Construction of accurate Kohn-Sham potentials for the lowest states of the helium atom: Accurate test of the ionization-potential theorem
Accurate local Kohn-Sham potentials have been constructed for the ground $1s^2 ^1S$ state and, in particular, for the lowest triplet $1s2s ^{3}S$ state of the helium atom, using electron densities from many-body calculations and the procedure of van Leeuwen and Baerends (Phys. Rev. A{\bf49}, 2138 (1994)). The resulting Kohn-Sham orbitals reproduce the many-body densities very accurately, and furthermore we have demonstrated that the negative of the energy eigenvalue of the outermost electron orbital agrees with the corresponding ionization energy with extreme accuracy. The procedure is also applied to the Hartree-Fock density of the $1s2s ^{3}S$ state, and the Kohn-Sham eigenvalue of the $2s$ orbital is found to agree very well with the corresponding Hartree-Fock eigenvalue, which is the negative of the ionization energy in this model due to Koopmans' theorem. The results for the $1s2s ^{3}S$ state clearly demonstrate that there is no conflict between the locality of the Kohn-Sham potential and the exclusion principle, as claimed by Nesbet (Phys. Rev. A{\bf58}, R12 (1998)).