Application of Exact Analytic Total Energy Functional for Hooke’s Atom to He, Li+ and Be++: An Examination of the Universality of the Energy Functional in DFT

We employ the recently generated energy density functional for Hooke’s atom Ludeña EV et al (2004) Intern J Quantum Chem 99:297], to which we introduce a simplification for the kinetic energy term, to evaluate the total energy of the helium atom and of the two-electron ions Li⁺ and Be⁺⁺. Using accurate representations for the one-particle densities of these systems we show that the energy density functional for Hooke’s atom leads, in these cases, to energy values that are below the exact ones. We discuss the implication of this finding with respect to the existence of a universal energy functional in DFT.