Elementary reaction steps for the catalytic cycle of thiophene desulfurization on Ni3Sy and Ni4Sy, clusters are investigated using density functional quantum chemical calculations. The Ni3S2 cluster is active while the Ni4Sy, cluster is relatively inactive for HDS catalysis. Adsorption and overall reaction energies are computed on complete geometry-optimized cluster-adsorbate systems. The nickel-sulfide cluster is found to significantly reorganize upon interaction with adsorbates. Sulfur readily rearranges between 3-fold and 2-fold binding sites. Hydrogen adsorbs molecularly and dissociates heterolytically over Ni3S2 to form both adsorbed sulfhydryl (SH) and hydryl (MH) species. The presence of coadsorbed hydrogen affects both the heat of adsorption and the coordination of thiophene. On the "bare" Ni3S2 cluster thiophene binds η4-coordinated, while in the presence of coadsorbed hydrogen thiophene prefers the η1 site. 2,5-Dihydrothiophene (DHT) adsorbs somewhat stronger than thiophene on the Ni3S2 cluster. In the preferred η3 configuration, the ethylene moiety of the DHT adsorbs at one nickel atom site while its sulfur adsorbs at the neighboring nickel atom site. For the HDS cycles initiated by η1 or η4 thiophene adsorption, the energy change associated with the carbon-sulfur bond scission step of adsorbed dihydrothiophene and that for the removal of sulfur via H2S are the most endothermic steps and are speculated to be rate limiting. Their comparable values indicate that the two steps compete. The cycle which is initiated by the removal of sulfur from Ni3S2 is energetically unfavorable.