Investigation of the correlation potential from Kohn-Sham perturbation theory

Perturbation theory on the basis of the Kohn-Sham Hamiltonian leads to an implicit density functional for the correlation energy E-c. In this contribution we investigate the corresponding correlation potential v(c). It is shown that for finite systems the v(c) obtained by direct application of the optimized potential method diverges in the asymptotic region. The presence of unoccupied states, inherent in any perturbative form of E-c, is identified as the origin of this unphysical behavior. An approximate variational procedure is developed in order to avoid this difficulty. The potential resulting from this method qualitatively reproduces the shell structure of the exact atomic v(c).