We have studied the adsorption of 4-mercaptopyridine (Mpy) on Au(111) using periodic density functional theory calculations. Isolated Mpy molecules adsorb preferentially at near-bridge sites in a tilted configuration. The interaction with water influences the adsorption of Mpy only weakly whereas the binding of ions to Mpy can lead to substantial structural changes in the Mpy adsorption geometry. At higher coverages, the molecules become more upright in order to allow for a denser packing in the self-assembled monolayers (SAMs). Simulated STM images of the 7 x mean square root of 3 and 5 x mean square root of 3 structures compare favorably with experimental results. Using an ab initio thermodynamics approach, we determined the most stable molecular structure as a function of the chemical potential of mercaptopyridine. The stability of the 7 x mean square root of 3 structure is confirmed, but the experimentally observed 5 x mean square root of 13 structure does not appear to be a thermodynamically stable structure. Several possible reasons for the discrepancy between theory and experiment are discussed.