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

Spiers Memorial Lecture: NMR crystallography

Chemical function is directly related to the spatial arrangement of atoms. Consequently, the determination of atomic-level three-dimensional structures has transformed molecular and materials science over the past 60 years. In this context, solid-state NMR has emerged to become the method of choice for atomic-level characterization of complex materials in powder form. In the following we present an overview of current methods for chemical shift driven NMR crystallography, illustrated with applications to complex materials.

Predicting 35-Cl electric field gradient tensors in crystalline solids using cluster and fragment-corrected planewave density functional theory

Planewave-corrected methods have proven effective for accurately modeling nuclear magnetic resonance (NMR) parameters in crystalline systems. Recent work extended the application of planewave-corrected calculations beyond the second row, predicting EFG tensor parameters for 35Cl using a simple molecular correction to projector augmented-wave (PAW) density functional theory (DFT). Here we extend this work using fragment and cluster-based calculations coupled with polarizable continuum (PCM) methods to improve further the accuracy of planewave-corrected 35Cl EFG tensor calculations. Benchmark data from a test set comprised of 105 individual 35Cl EFG tensor principal components for chlorine-containing molecular crystals and crystalline chloride salts shows fragment-corrected planewave calculations using the PBE0 hybrid density functional improve the accuracy of predicted EFG tensor components by 30 % relative to traditional planewave calculations. We compare the influence of different geometry optimization methods and density functionals on the accuracy of predicted 35Cl EFG tensor parameters. Four cases of spectral assignment are presented to demonstrate the utility of improving the accuracy of predicted 35Cl EFG tensor parameters.

Crystal structure validation of verinurad via proton-detected ultra-fast MAS NMR and machine learning

The recent development of ultra-fast magic-angle spinning (MAS) (>100 kHz) provides new opportunities for structural characterization in solids. Here, we use NMR crystallography to validate the structure of verinurad, a microcrystalline active pharmaceutical ingredient. To do this, we take advantage of 1H resolution improvement at ultra-fast MAS and use solely 1H-detected experiments and machine learning methods to assign all the experimental proton and carbon chemical shifts. This framework provides a new tool for elucidating chemical information from crystalline samples with limited sample volume and yields remarkably faster acquisition times compared to 13C-detected experiments, without the need to employ dynamic nuclear polarization.

The interplay of density functional selection and crystal structure for accurate NMR chemical shift predictions

Ab initio chemical shift prediction plays a central role in nuclear magnetic resonance (NMR) crystallography, and the accuracy with which chemical shifts can be predicted relative to experiment impacts the confidence with which structures can be assigned. For organic crystals, periodic density functional theory calculations with the gauge-including projector augmented wave (GIPAW) approximation and the PBE functional are widely used at present. Many previous studies have examined how using more advanced density functionals can increase the accuracy of predicted chemical shifts relative to experiment, but nearly all of those studies employed crystal structures that were optimized with generalized-gradient approximation (GGA) functionals. Here, we investigate how the accuracy of the predicted chemical shifts in organic crystals is affected by replacing GGA-level PBE-D3(BJ) crystal geometries with more accurate hybrid functional PBE0-D3(BJ) ones. Based on benchmark data sets containing 132 13C and 35 15N chemical shifts, plus case studies on testosterone, acetaminophen, and phenobarbital, we find that switching from GGA-level geometries and chemical shifts to hybrid-functional ones reduces 13C and 15N chemical shift errors by ∼40-60% versus experiment. However, most of the improvement stems from the use of the hybrid functional for the chemical shift calculations, rather than from the refined geometries. In addition, even with the improved geometries, we find that double-hybrid functionals still do not systematically increase chemical shift agreement with experiment beyond what hybrid functionals provide. In the end, these results suggest that the combination of GGA-level crystal structures and hybrid-functional chemical shifts represents a particularly cost-effective combination for NMR crystallography in organic systems.

Probing the Molecular and Macroscopic Structure of Solid Solutions by Dynamic Nuclear Polarization (DNP) Enhanced 13C and 15N Solid-State NMR Spectroscopy

Crystallization is a widely used purification technique in the manufacture of active pharmaceutical ingredients (APIs) and precursor molecules. However, when impurities and desired compounds have similar molecular structures, separation by crystallization may become challenging. In such cases, some impurities may form crystalline solid solutions with the desired product during recrystallization. Understanding the molecular structure of these recrystallized solid solutions is crucial to devise methods for effective purification. Unfortunately, there are limited analytical techniques that provide insights into the molecular structure or spatial distribution of impurities that are incorporated within recrystallized products. In this study, we investigated model solid solutions formed by recrystallizing salicylic acid (SA) in the presence of anthranilic acid (AA). These two molecules are known to form crystalline solid solutions due to their similar molecular structures. To overcome challenges associated with the long 1H longitudinal relaxation times (T1(1H)) of SA and AA, we employed dynamic nuclear polarization (DNP) and 15N isotope enrichment to enable solid-state NMR experiments. Results of solid-state NMR experiments and DFT calculations revealed that SA and AA are homogeneously alloyed as a solid solution. Heteronuclear correlation (HETCOR) experiments and plane-wave DFT structural models provide further evidence of the molecular-level interactions between SA and AA. This research provides valuable insights into the molecular structure of recrystallized solid solutions, contributing to the development of effective purification strategies and an understanding of the physicochemical properties of solid solutions.

