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

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