On the use of frequency-swept pulses and pulses designed with optimal control theory for the acquisition of ultra-wideline NMR spectra

Structure and bonding in rhodium coordination compounds: a 103Rh solid-state NMR and relativistic DFT study

This study demonstrates the application of 103Rh solid-state NMR (SSNMR) spectroscopy to inorganic and organometallic coordination compounds, in combination with relativistic density functional theory (DFT) calculations of 103Rh chemical shift tensors and their analysis with natural bond orbital (NBO) and natural localized molecular orbital (NLMO) protocols, to develop correlations between 103Rh chemical shift tensors, molecular structure, and Rh-ligand bonding. 103Rh is one of the least receptive NMR nuclides, and consequently, there are very few reports in the literature. We introduce robust 103Rh SSNMR protocols for stationary samples, which use the broadband adiabatic inversion-cross polarization (BRAIN-CP) pulse sequence and wideband uniform-rate smooth-truncation (WURST) pulses for excitation, refocusing, and polarization transfer, and demonstrate the acquisition of 103Rh SSNMR spectra of unprecedented signal-to-noise and uniformity. The 103Rh chemical shift tensors determined from these spectra are complemented by NBO/NLMO analyses of contributions of individual orbitals to the 103Rh magnetic shielding tensors to understand their relationship to structure and bonding. Finally, we discuss the potential for these experimental and theoretical protocols for investigating a wide range of materials containing the platinum group elements.

Broadband Cross-Polarization to Half-Integer Quadrupolar Nuclei: Wideline Static NMR Spectroscopy

Cross-polarization (CP) is a technique commonly used for the signal enhancement of NMR spectra; however, applications to quadrupolar nuclei have heretofore been limited due to a number of problems, including poor spin-locking efficiency, inconvenient relaxation times, and reduced CP efficiencies over broad spectral bandwidths─this is unfortunate, since they constitute 73% of NMR-active nuclei in the periodic table. The Broadband Adiabatic Inversion CP (BRAIN-CP) pulse sequence has proven useful for the signal enhancement of wideline and ultra-wideline (i.e., 250 kHz to several MHz in breadth) powder patterns arising from stationary samples; however, a comprehensive investigation of its application to half-integer quadrupolar nuclei (HIQN) is currently lacking. Herein, we present theoretical and experimental considerations for applying BRAIN-CP to acquire central-transition (CT, +1/2 ↔ -1/2) powder patterns of HIQN. Consideration is given to parameters crucial to the success of the experiment, such as the Hartmann-Hahn (HH) matching conditions and the phase modulation of the contact pulse. Modifications to the BRAIN-CP sequence such as flip-back (FB) pulses and ramped contact pulses applied to the 1H spins are used for the reduction of experimental times and increased CP bandwidth capabilities, respectively. Spectra for a series of quadrupolar nuclei with broad CT powder patterns, including 35Cl (S = 3/2), 55Mn (S = 5/2), 59Co (S = 7/2), and 93Nb (S = 9/2), are acquired via direct excitation (CPMG and WCPMG) and indirect excitation (CP/CPMG and BRAIN-CP) methods. We demonstrate that proper implementation of the sequence can enable 1H-S broadband CP over a bandwidth of 1 MHz, which to the best of our knowledge is the largest CP bandwidth reported to date. Finally, we establish the basic principles necessary for simplified optimization and execution of the BRAIN-CP pulse sequence for a wide range of HIQNs.

An automated multi-order phase correction routine for processing ultra-wideline NMR spectra

