We obtain the lowest energy 2D arrangements of atoms adsorbed on a hexagonal lattice, assuming rational coverage and a repulsive dipolar adsorbate-adsorbate interaction. To this end we exhaustively explore the ordered arrangements compatible with the coverage, including those that have multiatomic unit cells. For some coverages (theta=1/3, 1/4 and 1/7) we find a well defined ground state, and for others a nearly infinite degeneracy related to the possibility of creating dense arrays of linear defects with a negligible energy cost. We compare our results with some experimental determinations of surface structures in alkali overlayers on fcc (111) and hcp (0001) metal faces. Except for those systems that form islands, we have found agreement between our predicted ground states and experiment. Furthermore, no ordered structures with the coverages of our near degenerate states have been observed
