Recoupling in solid state NMR using γ prepared states and phase matching

The paper describes two-dimensional solid state NMR experiments that use powdered dephased antiphase coherence (γ preparation) to encode chemical shifts in the indirect dimension. Both components of this chemical shift encoded gamma-prepared states can be refocused into inphase coherence by a recoupling element. This helps to achieve sensitivity enhancement in 2D NMR experiments by quadrature detection. The powder dependence of the gamma-prepared states allows for manipulating them by suitable insertion of delays in the recoupling periods. This helps to design experiments that suppress diagonal peaks in 2D spectra, leading to improved resolution. We describe some new phase modulated heteronuclear and homonuclear recoupling pulse sequences that simplify the implementation of the described experiments based on γ prepared states. Recoupling in the heteronuclear spin system is achieved by matching the difference in the amplitude of the sine/cosine modulated phase on the two rf-channels to the spinning frequency while maintaining the same power on the two rf-channels.     

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.     

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.     

Heteronuclear decoupling interference during symmetry-based homonuclear recoupling in solid-state NMR

We examine the influence of continuous-wave heteronuclear decoupling on symmetry-based double-quantum homonuclear dipolar recoupling, using experimental measurements, numerical simulations, and average Hamiltonian theory. There are two distinct regimes in which the heteronuclear interference effects are minimized. The first regime utilizes a moderate homonuclear recoupling field and a strong heteronuclear decoupling field; the second regime utilizes a strong homonuclear recoupling field and a weak or absent heteronuclear decoupling field. The second regime is experimentally accessible at moderate or high magic-angle-spinning frequencies and is particularly relevant for many realistic applications of solid-state NMR recoupling experiments to organic or biological materials.     

The accuracy of distance measurements in solid-state NMR.

The accuracy with which distances can be measured using dipolar recoupling experiments in solid-state NMR is investigated. The relative precision of experiments in a three spin system versus an isolated spin pair is found to depend very strongly on the nature of the coupling Hamiltonian. The accuracy of distances measured in even the simplified three spin system is seen to be very poor for existing homonuclear recoupling Hamiltonians. This suggests that it would be difficult to exploit broadband homonuclear recoupling to measure geometrical information reliably in complex spin systems. These conclusions apply equally to both single-crystal studies and powder samples. In contrast, the presence of additional spins has marginal impact on the accuracy when the coupling Hamiltonians commute with each other, as in the case of heteronuclear recoupling. The possibility of creating such a Hamiltonian for homonuclear recoupling using a suitable rotor-synchronized pulse sequence is discussed.     

Selective Homonuclear Polarization Transfer in the Tilted Rotating Frame under Magic Angle Spinning in Solids

An application of the R2TR method (1995,Chem. Phys. Lett.232,424) to selective homonuclear polarization transfer under magic angle spinning is proposed. It is shown that, for a spinning speed fast enough to remove the maximum homonuclear dipolar coupling constant ω_Dinvolved, the flip-flop and flop-flop mechanisms are suitable for recoupling the spins with a chemical shift difference larger than ω_Dand a difference comparable to or smaller than ω_D, respectively. It is also shown that, for fast polarization transfer, the off-resonance frequencies should be much higher than the RF intensity in the flip-flop condition, while for the flop-flop condition, the off-resonance frequencies should be much lower than the RF intensity. Some one- and two-dimensional experiments are proposed by utilizing the capability of the R2TR method to abruptly switch on and off the recoupling condition, and are demonstrated for triply¹³C-enriched -alanine. The mixing time required for population transfer was found to be ca. 0.5 ms for the methine and methyl¹³C spins separated by 1.5 Å and ca. 5 ms for the methyl and the carboxyl carbons separated by 2.5 Å. The experimental results and theoretical simulations show that selective polarization transfer is achieved when the difference in the isotropic chemical shifts between the relevant pair of spins and a neighboring spin is more than 1000 Hz.     

