A periodic density functional theory study of thiophenic derivative cracking catalyzed by proton- or lithium-exchanged mordenite has been performed. The same qualitative trends in activation energies as those described employing the cluster approach method have been obtained. However, the zeolite framework appears not to stabilize the transition state complexes. This is explained by the zwitterionic nature of the thiophenic derivatives cracking transition state complexes. The zeolite framework has more subtle effect on reactivity, as shown by the alteration of the ionic nature of the transition state complex in the case of better fit with the zeolite cavity. Notwithstanding, thiophenic derivative cracking catalyzed by zeolites remains difficult. General comments concerning the use of zeolite catalysts in hydrodesulfurization are made. Predictions on zeolite-based catalysts more suitable to achieve hydrodesulfurization are described.