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 ) with experiment. We demonstrate a 31% reduction in the RMS error for the predicted ¹⁷O C 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 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 predictions is demonstrated by examining the disordered 4-Nitrobenzaldehyde crystal structure.