Calculations for H2S adsorption on X/MoS2 catalysts modeled by XMo2S10H6 (X = Zn, Cu, Ni, Co) clusters were carried out using ab initio Hartree-Fock and pseudopotential approaches. Two vertical adsorption modes were studied. The analysis of the electronic properties show that the adsorption energy depends not only on the metal promoter (Zn, Cu, Ni, or Co) but also,on the electronic state of the Mo2S10H6 moiety, which determine the electron distribution of the X atom. Results obtained optimizing the adsorbate geometry on the metallic center indicate that a small charge transfer from the H2S molecule to the XMo2S10H6 cluster occurs and the interaction phenomenon corresponds to a physisorption.