Predicting 51V nuclear magnetic resonance observables in molecular crystals

Solid-state nuclear magnetic resonance (NMR) spectroscopy and quantum chemical density functional theory (DFT) calculations are widely used to characterize vanadium centers in biological and pharmaceutically relevant compounds. Several techniques have been recently developed to improve the accuracy of predicted NMR parameters obtained from DFT. Fragment-based and planewave-corrected methods employing hybrid density functionals are particularly effective tools for solid-state applications. A recent benchmark study involving molecular crystal compounds found that fragment-based NMR calculations using hybrid density functionals improve the accuracy of predicted 51V chemical shieldings by 20% relative to traditional planewave methods. This work extends the previous study, including a careful analysis of 51V chemical shift anisotropy, electric field gradient calculations, and a more extensive test set. The accuracy of planewave-corrected techniques and recently developed fragment-based methods using electrostatic embedding based on the polarized continuum model (PCM) are found to be highly competitive with previous methods. Planewave-corrected methods achieve a 34% improvement in the errors of predicted 51V chemical shieldings relative to planewave. Additionally, planewave-corrected and fragment-based calculations were performed using PCM embedding, improving the accuracy of predicted 51V chemical shielding (CS) tensor principal values by 30% andC q values by 15% relative to traditional planewave methods. The performance of these methods is further examined using a redox-active oxovandium complex and a common 51V NMR reference compound.

Polymorph Identification for Flexible Molecules: Linear Regression Analysis of Experimental and Calculated Solution- and Solid-State NMR Data

The Δδ regression approach of Blade et al. [ J. Phys. Chem. A 2020, 124(43), 8959-8977] for accurately discriminating between solid forms using a combination of experimental solution- and solid-state NMR data with density functional theory (DFT) calculation is here extended to molecules with multiple conformational degrees of freedom, using furosemide polymorphs as an exemplar. As before, the differences in measured 1H and 13C chemical shifts between solution-state NMR and solid-state magic-angle spinning (MAS) NMR (Δδexperimental) are compared to those determined by gauge-including projector augmented wave (GIPAW) calculations (Δδcalculated) by regression analysis and a t-test, allowing the correct furosemide polymorph to be precisely identified. Monte Carlo random sampling is used to calculate solution-state NMR chemical shifts, reducing computation times by avoiding the need to systematically sample the multidimensional conformational landscape that furosemide occupies in solution. The solvent conditions should be chosen to match the molecule's charge state between the solution and solid states. The Δδ regression approach indicates whether or not correlations between Δδexperimental and Δδcalculated are statistically significant; the approach is differently sensitive to the popular root mean squared error (RMSE) method, being shown to exhibit a much greater dynamic range. An alternative method for estimating solution-state NMR chemical shifts by approximating the measured solution-state dynamic 3D behavior with an ensemble of 54 furosemide crystal structures (polymorphs and cocrystals) from the Cambridge Structural Database (CSD) was also successful in this case, suggesting new avenues for this method that may overcome its current dependency on the prior determination of solution dynamic 3D structures.

Carbon-13 chemical shift tensor measurements for nitrogen-dense compounds

This paper reports the principal values of the 13 C chemical shift tensors for five nitrogen-dense compounds (i.e., cytosine, uracil, imidazole, guanidine hydrochloride, and aminoguanidine hydrochloride). Although these are all fundamentally important compounds, the majority do not have 13 C chemical shift tensors reported in the literature. The chemical shift tensors are obtained from 1 H→13 C cross-polarization magic-angle spinning (CP/MAS) experiments that were conducted at a high field of 18.8 T to suppress the effects of 14 N-13 C residual dipolar coupling. Quantum chemical calculations using density functional theory are used to obtain the 13 C magnetic shielding tensors for these compounds. The best agreement with experiment arises from calculations using the hybrid functional PBE0 or the double-hybrid functional PBE0-DH, along with the triple-zeta basis sets TZ2P or pc-3, respectively, and intermolecular effects modeled using large clusters of molecules with electrostatic embedding through the COSMO approach. These measurements are part of an ongoing effort to expand the catalog of accurate 13 C chemical shift tensor measurements, with the aim of creating a database that may be useful for benchmarking the accuracy of quantum chemical calculations, developing nuclear magnetic resonance (NMR) crystallography protocols, or aiding in applications involving machine learning or data mining. This work was conducted at the National High Magnetic Field Laboratory as part of a 2-week school for introducing undergraduate students to practical laboratory experience that will prepare them for scientific careers or postgraduate studies.

Can simple 'molecular' corrections outperform projector augmented-wave density functional theory in the prediction of 35 Cl electric field gradient tensor parameters for chlorine-containing crystalline systems?

Many-body expansion (MBE) fragment approaches have been applied to accurately compute nuclear magnetic resonance (NMR) parameters in crystalline systems. Recent examples demonstrate that electric field gradient (EFG) tensor parameters can be accurately calculated for 14 N and 17 O. A key additional development is the simple molecular correction (SMC) approach, which uses two one-body fragment (i.e., isolated molecule) calculations to adjust NMR parameter values established using 'benchmark' projector augmented-wave (PAW) density functional theory (DFT) values. Here, we apply a SMC using the hybrid PBE0 exchange-correlation (XC) functional to see if this can improve the accuracy of calculated 35 Cl EFG tensor parameters. We selected eight organic and two inorganic crystal structures and considered 15 chlorine sites. We find that this SMC improves the accuracy of computed values for both the 35 Cl quadrupolar coupling constant (CQ ) and the asymmetry parameter ( η Q ) by approximately 30% compared with benchmark PAW DFT values. We also assessed a SMC that offers local improvements not only in terms of the quality of the XC functional but simultaneously in the quality of the description of relativistic effects via the inclusion of spin-orbit effects. As the inorganic systems considered contain heavy atoms bonded to the chlorine atoms, we find further improvements in the accuracy of calculated 35 Cl EFG tensor parameters when both a hybrid functional and spin-orbit effects are included in the SMC. On the contrary, for chlorine-containing organics, the inclusion of spin-orbit relativistic effects using a SMC does not improve the accuracy of computed 35 Cl EFG tensor parameters.

