Exact exchange in the Levy-Perdew-Sahni density-functional theory

We show that the Fermi-Amaldi functional constitutes the exact exchange contribution within the orbital-free Levy-Perdew-Sahni (LPS) density-functional scheme, which is based on a Schrödinger-like equation for the square root of the electron density. This result follows from interpreting the LPS scheme in terms of an auxiliary reference system of non-interacting particles occupying a single orbital. Unlike Kohn-Sham exact exchange, the exact LPS exchange is a pure density functional fully compatible with the orbital-free formalism. Self-consistent calculations for atoms and molecules show improved accuracy for light atoms relative to standard Kohn-Sham exchange approximations. These findings provide a basis for developing improved approximations to the remaining terms of the LPS total-energy functional.