The electronic contribution to the energy of surface phonons was decomposed into a wave-vector-dependent term which depends only on the response function in the surface region, plus a wavevector-independent term giving the energy change due to a uniform surface displacement. The wavevector-dependent term was evaluated for the unreconstructed Mo (001) surface, using the matching Green function method to calculate the electronic response function, and the rigid muffin-tin approximation to determine the electron-phonon matrix elements. It was found that the large density of the surface states at the Fermi energy, and the states bonding the surface atoms to the bulk, favour lateral displacements, through the wave-vector of the corresponding surface phonon anomaly disagrees with the experimentally observed reconstruction. Periodic vertical displacements of the surface atoms were energetically unfavourable.

Electronic Response to Surface Atomic Displacements on Mo (001). J.E.Inglesfield, A.Tagliacozzo: Journal of Physics C, 1984, 17[29], 5227-36