Exact-exchange self-consistent calculations of the Kohn-Sham potential, surface energy, and work function of jellium slabs are reported in the framework of the Optimized Effective Potential (OEP) scheme of Density Functional Theory. In the vacuum side of the jellium surface and at a distance $z$ that is larger than the slab thickness, the exchange-only Kohn-Sham potential is found to be image-like ($sim -e^2/z$) but with a coefficient that differs from that of the classical image potential $V_{im}(z)=-e^2/4z$. The three OEP contributions to the surface energy (kinetic, electrostatic, and exchange) are found to oscillate as a function of the slab thickness, as occurs in the case of the corresponding calculations based on the use of single-particle orbitals and energies obtained in the Local Density Approximation (LDA). The OEP work function presents large quantum size effects that are absent in the LDA and which reflect the intrinsic derivative discontinuity of the exact Kohn-Sham potential.
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