Orbital-free density-functional theory for metal slabs

Orbital-Free Density-Functional Theory (OF-DFT) is known to represent a promising alternative to the standard Kohn-Sham (KS) DFT, as it relies on the electron density alone, without the need to calculate all KS single-particle orbitals and energies. Here, we investigate the behavior of the main ingredients of this theory, which are the non-interacting kinetic-energy density (KED) and the Pauli potential, for metal slabs. We derive explicit density functionals for these quantities in the quantum limit where all electrons are in the same slab discrete level of energy, and we present numerical calculations beyond this quantum limit for slabs of various widths. We have found the first explicit KED functional for a realistic many-particle fermionic system, which we prove to be generally valid with no assumption about the KS potential. We also discuss the total non-interacting kinetic energy and the corresponding enhancement factor, which represent basic quantities for the practical implementation of OF-DFT.