The interactions of Na+ and Cu+ cations with a Cu(111) surface in the presence and absence of water molecules were investigated using cluster models and ab initio methods. Adsorption in aqueous solution was modeled with one to five water molecules around the adsorbing cation. The Cu surface was described with Cu-10 and Cu-18 cluster models and the computational method was MP2/RECP/6-31+G*. The effect of the basis set superposition error (BSSE) was taken into account with counterpoise (CP) correction, and the accuracy of HF-level results was examined. The interactions between Na+ and the Cu surface were found to be primarily electrostatic, and the energy differences among the different adsorption sites were small. The largest CP-corrected MP2 adsorption energy for the Cu-18 Cluster was -188 kJ/mol. When water molecules were added around it, Na+ receded from the Cu surface and finally was surrounded totally by the water molecules. The interactions between Cu+ and the Cu surface were dominated by orbital interactions, and Cu+ preferred to adsorb on sites where it could bind to more than one surface atom. The largest CP-corrected MP2 adsorption energy for the Cu-18 cluster was -447 kJ/mol. Adding water molecules around it did not cause Cu+ to draw away from the surface, but instead the water molecules began to form hydrogen bonds with one another. The magnitude of BSSE was substantial in most cases. CP corrections did not, however, have a significant impact on the relative trends among the interaction energies.