Recoupled Polarization-Transfer Methods for Solid-State H–C Heteronuclear Correlation in the Limit of Fast MAS

An in-depth account of the effects of homonuclear couplings and multiple heteronuclear couplings is given for a recently published technique for ¹H–¹³C dipolar correlation in solids under very fast MAS, where the heteronuclear dipolar coupling is recoupled by means of REDOR π-pulse trains. The method bears similarities to well-known solution-state NMR techniques, which form the framework of a heteronuclear multiple-quantum experiment. The so-called recoupled polarization-transfer (REPT) technique is versatile in that rotor-synchronized ¹H–¹³C shift correlation spectra can be recorded. In addition, weak heteronuclear dipolar coupling constants can be extracted by means of spinning sideband analysis in the indirect dimension of the experiment. These sidebands are generated by rotor encoding of the reconversion Hamiltonian. We present generalized variants of the initially described heteronuclear multiple-quantum correlation (HMQC) experiment, which are better suited for certain applications. Using these techniques, measurements on model compounds with ¹³C in natural abundance, as well as simulations, confirm the very weak effect of ¹H–¹H homonuclear couplings on the spectra recorded with spinning frequencies of 25–30 kHz. The effect of remote heteronuclear couplings on the spinning-sideband patterns of CH_n groups is discussed, and ¹³C spectral editing of rigid organic solids is shown to be practicable with these techniques.     

Recoupled polarization-transfer methods for solid-state (1)H--(13)C heteronuclear correlation in the limit of fast MAS

An in-depth account of the effects of homonuclear couplings and multiple heteronuclear couplings is given for a recently published technique for (1)H--(13)C dipolar correlation in solids under very fast MAS, where the heteronuclear dipolar coupling is recoupled by means of REDOR pi-pulse trains. The method bears similarities to well-known solution-state NMR techniques, which form the framework of a heteronuclear multiple-quantum experiment. The so-called recoupled polarization-transfer (REPT) technique is versatile in that rotor-synchronized (1)H--(13)C shift correlation spectra can be recorded. In addition, weak heteronuclear dipolar coupling constants can be extracted by means of spinning sideband analysis in the indirect dimension of the experiment. These sidebands are generated by rotor encoding of the reconversion Hamiltonian. We present generalized variants of the initially described heteronuclear multiple-quantum correlation (HMQC) experiment, which are better suited for certain applications. Using these techniques, measurements on model compounds with (13)C in natural abundance, as well as simulations, confirm the very weak effect of (1)H--(1)H homonuclear couplings on the spectra recorded with spinning frequencies of 25--30 kHz. The effect of remote heteronuclear couplings on the spinning-sideband patterns of CH(n) groups is discussed, and (13)C spectral editing of rigid organic solids is shown to be practicable with these techniques.     

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.     

Visualisation of enantiomers via insertion of a BIRD module in X-H correlation experiments in chiral liquid crystal solvent

Several 13C-1H NMR techniques are derived simplifying the visualisation of enantiomers in chiral ordering solvents. They proceed through various heteronuclear 2D experiments where a bilinear rotation decoupling sequence (BIRD) is inserted in the middle of the t1 evolution period. In this way, the small couplings are refocused while the large couplings are preserved. The methods allow extracting precise values of one-bond carbon-proton residual dipolar couplings for each enantiomer out of unresolved proton-coupled 13C or carbon-coupled 1H spectra. Illustrative examples are analysed and discussed using various pulse sequences.     

Multispin moments edited by multiple-quantum NMR: application to elastomers

The spin system response to the five-pulse sequence used for measurements of double-quantum and triple-quantum buildup curves is evaluated in the initial excitation/reconversion regime. The multispin dipolar network that is present also in many soft solids like elastomers was considered. It is proved rigorously that the relevant quantity for analysis of double-quantum build-up curves in the initial regime is the second van Vleck moment. The higher-order moments edited by double-quantum as well as higher-order coherences in the multiple-quantum build-up experiments are different from van Vleck moments. These results can be applied to compare (1)H residual moments edited by double-quantum and triple-quantum experiments with those measured by other NMR methods. The sensitivity of multiple-quantum coherences to the changes in the values of residual dipolar couplings for cross-linked natural rubber under uniaxial elongation is also discussed. Under such conditions (1)H second van Vleck moments were measured for different elongation ratios of a cross-linked natural rubber. Moreover, (1)H triple-quantum edited moments were also measured for the same sample under uniaxial compression. The dependence of the second van Vleck moment and the time of the maximum of the double-quantum buildup curve on the cross-link density of natural rubber measured at low magnetic field was also investigated.     

