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

The many-body expansion approach to ab initio calculation of electric field gradients in molecular crystals

Accurate calculation of electric field gradients (EFGs) in molecular crystals, despite big advances in ab initio techniques, is still a challenge. Here, we present a new approach to calculate the EFGs in molecular crystals by employing the many-body expansion (MBE) technique with electrostatic embedding. This allows for (i) a reduction in the computational cost or an alternative increase in the level of theory (we use the MP2/6-311++G) and (ii) the ability to monitor EFG convergence by progressively adding more surrounding molecules and/or adding higher many-body interactions. We focus on the ¹⁴N EFG and study four (model) compounds in more detail: solid nitrogen, ethylamine, methylamine, and ammonia. Solid nitrogen is rather insensitive to neighbors; for ethylamine and methylamine, the 3-body interactions are found sufficient for a converged EFG, whereas for ammonia, even the inclusion of 5-body interactions is insufficient although convergence is anticipated. We then validate our technique by comparing the experimental and ab initio¹⁴N EFGs for 116 organic compounds utilizing their known crystal structures and published EFG. Overall, we find a very good agreement, with a small EFG rms error, which is probably due to other sources, rather than the MBE approximation.

Mechanochemical Formation of Racemic Praziquantel Hemihydrate with Improved Biopharmaceutical Properties

Praziquantel (PZQ) is the first-line drug used against schistosomiasis, one of the most common parasitic diseases in the world. A series of crystalline structures including two new polymorphs of the pure drug and a series of cocrystals of PZQ have been discovered and deposited in the Cambridge Structural Database (CSD). This work adds to the list of multicomponent forms of PZQ a relevant example of a racemic hemihydrate (PZQ-HH), obtainable from commercial PZQ (polymorphic Form A) through mechanochemistry. Noteworthy, the formation of the new hemihydrate strongly depends on the initial polymorphic form of PZQ and on the experimental conditions used. The new PZQ-HH has been fully characterized by means of HPLC, Differential Scanning Calorimetry (DSC), Thermogravimetric Analysis (TGA), Hot-Stage Microscopy (SEM), Powder X-Ray Diffraction (PXRD), Scanning Electron Microscopy (SEM), FT-IR, polarimetry, solid-state NMR (SS-NMR), solubility and intrinsic dissolution rate (IDR), and in vitro tests on Schistosoma mansoni adults. The crystal structure was solved from the powder X-ray diffraction pattern and validated by periodic-DFT calculations. The new bioactive hemihydrate was physically stable for three months and showed peculiar biopharmaceutical features including enhanced solubility and a double intrinsic dissolution rate in water in comparison to the commercially available PZQ Form A.

GIAO versus GIPAW: Comparison of Methods To Calculate 11B NMR Shifts of Icosahedral Closo-Heteroboranes toward Boron-Rich Borides

In this work, we perform first-principle density functional theory calculations with the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional to compare the results of the gauge-including atomic orbital (GIAO) method with the gauge-including projector-augmented wave (GIPAW) approach for isotropic ¹¹B nuclear magnetic resonance shifts. GIPAW had been used successfully for the theoretical calculation of nuclear magnetic parameters of ¹¹B species in strong ionic solid-phase compounds such as borates but had been applied very rarely to structures where boron is mainly involved in complex covalent bonding situations, for example, in icosahedra of boron-rich borides. Thus, we investigate the accuracy of both well-known methods and reliability of the effective treatment of core electrons on a test set containing 16 experimentally known closo-(hetero)dodecaboranes. In general, we find very good agreement between GIAO and GIPAW when compared to experimental observations. However, accidental degeneracies of the shift values are better predicted by GIPAW. The optimized molecular geometries on the PBE level agree well with gaseous electron diffraction data and lead to theoretical isotropic chemical ¹¹B shifts with root-mean-square errors of 2.1 and 1.0 ppm depending on the used model of converting absolute shieldings to chemical shifts. The comparison with results from hybrid functionals (B3LYP, B3LYP-D2, and PBE0) shows a minor improvement in accuracy, which is in agreement with ¹³C shifts of sp³-hybridized species. In order to prove the reliability of the conversion parameters obtained by PBE, we report the calculated ¹¹B shifts of 1,2-, 1,7-, and 1,12-PCB₁₀H₁₁ with GIAO and GIPAW to our knowledge for the first time. Additionally, Bader's analysis is carried out on the converged electron density for all boron species within the molecular test set, yielding no simple direct relation between charge and isotropic shifts.

