We calculate the conductance spectra of a Co atom adsorbed on Cu(111), considering the Co $3d$ orbitals within a correlated multiple configurations model interacting through the substrate band with the Co $4s$ orbital, which is treated in a mean-field like approximation. By symmetry, only the $d_{z^2}$ orbital couples with the $s$ orbital through the Cu bands, and the interference between both conduction channels introduces a zero-bias anomaly in the conductance spectra. We find that, while the Kondo resonance is mainly determined by the interaction of the Co $d$ orbitals with the bulk states of the Cu(111) surface, a proper description of the contribution given by the coupling with the localized surface states to the Anderson widths is crucial to describe the interference line shape. We find that the coupling of the Co $4s$ orbital with the Shockley surface states is responsible of two main features observed in the measured conductance spectra, the dip shape around the Fermi energy and the resonance structure at the surface state low band edge.
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