Recoupled Polarization Transfer Heteronuclear H–C Multiple-Quantum Correlation in Solids under Ultra-fast MAS

A new approach for high-resolution solid-state heteronuclear multiple-quantum MAS NMR spectroscopy of dipolar-coupled spin- nuclei is introduced. The method is a heteronuclear chemical shift correlation technique of abundant spins, like ¹H with rare spins, like ¹³C in natural abundance. High resolution is provided by ultra-fast MAS and high magnetic fields, high sensitivity being ensured by a direct polarization transfer from the abundant protons to ¹³C. In a rotor-synchronized variant, the method can be used to probe heteronuclear through-space proximities, while the heteronuclear dipolar coupling constant can quantitatively be determined by measuring multiple-quantum spinning-sideband patterns. By means of recoupling, even weak heteronuclear dipolar interactions are accessible. The capabilities of the technique are demonstrated by measurements on crystalline -tyrosine hydrochloride salt.     

Effective dipolar couplings determined by dipolar dephasing of double-quantum coherences

It is shown how homonuclear distances and homonuclear dipolar lattice sums between spin-1/2 nuclei can be measured by a pulsed solid-state NMR experiment under magic-angle spinning conditions. The presented technique is based on double-quantum coherence filtering. Instead of measuring a build-up of double-quantum coherence the pulse sequence is designed to dephase double-quantum coherence. This is achieved by exciting double-quantum coherence either with the help of the through-space dipolar coupling or the through-bond dipolar coupling while the dephasing relies on the through-space dipolar coupling as selected by a gamma-encoded pulse sequence from the C/R symmetry class. Since dephasing curves can be normalized on zero dephasing, it is possible to analyze the initial dephasing regime and hence determine dipolar lattice sums (effective dipolar couplings) in multiple-spin systems. A formula for the effective dipolar coupling is derived theoretically and validated by numerical calculations and experiments on crystalline model compounds for (13)C and (31)P spin systems. The double-quantum dephasing experiment can be combined with constant-time data sampling to compensate for relaxation effects, consequently only two experimental data points are necessary for a single distance measurement. The phase cycling overhead for the constant-time experiment is minimal because a short cogwheel phase cycle exists. A 2D implementation is demonstrated on [(13)C(3)]alanine.     

Recoupled polarization transfer heteronuclear 1H-13C multiple-quantum correlation in solids under ultra-fast MAS.

A new approach for high-resolution solid-state heteronuclear multiple-quantum MAS NMR spectroscopy of dipolar-coupled spin-12 nuclei is introduced. The method is a heteronuclear chemical shift correlation technique of abundant spins, like 1H with rare spins, like 13C in natural abundance. High resolution is provided by ultra-fast MAS and high magnetic fields, high sensitivity being ensured by a direct polarization transfer from the abundant protons to 13C. In a rotor-synchronized variant, the method can be used to probe heteronuclear through-space proximities, while the heteronuclear dipolar coupling constant can quantitatively be determined by measuring multiple-quantum spinning-sideband patterns. By means of recoupling, even weak heteronuclear dipolar interactions are accessible. The capabilities of the technique are demonstrated by measurements on crystalline L-tyrosine hydrochloride salt.     

Enhanced sensitivity to residual dipolar couplings of elastomers by higher-order multiple-quantum NMR

The homonuclear and heteronuclear residual dipolar couplings in elastomers reflect changes in the cross-link density, temperature, the uniaxial and biaxial extension or compression as well as the presence of penetrant molecules. It is shown theoretically that for an isolated methyl group the relative changes in the intensity of the homonuclear double-quantum buildup curves in the initial time regime due to variation of the residual dipolar coupling strength is less sensitive than the changes in the triple-quantum filtered NMR signal when considering the same excitation/reconversion time. For a quadrupolar nucleus with spin I=2 the sensitivity enhancement was simulated for four-quantum, triple-quantum, and double-quantum buildup curves. In this case the four-quantum build-up curve shows the highest sensitivity to changes of spin couplings. This enhanced sensitivity to the residual dipolar couplings was tested experimentally by measuring 1H double-quantum, triple-quantum, and four-quantum buildup curves of differently cross-linked natural rubber samples. In the initial excitation/reconversion time regime, where the residual dipolar couplings can be measured model free, the relative changes in the intensity of the four-quantum buildup curves are about five times higher than those of the double-quantum coherences. For the first time proton four-quantum coherences were recorded for cross-linked elastomers.     

