Structural optimization and d-band holes in Cu monolayers

The equilibrium lattice parameter and bandstructure of copper monolayers, both in the square (100) and hexagonal (111) symmetry, have been determined using self-consistent full-potential local density approximation (LDA) calculations. Two quite different procedures have been employed: FILMS, a linear-combination-of-gaussian-type-orbitals method, and a full-potential linearized augmented plane-wave (F-LAPW) method. The copper monolayer is bound with respect to the atomic LSDA ground state in the configuration d¹⁰s¹. Nearest-neighbor distances a_nn are determined as 4.25 a.u. in the square geometry and 4.42 a.u. in hexagonal geometry, the latter being favored in energy by 0.33 eV/atom. Both monolayers thus exhibit a nearest-neighbor distance substantially shorter than that found in bulk copper, a_nn=4.8238 a.u. Excellent agreement between the two methods is obtained for the bandstructure, with no indication of a d-band hole at the M point (corner) of the Brillouin zone, in contrast to some other recent self-consistent calculations. Combined use of the von Barth-Hedin LDA and scalar-relativistic corrections produces the smallest gap at the M point, 0.15 eV, at the Hedin-Lundqvist equilibrium geometry. This may be suggestive evidence for the origin of d-band holes when combined with further approximations in the representation of the one-electron orbitals and the charge density.