Oil soluble catalysts are used in a process to hydrodesulfurize petroleum feedstock having a high concentration of sulfur-containing compounds and convert the feedstock to a higher value product. The catalyst complex includes at least one attractor species and at least one catalytic metal that are bonded to a plurality of organic ligands that make the catalyst complex oil-soluble. The attractor species selectively attracts the catalyst to sulfur sites in sulfur-containing compounds in the feedstock where the catalytic metal can catalyze the removal of sulfur. Because the attractor species selectively attracts the catalysts to sulfur sites, non-productive, hydrogen consuming side reactions are reduced and greater rates of hydrodesulfurization are achieved while consuming less hydrogen per unit sulfur removed.