Tomas Lunde Jensen

All molecular surfaces are equal: demanding invariance of predictions in linear single-variable models

ABSTRACT The molecular surface has been suggested to be a region of the molecule, where information of non-covalent intermolecular interactions is present. Many workers have pursued this idea by constructing models based on statistical parameters Φ extracted from the electrostatic potential on a particular molecular surface. We claim that a better approach is to define a family of equivalent molecular surfaces, each associated with a particular electron density ε. The demand that any model must give the same predictions on all such molecular surfaces yields a mathematical requirement restricting the space of permissible parameters. We prove that linear single-variable models of the form property = α Φ + β will only yield invariant predictions if the parameter values of Φ computed on equivalent surfaces are linearly related. This claim is not restricted to the use of the electrostatic potential, but holds for any parameter extracted from the surface of molecules. By using a set of 44 molecules, we also demonstrate that a frequently used aspect of the electrostatic potential, that of ‘imbalance’ of negative and positive values, fails to satisfy the linearity requirement. It is argued that multi-variable models should only include parameters that satisfy the single-variable requirement.

A critical investigation of proposed electrostatic corrections to quantum mechanical volumes: the importance of variation and the irrelevance of imbalance

ABSTRACT 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 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 optimised 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. 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.