An unusual ionic cocrystal of ponatinib hydrochloride: characterization by single-crystal X-ray diffraction and ultra-high field NMR spectroscopy.

This study describes the discovery of a unique ionic cocrystal of the active pharmaceutical ingredient (API) ponatinib hydrochloride (pon·HCl), and characterization using single-crystal X-ray diffraction (SCXRD) and solid-state NMR (SSNMR) spectroscopy. Pon·HCl is a multicomponent crystal that features an unusual stoichiometry, with an asymmetric unit containing both monocations and dications of the ponatinib molecule, three water molecules, and three chloride ions. Structural features include (i) a charged imidazopyridazine moiety that forms a hydrogen bond between the ponatinib monocations and dications and (ii) a chloride ion that does not feature hydrogen bonds involving any organic moiety, instead being situated in a "square" arrangement with three water molecules. Multinuclear SSNMR, featuring high and ultra-high fields up to 35.2 T, provides the groundwork for structural interpretation of complex multicomponent crystals in the absence of diffraction data. A 13C CP/MAS spectrum confirms the presence of two crystallographically distinct ponatinib molecules, whereas 1D 1H and 2D 1H-1H DQ-SQ spectra identify and assign the unusually deshielded imidazopyridazine proton. 1D 35Cl spectra obtained at multiple fields confirm the presence of three distinct chloride ions, with density functional theory calculations providing key relationships between the SSNMR spectra and H⋯Cl- hydrogen bonding arrangements. A 2D 35Cl → 1H D-RINEPT spectrum confirms the spatial proximities between the chloride ions, water molecules, and amine moieties. This all suggests future application of multinuclear SSNMR at high and ultra-high fields to the study of complex API solid forms for which SCXRD data are unavailable, with potential application to heterogeneous mixtures or amorphous solid dispersions.

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

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

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.

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

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

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

This study uses 35Cl and 14N solid-state NMR (SSNMR) spectroscopy and dispersion-corrected plane-wave density functional theory (DFT) calculations for the structural characterization of chloride salts of nutraceuticals in their bulk and dosage forms. For eight nutraceuticals, we measure the 35Cl EFG tensor parameters of the chloride ions and use plane-wave DFT calculations to elucidate relationships between NMR parameters and molecular-level structure, which provide rapid NMR crystallographic assessments of structural features. We employ both 35Cl direct excitation and 1H→35Cl cross-polarization methods to characterize a dosage form containing α-d-glucosamine HCl, observe possible impurity and/or adulterant phases, and quantify the weight percent of the active ingredient. To complement this, we also investigate 14N SSNMR spectroscopy and DFT calculations to characterize nitrogen atoms in the nutraceuticals. This includes a discussion of targeted acquisition experimental protocols (i.e., acquiring a select region of the overall pattern that features key discontinuities) that allow ultrawideline spectra to be acquired rapidly, even for unreceptive samples (i.e., those with long values of T1(14N), short values of T2eff(14N), or very broad patterns). It is hoped that these experimental and computational protocols will be useful for the characterization of various solid forms of nutraceuticals (i.e., salts, polymorphs, hydrates, solvates, cocrystals, amorphous solid dispersions, etc.), help detect impurity and counterfeit solid phases in dosage forms, and serve as a foundation for future NMR crystallographic studies of nutraceutical solid forms, including studies using ab initio crystal structure prediction algorithms.

Dispersion-Corrected DFT Methods for Applications in Nuclear Magnetic Resonance Crystallography.

