Multinuclear Residual Quadrupolar Couplings for Structure and Assignment

Most stable isotopes have a nuclear spin >1/2, but the quadrupole interaction poses challenge on their detection by nuclear magnetic resonance (NMR). On the other hand, the quadrupole interaction is a rich source of structural information that may be exploited for solution NMR in the form of residual quadrupolar couplings (RQCs) of weakly oriented samples. While 2H RQCs are now well established for structure verification and enantiomeric discrimination of organic molecules, we will in this article highlight some recent work on RQCs of other nuclei (especially 7Li and 11B).

NMR crystallography of amino acids

The development of NMR crystallography methods requires a reliable database of chemical shifts measured for systems with known crystal structure. We measured and assigned carbon and hydrogen chemical shifts of twenty solid natural amino acids of known polymorphic structure, meticulously determined using powder X-ray diffraction. We then correlated the experimental data with DFT-calculated isotropic shieldings. The small size of the unit cell of most amino acids allowed for advanced computations using various families of DFT functionals, including generalized gradient approximation (GGA), meta-GGA and hybrid DFT functionals. We tested several combinations of functionals for geometry optimizations and NMR calculations. For carbon shieldings, the widely used GGA functional PBE performed very well, although an improvement could be achieved by adding shielding corrections calculated for isolated molecules using a hybrid functional. For hydrogen nuclei, we observed the best performance for NMR calculations carried out with structures optimized at the hybrid DFT level. The high fidelity of the calculations made it possible to assign additional signals that could not be assigned based on experiments alone, for example signals of two non-equivalent molecules in the unit cell of some of the amino acids.

The need for operando modelling of 27Al NMR in zeolites: the effect of temperature, topology and water

Solid state (ss-) 27Al NMR is one of the most valuable tools for the experimental characterization of zeolites, owing to its high sensitivity and the detailed structural information which can be extracted from the spectra. Unfortunately, the interpretation of ss-NMR is complex and the determination of aluminum distributions remains generally unfeasible. As a result, computational modelling of 27Al ss-NMR spectra has grown increasingly popular as a means to support experimental characterization. However, a number of simplifying assumptions are commonly made in NMR modelling, several of which are not fully justified. In this work, we systematically evaluate the effects of various common models on the prediction of 27Al NMR chemical shifts in zeolites CHA and MOR. We demonstrate the necessity of operando modelling; in particular, taking into account the effects of water loading, temperature and the character of the charge-compensating cation. We observe that conclusions drawn from simple, high symmetry model systems such as CHA do not transfer well to more complex zeolites and can lead to qualitatively wrong interpretations of peak positions, Al assignment and even the number of signals. We use machine learning regression to develop a simple yet robust relationship between chemical shift and local structural parameters in Al-zeolites. This work highlights the need for sophisticated models and high-quality sampling in the field of NMR modelling and provides correlations which allow for the accurate prediction of chemical shifts from dynamical simulations.

Nuclear spin diffusion under fast magic-angle spinning in solid-state NMR

Solid-state nuclear spin diffusion is the coherent and reversible process through which spin order is transferred via dipolar couplings. With the recent increases in magic-angle spinning (MAS) frequencies and magnetic fields becoming routinely applied in solid-state nuclear magnetic resonance, understanding how the increased 1H resolution obtained affects spin diffusion is necessary for interpretation of several common experiments. To investigate the coherent contributions to spin diffusion with fast MAS, we have developed a low-order correlation in Liouville space model based on the work of Dumez et al. (J. Chem. Phys. 33, 224501, 2010). Specifically, we introduce a new method for basis set selection, which accounts for the resonance-offset dependence at fast MAS. Furthermore, we consider the necessity of including chemical shift, both isotropic and anisotropic, in the modeling of spin diffusion. Using this model, we explore how different experimental factors change the nature of spin diffusion. Then, we show case studies to exemplify the issues that arise in using spin diffusion techniques at fast spinning. We show that the efficiency of polarization transfer via spin diffusion occurring within a deuterated and 100% back-exchanged protein sample at 60 kHz MAS is almost entirely dependent on resonance offset. We additionally identify temperature-dependent magnetization transfer in beta-aspartyl L-alanine, which could be explained by the influence of an incoherent relaxation-based nuclear Overhauser effect.

Do Models beyond Hybrid Density Functionals Increase the Agreement with Experiment for Predicted NMR Chemical Shifts or Electric Field Gradient Tensors in Organic Solids?

