  Using an accurate semi-analytic wavefunction for two electron atoms, we
construct the external potential for varying strength of electron-electron
(e-e) interaction. Using this potential we explicitly calculate the energy of
their positive ion and show that the ionization-potential of these systems
remains unchanged with respect to the strength parameter for e-e interaction.
Furthermore, using total energies of these systems as a function of strength
parameter, we provide a new perspective into a variety of hybrid functionals.
