shift anisotropies.     

Efficient deuterium-carbon REDOR NMR spectroscopy

Phase modulated pulses for deuterium recoupling in (2)H-(13)C REDOR NMR spectroscopy have been introduced to improve dephasing of the detected (13)C nuclei. The deuterium inversion properties of phase modulated recoupling pulses have been studied experimentally on l-alanine-2-d(1) and theoretically using average Hamiltonian theory and exact simulations of the equation of motion of the density matrix. The best (13)C dephasing was observed when XYXYX (PM5) deuterium recoupling pulses were applied. A comparison to the 90 degrees -180 degrees -90 degrees (CPL) composite pulse scheme revealed an improvement of recoupling on the order of 2.5. Simple CW recoupling pulses of the same length of PM5 and CPL pulses showed the weakest (13)C dephasing. Simulations have shown that the (2)H recoupling efficiency of PM5 REDOR experiments approach the very efficient REAPDOR results. However, in our case a REAPDOR study of l-alanine-2-d(1) resulted in a significant decrease of the (13)C signal intensity due to pulse imperfections of (13)C pi-pulses. The new PM5-REDOR technique has been employed to study the torsion angle between C1/2 and C5 in ethylmalonic acid-4-d(2).     

Analytical theory of gamma-encoded double-quantum recoupling sequences in solid-state nuclear magnetic resonance

Many important double-quantum recoupling techniques in solid-state NMR are classified as being gamma-encoded. This means that the phase of the double-quantum effective Hamiltonian, but not its amplitude, depends on the third Euler angle defining the orientation of the molecular spin system in the frame of the magic-angle-spinning rotor. In this paper, we provide closed analytical solutions for the dependence of the powder-average double-quantum-filtered signal on the recoupling times, within the average Hamiltonian approximation for gamma-encoded pulse sequences. The validity of the analytical solutions is tested by numerical simulations. The internuclear distance in a (13)C(2)-labelled retinal is estimated by fitting the analytical curves to experimental double-quantum data.     

Comparison of several hetero-nuclear dipolar recoupling NMR methods to be used in MAS HMQC/HSQC

We compare several hetero-nuclear dipolar recoupling sequences available for HMQC or HSQC experiments applied to spin-1/2 and quadrupolar nuclei. These sequences, which are applied to a single channel, are based either on the rotary resonance recoupling (R3) irradiation, or on two continuous rotor-synchronized modulations (SFAM1 and SFAM2), or on four symmetry-based sequences (R2(1)1,SR4(1)2,R12(3)5,R20(5)9), or on the REDOR scheme. We analyze systems exhibiting purely hetero-nuclear dipolar interactions as well as systems where homo-nuclear dipolar interactions need to be canceled. A special attention is given to the behavior of these sequences at very fast MAS. It is shown that R3 methods behave poorly due to the narrowness of their rf-matching curves, and that the best methods are SR4(1)2 and SFAM (SFAM1 or SFAM2 if homo-nuclear interactions are not negligible). REDOR can also recouple efficiently hetero-nuclear dipolar interactions, provided the sequence is sent on the non-observed channel and homo-nuclear dipolar interactions are negligible. We anticipate that at ultra-fast spinning speed, SFAM1 and SFAM2 will be the most efficient methods.     

The Effect of RF Inhomogeneity on Heteronuclear Dipolar Recoupling in Solid State NMR: Practical Performance of SFAM and REDOR

Practical heteronuclear dipolar recoupling performances under magic angle spinning for SFAM and REDOR have been investigated under well-defined rf inhomogeneity environments with variation of resonance offsets for the irradiated nucleus. The heteronuclear dipolar recoupling efficiencies were quantitatively determined based on the experimentally obtained rf homogeneity. As a result, SFAM retains higher recoupling efficiency (>95%) at an 85% effective nutation frequency, and its recoupling efficiency is gradually reduced at lower effective nutation frequencies. On the other hand, although REDOR retains higher recoupling (>95%) efficiency at high (>92%) effective nutation frequency with an XY-8 compensation pulse sequence, the recoupling efficiency is dramatically decreased when the effective nutation frequency is below 90%. Over all, SFAM has significant advantages for insensitivity to carrier frequency offset and rf inhomogeneity.     