Exploring mechanochemical parameters using a DoE approach: Crystal structure solution from synchrotron XRPD and characterization of a new praziquantel polymorph

A rotated Doehlert matrix was utilized to explore the experimental design space around the milling parameters of Praziquantel (PZQ) polymorph B formation in terms of frequency and milling time. Three experimental responses were evaluated on the resulting ground samples: two quantitative responses, i.e. median particle size by Laser Light scattering (LLS) and drug recovery by HPLC, and one qualitative dependent variable, i.e. the obtained PZQ crystalline form, characterized through X-Ray Powder Diffraction (XRPD) and confirmed by Differential Scanning Calorimetry (DSC) and Thermogravimetric analysis (TGA). Temperature inside the jars was kept under constant control during the milling process by using temperature sensor equipped jars (thermojars), thus allowing evaluation of the obtained solid states at each experimental point, considering the specific temperature of the process. This explorative analysis led to the finding of a novel PZQ polymorph, named "Form C", produced without degradation, then fully characterized, including by means of Synchrotron XRPD, Polarimetric, FT-IR, SS-NMR, ESEM and saturation solubility. Crystal structure was solved from XRPD data and its geometry was optimized by DFT calculations (CASTEP). Finally, Form C and Form A activity against adult schistosoma mansoni were compared through in vitro testing, and Form C's physical stability checked. The new polymorph, crystallizing in space group I2/c, physically stable for approximately 2 months, showed a m.p. of 106.84 °C and displayed excellent biopharmaceutical properties (water solubility of 382.69±9.26 mg/l), while preserving excellent activity levels against adult schistosoma mansoni.

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.

Improving Predicted Nuclear Magnetic Resonance Chemical Shifts Using the Quasi-Harmonic Approximation

Ab initio nuclear magnetic resonance chemical shift prediction plays an important role in the determination or validation of crystal structures. The ability to predict chemical shifts more accurately can translate to increased confidence in the resulting chemical shift or structural assignments. Standard electronic structure predictions for molecular crystal structures neglect thermal expansion, which can lead to an appreciable underestimation of the molar volumes. This study examines this volume error and its impact on 68 ¹³C- and 28 ¹⁵N-predicted chemical shifts taken from 20 molecular crystals. It assesses the ability to recover more realistic room-temperature crystal structures using the quasi-harmonic approximation and how refining the structures impacts the chemical shifts. Several pharmaceutical molecular crystals are also examined in more detail. On the whole, accounting for quasi-harmonic expansion changes the ¹³C and ¹⁵N chemical shifts by 0.5 and 1.0 ppm on average. This, in turn, reduces the root-mean-square errors relative to experiment by 0.3 ppm for ¹³C and 0.7 ppm for ¹⁵N. Although the statistical impacts are modest, changes in individual chemical shifts can reach multiple ppm. Accounting for thermal expansion in molecular crystal chemical shift prediction may not be needed routinely, but the systematic trend toward improved accuracy with the experiment could be useful in cases where discrimination between structural candidates is challenging, as in the pharmaceutical theophylline.

