The Levy-Perdew-Sahni equation for the density: accurate effective potential and self-consistent solution for two-electron atomic systems

Levy-Perdew-Sahni (LPS) provided a proof of the connection between the density and ionization potential of a many-electron system using the equation for the density directly. This equation employs an effective potential which is derived by LPS from the many-electron wavefunction of the system. In this paper, we calculate this potential explicitly by employing an accurate wavefunction for two-electron systems. With this wavefunction connection the LPS equation is then solved self- consistently employing this potential and shown to lead to accurate densities and chemical potentials for these systems.