13C-1H HSQC experiment of probe molecules aligned in thermotropic liquid crystals: sensitivity and resolution enhancement in the indirect dimension

The spectra of molecules oriented in liquid crystalline media are dominated by partially averaged dipolar couplings. In the 13C-1H HSQC, due to the inefficient hetero-nuclear dipolar decoupling in the indirect dimension, normally carried out by using a pi pulse, there is a considerable loss of resolution. Furthermore, in such strongly orienting media the 1H-1H and 13C-1H dipolar couplings leads to fast dephasing of transverse magnetization causing inefficient polarization transfer and hence the loss of sensitivity in the indirect dimension. In this study we have carried out 13C-1H HSQC experiment with efficient polarization transfer from 1H to 13C for molecules aligned in liquid crystalline media. The homonuclear dipolar decoupling using FFLG during the INEPT transfer delays and also during evolution period combined with the pi pulse heteronuclear decoupling in the t1 period has been applied. The studies showed a significant reduction in partially averaged dipolar couplings and thereby enhancement in the resolution and sensitivity in the indirect dimension. This has been demonstrated on pyridazine and pyrimidine oriented in the liquid crystal. The two closely resonating carbons in pyrimidine are better resolved in the present study compared to the earlier work [H.S. Vinay Deepak, Anu Joy, N. Suryaprakash, Determination of natural abundance 15N-1H and 13C-1H dipolar couplings of molecules in a strongly orienting media using two-dimensional inverse experiments, Magn. Reson. Chem. 44 (2006) 553-565].     

Rotor-encoded heteronuclear MQ MAS NMR spectroscopy of half-integer quadrupolar and spin I=1/2 nuclei

A new two-dimensional heteronuclear multiple-quantum magic-angle spinning (MQ MAS) experiment is presented which combines high resolution for the half-integer quadrupolar nucleus with information about the dipolar coupling between the quadrupolar nucleus and a spin I=1/2 nucleus. Homonuclear MQ coherence is initially created for the half-integer quadrupolar nucleus by a single pulse as in a standard MQ MAS experiment. REDOR recoupling of the heteronuclear dipolar coupling then allows the creation of a heteronuclear multiple-quantum coherence comprising multiple- and single-quantum coherence of the quadrupolar and spin I=1/2 nucleus, respectively, which evolves during t1. Provided that the t1 increment is not rotor synchronized, rotor-encoded spinning-sideband patterns are observed in the indirect dimension. Simulated spectra for an isolated IS spin pair show that these patterns depend on the recoupling time, the magnitude of the dipolar coupling, the quadrupolar parameters, as well as the relative orientation of the quadrupolar and dipolar principal axes systems. Spectra are presented for Na2HPO4, with the heteronuclear 23Na-1HMQ MAS experiments beginning with the excitation of 23Na (spin I=3/2) three-quantum coherence. Coherence counting experiments demonstrate that four- and two-quantum coherences evolve during t1. The heteronuclear spinning-sideband patterns observed for the three-spin H-Na-H system associated with the Na(2) site are analyzed. For an IS2 system, simulated spectra show that, considering the free parameters, the spinning-sideband patterns are particularly sensitive to only, first, the angle between the two IS internuclear vectors and, second, the two heteronuclear dipolar couplings. It is demonstrated that the proton localization around the Na(2) site according to the literature crystal structure of Na2HPO4 is erroneous. Instead, the experimental data is consistent with two alternative different structural arrangements, whereby either there is a deviation of 10 degrees from linearity for the case of two identical Na-H distances, or there is a linear arrangement, but the two Na-H distances are different. Furthermore, the question of the origin of spinning-sidebands in the (homonuclear) MQ MAS experiment is revisited. It is shown that the asymmetric experimental MQ sideband pattern observed for the low-C(Q) Na(2) site in Na(2)HPO4 can only be explained by considering the 23Na chemical shift anisotropy.     

