First-principles calculation of the geometric and electronic structure of the Be(0001) surface

Linearized-augmented-plane-wave calculations for a nine-layer Be(0001) slab agree with the unusual experimental finding of a substantial outer-layer expansion relative to the truncated bulk lattice. They imply that the separation between the outer two layers should be 3.9% larger than in the bulk, while the second- to third-layer separation should be 2.2% larger. The surface expansion is accompanied by demotion of ${\mathit{p}}_{\mathrm{\sigma }}$ to s electrons on outer-layer Be’s. The surface Be’s loss of three neighbors makes the energy cost of s- to ${\mathit{p}}_{\mathrm{\sigma }}$-electron promotion, which is necessary for the formation of strong bonds to the next layer down, less profitable than in the bulk.