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. Her; 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 N-14, O-17, and Cl-35 EFG tensors from 95 materials. The most striking result is the degree by which calculations of Cl-35 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 center dot center dot 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 N-15 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.