Ab initio predictions of chemical shifts and electric field gradient (EFG) tensor components are frequently used to help interpret solid-state nuclear magnetic resonance (NMR) experiments. Typically, these predictions employ density functional theory (DFT) with generalized gradient approximation (GGA) functionals, though hybrid functionals have been shown to improve accuracy relative to experiment. Here, the performance of a dozen models beyond the GGA approximation are examined for the prediction of solid-state NMR observables, including meta-GGA, hybrid, and double-hybrid density functionals and second-order Møller-Plesset perturbation theory (MP2). These models are tested on organic molecular crystal data sets containing 169 experimental ¹³C and ¹⁵N chemical shifts and 114 ¹⁷O and ¹⁴N EFG tensor components. To make these calculations affordable, gauge-including projector augmented wave (GIPAW) Perdew-Burke-Ernzerhof (PBE) calculations with periodic boundary conditions are combined with a local intramolecular correction computed at the higher level of theory. Within the context of typical NMR property calculations performed on a static, DFT-optimized crystal structure, the benchmarking finds that the double-hybrid DFT functionals produce errors versus experiment that are no smaller than those of hybrid functionals in the best cases, and they can be larger. MP2 errors versus experiment are even bigger. Overall, no practical advantages are found for using any of the tested double-hybrid functionals or MP2 to predict experimental solid-state NMR chemical shifts and EFG tensor components for routine organic crystals, especially given the higher computational cost of those methods. This finding likely reflects error cancellation benefiting the hybrid functionals. Improving the accuracy of the predicted chemical shifts and EFG tensors relative to experiment would probably require more robust treatments of the crystal structures, their dynamics, and other factors.

A Crystalline Dimeric Steroidal Diboronate with Electronically Impeded Rotation

The dimeric steroid SMR-3, featuring a 1,4-phenyldiboronic ester flanked by two pregnan-triol frameworks, was synthesized to explore the intramolecular dynamics of its central component. The structural data from single-crystal X-ray diffraction studies and the Hirshfeld analyses indicate small steric effects around the aromatic ring that should favor the intended motion. However, solid-state NMR data obtained through VT ¹³C{¹H} CPMAS and ²H spin-echo experiments, using the deuterated analogue SMR-3D₄, revealed that this component is rigid even at temperatures where other reported steroidal molecular rotors experience fast rotation (85 °C). A combination of classical molecular dynamics, molecular mechanics, and correlated ab initio calculations allowed us to distinguish the steric and electronic factors that restrict the potential motion in this compound. The experimental and computational data reveal that electronic components dominate the behavior and are responsible for the high rotational barrier in the SMR-3 crystal.

Combining X-ray and NMR Crystallography to Explore the Crystallographic Disorder in Salbutamol Oxalate

Salbutamol is an active pharmaceutical ingredient commonly used to treat respiratory distress and is listed by the World Health Organization as an essential medicine. Here, we establish the crystal structure of its oxalate form, salbutamol oxalate, and explore the nature of its crystallographic disorder by combined X-ray crystallography and ¹³C cross-polarization (CP) magic-angle spinning (MAS) solid-state NMR. The *C-OH chiral center of salbutamol (note that the crystal structures are a racemic mixture of the two enantiomers of salbutamol) is disordered over two positions, and the tert-butyl group is rotating rapidly, as revealed by ¹³C solid-state NMR. The impact of crystallization conditions on the disorder was investigated, finding variations in the occupancy ratio of the *C-OH chiral center between single crystals and a consistency across samples in the bulk powder. Overall, this work highlights the contrast between investigating crystallographic disorder by X-ray diffraction and solid-state NMR experiment, and gauge-including projector-augmented-wave (GIPAW) density functional theory (DFT) calculations, with their combined use, yielding an improved understanding of the nature of the crystallographic disorder between the local (i.e., as viewed by NMR) and longer-range periodic (i.e., as viewed by diffraction) scale.

The steps of thermal treatment of Na-magadiite: a computational study using ab initio DFT calculations

We investigated each of the successive transformations of this material using ab initio calculations based on DFT. Possible structures produced from three reaction steps of the thermal treatment were simulated. Thermodynamic analysis was performed to assess the energy stability of each reaction. The dehydration of the interlamellar region confirmed the selective loss of water molecules, with axial H₂O being responsible for the first part of the mass loss experimentally observed in TG-DTA while the loss of equatorial H₂O molecules is observed above 150 °C. The reactions of the proposed intermediates after dehydration indicated that the formation of a zeolite Si₁₄O₂₈ is thermodynamically unfavorable in relation to zeolite sodium silicate. Kinetic effects and new heat treatment protocols should be studied to improve the understanding of these materials. The final steps indicated that after the condensation of the layers, sodium silicate was formed together with quartz.

High Level Electronic Structure Calculation of Molecular Solid-State NMR Shielding Constants

In this work, we present a quantum mechanics/molecular mechanics (QM/MM) approach for the computation of solid-state nuclear magnetic resonance (SS-NMR) shielding constants (SCs) for molecular crystals. Besides applying standard-DFT functionals like GGAs (PBE), meta-GGAs (TPSS), and hybrids (B3LYP), we apply a double-hybrid (DSD-PBEP86) functional as well as MP2, using the domain-based local pair natural orbital (DLPNO) formalism, to calculate the NMR SCs of six amino acid crystals. All the electronic structure methods used exhibit good correlation of the NMR shieldings with respect to experimental chemical shifts for both ¹H and ¹³C. We also find that local electronic structure is much more important than the long-range electrostatic effects for these systems, implying that cluster approaches using all-electron/Gaussian basis set methods might offer great potential for predictive computations of solid-state NMR parameters for organic solids.