Multiresolution 3D-DenseNet for Chemical Shift Prediction in NMR Crystallography

We have developed a deep learning algorithm for chemical shift prediction for atoms in molecular crystals that utilizes an atom-centered Gaussian density model for the 3D data representation of a molecule. We define multiple channels that describe different spatial resolutions for each atom type that utilizes cropping, pooling, and concatenation to create a multiresolution 3D-DenseNet architecture (MR-3D-DenseNet). Because the training and testing time scale linearly with the number of samples, the MR-3D-DenseNet can exploit data augmentation that takes into account the property of rotational invariance of the chemical shifts, thereby also increasing the size of the training data set by an order of magnitude without additional cost. We obtain very good agreement for ¹³C, ¹⁵N, and ¹⁷O chemical shifts when compared to ab initio quantum chemistry methods, with the highest accuracy found for ¹H chemical shifts that is comparable to the error between the ab initio results and experimental measurements. Principal component analysis (PCA) is used to both understand these greatly improved predictions for ¹H , as well as indicating that chemical shift prediction for ¹³C, ¹⁵N, and ¹⁷O, which have far fewer training environments than the ¹H atom type, will improve once more unique training samples are made available to exploit the deep network architecture.

Rapid Structure Determination of Molecular Solids Using Chemical Shifts Directed by Unambiguous Prior Constraints

NMR-based crystallography approaches involving the combination of crystal structure prediction methods, ab initio calculated chemical shifts and solid-state NMR experiments are powerful methods for crystal structure determination of microcrystalline powders. However, currently structural information obtained from solid-state NMR is usually included only after a set of candidate crystal structures has already been independently generated, starting from a set of single-molecule conformations. Here, we show with the case of ampicillin that this can lead to failure of structure determination. We propose a crystal structure determination method that includes experimental constraints during conformer selection. In order to overcome the problem that experimental measurements on the crystalline samples are not obviously translatable to restrict the single-molecule conformational space, we propose constraints based on the analysis of absent cross-peaks in solid-state NMR correlation experiments. We show that these absences provide unambiguous structural constraints on both the crystal structure and the gas-phase conformations, and therefore can be used for unambiguous selection. The approach is parametrized on the crystal structure determination of flutamide, flufenamic acid, and cocaine, where we reduce the computational cost by around 50%. Most importantly, the method is then shown to correctly determine the crystal structure of ampicillin, which would have failed using current methods because it adopts a high-energy conformer in its crystal structure. The average positional RMSE on the NMR powder structure is ⟨r_av⟩ = 0.176 Å, which corresponds to an average equivalent displacement parameter U_eq = 0.0103 Ų.

TensorView: A software tool for displaying NMR tensors

The representation of nuclear magnetic resonance (NMR) tensors as surfaces on three-dimensional molecular models is an information-rich presentation that highlights the geometric relationship between tensor principal components and the underlying molecular and electronic structure. Here, we describe a new computational tool, TensorView, for depicting NMR tensors on the molecular framework. This package makes use of the graphical interface and built-in molecular display functionality present within the Mathematica programming environment and is robust for displaying tensor properties from a broad range of commercial and user-specific computational chemistry packages. Two mathematical forms for representing tensor interaction surfaces are presented, the popular ellipsoidal construct and the more technically correct "ovaloid" form. Examples are provided for chemical shielding and shift tensors, dipole-dipole and quadrupolar couplings, and atomic anisotropic displacement parameters (thermal ellipsoids) derived from NMR crystallography.

Investigation of structure and dynamics in a photochromic molecular crystal by NMR crystallography

A photochromic anil, N-(3,5-di-t-butylsalicylidene)-4-amino-pyridine, has been studied by single-crystal X-ray diffraction, multinuclear magic-angle spinning NMR, and first-principles density functional theory (DFT) calculations. Interpretation of the solid-state NMR data on the basis of calculated chemical shifts confirms the structure is primarily composed of molecules in the ground-state enol tautomer, whereas thermally activated cis-keto and photoisomerised trans-keto states exist as low-level defects with populations that are too low to detect experimentally. Variable temperature ¹³ C NMR data reveal evidence for solid-state dynamics, which is found to be associated with fast rotational motion of t-butyl groups and 180° flips of the pyridine ring, contrasting the time-averaged structure obtained by X-ray diffraction. Comparison of calculated chemical shifts for the full crystal structure and an isolated molecule also reveals evidence for an intermolecular hydrogen bond involving the pyridine ring and an adjacent imine carbon, which facilitates the flipping motion. The DFT calculations also reveal that the molecular conformation in the crystal structure is very close to the energetic minimum for an isolated molecule, indicating that the ring dynamics arise as a result of considerable steric freedom of the pyridine ring and which also allows the molecule to adopt a favourable conformation for photochromism.

