Density Functional Theory Applied on Confined Many-Electron Atoms

Abstract

ln this report, Thomas-Fermi and Kohn-Sham models are used to study the electronic structure of confined atoms. The Slater and Krutter method is reviewed and it is applied on a modification of the Thomas-Fermi model, where the cusp condition is satisfied. By analyzing the equation involved in this discussion, it is found that in the Thomas-Fermi model a neutral atom cannot be confined in a sphere, of arbitrary radius, where the electron density is cancelled. By the side of the Kohn-Sham method, several exchange-correlation functionals were applied on atoms confined by rigid walls. It was found that the highest occupied molecular orbital, obtained by the considered exchange-correlation functionals, show large discrepancies with regard to those values obtained by the Hartree-Fock method, even for confinements where the asymptotic region is not relevant. Additionally, we found important differences, for the correlation energy, between the correlation functionals used and a wave function obtained by a Hylleraas wave functions expansion for two-electron system. Thus, we pointed out some relevant issues that must be addressed in the near future by the Kohn-Sham method applied to confined atoms.