Ab initio calculations of the dispersion of surface phonons of a c(2 × 2) CO overlayer on Ag(001).

We examine the phonon dispersion of c(2 × 2)-CO on Ag(001) by applying density functional perturbation theory with the generalized-gradient approximation. Our calculations indicate that the c(2 × 2)-CO overlayer on Ag(001) is dynamically stable. We find that the bond length of CO is expanded and its stretch mode (ν(1)) softened by ∼ 9 meV upon adsorption on Ag(001), in excellent agreement with experiments. We show that ν(1) at [Formula in text] alone cannot gauge the metal-CO interaction since it is not entirely determined by the C-O intramolecular force constant. Further softening of ν(1) on Ag(001) is obtained outside [Formula in text], indicative of CO-CO interactions even at a distance of ∼ 4 Å. The frequency of the Ag-CO stretch mode (ν(2)) is ∼ 30 meV and it is nearly dispersionless, implying that the perturbation corresponding to this mode is short-ranged. The frustrated rotation mode of CO (ν(3)) overlaps with the bulk band and mixes with substrate modes inside the SBZ, suggesting this as one of the key features for the enhanced diffusivity of CO on Ag surfaces over that on Cu surfaces. The frustrated translation mode of CO (ν(4)) is everywhere below ∼ 2.8 meV and therefore mixes with substrate modes in the region of the SBZ around [Formula in text]. Depending on the q vector, vertical and in-plane surface modes may soften or stiffen with respect to their counterpart on clean Ag(001). Although the response of most Ag(001) modes to CO adsorption is similar to that of corresponding Cu(001) modes, there are some contrasting features between the dynamics of the two surfaces concerning the changes in the surface force constants and mixing of S(6) with ν(3) on Ag(001).