Effect of c(2x2)-CO overlayer on the phonons of Cu(001): a first   principles study
  We have examined the effect of a c(2x2) overlayer of CO on the surface phonons of the substrate, Cu(001), by applying the density functional perturbation theory with both the local (LDA) and the generalized-gradient (GGA) density approximations, through the Hedin-Lundqvist and the Perdew-Burke-Ernzerhof functionals, respectively. Our results (GGA) trace the Rayleigh wave softening detected by helium atom scattering (HAS) experiments to changes in the force constants between the substrate surface atoms brought about by CO chemisorption, resolving an ongoing debate on the subject. The calculated surface phonon dispersion curves document the changes in the polarization of some modes and show those of the modes originally along the $\bar{Y}$ direction of the clean surface Brillouin zone (SBZ) which are back-folded along the $\bar{\Delta}$ direction of the chemisorbed SBZ, to be particularly consequential. The vertical and shear horizontal section of $S_1$ in the SBZ of the clean surface, for example, is back-folded as a longitudinal-vertical mode, indicating thereby that $S_1$ $-$ predicted a long time back along $\bar{\Delta}$ for the clean surface $-$ may be indirectly assessed at $\bar{X}$ upon CO adsorption by standard planar scattering techniques. These findings further suggest that some of the energy losses detected by HAS along $\bar{\Delta}$, which were associated to multiphonon excitations of the adlayer frustrated translation mode, may actually correspond to the back-folded substrate surface modes. 
Marisol Alc\'antara Ortigoza, Rolf Heid, Klaus-Peter Bohnen, Talat S.   Rahman