The Ad-MD method to calculate NMR shift including effects due to conformational dynamics: The 31 P NMR shift in DNA

A method for averaging of NMR parameters by molecular dynamics (MD) has been derived from the method of statistical averaging in MD snapshots, benchmarked and applied to structurally dynamic interpretation of the ³¹ P NMR shift (δ_31P ) in DNA phosphates. The method employs adiabatic dependence of an NMR parameter on selected geometric parameter(s) that is weighted by MD-calculated probability distribution(s) for the geometric parameter(s) (Ad-MD method). The usage of Ad-MD for polymers is computationally convenient when one pre-calculated structural dependence of an NMR parameter is employed for all chemically equivalent units differing only in dynamic behavior. The Ad-MD method is benchmarked against the statistical averaging method for δ_31P in the model phosphates featuring distinctively different structures and dynamic behavior. The applicability of Ad-MD is illustrated by calculating ³¹ P NMR spectra in the Dickerson-Drew DNA dodecamer. δ_31P was calculated with the B3LYP/IGLO-III/PCM(water) and the probability distributions for the torsion angles adjacent to the phosphorus atoms in the DNA phosphates were calculated using the OL15 force field.

Multi-Component Crystals Containing Urea: Mechanochemical Synthesis and Characterization by 35Cl Solid-State NMR Spectroscopy and DFT Calculations

Mechanochemical synthesis provides new pathways for the rational design of multi-component crystals (MCCs) involving anionic or cationic components, which offer molecular-level architectures unavailable to MCCs comprised of strictly neutral components....

Importance of Nuclear Quantum Effects for NMR Crystallography

The resolving power of solid-state nuclear magnetic resonance (NMR) crystallography depends heavily on the accuracy of computational predictions of NMR chemical shieldings of candidate structures, which are usually taken to be local minima in the potential energy. To test the limits of this approximation, we systematically study the importance of finite-temperature and quantum nuclear fluctuations for ¹H, ¹³C, and ¹⁵N shieldings in polymorphs of three paradigmatic molecular crystals: benzene, glycine, and succinic acid. The effect of quantum fluctuations is comparable to the typical errors of shielding predictions for static nuclei with respect to experiments, and their inclusion improves the agreement with measurements, translating to more reliable assignment of the NMR spectra to the correct candidate structure. The use of integrated machine-learning models, trained on first-principles energies and shieldings, renders rigorous sampling of nuclear fluctuations affordable, setting a new standard for the calculations underlying NMR structure determinations.

NMR spectroscopy probes microstructure, dynamics and doping of metal halide perovskites

Solid-state magic-angle spinning NMR spectroscopy is a powerful technique to probe atomic-level microstructure and structural dynamics in metal halide perovskites. It can be used to measure dopant incorporation, phase segregation, halide mixing, decomposition pathways, passivation mechanisms, short-range and long-range dynamics, and other local properties. This Review describes practical aspects of recording solid-state NMR data on halide perovskites and how these afford unique insights into new compositions, dopants and passivation agents. We discuss the applicability, feasibility and limitations of ¹H, ¹³C, ¹⁵N, ¹⁴N, ¹³³Cs, ⁸⁷Rb, ³⁹K, ²⁰⁷Pb, ¹¹⁹Sn, ¹¹³Cd, ²⁰⁹Bi, ¹¹⁵In, ¹⁹F and ²H NMR in typical experimental scenarios. We highlight the pivotal complementary role of solid-state mechanosynthesis, which enables highly sensitive NMR studies by providing large quantities of high-purity materials of arbitrary complexity and of chemical shifts calculated using density functional theory. We examine the broader impact of solid-state NMR on materials research and how its evolution over seven decades has benefitted structural studies of contemporary materials such as halide perovskites. Finally, we summarize some of the open questions in perovskite optoelectronics that could be addressed using solid-state NMR. We, thereby, hope to stimulate wider use of this technique in materials and optoelectronics research.

Analyzing Discrepancies in Chemical-Shift Predictions of Solid Pyridinium Fumarates

Highly accurate chemical-shift predictions in molecular solids are behind the success and rapid development of NMR crystallography. However, unusually large errors of predicted hydrogen and carbon chemical shifts are sometimes reported. An understanding of these deviations is crucial for the reliability of NMR crystallography. Here, recently reported large deviations of predicted hydrogen and carbon chemical shifts of a series of solid pyridinium fumarates are thoroughly analyzed. The influence of the geometry optimization protocol and of the computational level of NMR calculations on the accuracy of predicted chemical shifts is investigated. Periodic calculations with GGA, meta-GGA and hybrid functionals are employed. Furthermore, molecular corrections at the coupled-cluster singles-and-doubles (CCSD) level are calculated. The effect of nuclear delocalization on the structure and NMR shielding is also investigated. The geometry optimization with a computationally demanding hybrid functional leads to a substantial improvement in proton chemical-shift predictions.

A Review on Combination of Ab Initio Molecular Dynamics and NMR Parameters Calculations

This review focuses on a combination of ab initio molecular dynamics (aiMD) and NMR parameters calculations using quantum mechanical methods. The advantages of such an approach in comparison to the commonly applied computations for the structures optimized at 0 K are presented. This article was designed as a convenient overview of the applied parameters such as the aiMD type, DFT functional, time step, or total simulation time, as well as examples of previously studied systems. From the analysis of the published works describing the applications of such combinations, it was concluded that including fast, small-amplitude motions through aiMD has a noticeable effect on the accuracy of NMR parameters calculations.

