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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 hartree within four variants of the Kohn-Sham local-density approximation ͑LDA͒. The approximations considered are the local-density approximation, the local-spindensity 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 Zу40. 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.

We calculate the dielectric function e&(co) of silicon and germanium for frequencies below the direct band gap at the experimental lattice constant as well as the pressure dependence of the static dielectric constant e&(P). Our theory is an extension of the local-density approximation (LDA). We include self-energy effects by adding an operator to the usual LDA Hamiltonian; i.e. , H"=Hk "+AkP, k. This form leads to a Ward-identity replacement p~(c"k -Hk ") '(c, k -Hk)p. Our theory is in agreement with experiment for e&(cu) at the level of a few percent. For e&(P), we are in agreement with experiments for silicon and some of the conAicting experiments for germanium. A prediction is made for the pressure dependence of the dielectric function of silicon beyond the linear regime.

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