Nuclear electric field gradient (EFG) tensor parameters depend strongly on electronic structures, making their calculation from first principles an excellent metric for the prediction, refinement, and optimization of crystal structures. Here, we use plane-wave density functional theory (DFT) calculations of EFG tensors in organic solids to optimize the Grimme (D2) and Tkatchenko-Scheffler (TS) atomic-pairwise force field dispersion corrections. Refinements using these new force field correction methods result in better representations of true crystal structures, as gauged by calculations of 177 14N, 17O, and 35Cl EFG tensors from 95 materials. The most striking result is the degree by which calculations of 35Cl EFG tensors of chloride ions match with experiment, due to the ability of these new methods to properly locate the positions of hydrogen atoms participating in H···Cl- hydrogen bonds. These refined structures also feature atomic coordinates that are more similar to those of neutron diffraction structures than those obtained from calculations that do not employ the optimized force fields. Additionally, we assess the quality of these new energy-minimization protocols for the prediction of 15N magnetic shielding tensors and unit cell volumes, which complement the larger analysis using EFG tensors, since these quantities have different physical origins. It is hoped that these results will be useful in future nuclear magnetic resonance (NMR) crystallographic studies and will be of great interest to a wide variety of researchers, in fields including NMR spectroscopy, computational chemistry, crystallography, pharmaceutical sciences, and crystal engineering.

Chemical Shift Tensors of Cimetidine Form A Modeled with Density Functional Theory Calculations: Implications for NMR Crystallography.

The principal components of the 13C chemical shift tensors for the ten crystallographically distinct carbon atoms of the active pharmaceutical ingredient cimetidine Form A have been measured using the FIREMAT technique. Density functional theory (DFT) calculations of 13C and 15N magnetic shielding tensors are used to assign the 13C and 15N peaks. DFT calculations were performed on cimetidine and a training set of organic crystals using both plane-wave and cluster-based approaches. The former set of calculations allowed several structural refinement strategies to be employed, including calculations utilizing a dispersion-corrected force field that was parametrized using 13C and 15N magnetic shielding tensors. The latter set of calculations featured the use of resource-intensive hybrid-DFT methods for the calculation of magnetic shielding tensors. Calculations on structures refined using the new force-field correction result in improved values of 15N magnetic shielding tensors (as gauged by agreement with experimental chemical shift tensors), although little improvement is seen in the prediction of 13C shielding tensors. Calculations of 13C and 15N magnetic shielding tensors using hybrid functionals show better agreement with experimental values in comparison to those using GGA functionals, independent of the method of structural refinement; the shielding of carbon atoms bonded to nitrogen are especially improved using hybrid DFT methods.

High-resolution 13 C and 43 Ca solid-state NMR and computational studies of the ethylene glycol solvate of atorvastatin calcium.

We report 43 Ca and 13 C solid-state nuclear magnetic resonance (NMR) spectroscopic studies of the ethylene glycol solvate of atorvastatin calcium. The 13 C and 43 Ca chemical shift and 43 Ca quadrupolar coupling tensor parameters are reported. The results are interpreted in terms of the reported X-ray diffraction crystal structure of the solvate and are compared with the NMR parameters of atorvastatin calcium trihydrate, the active pharmaceutical ingredient in Lipitor®. Hartree-Fock and density functional theory calculations of the NMR parameters based on a cluster model derived from the optimized X-ray diffraction crystal structure of the ethylene glycol solvate of atorvastatin calcium are in reasonable agreement with the experimental 43 Ca and 13 C NMR measurables.

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

Frequency-swept (FS) pulses, such as wideband uniform-rate smooth-truncation (WURST) pulses, have found much success for the acquisition of ultra-wideline (UW) solid-state NMR spectra. In this preliminary study, new pulses and pulse sequences are explored in simulation and experimentally for several nuclei exhibiting UWNMR powder patterns under static conditions, including 119Sn (I = 1/2), 195Pt (I = 1/2), 2H (I = 1), and 71Ga (I = 3/2). First, hyperbolic secant (HS) and tanh/tan (THT) pulses are tested and implemented as excitation and refocusing pulses in spin-echo and Carr-Purcell/Meiboom Gill (CPMG)-type sequences, and shown to have comparable performances to analogous WURST pulses. Second, optimal control theory (OCT) is utilized for the design of new Optimal Control Theory Optimized Broadband Excitation and Refocusing (OCTOBER) pulses, using carefully parameterized WURST, THT, and HS pulses as starting points. Some of the new OCTOBER pulses used in spin-echo sequences are capable of efficient broadband excitation and refocusing, in some cases resulting in spectra with increased signal enhancements over those obtained in experiments using conventional FS pulses. Finally, careful consideration of the spin dynamics of several systems, by monitoring of the time evolution of the density matrix via the Liouville-von Neumann equation and analysis of the time-resolved Fourier transforms of the pulses, lends insight into the underlying mechanisms of the FS and OCTOBER pulses. This is crucial for understanding their performance in terms of generating uniformly excited patterns of high signal intensity, and for identifying trends that may offer pathways to generalized parameterization and/or new pulse shapes.

