Surface-phonon instabilities of W(001)

Tight-binding calculations of the surface-phonon dispersion curves for unreconstructed p(1×1) W(001) reveal a whole region of soft surface modes at the boundary of the surface Brillouin zone, caused by interactions with electronic surface states around ${\mathrm{E}}_{\mathrm{F}}$. An interplay of Fermi-surface nesting features and real-space d-orbital interactions leads to the maximum instability of the M${\mathrm{¯}}_5$ phonons, the basis of the observed c(2×2) reconstruction patterns. For small H coverages the electronic surface states are not removed but modified, probably in such a way as to produce incommensurate reconstructions.