Frontiers of molecular crystal structure prediction for pharmaceuticals and functional organic materials

The reliability of organic molecular crystal structure prediction has improved tremendously in recent years. Crystal structure predictions for small, mostly rigid molecules are quickly becoming routine. Structure predictions for larger, highly flexible molecules are more challenging, but their crystal structures can also now be predicted with increasing rates of success. These advances are ushering in a new era where crystal structure prediction drives the experimental discovery of new solid forms. After briefly discussing the computational methods that enable successful crystal structure prediction, this perspective presents case studies from the literature that demonstrate how state-of-the-art crystal structure prediction can transform how scientists approach problems involving the organic solid state. Applications to pharmaceuticals, porous organic materials, photomechanical crystals, organic semi-conductors, and nuclear magnetic resonance crystallography are included. Finally, efforts to improve our understanding of which predicted crystal structures can actually be produced experimentally and other outstanding challenges are discussed.

Calculating 13 C NMR chemical shifts of large molecules using the eXtended ONIOM method at high accuracy with a low cost

Fragmentation-based methods for nuclear magnetic resonance (NMR) chemical shift calculations have become more and more popular in first-principles calculations of large molecules. However, there are many options for a fragmentation-based method to select, such as theoretical methods, fragmentation schemes, the number of levels of theory, etc. It is important to study the optimal combination of the options to achieve a good balance between accuracy and efficiency. Here we investigate different combinations of options used by a fragmentation-based method, the eXtended ONIOM (XO) method, for 13 C chemical shift calculations on a set of organic and biological molecules. We found that: (1) introducing Hartree-Fock exchange into density functional theory (DFT) could reduce the calculation error due to fragmentation in contrast to pure DFT functionals, while a hybrid functional, xOPBE, is generally recommended; (2) fragmentation schemes generated from the molecular tailoring approach (MTA) with small level parameter n, for example, n = 2 and the degree-based fragmentation method (DBFM) with n = 1, are sufficient to achieve satisfactory accuracy; (3) the two-level XO (XO2) NMR calculation is superior to the calculation with only one level of theory, as the second level (i.e., low level) of theory provides a way to well describe the long-range effect. These findings are beneficial to practical applications of fragmentation-based methods for NMR chemical shift calculations of large molecules.

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.

Atomic-level structure determination of amorphous molecular solids by NMR

Structure determination of amorphous materials remains challenging, owing to the disorder inherent to these materials. Nuclear magnetic resonance (NMR) powder crystallography is a powerful method to determine the structure of molecular solids, but disorder leads to a high degree of overlap between measured signals, and prevents the unambiguous identification of a single modeled periodic structure as representative of the whole material. Here, we determine the atomic-level ensemble structure of the amorphous form of the drug AZD4625 by combining solid-state NMR experiments with molecular dynamics (MD) simulations and machine-learned chemical shifts. By considering the combined shifts of all 1H and 13C atomic sites in the molecule, we determine the structure of the amorphous form by identifying an ensemble of local molecular environments that are in agreement with experiment. We then extract and analyze preferred conformations and intermolecular interactions in the amorphous sample in terms of the stabilization of the amorphous form of the drug.

Discovering the Solid-State Secrets of Lorlatinib by NMR Crystallography: To Hydrogen Bond or not to Hydrogen Bond

Lorlatinib is an active pharmaceutical ingredient (API) used in the treatment of lung cancer. Here, an NMR crystallography analysis is presented whereby the single-crystal X-ray diffraction structure (CSD: 2205098) determination is complemented by multinuclear (1H, 13C, 14/15N, 19F) magic-angle spinning (MAS) solid-state NMR and gauge-including projector augmented wave (GIPAW) calculation of NMR chemical shifts. Lorlatinib crystallises in the P21 space group, with two distinct molecules in the asymmetric unit cell, Z' = 2. Three of the four NH2 hydrogen atoms form intermolecular hydrogen bonds, N30-H…N15 between the two distinct molecules and N30-H…O2 between two equivalent molecules. This is reflected in one of the NH21H chemical shifts being significantly lower, 4.0 ppm compared to 7.0 ppm. Two-dimensional 1H-13C, 14N-1H and 1H (double-quantum, DQ)-1H (single-quantum, SQ) MAS NMR spectra are presented. The 1H resonances are assigned and specific HH proximities corresponding to the observed DQ peaks are identified. The resolution enhancement at a 1H Larmor frequency of 1 GHz as compared to 500 or 600 MHz is demonstrated.

Weak, Broken, but Working-Intramolecular Hydrogen Bond in 2,2'-bipyridine

From an academic and practical point of view, it is desirable to be able to assess the possibility of the proton exchange of a given molecular system just by knowing the positions of the proton acceptor and the proton donor. This study addresses the difference between intramolecular hydrogen bonds in 2,2'-bipyridinium and 1,10-phenanthrolinium. Solid-state ¹⁵N NMR and model calculations show that these hydrogen bonds are weak; their energies are 25 kJ/mol and 15 kJ/mol, respectively. Neither these hydrogen bonds nor N-H stretches can be responsible for the fast reversible proton transfer observed for 2,2'-bipyridinium in a polar solvent down to 115 K. This process must have been caused by an external force, which was a fluctuating electric field present in the solution. However, these hydrogen bonds are the grain that tips the scales precisely because they are an integral part of a large system of interactions, including both intramolecular interactions and environmental influence.

