Solution of the Kohn–Sham equations for many-electron atoms confined by penetrable walls

Abstract

The solution of the Kohn–Sham equations in the Roothaan’s context is presented for atoms confined by penetrable walls. A new basis set is employed in this work, which was designed within the Hartree–Fock approach to ensure a correct decay on the electron density. Exchange-correlation functionals from local density and generalized gradient approximation are considered in the implementation of the Kohn–Sham method. The confinement effects on energies (total and orbital) and on the exchange potential are discussed when two exchange-only functionals are compared with the Hartree–Fock method, for closed-shell atoms confined by finite potentials. Clearly, the wrong asymptotic behavior exhibited by the exchange-only Kohn–Sham potentials, considered in this work, has a large impact on orbital energies when several confinements are tested. In fact, such exchange potentials predict orbital energies which are drastically different than those predicted by the Hartree–Fock method. These differences are not restricted just to absolute values, also the trend observed for exchange and orbital energies is quite different than that predicted by Hartree–Fock. Effects of the correlation contribution are also discussed on total and orbital energies, which show same trends than those obtained by exchange-only functionals. Unfortunately, there are no implementations of correlated methods based on the wave-function for this kind of problems, and consequently our results for correlation energy cannot be compared with a reference. With this implementation there is one possibility to test the performance of approximate exchange-correlation functionals, in addition to the sets commonly used in the design of new functionals.