Distance measurements in spin-1/2 systems by 13C and 31P solid-state NMR in dense dipolar networks

In this article solid-state NMR methods for the determination of internuclear dipole-dipole couplings between homonuclear spin-1/2 nuclei are presented. They are suitable for relatively dense dipolar networks which are still dominated by 2-spin interactions. C-/R-symmetry theory is applied to create a double-quantum average Hamiltonian using phase-modulated radio-frequency irradiation and magic-angle sample-rotation. Symmetry derived pulse sequences with improved compensation against chemical shift anisotropies were found assuming a small isotropic chemical shift difference and using numerical calculations of the spin dynamics. Moreover it is shown that a constant time procedure can be used to acquire reliable double-quantum build-up curves even in systems in which damping obscures oscillations in their symmetric build-up curve. This technique is demonstrated on four crystalline model compounds with 31P and 13C spin systems typical for inorganic and biological applications. Comparison to crystal structure data indicates that the distances derived this way from 31P and 13C double-quantum NMR carry only small systematic errors caused for example by anisotropic J-coupling, dipolar contributions from adjacent spins and relaxation.     

Sideband patterns from rotor-encoded longitudinal magnetization in MAS recoupling experiments

Recent multiple-quantum MAS NMR experiments have shown that a change in the rotor phase (and, hence, in the Hamiltonian) between the excitation and reconversion periods can lead to informative spinning-sideband patterns. However, such "rotor encoding" is not limited to multiple-quantum experiments. Here it is shown that longitudinal magnetization can also be rotor-encoded. Both homonuclear and heteronuclear rotor encoding of longitudinal magnetization (RELM) experiments are performed on dipolar-coupled spin-1/2 systems, and the corresponding sideband patterns in the indirect dimension are analyzed. In both cases, only even-order sidebands are produced, and their intensity distribution depends on the durations of the recoupling periods. In heteronuclear experiments using REDOR-type recoupling, purely dipolar sideband patterns that are entirely free of effects due to the chemical-shielding anisotropy can be generated. Advantages and disadvantages of the heteronuclear RELM experiment are discussed in the context of other methods used to measure heteronuclear dipolar couplings.     

Relaxation-induced dipolar exchange with recoupling-An MAS NMR method for determining heteronuclear distances without irradiating the second spin

A new magic-angle spinning NMR method for distance determination between unlike spins, where one of the two spins in question is not irradiated at all, is introduced. Relaxation-induced dipolar exchange with recoupling (RIDER) experiments can be performed with conventional double-resonance equipment and utilize the familiar π-pulse trains to recouple the heteronuclear dipolar interaction under magic-angle spinning conditions. Longitudinal relaxation of the passive spin during a delay between two recoupling periods results in a dephasing of the heteronuclear coherence and consequently a dephasing of the magnetization detected after the second recoupling period. The information about the dipolar coupling is obtained by recording normalized dephasing curves in a fashion similar to the REDOR experiment. At intermediate mixing times, the dephasing curves also depend on the relaxation properties of the passive spin, i.e., on single- and double-quantum longitudinal relaxation times for the case of I = 1 nuclei, and these relaxation times can be estimated with this new method. To a good approximation, the experiment does not depend on possible quadrupolar interactions of the passive spin, which makes RIDER an attractive method when distances to quadrupolar nuclei are to be determined. The new method is demonstrated experimentally with ¹⁴N and ²H as heteronuclei and observation of ¹³C in natural abundance.     

Double-quantum filtered MAS NMR in the presence of chemical shielding anisotropies and direct dipolar and J couplings

Double-quantum filtered MAS NMR spectra of an isolated homonuclear spin-1/2 pair are considered, at and away from rotational resonance conditions. The pulse sequence used is the solid-state NMR equivalent of double-quantum filtered COSY, known from solution-state NMR. The 119Sn spin pair in [(chex3Sn)2S] is characterized by a difference in isotropic chemical shielding smaller than the two chemical shielding anisotropies and by direct dipolar and isotropic J-coupling constants of similar magnitudes. At rotational resonance, one-dimensional double-quantum filtered 119Sn lineshapes yield the relative orientation of the two 119Sn chemical shielding tensors. Good double-quantum filtration efficiencies are found at and away from rotational resonance conditions, despite the presence of large chemical shielding anisotropies. Numerical simulations illustrate the interplay of the direct dipolar and J-coupling pathways and identify the latter as the main pathway even at rotational resonance conditions.     

Heteronuclear intermolecular single-quantum coherences in liquid nuclear magnetic resonance

This paper analyses the heteronuclear Cosy Revamped by Asymmetric Z-gradient Echo Detection pulse sequence. General theoretical expressions of the pulse sequence with arbitrary flip angles were derived by using dipolar field treatment and signals originating from heteronuclear intermolecular single-quantum coherences （iSQCs） in highly-polarized two spin-1/2 systems were mainly discussed in order to find the optimal flip angles. The results show that signals from heteronuclear iSQCs decay slower than those from intermolecular double-quantum coherences or intermolecular zero-quantum coherences. Magical angle experiments validate that the signals are from heteronuclear iSQCs and insensitive to the imperfection of radio-frequency flip angles. All experimental observations are in excellent agreement with theoretical predictions. The quantum-mechanical treatment leads to similar predictions to the dipolar field treatment.     