Broadband Polarization Transfer under Magic-Angle Spinning: Application to Total Through-Space-Correlation NMR Spectroscopy

A pulse sequence is described that leads to a broadband recoupling of the dipolar interaction in magic-angle-spinning solid-state NMR experiments of¹³C spins. The sequence is based on a combination of rotating frame and laboratory frame transfer periods. The recovered dipolar interaction is only weakly dependent on spectral parameters but is a faithful measure for the internuclear distances. Furthermore, a pure zero-quantum term is recovered (of the type found in static “spin-diffusion” experiments). This makes the pulse sequence particularly suited for incorporation into two-dimensional total through-space correlation experiments that deliver simultaneous information about all dipolar couplings in a single 2D experiment. It is found that the necessary decoupling from abundant protons is best performed in two steps: first, the strong homonuclear couplings between the high-γ spins are averaged by Lee–Goldburg irradiation and, second, the heteronuclear dipolar interaction is averaged by the combined application of an RF field to the low-γ spins and magic-angle sample spinning. Phase-inversion and amplitude attenuation in the rotating frame and refocusing pulses in the laboratory frame part of the pulse sequence are introduced to achieve an optimum chemical-shift offset-independence and for the suppression of unwanted double-quantum transitions. The design principles are explained in detail. Finally, the pulse scheme is applied to total-correlation spectroscopy of a uniformly labeled amino acid. The experimental cross-peak intensities are in qualitative agreement with the known crystal structure of the model compound.     

Heteronuclear polarization transfer by symmetry-based recoupling sequences in solid-state NMR

We demonstrate a new set of methods for transferring spin polarization between different nuclear isotopes in magic-angle-spinning solid-state NMR. The technique employs symmetry-based recoupling sequences on one irradiation channel and a simple sequence of between one and three strong radiofrequency pulses on the second channel. A phase shift of the recoupling sequences is applied at the same time as a pi/2 pulse on the second channel. The trajectory of the transferred polarization may be used to estimate heteronuclear distances. The method is particularly attractive for nuclei with low gyromagnetic ratios or for those experiencing strong anisotropic spin interactions, where conventional Hartmann-Hahn cross-polarization is difficult to apply. We demonstrate the method on 1H-13C, 1H-15N and 19F-109Ag systems.     

Broadband dipolar recoupling in rotating solids: a numerical comparison of some pulse schemes

A numerical comparison of the dipolar recoupling performance of several previously published homonuclear recoupling schemes under magic angle-spinning conditions is presented. Emphasis is put on the recoupled polarization transfer in a two-spin system where the efficiency is studied as a function of resonance offsets in the presence and absence of chemical-shielding anisotropies. In addition, the effect of the rf field strength is investigated. Powder pattern line shapes are shown in the on-resonance case that reveal the distribution of dipolar couplings for each recoupling scheme. These results are compared to data computed with a purposely misset rf field strength to estimate the pulse scheme sensitivity to rf-inhomogeneity and experimental missettings.     

Spinning-frequency-dependent narrowband RF-driven dipolar recoupling

Dipolar recoupling techniques of homonuclear spin pairs are commonly used for distance or orientation measurements in solids. Accurate measurements are interfered with by broadening mechanisms. In this publication narrowband RF-driven dipolar recoupling magnetization exchange experiments are performed as a function of the spinning frequency to reduce the effect of zero-quantum T(2) relaxation. To enhance the exchange of magnetization between the coupled spins, a fixed number of rotor-synchronous pi-pulses are applied at spinning frequencies approaching the rotational resonance (R(2)) conditions. The analysis of the powder averaged dipolar decay curves of the spin magnetizations as a function of the spinning frequency provides a quantitative measure of the dipolar coupling. An effective Hamiltonian for this experiment is derived, taking into account all chemical shift parameters of the spins. The length of the nbRFDR mixing time and the number of rotor cycles per pi-pulse are optimized by numerical simulations for sensitive probing of the dipolar coupling strength. The zero-quantum T(2) relaxation time can easily be taken into account in the data analysis, because the overall exchange time is almost constant in these experiments. Spinning-frequency-dependent nbRFDR experiments near the m = 1 and m = 2 R(2) condition are shown for doubly (13)C-labeled hydroxybutyric acid. Copyright 2000 Academic Press.