Density-determined orthonormal orbital approach to atomic energy functionalsa)

Orthonormal orbitals systematically constructed from the electron density are employed to obtain various closed expressions for approximate atomic energy functionals. A three-dimensional generalization of a construction originally due to Harriman is proposed. Numerical assessments are made of several new density functionals by evaluating them using accurate Hartree–Fock densities and by solving the corresponing Euler equations for electron density. The molecular virial theorem is stated and proved in a form particularly suitable for density functional theory.