Density-functional theory (DFT), morphologic, and quantum theory of atoms in molecules (QTAIM) studies of bilayer models of nonhydrogenated MoS 2 , CoMoS, and NiMoS phases have been performed. The QTAIM calculations have shown that for inactive catalysts, such as MoS 2 and Ni 3 S 2 , the basins of the outermost atoms of the particles on the exposed surfaces are almost covered by S atomic basins, giving reduced access to the Ni and Mo atoms. In contrast, for very active catalysts, such as NiMoS and RuS 2 , there are substantial open zones on the outermost S basin, giving considerable access to the metal atoms. Analysis of the electrostatic potential mapping onto the outermost atoms basins reveals soft Lewis acid zones for Ni 3 S 2 and MoS 2 and strong Lewis acid zones for NiMoS and RuS 2 . QTAIM and electrostatic potential calculations on hydrated MoS 2based monolayers have shown that the adsorption strengths (binding energies) of sulfur (H 2 S, thiophene, dibenzothiophene) and nitrogen (NH 3 and acridine) compounds on the exposed metallic sites are related to the Lewis basic−acid interaction of the minima at the molecule and the maxima at the metallic sites, whereas on the so-called BRIM sites, it is the result of the combination of Lewis and Brønsted acidity. The studied nitrogen and sulfur molecules exhibit just one and two lone pairs on the N and S atoms, respectively. In general, N minima ≫ S minima, showing the origin of the larger adsorption of the organonitrogen molecules, except on those metallic sites where both sulfur lone pairs adsorb at two neighboring metal maxima. The present results corroborate and explain the origin of the reported DFT findings.