Anomalous 1 H NMR chemical shift behavior of substituted benzoic acid esters

Benzoic acid esters represent key building blocks for many drug discovery and development programs and have been advanced as potent PDE4 inhibitors for inhaled administration for treatment of respiratory diseases. This class of compounds has also been employed in myriad industrial processes and as common food preservatives. Recent work directed toward the synthesis of intermediates for a proprietary medicinal chemistry program led us to observe that the ¹ H NMR chemical shifts of substituents ortho to the benzoic acid ester moiety defied conventional iterative chemical shift prediction protocols. To explore these unexpected results, we initiated a detailed computational study employing density functional theory (DFT) calculations to better understand the unexpectedly large variance in expected versus experimental NMR chemical shifts.

Benchmark accuracy of predicted NMR observables for quadrupolar 14 N and 17 O nuclei in molecular crystals

Nuclear quadrupole resonances for 14 N and ¹⁷ O nuclei are exquisitely sensitive to interactions with surrounding atoms. As a result, nitrogen and oxygen solid-state nuclear magnetic resonance (ssNMR) provides a powerful tool for investigating structure and dynamics in complex systems. First-principles calculations are increasingly used to facilitate spectral assignment and to evaluate and adjust crystal structures. Recent work combining the strengths of planewave density functional theory (DFT) calculations with a single molecule correction obtained using a higher level of theory has proven successful in improving the accuracy of predicted chemical shielding (CS) tensors and ¹⁷ O quadrupolar coupling constants ( C q ). Here we extend this work by examining the accuracy of predicted ¹⁴ N and ¹⁷ O electric field gradient (EFG) tensor components obtained using alternative planewave-corrections involving cluster and two-body fragment-based calculations. We benchmark the accuracy of CS and EFG tensor predictions for both nitrogen and oxygen using planewave, two-body fragment, and enhanced planewave-corrected techniques. Combining planewave and two-body fragment calculations reduces the error in predicted ¹⁷ O C q values by 35% relative to traditional planewave calculations. These enhanced planewave-correction methods improve the accuracy of ¹⁷ O and ¹⁴ N EFG tensor components by 15% relative to planewave DFT but yield minimal improvement relative to a simple molecular correction. However, in structural environments involving either high symmetry or strong intermolecular interactions, enhanced planewave-corrected methods provide a distinct advantage.

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.

Improving the accuracy of GIPAW chemical shielding calculations with cluster and fragment corrections

Ab initio methods for predicting NMR parameters in the solid state are an essential tool for assigning experimental spectra and play an increasingly important role in structural characterizations. Recently, a molecular correction (MC) technique has been developed which combines the strengths of plane-wave methods (GIPAW) with single molecule calculations employing Gaussian basis sets. The GIPAW + MC method relies on a periodic calculation performed at a lower level of theory to model the crystalline environment. The GIPAW result is then corrected using a single molecule calculation performed at a higher level of theory. The success of the GIPAW + MC method in predicting a range of NMR parameters is a result of the highly local character of the tensors underlying the NMR observable. However, in applications involving strong intermolecular interactions we find that expanding the region treated at the higher level of theory more accurately captures local many-body contributions to the N15 NMR chemical shielding (CS) tensor. We propose alternative corrections to GIPAW which capture interactions between adjacent molecules at a higher level of theory using either fragment or cluster-based calculations. Benchmark calculations performed on N15 and C13 data sets show that these advanced GIPAW-corrected calculations improve the accuracy of chemical shielding tensor predictions relative to existing methods. Specifically, cluster-based N15 corrections show a 24% and 17% reduction in RMS error relative to GIPAW and GIPAW + MC calculations, respectively. Comparing the benchmark data sets using multiple computational models demonstrates that N15 CS tensor calculations are significantly more sensitive to intermolecular interactions relative to C13. However, fragment and cluster-based corrections that include direct hydrogen bond partners are sufficient for optimizing the accuracy of GIPAW-corrected methods. Finally, GIPAW-corrected methods are applied to the particularly challenging NMR spectral assignment of guanosine dihydrate which contains two guanosine molecules in the asymmetric unit.

A Machine Learning Model of Chemical Shifts for Chemically and Structurally Diverse Molecular Solids

Nuclear magnetic resonance (NMR) chemical shifts are a direct probe of local atomic environments and can be used to determine the structure of solid materials. However, the substantial computational cost required to predict accurate chemical shifts is a key bottleneck for NMR crystallography. We recently introduced ShiftML, a machine-learning model of chemical shifts in molecular solids, trained on minimum-energy geometries of materials composed of C, H, N, O, and S that provides rapid chemical shift predictions with density functional theory (DFT) accuracy. Here, we extend the capabilities of ShiftML to predict chemical shifts for both finite temperature structures and more chemically diverse compounds, while retaining the same speed and accuracy. For a benchmark set of 13 molecular solids, we find a root-mean-squared error of 0.47 ppm with respect to experiment for ¹H shift predictions (compared to 0.35 ppm for explicit DFT calculations), while reducing the computational cost by over four orders of magnitude.

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.

