Optimized Effective Potential made simple: Orbital functionals, orbital shifts, and the exact Kohn-Sham exchange potential

Abstract

The optimized effective potential (OEP) is the exact Kohn-Sham potential for explicitly orbital-dependent energy functionals, e.g., the exact exchange energy. We give a proof for the OEP equation which does not depend on the chain rule for functional derivatives and directly yields the equation in its simplest form: a certain first-order density shift must vanish. This condition explains why the highest-occupied orbital energies of Hartree-Fock and exact-exchange OEP are so close. More importantly, we show that the exact OEP can be constructed iteratively from the first-order shifts of the Kohn-Sham orbitals, and that these can be calculated easily. The exact exchange potential $v_\mathrm{x}(\re)$ for spherical atoms and three-dimensional sodium clusters is calculated. Its long-range asymptotic behavior is investigated, including the approach of $v_\mathrm{x}(\re)$ to a non-vanishing constant in particular spatial directions. We calculate total and orbital energies and static electric dipole polarizabilities for the sodium clusters employing the exact exchange functional. Exact OEP results are compared to the Krieger-Li-Iafrate (KLI) and local density approximations.

15 pages, 3 figures. To appear in Physical Review B

References in corpus (9)

• Real-Space Mesh Techniques in Density Functional Theory
• Simple iterative construction of the optimized effective potential for orbital functionals, including exact exchange
• Assessment of exchange-correlation functionals for the calculation of dynamical properties of small clusters in TDDFT
• Excitonic optical spectrum of semiconductors obtained by time-dependent density-functional theory with the exact-exchange kernel
• Ionic and electronic structure of sodium clusters up to N=59
• Thermal expansion in small metal clusters and its impact on the electric polarizability
• Degeneracy in Density Functional Theory: Topology in v- and n-Space
• Exchange instability of the two-dimensional electron gas in semiconductor quantum wells
• Static Electric Dipole Polarizabilities of Na Clusters

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