Determination of the morphology and electronic properties of single-layer nanosize MoS2, particles is of considerable interest for a better understanding of the active phase of hydrotreating catalysts. We propose an original approach, based on density functional calculations applied to various types Of MoS2 clusters containing up to 200 atoms, to evaluate accurately the surface energies of the Mo-edge and S-edge terminated surfaces. The results are expressed as a function of the chemical potential of sulfur, which is in turn controlled by the temperature and the ratio of partial pressures of H2S and H-2. Gibbs-Curie-Wulff equilibrium morphologies reveal that a high chemical potential of sulfur leads to triangular-shaped particles terminated by the Mo-edge surface, giving an interpretation of the observations made recently by scanning tunneling microscopy (STM). Simulations of the STM images for the most stable clusters reveal a qualitatively good agreement with experiments. Moreover, our approach predicts that varying the potential of sulfur modifies the local Mo-edge structure and the shape of the nanoparticles. Finally, the thermodynamic diagram for a MoS2 particle with a realistic size shows that the creation of one sulfur vacancy at the corner and on the edge is possible under HDS working conditions.