Efficient acquisition of wideline solid-state nuclear magnetic resonance (NMR) spectra with patterns affected by large inhomogeneous broadening is accomplished with the use of broadband pulse sequences. These specialized pulse sequences often use frequency-swept pulses, which feature time-dependent phase and amplitude modulations that in turn deliver broad and uniform excitation across large spectral bandwidths. However, the resulting NMR spectra are often affected by complex frequency-dependent phase dispersions, owing to the interplay between the frequency-swept excitations and anisotropic resonance frequencies. Such phase distortions necessitate the use of multi-order non-linear corrections in order to obtain absorptive, distortion-free patterns with uniform phasing. Performing such corrections is often challenging due to the complex interdependence of the linear and non-linear phase contributions, and how these may affect the NMR signal. Hence, processing of these data usually involves calculating the spectra in magnitude mode wherein the phase information is discarded. Herein, we present a fully automated phasing routine that is capable of processing and phase correcting such wideline NMR spectra. Its performance is corroborated via processing of NMR data acquired using both the WURST-CPMG (Wideband, Uniform-Rate, Smooth Truncation with Carr-Purcell Meiboom-Gill acquisition) and BRAIN-CP (BRoadband Adiabatic Inversion Cross Polarization) pulse sequences for a variety of nuclei (i.e., 119Sn, 195Pt, 35Cl, 87Rb, and 14N). Based on both simulated and experimental NMR datasets, it is demonstrated that automatic phase corrections up to and including second order can be readily achieved without a priori information regarding the nature of the phase-distorted NMR datasets, and independently of the exact manner in which time-domain NMR data are collected and subsequently processed. In addition, it is shown that NMR spectra acquired at both single and multiple transmitter frequencies that are processed with this automated phasing routine have improved signal-to-noise properties than those processed with conventional magnitude calculations, along with powder patterns that better match those of ideal NMR spectra, even for datasets possessing low signal-to-noise ratios and/or affected by spectral artifacts.

Optimal control flow encoding for time-efficient magnetic resonance velocimetry

Phase contrast velocimetry relies on bipolar gradients to establish a direct and linear relationship between the phase of the magnetic resonance signal, and the corresponding fluid motion. Despite its utility, several limitations and drawbacks have been reported, the most important being the extended echo time due to the encoding after the excitation. In this study, we elucidate a new approach based on optimal control theory that circumvents some of these disadvantages. An excitation pulse, termed FAUCET (flow analysis under controlled encoding transients), is designed to encode velocity into phase already during the radiofrequency excitation. As a result of concurrent excitation and flow encoding, and hence elimination of post-excitation flow encoding, FAUCET achieves a shorter echo time than the conventional method. This achievement is a matter of significance not only because it decreases the loss of signal due to spin-spin relaxation and B₀ inhomogeneity, but also because a shorter echo time is always preferred in order to reduce the dimensionless dephasing parameter and the required residence time of the flowing sample in the detection coil. The method is able to establish a non-linear bijective relationship between phase and velocity, which can be employed to enhance the resolution over a specific range of velocities, for example along flow boundaries. A computational comparison between the phase contrast and optimal control methods reveals that the latter's encoding is more robust against remnant higher-order-moment terms of the Taylor expansion for faster voxels, such as acceleration, jerk, and snap.

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.

Hydrates of active pharmaceutical ingredients: A 35Cl and 2H solid-state NMR and DFT study

This study uses ³⁵Cl and ²H solid-state NMR (SSNMR) spectroscopy and dispersion-corrected plane-wave density functional theory (DFT) calculations to characterize the molecular-level structures and dynamics of hydrates of active pharmaceutical ingredients (APIs). We use ³⁵Cl SSNMR to measure the EFG tensors of the chloride ions to characterize hydrated forms of hydrochloride salts of APIs, along with two corresponding anhydrous forms. DFT calculations are used to refine the crystal structures of the APIs and determine relationships between the ³⁵Cl EFG tensors and the spatial arrangements of proximate hydrogen bonds, which are particularly influenced by interactions with water molecules. We find that the relationship between ³⁵Cl EFG tensors and local hydrogen bonding geometries is complex, but meaningful structure/property relationships can be garnered through use of DFT calculations. Specifically, for every case in which such a comparison could be made, we find that the hydrate has a smaller magnitude of C_Q than the corresponding anhydrous form, indicating a chloride ion environment with a ground-state electron density of higher spherical symmetry in the former. Finally, variable-temperature ³⁵Cl and ²H SSNMR experiments on a deuterium-exchanged sample of the API cimetidine hydrochloride monohydrate are used to monitor temperature-dependent influences on the spectra that may arise from motional influences on the ³⁵Cl and ²H EFG tensors. From the ²H SSNMR spectra, we determine that the motions of water molecules are characterized by jump-like motions about their C₂ rotational axes that occur on timescales that are unlikely to influence the ³⁵Cl central-transition (+1/2 ↔︎ -1/2) powder patterns (this is confirmed by ³⁵Cl SSNMR). Together, these methods show great promise for the future study of APIs in their bulk and dosage forms, especially variable hydrates in which crystallographic water content varies with external conditions such as humidity.

