Hartree-Fock method posed as a density-functional theory: Application to the Be atom

The Hartree-Fock ground-state energy and electron density are first shown to be derivable from a local one-body effective potential v(r). As a nontrivial example, attention is then focused on the Be atom and isoelectronic atomic ions, the wave functions being written in terms of the density amplitude and phase. Some related general comments on the two-level one-dimensional system are included; kinetic-energy density is shown to be a local functional of electron density generated by the harmonic-oscillator potential.