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.

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.

Variable-hydrate active pharmaceutical ingredients (APIs) are known to form thermodynamically and kinetically stabilized solid phases over a continuous range of nonstoichiometric hydration levels. Some of these forms can be problematic in the production of solid dosage forms (e.g., tablets and capsules), where manufacturing processes can induce changes in the hydration level of the API, resulting in transformations to undesirable solid phases that may affect product quality. In order to improve the development of variable-hydrate APIs for commercial use, reliable methods must be developed to not only measure the hydration levels, but also to probe the influences of water molecules on the molecular-level structures of APIs within dosage formulations. In this study, we examine a Genentech development compound, GNE-A, which is a hydrochloride (HCl) salt of an API that exhibits variable-hydrate behavior. Using a combination of 35Cl solid-state NMR (SSNMR), variable-relative humidity (RH) powder X-ray diffraction (PXRD), thermogravimetric analysis, and dispersion-corrected plane-wave density functional theory (DFT-D2*) calculations, we reveal the local and long-range structural effects of water under different storage and processing conditions. 35Cl SSNMR spectra are particularly sensitive to the presence of water and reveal distinct anionic Cl– environments in the hydrated and dehydrated forms of the HCl API. Our data demonstrate that complete dehydration of the material is surprisingly difficult, even with repeated drying cycles. Finally, 35Cl SSSNMR is shown to be very useful for probing the local structural environments of Cl– ions in tablets processed using either wet or dry granulation, since there are no interfering signals from the complex array of excipient molecules present in the formulation.

Nuclear electric field gradient (EFG) tensors obtained from solid-state NMR spectroscopy are highly responsive to variations in structural features. The orientations and principal components of EFG tensors show great variation between different molecular structures; hence, extraction of EFG tensor parameters, either experimentally or computationally, provides a powerful means for structure determination and refinement. Here, dispersion-corrected plane-wave density functional theory (DFT) is used to refine atomic coordinates in organic crystals determined initially through single-crystal Xray diffraction (XRD) or neutron diffraction methods. To accomplish this, an empirical parametrization of a two-body dispersion force field is illustrated, in which comparisons of experimental and calculated 14 N, 17 O, and 35 Cl EFG tensor parameters are used to assess the quality of energy-minimized structures. The parametrization is based on a training set of 17 organic solids. The analysis is applied subsequently to the structural refinements of structural models from over 60 different materials. For the prediction of 35 Cl EFG tensor parameters in particular, the optimization protocols described herein lead to a substantial improvement in agreement with experiment relative to structures obtained by XRD methods or by refinement with plane-wave DFT without the inclusion of the force field. The results further demonstrate that crystal structures with atomic coordinates refined with the present methods are able to pinpoint the positions of hydrogen atoms participating in H•••Cl − hydrogen bonding with a higher degree of precision than is possible through neutron diffraction. This methodology, which is facile to implement within most DFT software packages, should prove to be very useful for future structural refinements using NMR crystallographic methods.

The principal components of the 13 C 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 13 C and 15 N magnetic shielding tensors are used to assign the 13 C and 15 N 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 13 C and 15 N 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 15 N magnetic shielding tensors (as gauged by agreement with experimental chemical shift tensors), although little improvement is seen in the prediction of 13 C shielding tensors. Calculations of 13 C and 15 N 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.

The F 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 theF lines was observed under fast MAS conditions, at spinning frequencies above 50 kHz. The parameters characterizing the F 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 ofF 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 F-based MAS NMR structural analysis of proteins and protein assemblies.

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 O quadrupolar-coupling tensors that are systematically in close agreement with experiment. The predictions ofO 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, C,N, and O chemical-shift tensors andCl 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 O 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 ofCl 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 F 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 CFCl decreases the span. In calculations of F 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 mostF 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 F site.