A Critical Investigation of Proposed Electrostatic Corrections to Quantum Mechanical Volumes: The Importance of Variation and the Irrelevance of Imbalance

The crystal density of neutral and ionic molecular crystals is remarkably well approximated by the enclosed volume of molecular surfaces, where these surfaces are defined as regions of constant and small electron density. Several workers have proposed that estimates may be improved if one includes quantities extracted from the electrostatic potential on the surface of the molecule. The variation of the potential and the imbalance of positive and negative values have been considered to be of importance. In this study we demonstrate that whereas variation is important for improving crystal density predictions, imbalance is not. We present a density functional theory (DFT) study on a set of 44 neutral molecular crystals. Ten-fold cross-validations were performed on models that incorporate variation, imbalance, and combinations of both. Geometries were optimized using B3LYP and basis sets of type 6-31G(d). Electron densities and electrostatic potentials were computed with B3LYP and M05. Regardless of functional, models that correct for variation yield a relative decrease of 15%–18% in root-mean-square error of prediction (RMSEP). This correction appears to sharpen the error distribution about zero. Models based on imbalance yield no improvement, and we argue that it plays an insignificant role.