Structural characterisation of natural products by means of quantum chemical calculations of NMR parameters: new insights

In this review, we focus in all aspects of NMR simulation of natural products, from the fundamentals to the new computational toolboxes available, combining advanced quantum chemical calculations with upstream data processing and machine learning.

A curious case of dynamic disorder in pyrrolidine rings elucidated by NMR crystallography

A pharmaceutical exhibits differing dynamics in crystallographically distinct pyrrolidine rings despite being nearly related by symmetry, with one performing ring inversions while the other is constrained to torsional librations. Using ¹³C solid-state magic-angle spinning (MAS) NMR and DFT calculations, we show that this contrast originates from C-HH-C close contacts and less efficient C-Hπ intermolecular interactions observed in the transition state of the constrained pyrrolidine ring, highlighting the influence of the crystallographic environment on the molecular motion.

Parametrizing the Spatial Dependence of 1H NMR Chemical Shifts in π-Stacked Molecular Fragments

Most recently a renewed interest in several areas has arisen in factors governing the 1H NMR chemical shift (1H CS) of protons in aromatic systems. Therefore, it is important to describe how 1H CS values are affected by π-stacking intermolecular interactions. The parametrization of radial and angular dependences of the 1H CS is proposed, which is based on conventional gauge-independent atomic orbital (GIAO) calculations of explicit molecular fragments. Such a parametrization is exemplified for a benzene dimer with intermonomer vertical and horizontal distances which are in the range of values often found in crystals of organic compounds. Results obtained by the GIAO calculations combined with B3LYP and MP2 methods were compared, and revealed qualitatively the same trends in the 1H CS data. The parametrization was found to be quantitatively correct for the T-shaped benzene dimers, and its limitations were discussed. Parametrized 1H CS surfaces should become useful for providing additional restraints in the search of site-specific information through an analysis of structurally induced 1H CS changes.

Towards Accurate Predictions of Proton NMR Spectroscopic Parameters in Molecular Solids

The factors contributing to the accuracy of quantum-chemical calculations for the prediction of proton NMR chemical shifts in molecular solids are systematically investigated. Proton chemical shifts of six solid amino acids with hydrogen atoms in various bonding environments (CH, CH₂ , CH₃ , OH, SH and NH₃ ) were determined experimentally using ultra-fast magic-angle spinning and proton-detected 2D NMR experiments. The standard DFT method commonly used for the calculations of NMR parameters of solids is shown to provide chemical shifts that deviate from experiment by up to 1.5 ppm. The effects of the computational level (hybrid DFT functional, coupled-cluster calculation, inclusion of relativistic spin-orbit coupling) are thoroughly discussed. The effect of molecular dynamics and nuclear quantum effects are investigated using path-integral molecular dynamics (PIMD) simulations. It is demonstrated that the accuracy of the calculated proton chemical shifts is significantly better when these effects are included in the calculations.

Investigating discrepancies between experimental solid-state NMR and GIPAW calculation: NC-N 13C and OH⋯O 1H chemical shifts in pyridinium fumarates and their cocrystals

An NMR crystallography analysis is presented for four solid-state structures of pyridine fumarates and their cocrystals, using crystal structures deposited in the Cambridge Crystallographic Data Centre, CCDC. Experimental one-dimensional one-pulse ¹H and ¹³C cross-polarisation (CP) magic-angle spinning (MAS) nuclear magnetic resonance (NMR) and two-dimensional ¹⁴N-¹H heteronuclear multiple-quantum coherence MAS NMR spectra are compared with gauge-including projector augmented wave (GIPAW) calculations of the ¹H and ¹³C chemical shifts and the ¹⁴N shifts that additionally depend on the quadrupolar interaction. Considering the high ppm (>10 ​ppm) ¹H resonances, while there is good agreement (within 0.4 ​ppm) between experiment and GIPAW calculation for the hydrogen-bonded NH moieties, the hydrogen-bonded fumaric acid OH resonances are 1.2-1.9 ​ppm higher in GIPAW calculation as compared to experiment. For the cocrystals of a salt and a salt formed by 2-amino-5-methylpyridinium and 2-amino-6-methylpyridinium ions, a large discrepancy of 4.2 and 5.9 ​ppm between experiment and GIPAW calculation is observed for the quaternary ring carbon ¹³C resonance that is directly bonded to two nitrogens (in the ring and in the amino group). By comparison, there is excellent agreement (within 0.2 ​ppm) for the quaternary ring carbon ¹³C resonance directly bonded to the ring nitrogen for the salt and cocrystal of a salt formed by 2,6-lutidinium and 2,5-lutidinium, respectively.

NMR crystallography of molecular organics

Developments of NMR methodology to characterise the structures of molecular organic structures are reviewed, concentrating on the previous decade of research in which density functional theory-based calculations of NMR parameters in periodic solids have become widespread. With a focus on demonstrating the new structural insights provided, it is shown how "NMR crystallography" has been used in a spectrum of applications from resolving ambiguities in diffraction-derived structures (such as hydrogen atom positioning) to deriving complete structures in the absence of diffraction data. As well as comprehensively reviewing applications, the different aspects of the experimental and computational techniques used in NMR crystallography are surveyed. NMR crystallography is seen to be a rapidly maturing subject area that is increasingly appreciated by the wider crystallographic community.

