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.