Analysis of three‐dimensional molecular shape using surface area and molecular volume scaling descriptors

Continua of molecular surfaces have been proposed in the past as realistic approaches to modeling molecular shape. A continuum of fused-sphere surfaces combines the simplicity of computations involving hard spheres with a more accurate description of the “fuzzy” boundary of a molecule. In this work, we study some simple properties of a continuum of molecular surfaces derived by linearly scaling the van der Waals radii. We introduce some molecular shape descriptors derived from surface area and volume and study their dependence on a scaling parameter that “swells” the molecular surface. As one moves away from the nuclei, any transitions in molecular shape are reflected by changes in the descriptors. These descriptors convey essential shape features, in the sense that they are rather insensitive to molecular size. Even though the geometrical descriptors characterize the continuum globally, their behavior appears to be strongly determined by local molecular shape features. The procedure can also be extended to more realistic electron density surfaces. As a tool, the method can be helpful in assessing molecular similarity, as well as in studying properties of local neighborhoods within large clusters.