The structures of MoS2 crystallites present in industrial HDS/HYD catalysts in the reaction conditions are mimicked by using tiny single layer clusters (slabs) consisting of seven Mo atoms. These are the smallest clusters possessing the main structural features of the MoS2 slabs. The structures of the various clusters are optimized and examined by using ab initio MO approaches, in order to obtain the total energies at their stationary points. On the basis of the information obtained from the ab initio calculations, the different S atoms in the MoS2 structures are identified. As the real industrial catalysts work in a reducing atmosphere, the effect of removing S atoms from edges is discussed, providing information for a better understanding of the activation mechanisms of HDS/HYD catalysts. The cluster terminated by S atoms in all directions (i.e. with 24 S atoms) gains stability when containing two additional electrons. The charged and not charged clusters can readily form -SH (sulfhydryl) groups from terminal S atoms. Two-fold unsaturated coordination of Mo (2-CUS) is readily obtained by removal of these -SH groups. 3-CUS and 4-CUS Mo are formed by breaking one S-Mo bond of bridging S atoms or further removing all bridged S atoms. This needs a form of hydrogen more reactive than molecular hydrogen, e.g. a hydrogen atom, together with hydrogen molecules.