SORDOR pulses: expansion of the Böhlen-Bodenhausen scheme for low-power broadband magnetic resonance

A novel type of efficient broadband pulse, called second-order phase dispersion by optimised rotation (SORDOR), has recently been introduced. In contrast to adiabatic excitation, SORDOR-90 pulses provide effective transverse 90∘ rotations throughout their bandwidth, with a quadratic offset dependence of the phase in the x , y plane. Together with phase-matched SORDOR-180 pulses, this enables the Böhlen-Bodenhausen broadband refocusing approach for linearly frequency-swept pulses to be extended to any type of 90∘ /180∘ pulse-delay sequence. Example pulse shapes are characterised in theory and experiment, and an example application is given with a 19 F -PROJECT experiment for measuring relaxation times with reduced distortions due to J -coupling evolution.

Reducing the effects of weak homonuclear dipolar coupling with CPMG pulse sequences for static and spinning solids

The Carr-Purcell/Meiboom-Gill (CPMG) pulse sequence, initially introduced for measuring transverse relaxation time constants (T₂), can provide significant signal enhancements for solid-state NMR (SSNMR) spectra. The proper implementation of CPMG for acquiring spectra influenced by chemical shift anisotropies (CSAs), first and/or second order quadrupolar interactions, or paramagnetic broadening has been well documented to date, as have the effects of heteronuclear dipolar coupling on CPMG echo trains and T₂ lifetimes. Homonuclear dipolar coupling can also impact T₂ lifetimes and CPMG echo trains; these effects have been thoroughly investigated for spectra of homonuclear dipolar coupled spin-1/2 nuclei typically acquired under static conditions that are predominantly influenced by dipolar broadening (e.g., ¹H, ¹⁹F, etc.). In particular, it has been shown that short refocusing pulses with small flip angles can extend the effective T₂ (T₂^eff, the observed T₂ constant as impacted by experimental conditions) measured by CPMG sequences for strong homonuclear dipolar coupled spin-1/2 pairs under static conditions. To date, these effects have not been explored for (i) spin-1/2 nuclei that have significant CSAs and simultaneously feature weak homonuclear dipolar couplings, (ii) for quadrupolar nuclei that are also weakly homonuclear dipolar coupled, and (iii) for either of these cases under magic-angle spinning (MAS) conditions. Herein, we demonstrate that short refocusing pulses that cause small flip angles can reduce the attenuation of signal in CPMG echo trains resulting from dipolar dephasing caused by the weak homonuclear dipolar couplings. For both spin-1/2 and quadrupolar nuclei, this can lead to significant extensions in T₂^eff and signal enhancements of up to three times compared to conventional CPMG in favourable cases. These phenomena can occur under both static and magic-angle spinning (MAS) conditions, in the latter of which homonuclear couplings are reintroduced by rotational resonance (R²) recoupling. Experimental examples of ¹³C (I = 1/2), ²H (I = 1), ⁸⁷Rb (I = 3/2), ²³Na (I = 3/2), and ³⁵Cl (I = 3/2) NMR under static and MAS conditions, as well as simulations of these phenomena, are shown and discussed.

Improved design of frequency-swept pulse sequences

Frequency-swept pulses are extensively used in magnetic resonance spectroscopic techniques for the robust manipulation of spins across wide ranges of offset frequencies in the presence of B₁ field variations. Nevertheless, designing pulse sequences consisting of multiple frequency-swept pulses can be challenging, as they often require specific timings and parameter tweaking. In the present work we discuss a simple and general approach for constructing such sequences. We present new and improved pulse sequences for applications including broadband B₁-tolerant CPMG (CHORUS-CPMG), broadband chirped excitation with suppression of homonuclear J-modulation (PROCHORUS), and the further compression of frequency-swept pulse sequences by superposition of pulses which reduces pulse sequence durations by 25-40%. All sequence design strategies are accompanied by mathematical presentations, experimental results, and supporting simulations.

