On the differential geometry of interatomic surfaces

Using differential geometry, we propose the total curvature of interatomic surfaces to characterize bonds. In this way visual interpretations of interatomic surfaces are now rigorously quantified. The analysis of the intrinsic geometry of an interatomic surface is implemented in the program MORPHY 2.0. It is shown that the total curvature depends on anionic polarizability, electronegativity differences, and steric effects determined by the total chemical environment of the bonded atoms in question. In general the proposed index measures the external chemical distortion of an atom in a molecule. It can be used in the context of uniform electric fields and in conformational studies.