The exact Fermi potential yielding the Hartree-Fock electron density from orbital-free density functional theory

The exact expression for the Fermi potential yielding the Hartree-Fock electron density within an orbital-free density functional formalism is derived. The Fermi potential, which is defined as that part of the potential that depends on the particles' nature, is in this context given as the sum of the Pauli potential and the exchange potential. The exact exchange potential for an orbital-free density functional formalism is shown to be the Slater potential.