Nutraceuticals in Bulk and Dosage Forms: Analysis by 35Cl and 14N Solid-State NMR and DFT Calculations

This study uses ³⁵Cl and ¹⁴N solid-state NMR (SSNMR) spectroscopy and dispersion-corrected plane-wave density functional theory (DFT) calculations for the structural characterization of chloride salts of nutraceuticals in their bulk and dosage forms. For eight nutraceuticals, we measure the ³⁵Cl EFG tensor parameters of the chloride ions and use plane-wave DFT calculations to elucidate relationships between NMR parameters and molecular-level structure, which provide rapid NMR crystallographic assessments of structural features. We employ both ³⁵Cl direct excitation and ¹H→³⁵Cl cross-polarization methods to characterize a dosage form containing α-d-glucosamine HCl, observe possible impurity and/or adulterant phases, and quantify the weight percent of the active ingredient. To complement this, we also investigate ¹⁴N SSNMR spectroscopy and DFT calculations to characterize nitrogen atoms in the nutraceuticals. This includes a discussion of targeted acquisition experimental protocols (i.e., acquiring a select region of the overall pattern that features key discontinuities) that allow ultrawideline spectra to be acquired rapidly, even for unreceptive samples (i.e., those with long values of T₁(¹⁴N), short values of T₂^eff(¹⁴N), or very broad patterns). It is hoped that these experimental and computational protocols will be useful for the characterization of various solid forms of nutraceuticals (i.e., salts, polymorphs, hydrates, solvates, cocrystals, amorphous solid dispersions, etc.), help detect impurity and counterfeit solid phases in dosage forms, and serve as a foundation for future NMR crystallographic studies of nutraceutical solid forms, including studies using ab initio crystal structure prediction algorithms.

Broadband adiabatic inversion cross-polarization to integer-spin nuclei with application to deuterium NMR

Solid-state NMR (SSNMR) spectroscopy of integer-spin quadrupolar nuclei is important for the molecular-level characterization of a variety of materials and biological solids; of the integer spins, ² H (S = 1) is by far the most widely studied, due to its usefulness in probing dynamical motions. SSNMR spectra of integer-spin nuclei often feature very broad powder patterns that arise largely from the effects of the first-order quadrupolar interaction; as such, the acquisition of high-quality spectra continues to remain a challenge. The broadband adiabatic inversion cross-polarization (BRAIN-CP) pulse sequence, which is capable of cross-polarization (CP) enhancement over large bandwidths, has found success for the acquisition of SSNMR spectra of integer-spin nuclei, including ¹⁴ N (S = 1), especially when coupled with Carr-Purcell/Meiboom-Gill pulse sequences featuring frequency-swept WURST pulses (WURST-CPMG) for T₂ -based signal enhancement. However, to date, there has not been a systematic investigation of the spin dynamics underlying BRAIN-CP, nor any concrete theoretical models to aid in its parameterization for applications to integer-spin nuclei. In addition, the BRAIN-CP/WURST-CPMG scheme has not been demonstrated for generalized application to wideline or ultra-wideline (UW) ² H SSNMR. Herein, we provide a theoretical description of the BRAIN-CP pulse sequence for spin-1/2 → spin-1 CP under static conditions, featuring a set of analytical equations describing Hartmann-Hahn matching conditions and numerical simulations that elucidate a CP mechanism involving polarization transfer, coherence exchange, and adiabatic inversion. Several experimental examples are presented for comparison with theoretical models and previously developed integer-spin CP methods, demonstrating rapid acquisition of ² H NMR spectra from efficient broadband CP.

Field-stepped ultra-wideline NMR at up to 36 T: On the inequivalence between field and frequency stepping

Field-stepped NMR spectroscopy at up to 36 T using the series-connected hybrid (SCH) magnet at the U.S. National High Magnetic Field Laboratory is demonstrated for acquiring ultra-wideline powder spectra of nuclei with very large quadrupolar interactions. Historically, NMR evolved from the continuous-wave (cw) field-swept method in the early days to the pulsed Fourier-transform method in the modern era. Spectra acquired using field sweeping are generally considered to be equivalent to those acquired using the pulsed method. Here, it is shown that field-stepped wideline spectra of half-integer spin quadrupolar nuclei acquired using WURST/CPMG methods can be significantly different from those acquired with the frequency-stepped method commonly used with superconducting magnets. The inequivalence arises from magnetic field-dependent NMR interactions such as the anisotropic chemical shift and second-order quadrupolar interactions; the latter is often the main interaction leading to ultra-wideline powder patterns of half-integer spin quadrupolar nuclei. This inequivalence needs be taken into account to accurately and correctly determine the quadrupolar coupling and chemical shift parameters. A simulation protocol is developed for spectral fitting to facilitate analysis of field-stepped ultra-wideline NMR spectra acquired using powered magnets. A MATLAB program which implements this protocol is available on request.

