The local structure of the sulfur atom of methanethiolate and ethanethiolate on the Cu(111) and Cu(100) surfaces was investigated from first principles employing the periodic supercell approach in the framework of density functional theory. On the 111 surface, we investigated the (root 3 x root 3) R30 degrees and (2 x 2) structures, whereas on the 100 surface, we investigated the p(2 x 2) and c(2 x 2) structures. The landscape of the potential energy surface on each metal surface presents distinctive features that explain the local adsorption structure of thiolates found experimentally. On the Cu(111) surface, the energy difference between the hollow and bridge sites is only 3 kcal/mol, and consequently, adsorption sites ranging from the hollow to the bridge site were observed for increasing surface coverages. On the Cu(100) surface, there is a large energy difference of 12 kcal/mol between the hollow and bridge sites, and therefore, only the 4-fold coordination was observed. The high stabilization of thiolates on the hollow site of Cu(100) may be the driving force for the pseudosquare reconstruction observed experimentally on Cu(111). Density of states analysis and density difference plots were employed to characterize the bonding on different surface sites. Upon interaction with the metal d bands, the pi* orbital of methanethiolate splits into several peaks. The two most prominent peaks are located on either edge of the metal d band. They correspond to bonding and antibonding S-Cu interactions. In the case of ethanethiolate, all the back-bonds are affected by the surface bonding, leading to alternating regions of depletion and accumulation of charge in the successive bonds.