  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.
