From electron densities to Kohn-Sham kinetic energies, orbital energies, exchange-correlation potentials, and exchange-correlation energies

By developing our previous method Phys. Rev. A 46, 2337 (1992); J. Chem. Phys. 98, 543 (1993), we show how to calculate Kohn-Sham kinetic energies, orbitals, orbital energies, and exchange-correlation potentials, starting from accurate ground-state electron densities. In addition, given correct total energies, we also show how to obtain exchange-correlation energies. The scheme used is based on the Levy constrained-search method for determining the Kohn-Sham kinetic energy. In our preferred implementation, the total electron-electron repulsion is written as a Fermi-Amaldi term plus the rest, thereby assuring the correct long-range behavior of the exchange-correlation potential. Results are given for He, Be, Ne, and Ar. It is demonstrated that the exact exchange-correlation functional cannot be local.