A new NMR crystallographic approach to reveal the calcium local structure of atorvastatin calcium.

We combine experimental and computational determination of 43Ca solid-state NMR parameters (chemical shift tensors, quadrupolar coupling tensors, and Euler angles) to constrain the structure of the local calcium-ligand coordination environment. A new 43Ca NMR crystallographic approach which includes an extensive survey of the Cambridge Structural Database and a new symmetry benchmark is developed to enhance the selectivity of structural screening. The application of this method to quadrupolar NMR crystallographic investigations is demonstrated by unearthing the calcium local structure of the active pharmaceutical ingredient atorvastatin calcium trihydrate, the active ingredient in Lipitor®, in the absence of diffraction data. This method has been tested by applying it to calcium acetate monohydrate which has a known structure.

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.

19F Magic Angle Spinning NMR Spectroscopy and Density Functional Theory Calculations of Fluorosubstituted Tryptophans: Integrating Experiment and Theory for Accurate Determination of Chemical Shift Tensors.

The 19F chemical shift is a sensitive NMR probe of structure and electronic environment in organic and biological molecules. In this report, we examine chemical shift parameters of 4F-, 5F-, 6F-, and 7F-substituted crystalline tryptophan by magic angle spinning (MAS) solid-state NMR spectroscopy and density functional theory. Significant narrowing of the 19F lines was observed under fast MAS conditions, at spinning frequencies above 50 kHz. The parameters characterizing the 19F chemical shift tensor are sensitive to the position of the fluorine in the aromatic ring and, to a lesser extent, the chirality of the molecule. Accurate calculations of 19F magnetic shielding tensors require the PBE0 functional with a 50% admixture of a Hartree-Fock exchange term, as well as taking account of the local crystal symmetry. The methodology developed will be beneficial for 19F-based MAS NMR structural analysis of proteins and protein assemblies.

Role of Exact Exchange and Relativistic Approximations in Calculating 19F Magnetic Shielding in Solids Using a Cluster Ansatz.

Calculations of 19F magnetic shielding in various materials are presented. In calculations on gas-phase molecules, the variation of magnetic shielding with the amount of Hartree-Fock exchange (HFX) in the functional demonstrates that excellent agreement with experiment is obtained with an admixture of 50%, here denoted PBE0 (50%). Calculations at the PBE, PBE0 (25%), and PBE0 (50%) levels on 10 crystalline organofluorines and 15 crystalline inorganic fluorides, in which a cluster ansatz is used to model the lattice environment, were performed. For fluorine-containing aromatics, increasing the admixture of HFX results in the prediction of larger magnetic-shielding spans, whereas increasing the admixture of HFX in calculations for CFCl3 decreases the span. In calculations of 19F magnetic shielding of the inorganic fluorides, the use of sufficiently large clusters of inorganic fluorides results in accuracies similar to those calculated for the organofluorines. Relativistic effects on the magnetic shielding of inorganic fluorides, modeled with ZORA at both the scalar and spin-orbit levels, are dominated by the scalar terms that increase the shielding of most 19F sites over the non-relativistic results. These effects appear to scale with the atomic number of the cation. For most elements of the sixth row (Cs, Ba, La, and Pb), the scalar relativistic contribution to the magnetic shielding is in the range of 20-77 ppm. For elements of group XII (Zn, Cd, and Hg) bonded to fluorine, the scalar relativistic contribution results in deshielding of the 19F site.

Semi-empirical refinements of crystal structures using 17O quadrupolar-coupling tensors.

