Study of adiabatic connection in density functional theory with an accurate wavefunction for 2-electron atoms

Using an accurate semi-analytic wavefunction for two electron atoms, we construct the external potential v ext(~r) for varying strength of αVee(0 ≤ α ≤ 1) where α is the strength parameter and Vee is electron-electron 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 α. Furthermore, using total energies E of these systems as a function of α, we provide new perspective into a variety of hybrid functionals.