NMR of multipolar spin states excitated in strongly inhomogeneous magnetic fields

The possibility of exciting and filtering various multipolar spin states in proton NMR like dipolar encoded longitudinal magnetization (LM), double-quantum (DQ) coherences, and dipolar order (DO) in strongly inhomogeneous static and radio-frequency magnetic fields is investigated. For this purpose pulse sequences which label and manipulate the multipolar spin states in a specific way were implemented on the NMR-MOUSE (mobile universal surface explorer). The performance of the pulse sequences was also tested in homogeneous fields on a solid-state high-field NMR spectrometer. The theoretical justification of these procedures was shown for a rigid two-spin 1/2 system coupled by dipolar interactions. Dipolar encoded longitudinal magnetization decay curves, double-quantum and dipolar-order buildup curves, as well as double-quantum decay curves were recorded with the NMR-MOUSE for natural rubber samples with different crosslink density. The possibility of using these multipolar spin states for investigations of strained elastomers by NMR-MOUSE is also shown. These curves give access to quantitative values of the ratio of the total residual dipolar couplings of the protons in the series of samples which are in good agreement with those measured in homogeneous fields.     

Reduction of spin diffusion artifacts from 2D zfr-INADEQUATE MAS NMR spectra

The primary shortcoming of the z-filtered refocused INADEQUATE MAS NMR pulse sequence is the possibility of artifacts introduced during the z-filter due to spin diffusion where by extra peaks in the single-quantum dimension (from other sites in the molecule) appear correlated with a given double-quantum frequency. This is a problem when the spinning speeds are too slow (less than 15 kHz) to sufficiently average the proton-proton homonuclear dipolar couplings. This would be especially important when working with large volume rotors that are difficult to spin fast enough to completely average the homonuclear couplings. In our experiments we used the frequency-switched Lee-Goldberg (FSLG) method of homonuclear decoupling during the z-filter to remove the artifact peaks. This method has the advantage of being quite easy to setup and implement on most modern NMR spectrometers.     

1H NMR imaging of residual dipolar couplings in cross-linked elastomers: dipolar-encoded longitudinal magnetization, double-quantum, and triple-quantum filters.

Contrastfilters for NMR imaging of residual 1H dipolar couplings of elastomers are introduced based on dipolar-encoded longitudinal magnetization, as well as double- and triple-quantum coherences. The spin response is discussed in the initial excitation time regime for methylene, methyl, and methine protons applicable to poly(isoprene) and other elastomers, taking into account the hierarchy of dipolar couplings and the associated editing features of multiple-quantum experiments. The efficiency of these filters is investigated for a series of cross-linked poly(isoprene) samples. Spatially resolved dipolar-encoded longitudinal magnetization decays and double-quantum and triple-quantum buildup curves are presented for a phantom made of poly(isoprene) with different cross-link densities. Two-dimensional images representing residual dipolar couplings are presented using dipolar-encoded longitudinal magnetization, double-quantum, and triple-quantum contrast filters. Images from dipolar-encoded longitudinal magnetization and triple-quantum coherences show the highest resolution and contrast, respectively.     

Parameter maps of 1H residual dipolar couplings in tendon under mechanical load

Proton multipolar spin states associated with dipolar encoded longitudinal magnetization (DELM) and double-quantum (DQ) coherences of bound water are investigated for bovine and sheep Achilles tendon under mechanical load. DELM decay curves and DQ buildup and decay curves reveal changes of the 1H residual dipolar couplings for tendon at rest and under local compression forces. The multipolar spin states are used to design dipolar contrast filters for NMR 1H images of heterogeneous tendon. Heterogeneities in tendon samples were artificially generated by local compression parallel and perpendicular to the tendon plug axis. Quotient images obtained from DQ-filtered images by matched and mismatched excitation/reconversion periods are encoded only by the residual dipolar couplings. Semi-quantitative parameter maps of the residual dipolar couplings of bound water were obtained from these quotient images using a reference elastomer sample. This method can be used to quantify NMR imaging of injured ordered tissues.