Intermetallic compounds made of alkali metals and gold have intriguing electronic and structural properties that have not been extensively explored. We perform a systematic study of the phase diagram of one binary system belonging to this family, namely Na x Au 1−x , using the ab initio minima hopping structural prediction method. We discover that the most stable composition is NaAu 2 , in agreement with available experimental data. We also confirm the crystal structures of NaAu 2 and Na 2 Au, that were fully characterized in experiments, and identify a candidate ground-state structure for the experimental stoichiometry NaAu. Moreover, we obtain three other stoichiometries, namely