The atomic-scale structure of the Co-promoted MoS₂ catalyst (CoMoS), used for hydrodesulfurization and as a potential replacement for platinum in the acidic hydrogen evolution reaction has been analyzed by modeling its sites using density functional theory and applying thermochemical corrections to account for different reaction conditions. The equilibrium structures of the edges, basal plane and corners have been found and used to obtain a picture of an ideal CoMoS nanoparticle under hydrodesulfurization and hydrogen evolution reaction conditions. Under hydrodesulfurization conditions small energy differences between structures having an additional or missing sulfur atom relative to the equilibrium structures have been observed for the edges and corners explaining their activity towards hydrodesulfurization at the atomic scale. The lack of these small energy differences at the basal plane explains why it is inert towards hydrodesulfurization. The adsorption free energy of hydrogen was calculated and used as a descriptor for qualifying each site in the context of hydrogen evolution, finding that the corner site should perform better than the edges.