4fexcitation energies in rare-earth metals: Relativistic calculations

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We describe calculations of $4f$ electron binding energies for the rare-earth metals. Relativistic Hartree-Fock calculations for atomic configurations most closely approximating those of the metals are initially performed, and crystal potentials are constructed by means of the renormalized-atom method. Relativistic band calculations are iterated to crude self-consistency and total band energies obtained. Correlation effects identical to those in the free atoms are assumed. Within the assumption of a completely screened final state, in which the atomic site having the $4f$ hole is electrically neutral, $4f$ binding energies are estimated which are in at least as good agreement with experiment as previous, less complete calculations. The impact of the complete screening approximation is assessed by estimating the binding energies corresponding to atomic sites which are ionized in their final states; we find that the presence of an additional screening electron lowers the $4f$ binding energy by 4-6 eV.