The local-scaling version of density functional theory: A practical method for rigorous calculations of many-electron systems

Abstract

The local-scaling transformation version of density functional theory is reviewed in the present work. Emphasis is placed in showing how in the context of this theory, the N -and v -representability problems for the energy functionals are solved, and how the theory provides systematic ways for constructing energy density functionals which lead to upper bounds to the exact energies. The importance of the concept of “orbit” is indicated. Several theoretical methods leading to intra-orbit and inter-orbit optimization are discussed and results of the total energy of sample systems are given. Also, numerical results are reported on the use of local-scaling transformations for the direct solution of the Kohn-Sham equations. Finally, calculations are presented showing how this method can be extended in order to provide a rigorous treatment of excited states.