Effects of Li Confined Motion on NMR Quadrupolar Interactions: A Combined 7 Li NMR and DFT-MD Study of LiR2 (PO4 )3 (R=Ti or Zr) Phases

Ab initio molecular dynamics (MD) simulations and NMR GIPAW (gauge including projector augmented wave) calculations have been used to analyze the coordination and mobility of Li ions in LiTi₂ (PO₄ )₃ (rhombohedral), LiZr₂ (PO₄ )₃ (triclinic), and LiZr₂ (PO₄ )₃ (rhombohedral) phases. Significant discrepancies are observed between static calculations of ⁷ Li quadrupolar parameters and experimental values. The dynamical origin of this disagreement is demonstrated by incorporating in the calculations thermal vibrations and local motion of atoms with MD simulations. For LiTi₂ (PO₄ )₃ , the quadrupolar constant associated with Li ions grows with temperature because the local symmetry of the system decreases, whereas for the Zr phases, the quadrupolar constant decreases because thermal vibrations reduce the anisotropy of the interaction. Finally, for both Zr phases, MD yields Li distributions that compare well with disorder reported from diffraction studies.

Resolving alternative organic crystal structures using density functional theory and NMR chemical shifts

Alternative (‘repeat’) determinations of organic crystal structures deposited in the Cambridge Structural Database are analysed to characterise the nature and magnitude of the differences between structure solutions obtained by diffraction methods. Of the 3132 structure pairs considered, over 20% exhibited local structural differences exceeding 0.25 Å. In most cases (about 83%), structural optimisation using density functional theory (DFT) resolved the differences. Many of the cases where distinct and chemically significant structural differences remained after optimisation involved differently positioned hydroxyl groups, with obvious implications for the correct description of hydrogen bonding. ¹H and ¹³C chemical shifts from solid-state NMR experiments are proposed as an independent methodology in cases where DFT optimisation fails to resolve discrepancies.

DFT optimisation often resolves conflicting crystal structure determinations, with NMR shifts helping in cases where optimisation diverges to different structures.

A Bayesian approach to NMR crystal structure determination

Nuclear Magnetic Resonance (NMR) spectroscopy is particularly well suited to determine the structure of molecules and materials in powdered form. Structure determination usually proceeds by finding the best match between experimentally observed NMR chemical shifts and those of candidate structures. Chemical shifts for the candidate configurations have traditionally been computed by electronic-structure methods, and more recently predicted by machine learning. However, the reliability of the determination depends on the errors in the predicted shifts. Here we propose a Bayesian framework for determining the confidence in the identification of the experimental crystal structure, based on knowledge of the typical errors in the electronic structure methods. We demonstrate the approach on the determination of the structures of six organic molecular crystals. We critically assess the reliability of the structure determinations, facilitated by the introduction of a visualization of the similarity between candidate configurations in terms of their chemical shifts and their structures. We also show that the commonly used values for the errors in calculated ¹³C shifts are underestimated, and that more accurate, self-consistently determined uncertainties make it possible to use ¹³C shifts to improve the accuracy of structure determinations. Finally, we extend the recently-developed ShiftML model to render it more efficient, accurate, and, most importantly, to evaluate the uncertainties in its predictions. By quantifying the confidence in structure determinations based on ShiftML predictions we further substantiate that it provides a valid replacement for first-principles calculations in NMR crystallography.

Understanding hydrogen-bonding structures of molecular crystals via electron and NMR nanocrystallography

Understanding hydrogen-bonding networks in nanocrystals and microcrystals that are too small for X-ray diffractometry is a challenge. Although electron diffraction (ED) or electron 3D crystallography are applicable to determining the structures of such nanocrystals owing to their strong scattering power, these techniques still lead to ambiguities in the hydrogen atom positions and misassignments of atoms with similar atomic numbers such as carbon, nitrogen, and oxygen. Here, we propose a technique combining ED, solid-state NMR (SSNMR), and first-principles quantum calculations to overcome these limitations. The rotational ED method is first used to determine the positions of the non-hydrogen atoms, and SSNMR is then applied to ascertain the hydrogen atom positions and assign the carbon, nitrogen, and oxygen atoms via the NMR signals for ¹H, ¹³C, ¹⁴N, and ¹⁵N with the aid of quantum computations. This approach elucidates the hydrogen-bonding networks in l-histidine and cimetidine form B whose structure was previously unknown.

Electron diffraction can be used to determine nanocrystal structures, but is unsuitable for locating hydrogen atoms. Here the authors combine electron diffraction, solid-state NMR and first-principles calculations to resolve the crystal structures and hydrogen-bonding networks of L-histidine and cimetidine form B.

