Refining Crystal Structures with Quadrupolar NMR and Dispersion-Corrected Density Functional Theory

Abstract

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 X-ray 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 14N, 17O, and 35Cl 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 35Cl 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.