The shell structure of atoms

The total electron density distribution of an isolated atom or an atom in a molecule does not reveal an atomic shell structure. Many localization functions, such as the radial averaged electron density, the Laplacian of the electron density, or the electron localization function have been proposed to visualize and analyze the shell structure of atoms. It was found that for light main group elements the correct number of shells is revealed by such functions. Later it was recognized that for heavy main group elements and for transition metals many of these diagnostic tools fail to reveal the full set of electronic shells as expected from the periodic table. In this work we focus on the radial structure of isolated atoms as revealed by the Laplacian of the electron density. We will demonstrate that it is the nodal structure of the orbitals of the inner shells which is responsible for the diminishing of at least one valence shell of third row transition metal atoms. Particular attention is paid to the effect of different electronic configurations on the shell structure of atoms and the question if the changes observed in the Laplacian of the radial density are sufficiently large for experimental studies on the topology of the electron density. Our presentation is as general as possible and, hence, employs a fully relativistic, i.e., four-component picture and a multiconfigurational ansatz for the wave function, which is thus valid for the whole periodic table of elements.