The total energies of atoms and with atomic number Z from 1 to 92 and singly charged cations with Z from 2 to 92 have been calculated to an accuracy of 1 μhartree within four variants of the Kohn-Sham local-density approximation (LDA). The approximations considered are the local-density approximation, the local-spin-density approximation, the relativistic local-density approximation, and the scalar-relativistic local-density approximation. The total energies for the LDA are found to be in 0.1% agreement with a large atomic number expansion from many-body theory for Z⩾40. A comparison to experiment is made for the ionization energies and spin-orbit splittings; also the total energies and eigenvalues of the various theories are compared among themselves.

DOI:https://doi.org/10.1103/PhysRevA.55.191