Incipient manifestation of the shell structure of atoms within the WDA model for the exchange and kinetic energy density functionals

Abstract

The radial electron density obtained for all the atoms of the main groups of the Periodic Table through the solution of the Euler equation associated with the nonlocal weighted density approximation (WDA) for the exchange and kinetic energy density functionals shows an incipient shell structure which is absent in other calculations using kinetic energy functionals based on the electronic density. The WDA radial density reveals two local maxima and the position of the first maximum correlates with the position of the maximum for the 1s orbital in the Hartree-Fock approximation. The cusp condition at the nucleus is fulfilled accurately. Also we study the density-based electron localization function (DELF) as a complementary procedure for the visualization of shells.