The use of variable temperature 13 C solid-state MAS NMR and GIPAW DFT calculations to explore the dynamics of diethylcarbamazine citrate

Experimental ¹³ C solid-state magic-angle spinning (MAS) Nuclear Magnetic Resonance (NMR) as well as Density-Functional Theory (DFT) gauge-including projector augmented wave (GIPAW) calculations were used to probe disorder and local mobility in diethylcarbamazine citrate, (DEC)⁺ (citrate)^- . This compound has been used as the first option drug for the treatment of filariasis, a disease endemic in tropical countries and caused by adult worms of Wuchereria bancrofti, which is transmitted by mosquitoes. We firstly present 2D ¹³ C─¹ H dipolar-coupling-mediated heteronuclear correlation spectra recorded at moderate spinning frequency, to explore the intermolecular interaction between DEC and citrate molecules. Secondly, we investigate the dynamic behavior of (DEC)⁺ (citrate)^- by varying the temperature and correlating the experimental MAS NMR results with DFT GIPAW calculations that consider two (DEC)⁺ conformers (in a 70:30 ratio) for crystal structures determined at 293 and 235 K. Solid-state NMR provides insights on slow exchange dynamics revealing conformational changes involving particularly the DEC ethyl groups.

How does the NMR thermometer work? Application of combined quantum molecular dynamics and GIPAW calculations into the study of lead nitrate

Lead nitrate is an inorganic salt, commonly used for the accurate temperature determination in the solid state NMR spectroscopy, due to the strong temperature dependence of the ²⁰⁷ Pb chemical shift. As the reason for this phenomenon remained unknown, the main purpose of this study was to explain this temperature dependence at the molecular level. To achieve this, combined CASTEP geometry optimization, quantum molecular dynamics at chosen temperatures and GIPAW NMR computations were performed. Due to the previous literature reports on inaccuracy in the calculation of ²⁰⁷ Pb NMR parameters using GIPAW, a large emphasis was put on the optimization of computational method. The application of quantum molecular dynamics provided the simulation of the temperature-dependent vibrational motions and enabled to accurately compute the changes in the value of Pb δ_iso resulting from them. © 2018 Wiley Periodicals, Inc.

Accurate 13-C and 15-N molecular crystal chemical shielding tensors from fragment-based electronic structure theory

Standard nuclear magnetic resonance (NMR) spectroscopy experiments measure isotropic chemical shifts, but measuring the chemical shielding anisotropy (CSA) tensor can provide additional insights into solid state chemical structures. Interpreting the principal components of these tensors is facilitated by first-principles chemical shielding tensor predictions. Here, the ability to predict molecular crystal CSA tensor components for ¹³C and ¹⁵N nuclei with fragment-based electronic structure techniques is explored. Similar to what has been found previously for isotropic chemical shifts, the benchmarking demonstrates that fragment-based techniques can accurately reproduce CSA tensor components. The use of hybrid density functionals like PBE0 or B3LYP provide higher accuracy than generalized gradient approximation functionals like PBE. Unlike for planewave density functional techniques, hybrid density functionals can be employed routinely with modest computational cost in fragment approaches. Finally, good consistency between the regression parameters used to map either isotropic shieldings or CSA tensor components is demonstrated, providing further evidence for the quality of the models and highlighting that models trained for isotropic shifts can also be applied to CSA tensor components.

NMR Crystallography of the Polymorphs of Metergoline

Two polymorphs of the drug compound metergoline (C25H29N3O2) were investigated in detail by solid-state NMR measurements. The results have been analysed by an advanced procedure, which uses experimental input together with the results of quantum chemical calculations that were performed for molecular crystals. In this way, it was possible to assign the total of 40 1H–13C correlation pairs in a highly complex system, namely, in the dynamically disordered polymorph with two independent molecules in the unit cell of a large volume of 4234 Å3. For the simpler polymorph, which exhibits only small-amplitude motions and has just one molecule in the unit cell with a volume of 529.0 Å3, the values of the principal elements of the 13C chemical shift tensors were measured. Additionally, for this polymorph, a set of crystal structure predictions were generated, and the {13C, 1H} isotropic and 13C anisotropic chemical shielding data were computed while using the gauge-including projector augmented-wave approach combined with the “revised Perdew-Burke-Ernzerhof“ exchange-correlation functional (GIPAW-RPBE). The experimental and theoretical results were combined in an application of the newly developed strategy to polymorph discrimination. This research thus opens up new routes towards more accurate characterization of the polymorphism of drug formulations.

Perspective: Current advances in solid-state NMR spectroscopy

In contrast to the rapid and revolutionary impact of solution-state Nuclear Magnetic Resonance (NMR) on modern chemistry, the field of solid-state NMR has matured more slowly. This reflects the major technical challenges of much reduced spectral resolution and sensitivity in solid-state as compared to solution-state spectra, as well as the relative complexity of the solid state. In this perspective, we outline the technique developments that have pushed resolution to intrinsic limits and the approaches, including ongoing major developments in the field of Dynamic Nuclear Polarisation, that have enhanced spectral sensitivity. The information on local structure and dynamics that can be obtained using these gains in sensitivity and resolution is illustrated with a diverse range of examples from large biomolecules to energy materials and pharmaceuticals and from both ordered and highly disordered materials. We discuss how parallel developments in quantum chemical calculation, particularly density functional theory, have enabled experimental data to be translated directly into information on local structure and dynamics, giving rise to the developing field of "NMR crystallography."