Local-structure effects on 31P NMR chemical shift tensors in solid state

The effect of the local structure on the ³¹P NMR chemical shift tensor (CST) has been studied experimentally and simulated theoretically using the density functional theory gauge-independent-atomic-orbital approach. It has been shown that the dominating impact comes from a small number of noncovalent interactions between the phosphorus-containing group under question and the atoms of adjacent molecules. These interactions can be unambiguously identified using the Bader analysis of the electronic density. A robust and computationally effective approach designed to attribute a given experimental ³¹P CST to a certain local morphology has been elaborated. This approach can be useful in studies of surfaces, complex molecular systems, and amorphous materials.

A DFT/ZORA Study of Cadmium Magnetic Shielding Tensors: Analysis of Relativistic Effects and Electronic-State Approximations

Theoretical considerations are discussed for the accurate prediction of cadmium magnetic shielding tensors using relativistic density functional theory (DFT). Comparison is made between calculations that model the extended lattice of the cadmium-containing solids using periodic boundary conditions and pseudopotentials with calculations that use clusters of atoms. The all-electron cluster-based calculations afford an opportunity to examine the importance of (i) relativistic effects on cadmium magnetic shielding tensors, as introduced through the ZORA Hamiltonian at either the scalar (SC) or spin-orbit (SO) levels and (ii) variation in the class of the DFT approximation. Twenty-three combinations of pseudopotentials or all-electron methods, DFT functionals, and relativistic treatments are assessed for the prediction of the principal components of the magnetic shielding tensors of 30 cadmium sites. We find that the inclusion of SO coupling can increase the cadmium magnetic shielding by as much as ca. 1100 ppm for a certain principal values; these effects are most pronounced for cadmium sites featuring bonds to other heavy atoms such as cadmium, iodine, or selenium. The best agreement with experimental values is found at the ZORA SO level in combination with a hybrid DFT method featuring a large admixture of Hartree-Fock exchange such as BH&HLYP. Finally, a theoretical examination is presented of the magnetic shielding tensor of the Cd(I) site in Cd₂(AlCl₄)₂.

Improving the accuracy of solid-state nuclear magnetic resonance chemical shift prediction with a simple molecular correction

A fast, straightforward method for computing NMR chemical shieldings of crystalline solids is proposed. The method combines the advantages of both conventional approaches: periodic calculations using plane-wave basis sets and molecular computational approaches. The periodic calculations capture the periodic nature of crystalline solids, but the computational level of the electronic structure calculation is limited to general-gradient-approximation (GGA) density functionals. It is demonstrated that a correction to the GGA result calculated on an isolated molecule at a higher level of theory significantly improves the correlations between experimental and calculated chemical shifts while adding almost no additional computational cost. Corrections calculated with a hybrid density functional improved the accuracy of 13C, 15N and 17O chemical shift predictions significantly and allowed identifying errors in previously published experimental data. Applications of the approach to crystalline isocytosine, methacrylamide, and testosterone are presented.

An XRD and NMR crystallographic investigation of the structure of 2,6-lutidinium hydrogen fumarate

A crystallographic study highlighting the benefits of a combined XRD and NMR approach in investigating both stability and variation within an organic multicomponent crystal.

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.

