Contribution to the electron distribution analysis. I. Shell structure of atoms

Relativistic spherically averaged numerical all-electron densities ρ were computed for the atoms Be–Ba, B–Tl, C–Pb, Cu–Au, and Zn–Hg. The Laplacian of these densities is not able to resolve the valence shell from the inner shells in case of heavy atoms, starting with the fourth row. The distribution of the local kinetic energy Ekin shows a valence maximum even for these heavy atoms, unfortunately, in a region of negative kinetic energy; i.e., nonclassically allowed. The quantity −‖∇ρ‖/ρ was also investigated. For all computed atoms, the −‖∇ρ‖/ρ diagrams are capable of describing the complete shell structure. −‖∇ρ‖/ρ is sensitive to basis set quality: poor Gaussian basis sets exhibit spurious oscillations and a premature onset of the linear decay. For the atoms B–Tl, Ba, Au, Hg, and Pb, nonrelativistic numerical calculations were performed to examine the effect of the relativity on the aforementioned quantities. Tests with pseudopotential densities reveal that for pseudopotential calculations, it is advisable to use at least two outermost shells in order to reproduce the all-electron values of ∇ 2ρ, Ekin, and −‖∇ρ‖/ρ in the valence region.