## 5 Computational Results  
### Stability of Desulfurization Intermediates  
The simulations first evaluated the stability of CO\({}_{2}\)*, COS*, and CO* on pristine CuO(111) where * represents a molecule adsorbed on the surface. The Cu\({}_{\text{sat}}\) and Cu\({}_{\text{cus}}\) top sites on CuO(111) were compared to investigate the favorable adsorption site for each adsorbate. DFT predicts that both COS* and CO\({}_{2}\)* do not adsorb on the Cu\({}_{\text{sat}}\) site but are instead pushed and converged toward the Cu\({}_{\text{cus}}\) site. The CO* on Cu\({}_{\text{cus}}\) was predicted to be ~24 kJ/mol more stable than CO* on Cu\({}_{\text{sat}}\). Therefore, all the proposed results are based on the molecules adsorbing on Cu\({}_{\text{cus}}\) site. Figure 11a,e,i shows the relaxed adsorbates of CO\({}_{2}\)*, COS*, and CO* on the pristine CuO(111). Each adsorption energy could be found immediately below at each relaxed image in Figure 11. The DFT results show that the desulfurization intermediates of CO\({}_{2}\)*, COS*, and CO* bind weakly to the CuO(111) surface; the predicted adsorption energies are <35 kJ/mol. In particular, the low stability of COS* would prefer to desorb from the surface and rarely lead to activating the initial desulfurization step for CO-S bond dissociation if the reaction has a relatively large energy barrier. In comparison with the experimental data, the predicted weak binding of COS does not correspond to the high desulfurization performance of CuO. This study focused on other surface environments, including a defect surface and a sulfurized surface potentially generated during the desulfurization reactions to resolve the inconsistency. For the defect surface, the defect surface was modeled by introducing a surface oxygen vacancy and evaluating the stabilities of the adsorbed CO\({}_{2}\)*, COS*, and CO* on the CuO(111) surface. Figure 11b,f,j presents the relaxed adsorbate images with oxygen vacancies; the vacancy site is illustrated by a white dashed circle. The CO\({}_{2}\)* (9.0 kJ/mol) still binds weakly to an oxygen vacancy on CuO(111). In contrast to CO\({}_{2}\)*, an adjacent oxygen vacancy stabilizes the adsorbed CO*(99.7 kJ/mol) and COS*(29.3 kJ/mol). The oxygen vacancy defect provides high stability with CO*, and the results suggest that the presence of oxygen vacancies on the surface provides active sites for the CO molecule. The adjacent oxygen vacancy affects the electronic structures of the adjacent Cu\({}_{\text{cus}}\) site significantly. It would trigger stronger back donation from Cu\({}_{\text{cus}}\) to the adsorbed CO* molecule, thereby providing the  
Figure 10: CO concentration vs. time by desulfurization tests over pellet type of 15 wt % CuO-based desulfurization sorbents: CuO/\(\gamma\)-Al\({}_{2}\)O\({}_{3}\) and CuO/macro-porous Al\({}_{2}\)O\({}_{3}\). high stability of adsorbed CO* [37]. Such effects of oxygen vacancies have been reported in other reactions on CuO surfaces and other transition metal oxides [37; 38; 39]. Figure 11: Top and side views of adsorbed CO\({}_{2}\), COS, and CO on CuO(111) surface with and without an oxygen vacancy and a surface sulfur (yellow). The DFT predicted adsorption energy is presented below each figure. In terms of the sulfurized surface modeled by replacing surface O atom with S atom, the relaxed adsorbate images are provided in Figure 11c,g,k. A black dashed circle indicates the S surface insulted sites. The surface S atom does not significantly impact the stability of adsorbed CO2* (1.6 kJ/mol) and CO* (30.9 kJ/mol). On the other hand, it stabilizes the COS* (33.3 kJ/mol) on the surface. Finally, adsorption behaviors of the adsorbates on the surface with both a surface oxygen vacancy and a surface sulfur atom were studied. Figure 11d,h,l shows the relaxed adsorbate images. The stability of CO2*(30.8 kJ/mol) was enhanced by -30 kJ/mol when both surface defect and S surface atom were present, but COS* (7.81 kJ/mol) still binds weakly to the surface.