Explicit density functionals for the energy by means of padé approximants to local-scaling transformations

We review in the present work the explicit construction of energy density functionals within the local-scaling transformation version of density functional theory, LS-DFT, as accomplished through the use of Padé approximants. The various stages in the development of density functional theory are briefly surveyed. A general way for constructing explicit Hartree-Fock energy density functionals for atoms is advanced and specific functionals for selected first-row atoms are displayed. It is found that these functionals contain universal factors whose leading terms are π ^5/3 for the kinetic energy and π ^4/3 for the exchange energy. But, in addition, they contain specific modulating factors that depend on the number of particles N, on the angular momentum and on the spin symmetry of the particular atomic ground states under consideration. Numerical examples attesting to the accuracy of the proposed functionals are given. Also, some problems pertaining to the extension of these ideas to the electronic correlation problem in atoms are discussed and explicit density functionals are obtained for the dominant electron correlation term.