Enhancing sensitivity or resolution of homonuclear correlation experiment for half-integer quadrupolar nuclei

We have recently introduced double-quantum homonuclear correlation NMR experiment for half-integer quadrupolar nuclei in solids, which was based on rotary resonance recoupling [J. Chem. Phys. 120 (2004) 2835]. In this contribution we show on two 23Na (I=3/2) containing samples, Na2SO4 and Na2HPO4, that the efficiency of the experiment can be substantially enhanced by adding rotor assisted population transfer (RAPT) and Carr-Purcell-Meiboom-Gill (CPMG) sequences to it. We also present an upgraded two-dimensional experiment, in which double- and six-quantum coherences are correlated during t1 evolution period, yielding a high-resolution isotropic spectrum along an indirectly detected dimension. The sensitivity of the upgraded experiment is, however, greatly reduced compared to the sensitivity of the original experiment, so that its application is feasible only when RAPT and CPMG can be used as well.     

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.     

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.     

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.     

Double-quantum homonuclear correlations of spin I=5/2 nuclei

The challenges associated with acquiring double-quantum homonuclear Nuclear Magnetic Resonance correlation spectra of half-integer quadrupolar nuclei are described. In these experiments the radio-frequency irradiation amplitude is necessarily weak in order to selectively excite the central transition. In this limit only one out of the 25 double-quantum coherences possible for two coupled spin I=5/2 nuclei is excited. An investigation of all the 25 two spins double quantum transitions reveals interesting effects such as a compensation of the first-order quadrupolar interaction between the two single quantum transitions involved in the double quantum coherence. In this paper a full numerical study of a hypothetical two spin I=5/2 system is used to show what happens when the RF amplitude during recoupling is increased. In principle this is advantageous, since the required double quantum coherence should build up faster, but in practice it also induces adiabatic passage transfer of population and coherence which impedes any build up. Finally an optimized rotary resonance recoupling (oR(3)) sequence is introduced in order to decrease these transfers. This sequence consists of a spin locking irradiation whose amplitude is reduced four times during one rotor period, and allows higher RF powers to be used during recoupling. The sequence is used to measure (27)Al DQ dipolar correlation spectra of Y(3)Al(5)O(12) (YAG) and gamma alumina (γAl(2)O(3)). The results prove that aluminium vacancies in gamma alumina mainly occur in the tetrahedral sites.     

Triple-quantum dynamics in multiple-spin systems undergoing magic-angle spinning: application to 13C homonuclear correlation spectroscopy

We analyze the multiple-quantum dynamics governed by a new homonuclear recoupling strategy effecting an average dipolar Hamiltonian comprising three-spin triple-quantum operators (e.g., S(p)+S(q)+S(r)+) under magic-angle spinning conditions. Analytical expressions are presented for polarization transfer processes in systems of three and four coupled spins-1/2 subject to triple-quantum filtration (3QF), and high-order multiple-quantum excitation is investigated numerically in moderately large clusters, comprising up to seven spins. This recoupling approach gives highly efficient excitation of triple-quantum coherences: ideally, up to 67% of the initial polarization may be recovered by 3QF in three-spin systems in polycrystalline powders. Two homonuclear 2D correlation strategies are demonstrated experimentally on powders of uniformly 13C-labeled alanine and tyrosine: the first correlates the single-quantum spectrum in the first dimension with the corresponding 3QF spectrum along the other. The second protocol correlates triple-quantum coherences with their corresponding single-quantum coherences within triplets of coupled spins.     

Measurement of interfluorine distances in solids

(19)F homonuclear dipolar recoupling methods were used to measure internuclear distances ranging from 5 to 12 A in fluorinated organic compounds in the solid state. Magic-angle-spinning-based high-resolution techniques were utilized. Trifluoromethyl and aromatic fluorine groups were separated by rigid aromatic spacers; these compounds were diluted into nonfluorinated host molecule matrices to give isolated homonuclear spin pairs with known internuclear distances. Radiofrequency-driven recoupling (RFDR) was used to elicit magnetization exchange between the spin pairs in 1D and 2D experiments. Simulation of the exchange was accomplished using a Monte Carlo-type algorithm to search the parameter space. These methods allow the determination of distances with an accuracy of 1 A at shorter distances and 2 A at longer distances, with the assumption of no prior knowledge of T(2)(ZQ).     

