On the use of single-frequency versus double-frequency satellite-transition pulses for MQMAS

High-resolution indirect detection of spin-3/2 quadrupolar nuclei in solids using multiple-quantum-filtered through-space D-HMQC experiments

Through-space heteronuclear correlation experiments under magic-angle spinning (MAS) conditions can provide unique insights into inter-atomic proximities. In particular, it has been shown that experiments based on two consecutive coherence transfers, 1H → I → 1H, like D-HMQC (dipolar-mediated heteronuclear multiple-quantum correlation), are usually more sensitive for the indirect detection via protons of spin-3/2 quadrupolar nuclei with low gyromagnetic ratio. Nevertheless, the resolution is often decreased by the second-order quadrupolar broadening along the indirect dimension. To circumvent this issue, we incorporate an MQMAS (multiple-quantum MAS) quadrupolar filter into the t1 evolution period of the D-HMQC sequence, which results in a novel pulse sequence called D-HMQC-MQ. The triple-quantum coherences evolving during this filter are excited and reconverted using cosine-modulated long-pulses synchronized with the sample rotation to avoid spinning sidebands in the indirect dimension. The desired coherence transfer pathways during this sequence are selected using two nested cogwheel phase cycles with 56 steps. This high-resolution heteronuclear correlation technique is demonstrated experimentally for the indirect detection via 1H of spin-3/2 isotopes, such as 11B, 23Na and 35Cl, in zinc borate hydrate, NaH2PO4 and l-histidine hydrochloride, respectively. We show that this experiment can be applied at high magnetic fields up to 28.2 T for protons subject to chemical shift anisotropies larger than 20 ppm, provided the MAS frequency is sufficiently stable since the D-HMQC-MQ experiment, like the parent D-HMQC, is sensitive to MAS fluctuations, which can produce t1-noise.

High-resolution heteronuclear correlations between spin-1/2 and half-integer quadrupolar nuclei under fast MAS solid-state NMR

High isotropic resolution is essential for the structural elucidation of samples with multiple sites. In this study, utilizing the benefits of TRAPDOR-based heteronuclear multiple quantum coherence (T-HMQC) and a pair of one rotor period long cosine amplitude modulated low-power (cos-lp) pulse-based symmetric-split-t1 multiple-quantum magic angle spinning (MQMAS) methods, we have developed a proton-detected 2D 35Cl/1H T-HMQC-MQMAS pulse sequence under fast MAS (70 kHz) to achieve high-resolution in the indirect dimension of the spin-3/2 (35Cl) nuclei connected via protons. As T-HMQC polarizes not only single-quantum central transition (SQCT) but also triple-quantum (TQ) coherences, the proposed 2D pulse sequence is implemented via selection of two coherence pathways (SQCT→TQ →SQCT and TQ → SQCT→TQ) resulting in the 35Cl isotropic dimension and is superior to the existing double-quantum satellite-transition (DQST) T-HMQC in terms of resolution.

On the applicability of cosine-modulated pulses for high-resolution solid-state NMR of quadrupolar nuclei with spin > 3/2

In MQMAS-based high-resolution solid-state NMR experiments of half-integer spin quadrupolar nuclei, the high radiofrequency (RF) field requirement for the MQ excitation and conversion steps with two hard-pulses is often a sensitivity limiting factor in many practical applications. Recently, the use of two cosine-modulated (cos) low-power (lp) pulses, lasting one-rotor period each, was successfully introduced for efficient MQ excitation and conversion of spin-3/2 nuclei with a reduced RF amplitude. In this study, we extend our previous investigations of spin-3/2 nuclei to systems with higher spin values and discuss the applicability of coslp-MQ excitation and conversion in MQMAS and MQ-HETCOR experiments under slow and fast spinning conditions. For the numerical simulations and experiments we used a moderate magnetic field of 14.1 T. Two spin-5/2 nuclei (⁸⁵Rb and ²⁷Al) are mainly employed with a large variety of C_Q values, but we show that the practical set up is also available for higher spin values, such as spin-9/2 with ⁹³Nb in Cs₄Nb₁₁O₃₀. We demonstrate for nuclei with spin value larger than 3/2 a preferential use of coslp-MQ acquisition for low-gamma nuclei and/or large C_Q values with a much reduced RF-field with respect to that of hard-pulses used with conventional methods.