Predicting anisotropic thermal displacements for hydrogens from solid-state NMR: a study on hydrogen bonding in polymorphs of palmitic acid

The hydrogen-bonding environments at the COOH moiety in eight polycrystalline polymorphs of palmitic acid are explored using solid-state NMR. Although most phases have no previously reported crystal structure, measured 13C chemical shift tensors for COOH moieties, combined with DFT modeling establish that all phases crystallize with a cyclic dimer (R22(8)) hydrogen bonding arrangement. Phases A2, Bm and Em have localized OH hydrogens while phase C has a dynamically disordered OH hydrogen. The phase designated As is a mix of five forms, including 27.4% of Bm and four novel phases not fully characterized here due to insufficient sample mass. For phases A2, Bm, Em, and C the anisotropic uncertainties in the COOH hydrogen atom positions are established using a Monte Carlo sampling scheme. Sampled points are retained or rejected at the ±1σ level based upon agreement of DFT computed 13COOH tensors with experimental values. The collection of retained hydrogen positions bear a remarkable resemblance to the anisotropic displacement parameters (i.e. thermal ellipsoids) from diffraction studies. We posit that this similarity is no mere coincidence and that the two are fundamentally related. The volumes of NMR-derived anisotropic displacement ellipsoids for phases with localized OH hydrogens are 4.1 times smaller than those derived from single crystal X-ray diffraction and 1.8 times smaller than the volume of benchmark single crystal neutron diffraction values.

Electron-phonon coupling from finite differences

The interaction between electrons and phonons underlies multiple phenomena in physics, chemistry, and materials science. Examples include superconductivity, electronic transport, and the temperature dependence of optical spectra. A first-principles description of electron-phonon coupling enables the study of the above phenomena with accuracy and material specificity, which can be used to understand experiments and to predict novel effects and functionality. In this topical review, we describe the first-principles calculation of electron-phonon coupling from finite differences. The finite differences approach provides several advantages compared to alternative methods, in particular (i) any underlying electronic structure method can be used, and (ii) terms beyond the lowest order in the electron-phonon interaction can be readily incorporated. But these advantages are associated with a large computational cost that has until recently prevented the widespread adoption of this method. We describe some recent advances, including nondiagonal supercells and thermal lines, that resolve these difficulties, and make the calculation of electron-phonon coupling from finite differences a powerful tool. We review multiple applications of the calculation of electron-phonon coupling from finite differences, including the temperature dependence of optical spectra, superconductivity, charge transport, and the role of defects in semiconductors. These examples illustrate the advantages of finite differences, with cases where semilocal density functional theory is not appropriate for the calculation of electron-phonon coupling and many-body methods such as the GW approximation are required, as well as examples in which higher-order terms in the electron-phonon interaction are essential for an accurate description of the relevant phenomena. We expect that the finite difference approach will play a central role in future studies of the electron-phonon interaction.

Exploiting 13C/14N solid-state NMR distance measurements to assign dihedral angles and locate neighboring molecules

The RESPDOR NMR method rapidly provides multiple ¹³C/¹⁴N distance measurements in natural abundance solids.

Furosemide's one little hydrogen atom: NMR crystallography structure verification of powdered molecular organics

The potential of NMR crystallography to verify molecular crystal structures deposited in structural databases is evaluated, with two structures of the pharmaceutical furosemide serving as examples. While the structures differ in the placement of one H atom, using this approach, we verify one of the structures in the Cambridge Structural Database using quantitative tools, while establishing that the other structure does not meet the verification criteria.

Exploring Systematic Discrepancies in DFT Calculations of Chlorine Nuclear Quadrupole Couplings

Previous studies have revealed significant discrepancies between density functional theory (DFT)-calculated and experimental nuclear quadrupolar coupling constants (C_Q) for chlorine atoms, particularly in ionic solids. Various aspects of the computations are systematically investigated here, including the choice of the DFT functional, basis set convergence, and geometry optimization protocol. The effects of fast (fs) time-scale dynamics are probed using molecular dynamics (MD) and nuclear quantum effects (NQEs) are considered using path-integral MD calculations. It is shown that the functional choice is the most important factor related to improving the accuracy of the quadrupolar coupling calculations, and that functionals beyond the generalized gradient approximation (GGA) level, such as hybrid and meta-GGA functionals, are required for good correlations with experiment. The influence of molecular dynamics and NQEs is less important than the functional choice in the studied systems. A method which involves scaling the calculated quadrupolar coupling constant is proposed here; its application leads to good agreement with experimental data.

The application of tailor-made force fields and molecular dynamics for NMR crystallography: a case study of free base cocaine

Motional averaging has been proven to be significant in predicting the chemical shifts in ab initio solid-state NMR calculations, and the applicability of motional averaging with molecular dynamics has been shown to depend on the accuracy of the molecular mechanical force field. The performance of a fully automatically generated tailor-made force field (TMFF) for the dynamic aspects of NMR crystallography is evaluated and compared with existing benchmarks, including static dispersion-corrected density functional theory calculations and the COMPASS force field. The crystal structure of free base cocaine is used as an example. The results reveal that, even though the TMFF outperforms the COMPASS force field for representing the energies and conformations of predicted structures, it does not give significant improvement in the accuracy of NMR calculations. Further studies should direct more attention to anisotropic chemical shifts and development of the method of solid-state NMR calculations.

Internal dynamics in helical molecules studied by X-ray diffraction, NMR spectroscopy and DFT calculations

Unexpected flexibility of helical molecules is observed both in solution and solid phases.

