Surface shift of the occupied and unoccupied 4f levels of the rare-earth metals

The surface energy shifts of the occupied and unoccupied 4f levels for the lanthanide metals have been calculated from first principles by means of a Green’s-function technique within the tight-binding linear muffin-tin orbitals method. We use the concept of complete screening to identify the occupied and unoccupied 4f energy level shifts as the surface segregation energy of a 4${\mathit{f}}^{\mathit{n}\mathrm{-}1}$ and 4${\mathit{f}}^{\mathit{n}+1\mathrm{}}$ impurity atom, respectively, in a 4${\mathit{f}}^{\mathit{n}}$ host metal. The calculations include both initial- and final-state effects and give values that are considerably lower than those measured on polycrystalline samples as well as those found in previous initial-state model calculations. The present theory agrees well with very recent high-resolution, single-crystal film measurements for Gd, Tb, Dy, Ho, Er, Tm, and Lu. We furthermore utilize the unique possibility offered by the lanthanide metals to clarify the roles played by the initial and the different final states of the core-excitation process, permitted by the fact that the so-called initial-state effect is identical upon 4f removal and 4f addition. Surface energy and work function calculations are also reported.