Pushing the limit of MQMAS for low-γ quadrupolar nuclei in pharmaceutical hydrochlorides

Solid-state NMR of quadrupolar nuclei such as 35Cl has become a useful tool to characterize polymorphism in pharmaceutical hydrochlorides. The two-dimensional multiple-quantum magic-angle spinning (MQMAS) experiment can achieve isotropic resolution, and separate quadrupolar line shapes for samples with multiple sites but the pulse sequence efficiency is often low, limiting applications due to the intrinsically low NMR signals and rf field from the low gyromagnetic ratios γ. The use of cosine low-power MQMAS pulse sequences and high magnetic fields is presented to push the limit of MQMAS for insensitive low-γ quadrupolar nuclei. The improved efficiency and fields up to 35.2 T enable the acquisition of MQMAS spectra for pharmaceutical samples with multiple 35Cl sites, large quadrupolar couplings and/or in diluted dosage forms.

Satellite-transition double cross-polarization HETCOR under fast MAS

Double-cross polarization to the satellite-transitions (STs) of half-integer quadrupolar nuclei is demonstrated using proton-detected heteronuclear correlation (HETCOR) under fast magic-angle spinning (MAS). By placing the rf frequency away from the central-transition (CT) and selective to the STs, average Hamiltonian theory shows a scaled effective rf field with a phase equal to the complex ST spinning sideband being irradiated. Such an effective rf field can excite and spinlock STs but the phase spread usually leads to signal cancellation in one-step excitation or cross polarization experiments. The cancellation does not occur for two-step double cross-polarization (DCP) HETCOR experiments, therefore high efficiencies can be obtained. With careful magic-angle calibration, ST and double-quantum ST (DQST) HETCOR experiments are demonstrated with the ³⁵Cl nuclei in histidine·HCl·H₂O. These experiments provide additional information over the commonly observed CT spectra and near isotropic resolution in the case of DQST of spin S = 3/2 quadrupolar nuclei.

DESPERATE: A Python library for processing and denoising NMR spectra

NMR spectroscopy is an inherently insensitive technique with respect to the amount of observable signal. A common element in all NMR spectra is random thermal noise that is often characterized by a signal-to-noise ratio (SNR). SNR can be generically improved experimentally with repetitive signal averaging or during post-processing with apodization; the former of which often results in long experimental times and the latter results in the loss of spectral resolution. Denoising techniques can instead be used during post-processing to enhance SNR without compromising resolution. The most common approach relies on the singular-value decomposition (SVD) to discard noisy components of NMR data. SVD-based approaches work well, such as Cadzow and PCA, but are computationally expensive when used for large datasets that are often encountered in NMR (e.g., Carr-Purcell/Meiboom-Gill and nD datasets). Herein, we describe the implementation of a new wavelet transform (WT) routine for the fast and robust denoising of 1D and 2D NMR spectra. Several simulated and experimental datasets are denoised with both SVD-based Cadzow or PCA and WT's, and the resulting SNR enhancements and spectral uniformity are compared. WT denoising offers similar and improved denoising compared with SVD and operates faster by several orders-of-magnitude in some cases. All denoising and processing routines used in this work are included in a free and open-source Python library called DESPERATE.

Improved resolution for spin-3/2 isotopes in solids via the indirect NMR detection of triple-quantum coherences using the T-HMQC sequence

The indirect NMR detection of quadrupolar nuclei in solids under magic-angle spinning (MAS) is possible with the through-space HMQC (heteronuclear multiple-quantum coherence) scheme incorporating the TRAPDOR (transfer of population in double-resonance) dipolar recoupling. This sequence, called T-HMQC, exhibits limited t₁-noise. In this contribution, with the help of numerical simulations of spin dynamics, we show that most of the time, the fastest coherence transfer in the T-HMQC scheme is achieved when TRAPDOR recoupling employs the highest radiofrequency (rf) field compatible with the probe specifications. We also demonstrate how the indirect detection of the triple-quantum (3Q) coherences of spin-3/2 quadrupolar nuclei in solids improves the spectral resolution for these isotopes. The sequence is then called T-HMQC₃. We demonstrate the gain in resolution provided by this sequence for the indirect proton detection of ³⁵Cl nuclei in l-histidine∙HCl and l-cysteine∙HCl, as well as that of ²³Na isotope in NaH₂PO₄. These experiments indicate that the gain in resolution depends on the relative values of the chemical and quadrupolar-induced shifts (QIS) for the different spin-3/2 species. In the case of NaH₂PO₄, we show that the transfer efficiency of the T-HMQC₃ sequence employing an rf-field of 80 kHz with a MAS frequency of 62.5 kHz reaches 75% of that of the t₁-noise eliminated (TONE) dipolar-mediated HMQC (D-HMQC) scheme.

