New Approximation for Screened Exchange and the Dielectric Constant of Metals

Using self-consistent-field techniques, we derive the dynamic dielectric constants appropriate to electrons and to test charges which differ with the inclusion of screened Hartree-Fock exchange. For large wave vector (in the static limit), the exchange contributions exceed the Coulomb contributions, and the electronic dielectric constant becomes less than unity. We also derive a screened exchange potential linearly dependent on the charge density, which seems preferable to the Slater ρ1/3(r) approximation for energy-band calculations.