We used a (3  3) surface unit cell and performed geometry optimizations using a 3  3  1 -centered k-point grid. For the various structures studied here we used the following notation: AgnL/Pt(111) denotes a structure with n pseudomorphic silver overlayers above the Pt(111) substrate, Pt1-xAgx/Pt(111) denotes a surface alloy in the topmost layer, and Pt1-xAgx/AgnL/Pt(111) denotes a structure with a surface alloy at the topmost overlayer and n pseudomorphic Ag layers underneath. Finally, we would like to add that because of the similarity in these calculations we expect relative changes by 0.01 eV to be significant, both for formation enthalpies and adsorption energies.