Practical considerations on the use of low RF-fields and cosine modulation in high-resolution NMR of I = 3/2 spin quadrupolar nuclei in solids

Despite its ease in experimental set up, the low sensitivity of MQMAS experiments is often a limiting factor in many practical applications. This is mainly due to the large radiofrequency (RF) field requirement of the two short hard-pulses often used for the optimum MQ excitation and conversion steps. Very recently, two novel MQMAS experiments have been proposed for I = 3/2 nuclei, namely lp-MQMAS and coslp-MQMAS, enabling an efficient MQ excitation/conversion with a reduced RF requirement, by utilizing two long pulses lasting one rotor period each, with or without cosine modulation. In this study, we focus on the practical considerations of these new methods and discuss their pros and cons to elucidate their appropriate use under both moderate and fast spinning conditions. Using four I = 3/2 (⁸⁷Rb, ⁷¹Ga, ³⁵Cl and ²³Na) nuclei at a moderate magnetic field (B₀ = 14.1 T), we show the superior use of these experiments, especially for samples with large C_Q values and/or low-gamma nuclei. Compared to all other existing sequences, the coslp-MQMAS method with initial WURST signal enhancement is the most robust, efficient and resolved high-resolution 2D method for spin 3/2 nuclei. Furthermore, using {²³Na}-¹H spin systems, we demonstrate the sensitivity advantage of the WURST coslp-MQ-HETCOR acquisition upon ¹H detection and fast MAS conditions.

Residue-Specific High-Resolution 17O Solid-State Nuclear Magnetic Resonance of Peptides: Multidimensional Indirect 1H Detection and Magic-Angle Spinning

Oxygen is an integral component of proteins but remains sparsely studied because its only NMR active isotope, ¹⁷O, has low sensitivity, low resolution, and large quadrupolar couplings. These issues are addressed here with efficient isotopic labeling, high magnetic fields, fast sample spinning, and ¹H detection in conjunction with multidimensional experiments to observe oxygen sites specific to each amino acid residue. Notably, cross-polarization at high sample spinning frequencies provides efficient ¹³C ↔ ¹⁷O polarization transfer. The use of ¹⁷O for initial polarization is found to provide better sensitivity per unit time compared to ¹H. Sharp isotropic ¹⁷O peaks are obtained by using a low-power multiple-quantum sequence, which in turn allows extraction of quadrupolar parameters for each oxygen site. Finally, the potential to determine sequential assignments and long-range distance restraints is demonstrated by using 3D ¹H/¹³C/¹⁷O experiments, suggesting that such methods can become an essential tool for biomolecular structure determination.

3D Relaxation-Assisted Separation of Wideline Solid-State NMR Patterns for Achieving Site Resolution

There are currently no methods for the acquisition of ultra-wideline (UW) solid-state NMR spectra under static conditions that enable reliable separation and resolution of overlapping powder patterns arising from magnetically...

Accelerating the acquisition of high-resolution quadrupolar MQ/ST-HETCOR 2D spectra under fast MAS via 1H detection and through-space population transfers

Recently, we established an experimental setup protocol to perform the population transfer from half-integer quadrupolar spin to ¹H nuclei under fast MAS in the context of MQ-HETCOR experiments. In this article, we further develop the high-resolution 2D HETCOR methods by ST-based approaches, making use of the sensitivity advantage of STMAS over its MQMAS counterpart. In a similar manner to the previous work, which utilized CP and RINEPT for the population transfer, we also demonstrate the experimental setup protocol for PRESTO. Using {²³Na}-¹H and {²⁷Al}-¹H spin systems of powder samples, we compare a series of MQ/ST-HETCOR 2D spectra to discuss the pros and cons of the distinct MQ/ST-based approaches for spin 3/2 and 5/2 nuclei, respectively. We also incorporate two experimental tricks to reduce the experimental time of such long 2D experiments, the Optimized Rotor-Synchronization (ORS) and the Non-Uniform Sampling (NUS), in the context of high-resolution spectra of half-integer quadrupolar spin nuclei.

A comparison of through-space population transfers from half-integer spin quadrupolar nuclei to 1H using MQ-HETCOR and MQ-SPAM-HETCOR under fast MAS

In this article, we compare the various schemes of magnetization transfer from half-integer quadrupolar spins to ¹H nuclei and we establish an efficient protocol to perform these transfers under MQMAS high-resolution with the MQ-HETCOR and MQ-SPAM-HETCOR experiments under fast MAS. The MQMAS efficiencies are analyzed with SIMPSON simulations, and the CPMAS and RINEPT magnetization transfers are compared at 62.5 kHz MAS using {²³Na}-¹H and {²⁷Al}-¹H MQ-HETCOR and MQ-SPAM-HETCOR experiments performed on NaH₂PO4, Na₂HPO₄, Na citrate dihydrate and ipa-AlPO-14 powder samples. We discuss the pros and cons of these approaches, aiming to record 2D spectra of the best possible quality under fast MAS. We also incorporate some experimental approaches to reduce the total experiment time of such long 2D experiments.