Accurate Kohn-Sham potential for the 1s2s 3S state of the helium atom: Tests of the locality and the ionization-potential theorems

The local Kohn–Sham potential is constructed for the 1s2s 3S state of the helium atom, using the procedure proposed by van Leeuwen and Baerends (Phys. Rev. A, 49, 2138 (1994)) and the many-body electron density, obtained from the pair-correlation program of Salomonson and Öster (Phys. Rev. A, 40, 5559 (1989)). The Kohn–Sham orbitals reproduce the many-body density very accurately, demonstrating the validity of the Kohn–Sham model and the locality theorem in this case. The ionization-potential theorem, stating that the Kohn–Sham energy eigenvalue of the outermost electron orbital agrees with the negative of the corresponding many-body ionization energy (including electronic relaxation), is verified in this case to nine digits. A Kohn–Sham potential is also constructed to reproduce the Hartree–Fock density of the same state, and the Kohn–Sham 2s eigenvalue is then found to agree with the same accuracy with the corresponding Hartree–Fock eigenvalue. This is consistent with the fact that in this model the energy eigenvalue equals the negative of the ionization energy without relaxation due to Koopmans' theorem. Related calculations have been performed previously, particularly for atomic and molecular ground states, but none of matching accuracy. In the computations presented here there is no conflict between the locality of the Kohn–Sham potential and the exclusion principle, as claimed by Nesbet (Phys. Rev. A, 58, R12 (1998)). PACS Nos.: 31.15.Ew, 31.15.Pf, 02.30.Sa