Direct comparison of optimized effective potential and Hartree-Fock self-consistent calculations for jellium slabs

We present a direct comparison of the exchange-only optimized effective potential (x-OEP) method, originating from density functional theory, with Hartree-Fock (HF) results for jellium slabs of finite width, based on fully self-consistent calculations. The nonlocal character of the HF exchange potential causes a coupling of the momentum parallel to the slab surface with the perpendicular component of the orbitals. This results in an entirely different energy-band structure close to the Fermi surface and in terms of bandwidth, as compared with the x-OEP energy-band structure. Good agreement between x-OEP and HF calculations for jellium slabs has been observed for Friedel oscillations of the electron density, surface energies, and dipole barriers, as well as for electrostatic and averaged exchange potentials. However, marked differences appear between x-OEP and HF work functions for narrow slabs, which is in contrast to the good agreement of ionization energies reported for finite systems. On the other hand, we present evidence that both work functions are very similar in the limit of very wide slabs.