Enhanced NMR Discrimination of Pharmaceutically Relevant Molecular Crystal Forms through Fragment-Based Ab Initio Chemical Shift Predictions

Chemical shift prediction plays an important role in the determination or validation of crystal structures with solid-state nuclear magnetic resonance (NMR) spectroscopy. One of the fundamental theoretical challenges lies in discriminating variations in chemical shifts resulting from different crystallographic environments. Fragment-based electronic structure methods provide an alternative to the widely used plane wave gauge-including projector augmented wave (GIPAW) density functional technique for chemical shift prediction. Fragment methods allow hybrid density functionals to be employed routinely in chemical shift prediction, and we have recently demonstrated appreciable improvements in the accuracy of the predicted shifts when using the hybrid PBE0 functional instead of generalized gradient approximation (GGA) functionals like PBE. Here, we investigate the solid-state ¹³C and ¹⁵N NMR spectra for multiple crystal forms of acetaminophen, phenobarbital, and testosterone. We demonstrate that the use of the hybrid density functional instead of a GGA provides both higher accuracy in the chemical shifts and increased discrimination among the different crystallographic environments. Finally, these results also provide compelling evidence for the transferability of the linear regression parameters mapping predicted chemical shieldings to chemical shifts that were derived in an earlier study.

Crystallographic and Dynamic Aspects of Solid-State NMR Calibration Compounds: Towards ab Initio NMR Crystallography

The excellent results of dispersion-corrected density functional theory (DFT-D) calculations for static systems have been well established over the past decade. The introduction of dynamics into DFT-D calculations is a target, especially for the field of molecular NMR crystallography. Four (13) C ss-NMR calibration compounds are investigated by single-crystal X-ray diffraction, molecular dynamics and DFT-D calculations. The crystal structure of 3-methylglutaric acid is reported. The rotator phases of adamantane and hexamethylbenzene at room temperature are successfully reproduced in the molecular dynamics simulations. The calculated (13) C chemical shifts of these compounds are in excellent agreement with experiment, with a root-mean-square deviation of 2.0 ppm. It is confirmed that a combination of classical molecular dynamics and DFT-D chemical shift calculation improves the accuracy of calculated chemical shifts.

Benchmark fragment-based (1)H, (13)C, (15)N and (17)O chemical shift predictions in molecular crystals

The performance of fragment-based ab initio(1)H, (13)C, (15)N and (17)O chemical shift predictions is assessed against experimental NMR chemical shift data in four benchmark sets of molecular crystals. Employing a variety of commonly used density functionals (PBE0, B3LYP, TPSSh, OPBE, PBE, TPSS), we explore the relative performance of cluster, two-body fragment, and combined cluster/fragment models. The hybrid density functionals (PBE0, B3LYP and TPSSh) generally out-perform their generalized gradient approximation (GGA)-based counterparts. (1)H, (13)C, (15)N, and (17)O isotropic chemical shifts can be predicted with root-mean-square errors of 0.3, 1.5, 4.2, and 9.8 ppm, respectively, using a computationally inexpensive electrostatically embedded two-body PBE0 fragment model. Oxygen chemical shieldings prove particularly sensitive to local many-body effects, and using a combined cluster/fragment model instead of the simple two-body fragment model decreases the root-mean-square errors to 7.6 ppm. These fragment-based model errors compare favorably with GIPAW PBE ones of 0.4, 2.2, 5.4, and 7.2 ppm for the same (1)H, (13)C, (15)N, and (17)O test sets. Using these benchmark calculations, a set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided and their robustness assessed using statistical cross-validation. We demonstrate the utility of these approaches and the reported scaling parameters on applications to 9-tert-butyl anthracene, several histidine co-crystals, benzoic acid and the C-nitrosoarene SnCl2(CH3)2(NODMA)2.

Combining solid-state NMR spectroscopy with first-principles calculations - a guide to NMR crystallography

Recent advances in the application of first-principles calculations of NMR parameters to periodic systems have resulted in widespread interest in their use to support experimental measurement. Such calculations often play an important role in the emerging field of "NMR crystallography", where NMR spectroscopy is combined with techniques such as diffraction, to aid structure determination. Here, we discuss the current state-of-the-art for combining experiment and calculation in NMR spectroscopy, considering the basic theory behind the computational approaches and their practical application. We consider the issues associated with geometry optimisation and how the effects of temperature may be included in the calculation. The automated prediction of structural candidates and the treatment of disordered and dynamic solids are discussed. Finally, we consider the areas where further development is needed in this field and its potential future impact.

Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.

Temperature Dependence of NMR Parameters Calculated from Path Integral Molecular Dynamics Simulations

The influence of temperature on NMR chemical shifts and quadrupolar couplings in model molecular organic solids is explored using path integral molecular dynamics (PIMD) and density functional theory (DFT) calculations of shielding and electric field gradient (EFG) tensors. An approach based on convoluting calculated shielding or EFG tensor components with probability distributions of selected bond distances and valence angles obtained from DFT-PIMD simulations at several temperatures is used to calculate the temperature effects. The probability distributions obtained from the quantum PIMD simulations, which includes nuclear quantum effects, are significantly broader and less temperature dependent than those obtained with conventional DFT molecular dynamics or with 1D scans through the potential energy surface. Predicted NMR observables for the model systems were in excellent agreement with experimental data.