The Hartree product and the description of local and global quantities in atomic systems: A study within Kohn-Sham theory

The Hartree product is analyzed in the context of Kohn-Sham theory. The dif ferential equations that emerge from this theory are solved with the optimi zed effective potential using the Krieger, Li, and Iafrate approximation, i n order to get a local potential as required by the ordinary Kohn-Sham proc edure. Because the diagonal terms of the exact exchange energy are included in Hartree theory, it is self-interaction free and the exchange potential has the proper asymptotic behavior. We have examined the impact of this cor rect asymptotic behavior on local and global properties using this simple m odel to approximate the exchange energy. Local quantities, such as the exch ange potential and the average local electrostatic potential are used to ex amine whether the shell structure in an atom is revealed by this theory. Gl obal quantities, such as the highest occupied orbital energy (related to th e ionization potential) and the exchange energy are also calculated. These quantities are contrasted with those obtained from calculations with the lo cal density approximation, the generalized gradient approximation, and the self-interaction correction approach proposed by Perdew and Zunger. We conc lude that the main characteristics in an atomic system are preserved with t he Hartree theory. In particular, the behavior of the exchange potential ob tained in this theory is similar to those obtained within other Kohn-Sham a pproximations. (C) 2000 American Institute of Physics. [S0021-9606(00)31401 -5].