We demonstrate a modification of Grimme's two-parameter empirical dispersion force field (referred to as the PW91-D2* method), in which the damping function has been optimized to yield geometries that result in predictions of the principal values of 17O quadrupolar-coupling tensors that are systematically in close agreement with experiment. The predictions of 17O quadrupolar-coupling tensors using PW91-D2*-refined structures yield a root-mean-square deviation (RMSD) (0.28 MHz) for twenty-two crystalline systems that is smaller than the RMSD for predictions based on X-ray diffraction structures (0.58 MHz) or on structures refined with PW91 (0.53 MHz). In addition, 13C, 15N, and 17O chemical-shift tensors and 35Cl quadrupolar-coupling tensors determined with PW91-D2*-refined structures are compared to the experiment. Errors in the prediction of chemical-shift tensors and quadrupolar-coupling tensors are, in these cases, substantially lowered, as compared to predictions based on PW91-refined structures. With this PW91-D2*-based method, analysis of 42 17O chemical-shift-tensor principal components gives a RMSD of only 18.3 ppm, whereas calculations on unrefined X-ray structures give a RMSD of 39.6 ppm and calculations of PW91-refined structures give an RMSD of 24.3 ppm. A similar analysis of 35Cl quadrupolar-coupling tensor principal components gives a RMSD of 1.45 MHz for the unrefined X-ray structures, 1.62 MHz for PW91-refined structures, and 0.59 MHz for the PW91-D2*-refined structures.

Calculations of solid-state 43 Ca NMR parameters: A comparison of periodic and cluster approaches and an evaluation of DFT functionals.

We present a computational study of magnetic-shielding and quadrupolar-coupling tensors of 43 Ca sites in crystalline solids. A comparison between periodic and cluster-based approaches for modeling solid-state interactions demonstrates that cluster-based approaches are suitable for predicting 43 Ca NMR parameters. Several model chemistries, including Hartree-Fock theory and 17 DFT approximations (SVWN, CA-PZ, PBE, PBE0, PW91, B3PW91, rPBE, PBEsol, WC, PKZB, BMK, M06-L, M06, M06-2X, M06-HF, TPSS, and TPSSh), are evaluated for the prediction of 43 Ca NMR parameters. Convergence of NMR parameters with respect to basis sets of the form cc-pVXZ (X = D, T, Q) is also evaluated. All DFT methods lead to substantial, and frequently systematic, overestimations of experimental chemical shifts. Hartree-Fock calculations outperform all DFT methods for the prediction of 43 Ca chemical-shift tensors. © 2017 Wiley Periodicals, Inc.

Spin-orbit effects on the (119)Sn magnetic-shielding tensor in solids: a ZORA/DFT investigation.

Periodic-boundary and cluster calculations of the magnetic-shielding tensors of (119)Sn sites in various co-ordination and stereochemical environments are reported. The results indicate a significant difference between the predicted NMR chemical shifts for tin(ii) sites that exhibit stereochemically-active lone pairs and tin(iv) sites that do not have stereochemically-active lone pairs. The predicted magnetic shieldings determined either with the cluster model treated with the ZORA/Scalar Hamiltonian or with the GIPAW formalism are dependent on the oxidation state and the co-ordination geometry of the tin atom. The inclusion of relativistic effects at the spin-orbit level removes systematic differences in computed magnetic-shielding parameters between tin sites of differing stereochemistries, and brings computed NMR shielding parameters into significant agreement with experimentally-determined chemical-shift principal values. Slight improvement in agreement with experiment is noted in calculations using hybrid exchange-correlation functionals.

Analysis of the bond-valence method for calculating (29) Si and (31) P magnetic shielding in covalent network solids.

