Density Functional Theory Applied on Confined Many-Electron Atoms
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.
This work has been supported by CONACYT, México, through the projects 154784, 155698 and 155070. The authors thank the facilities provided by the Laboratorio de Supercómputo y Visualización en Paralelo at the Universidad Autónoma Metropolitana-Iztapalapa.
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