Single-Electron Energies, Many-Electron Effects, and the Renormalized-Atom Scheme as Applied to Rare-Earth Metals

A systematic investigation of certain electronic properties of the rare-earth metals is reported. Calculations are performed within the framework of the renormalized-atom method in which Hartree-Fock free-atom solutions, with electronic configurations appropriate to the metal, are initially computed; the wave functions are then renormalized to the Wigner-Seitz sphere and used to construct l-dependent Hartree-Fock-Wigner-Seitz crystal potentials. The following results are obtained: (i) Recent spectral information together with the free-atom solutions permits us to estimate the change in neutral-atom correlation energy associated with changing the 4f electron count; contrary to expectation, we find that correlation effects are more significant in a configuration with one fewer 4f and one more 5d electron. (ii) Band extrema and Fermi levels are placed. (iii) The positions of occupied and unoccupied 4f levels are estimated in both a one-electron approach and a multielectron method taking screening and relaxation effects into account in a definite way. The one-electron approximation for the 4f levels fails badly in reproducing the results of recent photoemission experiments, while the multielectron calculations are in surprisingly good accord with experiment. The effective Coulomb-interaction energy between two 4f electrons at the same site, the familiar U, is reduced from the single-particle value of approximately 27 eV to about 7 eV with the inclusion of multielectron effects. (iv) Hartree-Fock values for the 4s- and 5s-shell exchange splittings are compared with soft-x-ray photoemission studies of the rare-earth fluorides and oxides; the calculated 4s splittings are roughly twice as large as experiment while, unexpectedly, the 5s results are in almost precise agreement.