Study of adiabatic connection in density functional theory with an accurate wavefunction for two‐electron spherical systems

An accurate semianalytic wavefunction is proposed for the Hookium and two‐electron atoms for varying strength of where is the strength parameter and is coulomb interaction between two electrons. The wavefunction leads to energies that are as accurate as those from the Coupled cluster singles and doubles (CCSD) calculations. Using this wavefunction, we construct the external potential such that the density of the system remains unchanged as is varied. The work thus gives a unified picture of adiabatic connection for these systems based on an easy to use wavefunction and complements the past investigations done in this direction. Using the potential obtained, we explicitly calculate the energy of the corresponding positive ions and show that the chemical potential—calculated as the difference between the energies of the two‐electron system and its positive ion—is equal to the experimental ionization energy and remains unchanged as is varied. Furthermore, using total energies of these systems as a function of , we provide a new perspective into a variety of hybrid functionals.