Chemical shifts in molecular solids by machine learning

Due to their strong dependence on local atonic environments, NMR chemical shifts are among the most powerful tools for strucutre elucidation of powdered solids or amorphous materials. Unfortunately, using them for structure determination depends on the ability to calculate them, which  comes at the cost of high accuracy first-principles calculations. Machine learning has recently emerged as a way to overcome the need for quantum chemical calculations, but for chemical shifts in solids it is hindered by the chemical and combinatorial space spanned by molecular solids, the strong dependency of chemical shifts on their environment, and the lack of an experimental database of shifts. We propose a machine learning method based on local environments to accurately predict chemical shifts of molecular solids and their polymorphs to within DFT accuracy. We also demonstrate that the trained model is able to determine, based on the match between experimentally measured and ML-predicted shifts, the structures of cocaine and the drug 4-[4-(2-adamantylcarbamoyl)-5-tert-butylpyrazol-1-yl]benzoic acid.

Solid-state nuclear magnetic resonance combined with quantum chemical shift predictions is limited by high computational cost. Here, the authors use machine learning based on local atomic environments to predict experimental chemical shifts in molecular solids with accuracy similar to density functional theory.

Elucidating an Amorphous Form Stabilization Mechanism for Tenapanor Hydrochloride: Crystal Structure Analysis Using X-ray Diffraction, NMR Crystallography, and Molecular Modeling

By the combined use of powder and single-crystal X-ray diffraction, solid-state NMR, and molecular modeling, the crystal structures of two systems containing the unusually large tenapanor drug molecule have been determined: the free form, ANHY, and a dihydrochloride salt form, 2HCl. Dynamic nuclear polarization (DNP) assisted solid-state NMR (SSNMR) crystallography investigations were found essential for the final assignment and were used to validate the crystal structure of ANHY. From a structural informatics analysis of ANHY and 2HCl, conformational ring differences in one part of the molecule were observed which influence the relative orientation of a methyl group on a ring nitrogen and thereby impact the crystallizability of the dihydrochloride salt. From quantum chemistry calculations, the dynamics between different ring conformations in tenapanor is predicted to be fast. Addition of HCl to tenapanor results in general in a mixture of protonated ring conformers and hence a statistical mix of diastereoisomers which builds up the amorphous form, a-2HCl. This was qualitatively verified by ¹³C CP/MAS NMR investigations of the amorphous form. Thus, to form any significant amount of the crystalline material 2HCl, which originates from the minor (i.e., energetically less stable) ring conformations, one needs to involve nitrogen deprotonation to allow exchange between the minor and major conformations of ANHY in solution. Thus, by controlling the solution pH value to well below the p K_a of ANHY, the equilibrium between ANHY and 2HCl can be controlled and by this mechanism the crystallization of 2HCl can be avoided and the amorphous form of the dichloride salt can therefore be stabilized.

Improved Electrostatic Embedding for Fragment-Based Chemical Shift Calculations in Molecular Crystals

Fragment-based methods predict nuclear magnetic resonance (NMR) chemical shielding tensors in molecular crystals with high accuracy and computational efficiency. Such methods typically employ electrostatic embedding to mimic the crystalline environment, and the quality of the results can be sensitive to the embedding treatment. To improve the quality of this embedding environment for fragment-based molecular crystal property calculations, we borrow ideas from the embedded ion method to incorporate self-consistently polarized Madelung field effects. The self-consistent reproduction of the Madelung potential (SCRMP) model developed here constructs an array of point charges that incorporates self-consistent lattice polarization and which reproduces the Madelung potential at all atomic sites involved in the quantum mechanical region of the system. The performance of fragment- and cluster-based ¹H, ¹³C, ¹⁴N, and ¹⁷O chemical shift predictions using SCRMP and density functionals like PBE and PBE0 are assessed. The improved embedding model results in substantial improvements in the predicted ¹⁷O chemical shifts and modest improvements in the ¹⁵N ones. Finally, the performance of the model is demonstrated by examining the assignment of the two oxygen chemical shifts in the challenging γ-polymorph of glycine. Overall, the SCRMP-embedded NMR chemical shift predictions are on par with or more accurate than those obtained with the widely used gauge-including projector augmented wave (GIPAW) model.

