Geometrically Faithful Homeomorphisms Between the Electron Density and the Bare Nuclear Potential

The topology of the nuclear potential, V-nuc(r), of just over 130 molecules and molecular complexes is investigated and compared with the topology of the electron density p(r). As nuclear positions are kept fixed in this comparison, this work screens for geonietrically faithful homeomorphisms between rho(r) and V-nuc(r). In this set of molecules spanning simple inorganic moieties, strained (and cyclic) hydrocarbons, (fused) aromatics, boranes, van der Waals complexes, water clusters, and a few biomolecules, about 70% of the systems show this homeomorphism. A simple analytical formula is derived, expressing the position of a (3,-1) critical point in any diatomic as a function of the participating atomic numbers. The topology of V-nuc(r) at one location of a molecule can sensitively depend on the presence or absence of a substituent far away from this location. (C) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 109: 2542-2553, 2009