MPI - CPfS

Shell Structure

The term "atomic shell" is actually used for two different, but related representations. For clarity, we write in this section the terms referring to the orbital picture in italic and the terms concerning the spatial picture in bold.

An atomic shell in the orbital picture is given by orbitals with the same principal quantum number, therefore spreading over the whole real space. The charge densities of the atomic shells interpenetrate.

In contrast, ELF for an atom reveals a radial sequence of local ELF maxima around the nucleus [BECKE1990]. Between two successive local maxima a local minimum is situated, which is used as the separatrix between two shell regions. Each shell region is thus separated from the neighboring shell regions by surfaces of zero flux in ELF gradient and constitutes an ELF basin. An "atomic shell" defined this way in direct space as an atomic shell basin is strictly confined to a unique spacial region.

ELF has been shown to exhibit the shell structure of atoms not only in a qualitative manner, i.e. the number of atomic shell basins equals the number of atomic shells following from the Aufbau principle, but also in a quantitative manner: the electron density integrated within each atomic shell basin yields shell populations very close to the one expected from the Aufbau principle [KOHOUT1996]. From the orbital point of view, the charge found in a particular atomic shell basin originates mainly from orbitals with the same principal quantum number. The additional charge coming from orbitals with other principal numbers yields the observed "correct" electron population of the atomic shell basin.

For chemical aggregates of atoms, e. g. molecules, the spherical symmetry is broken. (Remark: In fact, all the spherical maxima and minima of ELF for an isolated atom are degenerate critical points, which means that this situation is topologically unstable and the very slightest non-spherical perturbation is sufficient to break the spherical symmetry.) The atomic shell basin decomposes into several smaller basins interconnected by separatrices. Given our definition of a basin set (see section Topological Analysis) we can now state the following observation: Usually each inner atomic shell basin decomposes into a number of basins which all together form the shell basin set. A sufficient condition for this finding is, that the highest inter-shell basin interconnection points (bips) obviously have lower η-values than the lowest intra-shell ones.

The common outermost basin set regions of all atoms constitute the valence region of the chemical system. The analysis of the topology of ELF in this region has been proven to be an excellent tool to discuss various types of chemical bonding situations [SAVIN1997].

last update: 03.07.2002