Self-consistent electronic structure of surfaces: Surface states and surface resonances on W(001)

Surface states (SS) and surface resonances (SR) on the W(001) surface have been determined from the first self-consistent energy-band study of this metal surface. The calculations were performed for a seven-layer film using our thin-film linearized augmented-plane-wave method which includes all relativistic corrections except the spin-orbit interaction. Self-consistency was found to be essential for obtaining an accurate value of the work function-4.5±0.2 eV, in excellent agreement with experiment. No evidence was found for surface core-level shifts as observed in photoemission from the (110) surface, indicating the possible importance of final-state effects. A complete description of all three experimentally observed resonance bands is given for the first time: SS and SR states are found to exist in different portions of the two-dimensional Brillouin zone; their location and symmetry are in very good agreement with structure observed in photoemission at 0.3, 0.8, and 4.2 eV below the Fermi energy, $E_F$. Particularly interesting is the close agreement of the never before obtained ${\overrightarrow{\mathrm{k}}}_{\parallel }=0\mathrm{}$ true SS (at - 0.3 eV) with experiment.