Computational 1 H and 13 C NMR in structural and stereochemical studies

Present review outlines the advances and perspectives of computational ¹ H and ¹³ C NMR applied to the stereochemical studies of inorganic, organic, and bioorganic compounds, involving in particular natural products, carbohydrates, and carbonium ions. The first part of the review briefly outlines theoretical background of the modern computational methods applied to the calculation of chemical shifts and spin-spin coupling constants at the DFT and the non-empirical levels. The second part of the review deals with the achievements of the computational ¹ H and ¹³ C NMR in the stereochemical investigation of a variety of inorganic, organic, and bioorganic compounds, providing in an abridged form the material partly discussed by the author in a series of parent reviews. Major attention is focused herewith on the publications of the recent years, which were not reviewed elsewhere.

Complete resonance assignment of a pharmaceutical drug at natural isotopic abundance from DNP-Enhanced solid-state NMR

Solid-state dynamic nuclear polarization enhanced magic angle spinning (DNP-MAS) NMR measurements coupled with density functional theory (DFT) calculations enable the full resonance assignment of a complex pharmaceutical drug molecule without the need for isotopic enrichment. DNP dramatically enhances the NMR signals, thereby making possible previously intractable two-dimensional correlation NMR spectra at natural abundance. Using inputs from DFT calculations, herein we describe a significant improvement to the structure elucidation process for complex organic molecules. Further, we demonstrate that a series of two-dimensional correlation experiments, including ¹⁵N-¹³C TEDOR, ¹³C-¹³C INADEQUATE/SARCOSY, ¹⁹F-¹³C HETCOR, and ¹H-¹³C HETCOR, can be obtained at natural isotopic abundance within reasonable experiment times, thus enabling a complete resonance assignment of sitagliptin, a pharmaceutical used for the treatment of type 2 diabetes.

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.

Resolving alternative structure determinations of indapamide using 13C solid-state NMR

The conflict between alternative crystal structures in the Cambridge Structural Database for the diuretic drug indapamide hemihydrate (IND) has been resolved with the aid of ¹³C solid-state NMR. IND is seen to contain multiple distinct molecules in the asymmetric unit (Z' = 4) rather than exhibiting disorder in the orientation of sulfonamide groups. The NMR crystallographic approach is a more effective tool for distinguishing between alternative structures than naïve judgements of quality based on crystallographic refinement agreement factors.

Atomic-resolution chemical characterization of (2x)72-kDa tryptophan synthase via four- and five-dimensional 1H-detected solid-state NMR

NMR chemical shifts provide detailed information on the chemical properties of molecules, thereby complementing structural data from techniques like X-ray crystallography and electron microscopy. Detailed analysis of protein NMR data, however, often hinges on comprehensive, site-specific assignment of backbone resonances, which becomes a bottleneck for molecular weights beyond 40 to 45 kDa. Here, we show that assignments for the (2x)72-kDa protein tryptophan synthase (665 amino acids per asymmetric unit) can be achieved via higher-dimensional, proton-detected, solid-state NMR using a single, 1-mg, uniformly labeled, microcrystalline sample. This framework grants access to atom-specific characterization of chemical properties and relaxation for the backbone and side chains, including those residues important for the catalytic turnover. Combined with first-principles calculations, the chemical shifts in the β-subunit active site suggest a connection between active-site chemistry, the electrostatic environment, and catalytically important dynamics of the portal to the β-subunit from solution.

Imaging active site chemistry and protonation states: NMR crystallography of the tryptophan synthase α-aminoacrylate intermediate

NMR-assisted crystallography-the integrated application of solid-state NMR, X-ray crystallography, and first-principles computational chemistry-holds significant promise for mechanistic enzymology: by providing atomic-resolution characterization of stable intermediates in enzyme active sites, including hydrogen atom locations and tautomeric equilibria, NMR crystallography offers insight into both structure and chemical dynamics. Here, this integrated approach is used to characterize the tryptophan synthase α-aminoacrylate intermediate, a defining species for pyridoxal-5'-phosphate-dependent enzymes that catalyze β-elimination and replacement reactions. For this intermediate, NMR-assisted crystallography is able to identify the protonation states of the ionizable sites on the cofactor, substrate, and catalytic side chains as well as the location and orientation of crystallographic waters within the active site. Most notable is the water molecule immediately adjacent to the substrate β-carbon, which serves as a hydrogen bond donor to the ε-amino group of the acid-base catalytic residue βLys87. From this analysis, a detailed three-dimensional picture of structure and reactivity emerges, highlighting the fate of the L-serine hydroxyl leaving group and the reaction pathway back to the preceding transition state. Reaction of the α-aminoacrylate intermediate with benzimidazole, an isostere of the natural substrate indole, shows benzimidazole bound in the active site and poised for, but unable to initiate, the subsequent bond formation step. When modeled into the benzimidazole position, indole is positioned with C3 in contact with the α-aminoacrylate Cβ and aligned for nucleophilic attack. Here, the chemically detailed, three-dimensional structure from NMR-assisted crystallography is key to understanding why benzimidazole does not react, while indole does.

