It is shown that ab initio MO approaches are suitable to simulate the relatively large hexagonal MoS2 slab corresponding to the average initial size (15-20 Angstrom) of MoS2 on alumina-supported catalysts used in hydrodesulfurization (HDS) and hydrogenation (HYD) of petroleum fractions. By using a general ab initio MO program, GAMESS, the structure optimization of the Mo27S54 slab is possible at the UHF/MINI/ECP=SBK level of theory, providing helpful information on the structural and electronic properties of the slab. The improvement, compared to other theoretical calculations based on simplified structural models, is that the different bonding and electronic properties of the Mo and S atoms in basal plane and on different edges and corners of the slab can clearly be distinguished. The structure of the slab is relaxed toward the edges. The 2-fold coordinatively unsaturated sites (CUS) on corners have-both electron-donating and -accepting properties, making them potentially active for HDS (and HYD) reactions. The 2-fold CUS's on the edges ("reduced edges") seem to permit only the HYD reaction or CO hydrogenation. The removal of the basal plane S atoms requires activated atomic hydrogen species. The unreduced ((1) over bar 010) edges do not seem to be potentially active catalytically. This deepens the understanding of the catalytic nature of the MoS2 structure for several reactions, especially HDS and HYD (hydrotreating reactions) and CO hydrogenation.