Investigation of the correlation potential from Kohn-Sham perturbation theory

Perturbation theory on the basis of the Kohn-Sham Hamiltonian leads to an i mplicit density functional for the correlation energy E-c. In this contribu tion we investigate the corresponding correlation potential v(c). It is sho wn that for finite systems the v(c) obtained by direct application of the o ptimized potential method diverges in the asymptotic region. The presence o f unoccupied states, inherent in any perturbative form of E-c, is identifie d as the origin of this unphysical behavior. An approximate variational pro cedure is developed in order to avoid this difficulty. The potential result ing from this method qualitatively reproduces the shell structure of the ex act atomic v(c).