A toolbox for improving the workflow of NMR crystallography

NMR crystallography is a powerful tool with applications in structural characterization and crystal structure verification, to name two. However, applying this tool presents several challenges, especially for industrial users, in terms of consistency, workflow, time consumption, and the requirement for a high level of understanding of experimental solid-state NMR and GIPAW-DFT calculations. Here, we have developed a series of fully parameterized scripts for use in Materials Studio and TopSpin, based on the .magres file format, with a focus on organic molecules (e.g. pharmaceuticals), improving efficiency, robustness, and workflow. We separate these tools into three major categories: performing the DFT calculations, extracting & visualizing the results, and crystallographic modelling. These scripts will rapidly submit fully parameterized CASTEP jobs, extract data from the calculations, assist in visualizing the results, and expedite the process of structural modelling. Accompanied with these tools is a description on their functionality, documentation on how to get started and use the scripts, and links to video tutorials for guiding new users. Through the use of these tools, we hope to facilitate NMR crystallography and to harmonize the process across users.

Bayesian probabilistic assignment of chemical shifts in organic solids

A prerequisite for NMR studies of organic materials is assigning each experimental chemical shift to a set of geometrically equivalent nuclei. Obtaining the assignment experimentally can be challenging and typically requires time-consuming multidimensional correlation experiments. An alternative solution for determining the assignment involves statistical analysis of experimental chemical shift databases, but no such database exists for molecular solids. Here, by combining the Cambridge Structural Database with a machine learning model of chemical shifts, we construct a statistical basis for probabilistic chemical shift assignment of organic crystals by calculating shifts for more than 200,000 compounds, enabling the probabilistic assignment of organic crystals directly from their two-dimensional chemical structure. The approach is demonstrated with the ¹³C and ¹H assignment of 11 molecular solids with experimental shifts and benchmarked on 100 crystals using predicted shifts. The correct assignment was found among the two most probable assignments in more than 80% of cases.

Fast and Accurate Electric Field Gradient Calculations in Molecular Solids With Density Functional Theory

Modern approaches for calculating electric field gradient (EFF) tensors in molecular solids rely upon plane-wave calculations employing periodic boundary conditions (PBC). In practice, models employing PBCs are limited to generalized gradient approximation (GGA) density functionals. Hybrid density functionals applied in the context of gauge-including atomic orbital (GIAO) calculations have been shown to substantially improve the accuracy of predicted NMR parameters. Here we propose an efficient method that effectively combines the benefits of both periodic calculations and single-molecule techniques for predicting electric field gradient tensors in molecular solids. Periodic calculations using plane-wave basis sets were used to model the crystalline environment. We then introduce a molecular correction to the periodic result obtained from a single-molecule calculation performed with a hybrid density functional. Single-molecule calculations performed using hybrid density functionals were found to significantly improve the agreement of predicted 17O quadrupolar coupling constants (C q ) with experiment. We demonstrate a 31% reduction in the RMS error for the predicted 17O C q values relative to standard plane-wave methods using a carefully constructed test set comprised of 22 oxygen-containing molecular crystals. We show comparable improvements in accuracy using five different hybrid density functionals and find predicted C q values to be relatively insensitive to the choice of basis set used in the single molecule calculation. Finally, the utility of high-accuracy 17O C q predictions is demonstrated by examining the disordered 4-Nitrobenzaldehyde crystal structure.

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.

Accurate fragment-based 51-V chemical shift predictions in molecular crystals

Nuclear magnetic resonance (NMR) spectroscopy plays a crucial role in determining molecular structure for complex biological and pharmaceutical compounds. NMR investigations are increasingly reliant on computation for mapping spectral features to chemical structures. Here we benchmark the accuracy of fragment-based ⁵¹V chemical shielding tensor calculations using a training set comprised of 10 biologically and pharmaceutically relevant oxovanadium complexes. Using our self-consistent reproduction of the Madelung potential (SCRMP) electrostatic embedding model, we demonstrate comparable performance between fragment methods and computationally demanding cluster-based techniques. Specifically, fragment methods employing hybrid density functionals are capable of reproducing the experimental ⁵¹V isotropic chemical shifts with a training set rms error of ~9 ​ppm, representing a 20% improvement over traditional plane wave techniques. We provide training set-derived linear regression models for mapping the absolute shieldings obtained from computation to the experimentally determined chemical shifts using four common density functionals; PBE0, B3LYP, PBE, and BLYP. Finally, we establish the utility of fragment methods and the reported regression parameters examining four oxovanadium structures excluded from the training set including the tetracoordinate oxovanadium silicate [Formula: see text] , VO¹⁵NGlySalbz which contains redox-active ligands, and the solid-state form of the common ⁵¹V NMR reference compound VOCl₃.

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.

Structure determination of an amorphous drug through large-scale NMR predictions

Knowledge of the structure of amorphous solids can direct, for example, the optimization of pharmaceutical formulations, but atomic-level structure determination in amorphous molecular solids has so far not been possible. Solid-state nuclear magnetic resonance (NMR) is among the most popular methods to characterize amorphous materials, and molecular dynamics (MD) simulations can help describe the structure of disordered materials. However, directly relating MD to NMR experiments in molecular solids has been out of reach until now because of the large size of these simulations. Here, using a machine learning model of chemical shifts, we determine the atomic-level structure of the hydrated amorphous drug AZD5718 by combining dynamic nuclear polarization-enhanced solid-state NMR experiments with predicted chemical shifts for MD simulations of large systems. From these amorphous structures we then identify H-bonding motifs and relate them to local intermolecular complex formation energies.

