Some fundamental problems with zero flux partitioning of electron densities

A number of fundamental problems with the topological analysis of molecular electron densities using thtr atoms in molecules (AIM) theory developed by Bader and coworkers are highlighted. In particular, contrary to statements made in the literature, we show that the local zero flux condition used in the AIR;I theory to define an atom in a molecule does not follow from the Schwinger variation principle, nor does it define unambiguously the atomic domains. Serious limitations of the definition of an atom in AIM theory also arise due to vibrational effects. A general definition of the structure of a molecular isomer based on a generalisation of the Born-Oppenheimer potential energy surface allow these limitations to be overcome.