(29) Si and (31) P magnetic-shielding tensors in covalent network solids have been evaluated using periodic and cluster-based calculations. The cluster-based computational methodology employs pseudoatoms to reduce the net charge (resulting from missing co-ordination on the terminal atoms) through valence modification of terminal atoms using bond-valence theory (VMTA/BV). The magnetic-shielding tensors computed with the VMTA/BV method are compared to magnetic-shielding tensors determined with the periodic GIPAW approach. The cluster-based all-electron calculations agree with experiment better than the GIPAW calculations, particularly for predicting absolute magnetic shielding and for predicting chemical shifts. The performance of the DFT functionals CA-PZ, PW91, PBE, rPBE, PBEsol, WC, and PBE0 are assessed for the prediction of (29) Si and (31) P magnetic-shielding constants. Calculations using the hybrid functional PBE0, in combination with the VMTA/BV approach, result in excellent agreement with experiment. © 2016 Wiley Periodicals, Inc.

Carbon-13 chemical-shift tensors in indigo: A two-dimensional NMR-ROCSA and DFT Study.

The principal components of the (13)C NMR chemical-shift tensors for the eight unique carbon sites of crystalline indigo have been measured using the ROCSA pulse sequence. The chemical shifts have been assigned unambiguously to their respective nuclear sites through comparison of the experimental data to the results of density-functional calculations employing a refined X-ray diffraction structure. These measurements expand the database of measured aromatic (13)C chemical-shift tensors to the indole ring. Magnetic shielding calculations for hypoxanthine and adenosine are also reported. Comparisons of calculations that include the effect of the crystalline lattice with calculations that model indigo as an isolated molecule give an estimate of the intermolecular contribution to the magnetic shielding.

Critical Analysis of Cluster Models and Exchange-Correlation Functionals for Calculating Magnetic Shielding in Molecular Solids.

Calculations of the principal components of magnetic-shielding tensors in crystalline solids require the inclusion of the effects of lattice structure on the local electronic environment to obtain significant agreement with experimental NMR measurements. We assess periodic (GIPAW) and GIAO/symmetry-adapted cluster (SAC) models for computing magnetic-shielding tensors by calculations on a test set containing 72 insulating molecular solids, with a total of 393 principal components of chemical-shift tensors from 13C, 15N, 19F, and 31P sites. When clusters are carefully designed to represent the local solid-state environment and when periodic calculations include sufficient variability, both methods predict magnetic-shielding tensors that agree well with experimental chemical-shift values, demonstrating the correspondence of the two computational techniques. At the basis-set limit, we find that the small differences in the computed values have no statistical significance for three of the four nuclides considered. Subsequently, we explore the effects of additional DFT methods available only with the GIAO/cluster approach, particularly the use of hybrid-GGA functionals, meta-GGA functionals, and hybrid meta-GGA functionals that demonstrate improved agreement in calculations on symmetry-adapted clusters. We demonstrate that meta-GGA functionals improve computed NMR parameters over those obtained by GGA functionals in all cases, and that hybrid functionals improve computed results over the respective pure DFT functional for all nuclides except 15N.

Density functional investigation of intermolecular effects on 13C NMR chemical-shielding tensors modeled with molecular clusters.

A quantum-chemical method for modeling solid-state nuclear magnetic resonance chemical-shift tensors by calculations on large symmetry-adapted clusters of molecules is demonstrated. Four hundred sixty five principal components of the (13)C chemical-shielding tensors of 24 organic materials are analyzed. The comparison of calculations on isolated molecules with molecules in clusters demonstrates that intermolecular effects can be successfully modeled using a cluster that represents a local portion of the lattice structure, without the need to use periodic-boundary conditions (PBCs). The accuracy of calculations which model the solid state using a cluster rivals the accuracy of calculations which model the solid state using PBCs, provided the cluster preserves the symmetry properties of the crystalline space group. The size and symmetry conditions that the model cluster must satisfy to obtain significant agreement with experimental chemical-shift values are discussed. The symmetry constraints described in the paper provide a systematic approach for incorporating intermolecular effects into chemical-shielding calculations performed at a level of theory that is more advanced than the generalized gradient approximation. Specifically, NMR parameters are calculated using the hybrid exchange-correlation functional B3PW91, which is not available in periodic codes. Calculations on structures of four molecules refined with density plane waves yield chemical-shielding values that are essentially in agreement with calculations on clusters where only the hydrogen sites are optimized and are used to provide insight into the inherent sensitivity of chemical shielding to lattice structure, including the role of rovibrational effects.