Modeling Small Structural and Environmental Differences in Solids with 15 N NMR Chemical Shift Tensors

The ability to theoretically predict accurate NMR chemical shifts in solids is increasingly important due to the role such shifts play in selecting among proposed model structures. Herein, two theoretical methods are evaluated for their ability to assign ¹⁵ N shifts from guanosine dihydrate to one of the two independent molecules present in the lattice. The NMR data consist of ¹⁵ N shift tensors from 10 resonances. Analysis using periodic boundary or fragment methods consider a benchmark dataset to estimate errors and predict uncertainties of 5.6 and 6.2 ppm, respectively. Despite this high accuracy, only one of the five sites were confidently assigned to a specific molecule of the asymmetric unit. This limitation is not due to negligible differences in experimental data, as most sites exhibit differences of >6.0 ppm between pairs of resonances representing a given position. Instead, the theoretical methods are insufficiently accurate to make assignments at most positions.

Revving up 13C NMR shielding predictions across chemical space: benchmarks for atoms-in-molecules kernel machine learning with new data for 134 kilo molecules

The requirement for accelerated and quantitatively accurate screening of nuclear magnetic resonance spectra across the small molecules chemical compound space is two-fold: (1) a robust ‘local’ machine learning (ML) strategy capturing the effect of the neighborhood on an atom’s ‘near-sighted’ property—chemical shielding; (2) an accurate reference dataset generated with a state-of-the-art first-principles method for training. Herein we report the QM9-NMR dataset comprising isotropic shielding of over 0.8 million C atoms in 134k molecules of the QM9 dataset in gas and five common solvent phases. Using these data for training, we present benchmark results for the prediction transferability of kernel-ridge regression models with popular local descriptors. Our best model, trained on 100k samples, accurately predicts isotropic shielding of 50k ‘hold-out’ atoms with a mean error of less than 1.9 ppm. For the rapid prediction of new query molecules, the models were trained on geometries from an inexpensive theory. Furthermore, by using a Δ-ML strategy, we quench the error below 1.4 ppm. Finally, we test the transferability on non-trivial benchmark sets that include benchmark molecules comprising 10–17 heavy atoms and drugs.

Automated fragmentation quantum mechanical calculation of 13C and 1H chemical shifts in molecular crystals

In this work, the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach was applied to calculate the ¹³C and ¹H nuclear magnetic resonance (NMR) chemical shifts in molecular crystals. Two benchmark sets of molecular crystals were selected to calculate the NMR chemical shifts. Systematic investigation was conducted to examine the convergence of AF-QM/MM calculations and the impact of various density functionals with different basis sets on the NMR chemical shift prediction. The result demonstrates that the calculated NMR chemical shifts are close to convergence when the distance threshold for the QM region is larger than 3.5 Å. For ¹³C chemical shift calculations, the mPW1PW91 functional is the best density functional among the functionals chosen in this study (namely, B3LYP, B3PW91, M06-2X, M06-L, mPW1PW91, OB98, and OPBE), while the OB98 functional is more suitable for the ¹H NMR chemical shift prediction of molecular crystals. Moreover, with the B3LYP functional, at least a triple-ζ basis set should be utilized to accurately reproduce the experimental ¹³C and ¹H chemical shifts. The employment of diffuse basis functions will further improve the accuracy for ¹³C chemical shift calculations, but not for the ¹H chemical shift prediction. We further proposed a fragmentation scheme of dividing the central molecule into smaller fragments. By comparing with the results of the fragmentation scheme using the entire central molecule as the core region, the AF-QM/MM calculations with the fragmented central molecule can not only achieve accurate results but also reduce the computational cost. Therefore, the AF-QM/MM approach is capable of predicting the ¹³C and ¹H NMR chemical shifts for molecular crystals accurately and effectively, and could be utilized for dealing with more complex periodic systems such as macromolecular polymers and biomacromolecules. The AF-QM/MM program for molecular crystals is available at https://github.com/shiman1995/NMR.

Solid-state NMR spectroscopy

Solid-state nuclear magnetic resonance (NMR) spectroscopy is an atomic-level method used to determine the chemical structure, three-dimensional structure, and dynamics of solids and semi-solids. This Primer summarizes the basic principles of NMR as applied to the wide range of solid systems. The fundamental nuclear spin interactions and the effects of magnetic fields and radiofrequency pulses on nuclear spins are the same as in liquid-state NMR. However, because of the anisotropy of the interactions in the solid state, the majority of high-resolution solid-state NMR spectra is measured under magic-angle spinning (MAS), which has profound effects on the types of radiofrequency pulse sequences required to extract structural and dynamical information. We describe the most common MAS NMR experiments and data analysis approaches for investigating biological macromolecules, organic materials, and inorganic solids. Continuing development of sensitivity-enhancement approaches, including 1H-detected fast MAS experiments, dynamic nuclear polarization, and experiments tailored to ultrahigh magnetic fields, is described. We highlight recent applications of solid-state NMR to biological and materials chemistry. The Primer ends with a discussion of current limitations of NMR to study solids, and points to future avenues of development to further enhance the capabilities of this sophisticated spectroscopy for new applications.

5-amino-2-methylpyridinium hydrogen fumarate: An XRD and NMR crystallography analysis

Single-crystal X-ray diffraction structures of the 5-amino-2-methylpyridinium hydrogen fumarate salt have been solved at 150 and 300 K (CCDC 1952142 and 1952143). A base-acid-base-acid ring is formed through pyridinium-carboxylate and amine-carboxylate hydrogen bonds that hold together chains formed from hydrogen-bonded hydrogen fumarate ions. ¹ H and ¹³ C chemical shifts as well as ¹⁴ N shifts that additionally depend on the quadrupolar interaction are determined by experimental magic angle spinning (MAS) solid-state nuclear magnetic resonance (NMR) and gauge-including projector-augmented wave (GIPAW) calculation. Two-dimensional homonuclear ¹ H-¹ H double-quantum (DQ) MAS and heteronuclear ¹ H-¹³ C and ¹⁴ N-¹ H spectra are presented. Only small differences of up to 0.1 and 0.6 ppm for ¹ H and ¹³ C are observed between GIPAW calculations starting with the two structures solved at 150 and 300 K (after geometry optimisation of atomic positions, but not unit cell parameters). A comparison of GIPAW-calculated ¹ H chemical shifts for isolated molecules and the full crystal structures is indicative of hydrogen bonding strength.

