First-principles chemical shielding tensor predictions play a critical role in studying molecular crystal structures using nuclear magnetic resonance. Fragment-based electronic structure methods have dramatically improved the ability to model molecular crystal structures and energetics using high-level electronic structure methods. Here, a many-body expansion fragment approach is applied to the calculation of chemical shielding tensors in molecular crystals. We begin by exploring the impact of truncating the many-body expansion at different orders and the role of electrostatic embedding are examined on a series of molecular clusters extracted from molecular crystals.
We then assess the quality of fragment-based ab initio isotropic $^{13}$C, $^{15}$N and $^{17}$O chemical shift predictions for a collection of molecular crystals with a variety of commonly used density functionals. We explore the relative performance of cluster, two-body fragment, combined cluster/fragment, and the planewave gauge-including projector augmented wave (GIPAW) models relative to experiment. When electrostatic embedding is employed to capture many-body polarization effects, the simple and computationally inexpensive two-body fragment model predicts isotropic $^{13}$C chemical shifts and the chemical shielding tensors as well as both cluster models and the GIPAW approach. Compared with $^{13}$C, fragment-methods give larger RMS errors relative to experiment for both $^{15}$N and $^{17}$O nuclei. However, $^{15}$N displays similar performance to $^{13}$C with electrostatically embedded two-body fragment methods yielding comparable performance with both cluster and cluster/fragment methods. In the case of $^{17}$O, local many-body effects make a combined cluster/fragment approach necessary for accurate treatment of the chemical shielding. In every case, hybrid functionals predict chemical shifts in noticeably better agreement with experiment than generalized gradient approximation (GGA) functionals.
Finally, we asses the ability of these techniques to correctly identify molecular crystal polymorphs and to assign experimental chemical shifts to atoms on individual monomers in the asymmetric unit cell for: sulfanilamide, testosterone, 2-aminobenzoic acid, phenobarbital, and the three colored polymorphs of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile. Many of these systems provide challenging examples of NMR crystallography that require the discrimination among spectra whose $^{13}$C chemical shifts differ by only a few parts per million (ppm) across the different polymorphs. Fragment-based PBE0/6-311+G(2d,p) level chemical shielding predictions correctly assign the polymorphic forms for each of these systems, often reproducing the experimental $^{13}$C chemical shifts with 1 ppm accuracy.