Frequency-Swept Ultra-Wideline Magic-Angle Spinning NMR Spectroscopy

Recent years have witnessed the development of solid-state NMR techniques that allow the direct investigation of extremely wide inhomogeneously broadened resonance lines. To date, this typically involves the application of frequency sweeps as offered by wideband uniform rate smooth truncation (WURST) pulses. While the effects of such advanced irradiation schemes on static samples are well understood, the interference between the varying carrier frequency and the time-dependent evolution of the spin system under magic-angle spinning (MAS) conditions is more complex. Herein, we introduce the well-known WURST-Carr-Purcell-Meiboom-Gill (WCPMG) pulse sequence for spinning samples. Using numerical spin-density matrix analysis, an ideal design based on fast frequency sweeps and high truncation of the incorporated WURST pulses is presented that enables uniform excitation/refocusing under MAS conditions with low-to-moderate radio-frequency power requirements. This permits the acquisition of ultra-wideline MAS NMR lines exceeding 500 kHz with chemical shift resolution in a single transmitter step.

Chirped ordered pulses for ultra-broadband ESR spectroscopy

Recently, applications of swept-frequency pulses proved to be a useful approach to circumvent the problem of limited excitation bandwidth in pulsed ESR posed by conventional pulses. Here, we present a chirped excitation sequence, CHirped ORdered pulses for Ultra-broadband Spectroscopy (CHORUS), for ultra-broadband ESR spectroscopy. It will be demonstrated that the application of this sequence can address the problems of excitation non-uniformity and sensitivity to instrumental instabilities to a greater extent compared to the current state of the art. This sequence is highly promising for finding applications beyond single excitation in many ESR experiments. Theoretical and experimental results for the proposed method are presented along with calibration strategies for experimental implementation.

Broadband adiabatic inversion experiments for the measurement of longitudinal relaxation time constants

Accurate measurements of longitudinal relaxation time constants (T₁) in solid-state nuclear magnetic resonance (SSNMR) experiments are important for the study of molecular-level structure and dynamics. Such measurements are often made under magic-angle spinning conditions; however, there are numerous instances where they must be made on stationary samples, which often give rise to broad powder patterns arising from large anisotropic NMR interactions. In this work, we explore the use of wideband uniform-rate smooth-truncation pulses for the measurement of T₁ constants. Two experiments are introduced: (i) BRAIN-CPT1, a modification of the BRAIN-CP (BRoadband Adiabatic-INversion-Cross Polarization) sequence, for broadband CP-based T₁ measurements and (ii) WCPMG-IR, a modification of the WURST-CPMG sequence, for direct-excitation (DE) inversion-recovery experiments. A series of T₁ constants are measured for spin-1/2 and quadrupolar nuclei with broad powder patterns, such as ¹¹⁹Sn (I = 1/2), ³⁵Cl (I = 3/2), ²H (I = 1), and ¹⁹⁵Pt (I = 1/2). High signal-to-noise spectra with uniform patterns can be obtained due to signal enhancements from T₂ ^eff-weighted echo trains, and in favorable cases, BRAIN-CPT1 allows for the rapid measurement of T₁ in comparison to DE experiments. Protocols for spectral acquisition, processing, and analysis of relaxation data are discussed. In most cases, relaxation behavior can be modeled with either monoexponential or biexponential functions based upon measurements of integrated powder pattern intensity; however, it is also demonstrated that one must interpret such T₁ values with caution, as demonstrated by measurements of T₁ anisotropy in ¹¹⁹Sn, ²H, and ¹⁹⁵Pt NMR spectra.

Comprehensive and High-Throughput Exploration of Chemical Space Using Broadband 19 F NMR-Based Screening

Fragment-based lead discovery has become a fundamental approach to identify ligands that efficiently interact with disease-relevant targets. Among the numerous screening techniques, fluorine-detected NMR has gained popularity owing to its high sensitivity, robustness, and ease of use. To effectively explore chemical space, a universal NMR experiment, a rationally designed fragment library, and a sample composition optimized for a maximal number of compounds and minimal measurement time are required. Here, we introduce a comprehensive method that enabled the efficient assembly of a high-quality and diverse library containing nearly 4000 fragments and screening for target-specific binders within days. At the core of the approach is a novel broadband relaxation-edited NMR experiment that covers the entire chemical shift range of drug-like ¹⁹ F motifs in a single measurement. Our approach facilitates the identification of diverse binders and the fast ligandability assessment of new targets.