Ab initio random structure searching of organic molecular solids: assessment and validation against experimental data

This paper explores the capability of using the DFT-D ab initio random structure searching (AIRSS) method to generate crystal structures of organic molecular materials, focusing on a system (m-aminobenzoic acid; m-ABA) that is known from experimental studies to exhibit abundant polymorphism. Within the structural constraints selected for the AIRSS calculations (specifically, centrosymmetric structures with Z = 4 for zwitterionic m-ABA molecules), the method is shown to successfully generate the two known polymorphs of m-ABA (form III and form IV) that have these structural features. We highlight various issues that are encountered in comparing crystal structures generated by AIRSS to experimental powder X-ray diffraction (XRD) data and solid-state magic-angle spinning (MAS) NMR data, demonstrating successful fitting for some of the lowest energy structures from the AIRSS calculations against experimental low-temperature powder XRD data for known polymorphs of m-ABA, and showing that comparison of computed and experimental solid-state NMR parameters allows different hydrogen-bonding motifs to be discriminated.

Quantum mechanical force fields for condensed phase molecular simulations

Molecular simulations are powerful tools for providing atomic-level details into complex chemical and physical processes that occur in the condensed phase. For strongly interacting systems where quantum many-body effects are known to play an important role, density-functional methods are often used to provide the model with the potential energy used to drive dynamics. These methods, however, suffer from two major drawbacks. First, they are often too computationally intensive to practically apply to large systems over long time scales, limiting their scope of application. Second, there remain challenges for these models to obtain the necessary level of accuracy for weak non-bonded interactions to obtain quantitative accuracy for a wide range of condensed phase properties. Quantum mechanical force fields (QMFFs) provide a potential solution to both of these limitations. In this review, we address recent advances in the development of QMFFs for condensed phase simulations. In particular, we examine the development of QMFF models using both approximate and ab initio density-functional models, the treatment of short-ranged non-bonded and long-ranged electrostatic interactions, and stability issues in molecular dynamics calculations. Example calculations are provided for crystalline systems, liquid water, and ionic liquids. We conclude with a perspective for emerging challenges and future research directions.

A Modular Implementation for the Simulation of 1D and 2D Solid-State NMR Spectra of Quadrupolar Nuclei in the Virtual Multifrequency Spectrometer-Draw Graphical Interface

We present the implementation of the solid state (SoS)NMR module for the simulation of several 1D and 2D NMR spectra of all the elements in the periodic table in the virtual multifrequency spectrometer (VMS). This module is fully integrated with the graphical user interface of VMS (VMS-Draw) [Licari et al., J. Comput. Chem. 36, 2015, 321-334], a freeware tool which allows a user-friendly handling of structures and analyses of advanced spectroscopical properties of chemical compounds-from model systems to real-world applications. Besides the numerous modules already available in VMS for the study of electronic, optical, vibrational, vibronic, and EPR properties, here the simulation of NMR spectra is presented with a particular emphasis on those techniques usually employed to investigate solid state systems. The SoSNMR module benefits from its ability to work under both periodic and nonperiodic conditions, such that small molecules/molecular clusters can be treated, as well as extended three-dimensional systems enforcing (or not) translational periodicity. These features allow VMS to simulate spectra resulting from NMR calculations by some popular quantum chemistry codes, namely Gaussian09/16, Castep, and Quantum Espresso. The effectiveness of the SoSNMR module of VMS is examined throughout the manuscript, and applied to simulate 1D static, MAS, and VAS NMR spectra as well as 2D correlation (90°, MAS) and MQMAS spectra of active NMR nuclei embedded in different amorphous and crystalline systems of actual interest in chemistry and material science. Finally, the program is able to simulate the spectra of both the total ensemble of spin-active nuclei present in the system and of subensembles differentiated depending on the chemical environment of the first and second coordination sphere in a very general way applicable to any kind of systems.

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.