BaBa-xy16: robust and broadband homonuclear DQ recoupling for applications in rigid and soft solids up to the highest MAS frequencies

We here present a substantially improved version of the popular Back-to-Back (BaBa) homonuclear double-quantum (DQ) MAS recoupling pulse sequence. By combining the original pulse sequence with a virtual π pulse train with xy-16 phase cycling along with time-reversed DQ reconversion, a truly broadband and exceptionally robust pulse sequence is obtained. The sequence has moderate radio-frequency power requirements, amounting to only one 360° nutation per rotor cycle, it is robust with respect to rf power and tune-up errors, and its broadband performance increases with increasing spinning frequency, here tested up to 63 kHz. The experiment can be applied to many spin-1/2 nuclei in rigid solids with substantial frequency offsets and CSAs, which is demonstrated on the example of 31P NMR of a magnesium ultraphosphate, comparing experimental data with multi-spin simulations, and we also show simulations addressing the performance in 13C NMR of bio(macro)molecules. 1H-based studies of polymer dynamics are highlighted for the example of a rigid solid with strongly anisotropic mobility, represented by a polymer inclusion compound, and for the example of soft materials with weak residual dipole-dipole couplings, represented by homogeneous and inhomogeneous elastomers. We advocate the use of normalized (relaxation-corrected) DQ build-up curves for a quantitative assessment of weak average dipole-dipole couplings and even distributions thereof.     

Sensitivity enhanced recoupling experiments in solid-state NMR by gamma preparation

In this paper, we introduce a class of dipolar recoupling experiments under magic angle spinning (MAS), which use gamma dependent antiphase polarization during the t1 evolution period. We show that this helps us to design dipolar recoupling experiments that transfer both components of the transverse magnetization of spin S to a coupled spin I in the mixing step of a 2D NMR experiment. We show that it is possible to design such transfer schemes and make them insensitive to the orientation dependency of the couplings in powders. This helps us to develop sensitivity enhanced 2D NMR experiments of powder samples under MAS.     

1H-1H MAS correlation spectroscopy and distance measurements in a deuterated peptide

In this Communication, we demonstrate the use of deuteration together with back substitution of exchangeable protons as a means of attenuating the strong 1H-1H couplings that broaden 1H magic angle spinning (MAS) spectra of solids. The approach facilitates 15N-1H correlation experiments as well as experiments for the measurement of 1H-1H distances. The distance measurement relies on the excellent resolution in the 1H MAS spectrum and homonuclear double quantum recoupling techniques. The 1H-1H dipolar recoupling can be analyzed in an analytical fashion by fitting the data to a 2- or 3-spin system. The experiments are performed on a sample of the dipeptide N-Ac-Val-Leu-OH, which was synthesized from uniformly [2H, 15N] labeled materials and back-exchanged in H2O.     

Spin-locking and recoupling of homonuclear dipolar interaction between spin-3/2 nuclei under magic-angle sample spinning

Numerical simulations and experiments were used to examine the possibility of employing strong spin-lock fields for recoupling of homonuclear dipolar interactions between spin-3/2 quadrupolar nuclei and to compare it to the rotary-resonance recoupling at weak spin-lock fields. It was shown that strong spin-lock pulses under MAS conditions can lead to recoupling, provided that the electric-field gradient principal axes systems of the coupled nuclei are aligned and that their quadrupolar coupling constants are approximately the same. The phenomenon is based on the fact that strong spin-lock pulses induce adiabatic transfer of magnetization between the central-transition coherence and the triple-quantum coherence with equal periodicity as is the periodicity of the time-dependent dipolar coupling. Because of the synchronous variation of the state of the spin system and of the dipolar interaction, the effect of the latter on the central-transition coherence and on the triple-quantum coherence is not averaged out by sample rotation. The approach is, however, very sensitive to the relative orientation of the electric-field gradient principal axes systems and therefore less robust than the approach based on weak spin-lock pulses that satisfy rotary-resonance condition.     

1H-1H double-quantum CRAMPS NMR at very-fast MAS (nuR=35 kHz): a resolution enhancement method to probe 1H-1H proximities in solids

A High-resolution two-dimensional (2D) (1)H double-quantum (DQ) homonuclear recoupling experiments, combined with smooth amplitude-modulation (SAM) homonuclear decoupling is presented. The experiment affords highly resolved and clean (1)H DQ-SQ 2D spectra at very-fast MAS rates (nu(R)=35 kHz). The method is well suited to probe (1)H-(1)H distances in powdered solids and demonstrations are applied on a NaH(2)PO(4) powdered sample, an inorganic compound having hydrogen bonding networks.     

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.