Bridging photochemistry and photomechanics with NMR crystallography: the molecular basis for the macroscopic expansion of an anthracene ester nanorod

Crystals composed of photoreactive molecules represent a new class of photomechanical materials with the potential to generate large forces on fast timescales. An example is the photodimerization of 9-tert-butyl-anthracene ester (9TBAE) in molecular crystal nanorods that leads to an average elongation of 8%. Previous work showed that this expansion results from the formation of a metastable crystalline product. In this article, it is shown how a novel combination of ensemble oriented-crystal solid-state NMR, X-ray diffraction, and first principles computational modeling can be used to establish the absolute unit cell orientations relative to the shape change, revealing the atomic-resolution mechanism for the photomechanical response and enabling the construction of a model that predicts an elongation of 7.4%, in good agreement with the experimental value. According to this model, the nanorod expansion does not result from an overall change in the volume of the unit cell, but rather from an anisotropic rearrangement of the molecular contents. The ability to understand quantitatively how molecular-level photochemistry generates mechanical displacements allows us to predict that the expansion could be tuned from +9% to -9.5% by controlling the initial orientation of the unit cell with respect to the nanorod axis. This application of NMR-assisted crystallography provides a new tool capable of tying the atomic-level structural rearrangement of the reacting molecular species to the mechanical response of a nanostructured sample.

Computation of NMR Shielding Constants for Solids Using an Embedded Cluster Approach with DFT, Double-Hybrid DFT, and MP2

In this work, we explore the accuracy of post-Hartree–Fock (HF) methods and double-hybrid density functional theory (DFT) for the computation of solid-state NMR chemical shifts. We apply an embedded cluster approach and investigate the convergence with cluster size and embedding for a series of inorganic solids with long-range electrostatic interactions. In a systematic study, we discuss the cluster design, the embedding procedure, and basis set convergence using gauge-including atomic orbital (GIAO) NMR calculations at the DFT and MP2 levels of theory. We demonstrate that the accuracy obtained for the prediction of NMR chemical shifts, which can be achieved for molecular systems, can be carried over to solid systems. An appropriate embedded cluster approach allows one to apply methods beyond standard DFT even for systems for which long-range electrostatic effects are important. We find that an embedded cluster should include at least one sphere of explicit neighbors around the nuclei of interest, given that a sufficiently large point charge and boundary effective potential embedding is applied. Using the pcSseg-3 basis set and GIAOs for the computation of nuclear shielding constants, accuracies of 1.6 ppm for ⁷Li, 1.5 ppm for ²³Na, and 5.1 ppm for ³⁹K as well as 9.3 ppm for ¹⁹F, 6.5 ppm for ³⁵Cl, 7.4 ppm for ⁷⁹Br, and 7.5 ppm for ²⁵Mg as well as 3.8 ppm for ⁶⁷Zn can be achieved with MP2. Comparing various DFT functionals with HF and MP2, we report the superior quality of results for methods that include post-HF correlation like MP2 and double-hybrid DFT.

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.

Polarizable continuum models provide an effective electrostatic embedding model for fragment-based chemical shift prediction in challenging systems

Ab initio nuclear magnetic resonance chemical shift prediction provides an important tool for interpreting and assigning experimental spectra, but it becomes computationally prohibitive in large systems. The computational costs can be reduced considerably by fragmentation of the large system into a series of contributions from many smaller subsystems. However, the presence of charged functional groups and the need to partition the system across covalent bonds create complications in biomolecules that typically require the use of large fragments and careful descriptions of the electrostatic environment. The present work shows how a model that combines chemical shielding contributions from non-overlapping monomer and dimer fragments embedded in a polarizable continuum model provides a simple, easy-to-implement, and computationally inexpensive approach for predicting chemical shifts in complex systems. The model's performance proves rather insensitive to the continuum dielectric constant, making the selection of the optimal embedding dielectric less critical. The PCM-embedded fragment model is demonstrated to perform well across systems ranging from molecular crystals to proteins.

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.

Accurate Backbone 13 C and 15 N Chemical Shift Tensors in Galectin-3 Determined by MAS NMR and QM/MM: Details of Structure and Environment Matter

Chemical shift tensors obtained from solid-state NMR spectroscopy are very sensitive reporters of structure and dynamics in proteins. While accurate 13 C and 15 N chemical shift tensors are accessible by magic angle spinning (MAS) NMR, their quantum mechanical calculations remain challenging, particularly for 15 N atoms. Here we compare experimentally determined backbone 13 Cα and 15 NH chemical shift tensors by MAS NMR with hybrid quantum mechanics/molecular mechanics/molecular dynamics (MD-QM/MM) calculations for the carbohydrate-binding domain of galectin-3. Excellent agreement between experimental and computed 15 NH chemical shift anisotropy values was obtained using the Amber ff15ipq force field when solvent dynamics was taken into account in the calculation. Our results establish important benchmark conditions for improving the accuracy of chemical shift calculations in proteins and may aid in the validation of protein structure models derived by MAS NMR.