NMR Crystallography of a Carbanionic Intermediate in Tryptophan Synthase: Chemical Structure, Tautomerization, and Reaction Specificity

Carbanionic intermediates play a central role in the catalytic transformations of amino acids performed by pyridoxal-5'-phosphate (PLP)-dependent enzymes. Here, we make use of NMR crystallography-the synergistic combination of solid-state nuclear magnetic resonance, X-ray crystallography, and computational chemistry-to interrogate a carbanionic/quinonoid intermediate analogue in the β-subunit active site of the PLP-requiring enzyme tryptophan synthase. The solid-state NMR chemical shifts of the PLP pyridine ring nitrogen and additional sites, coupled with first-principles computational models, allow a detailed model of protonation states for ionizable groups on the cofactor, substrates, and nearby catalytic residues to be established. Most significantly, we find that a deprotonated pyridine nitrogen on PLP precludes formation of a true quinonoid species and that there is an equilibrium between the phenolic and protonated Schiff base tautomeric forms of this intermediate. Natural bond orbital analysis indicates that the latter builds up negative charge at the substrate Cα and positive charge at C4' of the cofactor, consistent with its role as the catalytic tautomer. These findings support the hypothesis that the specificity for β-elimination/replacement versus transamination is dictated in part by the protonation states of ionizable groups on PLP and the reacting substrates and underscore the essential role that NMR crystallography can play in characterizing both chemical structure and dynamics within functioning enzyme active sites.

Predicting Molecular Crystal Properties from First Principles: Finite-Temperature Thermochemistry to NMR Crystallography

Molecular crystals occur widely in pharmaceuticals, foods, explosives, organic semiconductors, and many other applications. Thanks to substantial progress in electronic structure modeling of molecular crystals, attention is now shifting from basic crystal structure prediction and lattice energy modeling toward the accurate prediction of experimentally observable properties at finite temperatures and pressures. This Account discusses how fragment-based electronic structure methods can be used to model a variety of experimentally relevant molecular crystal properties. First, it describes the coupling of fragment electronic structure models with quasi-harmonic techniques for modeling the thermal expansion of molecular crystals, and what effects this expansion has on thermochemical and mechanical properties. Excellent agreement with experiment is demonstrated for the molar volume, sublimation enthalpy, entropy, and free energy, and the bulk modulus of phase I carbon dioxide when large basis second-order Møller-Plesset perturbation theory (MP2) or coupled cluster theories (CCSD(T)) are used. In addition, physical insight is offered into how neglect of thermal expansion affects these properties. Zero-point vibrational motion leads to an appreciable expansion in the molar volume; in carbon dioxide, it accounts for around 30% of the overall volume expansion between the electronic structure energy minimum and the molar volume at the sublimation point. In addition, because thermal expansion typically weakens the intermolecular interactions, neglecting thermal expansion artificially stabilizes the solid and causes the sublimation enthalpy to be too large at higher temperatures. Thermal expansion also frequently weakens the lower-frequency lattice phonon modes; neglecting thermal expansion causes the entropy of sublimation to be overestimated. Interestingly, the sublimation free energy is less significantly affected by neglecting thermal expansion because the systematic errors in the enthalpy and entropy cancel somewhat. Second, because solid state nuclear magnetic resonance (NMR) plays an increasingly important role in molecular crystal studies, this Account discusses how fragment methods can be used to achieve higher-accuracy chemical shifts in molecular crystals. Whereas widely used plane wave density functional theory models are largely restricted to generalized gradient approximation (GGA) functionals like PBE in practice, fragment methods allow the routine use of hybrid density functionals with only modest increases in computational cost. In extensive molecular crystal benchmarks, hybrid functionals like PBE0 predict chemical shifts with 20-30% higher accuracy than GGAs, particularly for ¹H, ¹³C, and ¹⁵N nuclei. Due to their higher sensitivity to polarization effects, ¹⁷O chemical shifts prove slightly harder to predict with fragment methods. Nevertheless, the fragment model results are still competitive with those from GIPAW. The improved accuracy achievable with fragment approaches and hybrid density functionals increases discrimination between different potential assignments of individual shifts or crystal structures, which is critical in NMR crystallography applications. This higher accuracy and greater discrimination are highlighted in application to the solid state NMR of different acetaminophen and testosterone crystal forms.

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.