## 5 Computational Results
### Mechanism of the Initial Desulfurization Kinetics  
Desulfurization kinetics must include two surface reactions, such as CO-S bond-breaking from COS and subsequent CO2 formation. The two reactions proceed sequentially, and the reaction steps are described as follows:  
\[ \begin{array}{ll}\text{COS}(\text{g})+*\ \rightarrow\text{COS}^{*}&(step\ 1)\\ \text{COS}^{*}+10\text{vac}\ site\rightarrow\text{CO}^{*}+\text{S}^{*}&(step 2)\\ \text{CO}^{*}+\text{S}^{*}+\text{O}_{\text{surf}}\rightarrow\text{CO}_{2}{}^{* }+\text{S}^{*}&(step\ 3)\end{array} \]  
Initially, gas-phase COS adsorbs on an active site *, and the COS* undergoes CO-S bond dissociation into CO* and S*, which occupies a surface oxygen vacancy. The dissociated CO* then grabs a surface oxygen atom to form CO2 on the surface. The described three steps were evaluated on three different CuO(111) surface local environments (1. pristine surface, 2. defected surface with one surface oxygen vacancy, and 3. surface with both surface sulfur and surface oxygen vacancies). All surface environments initially included an additional oxygen vacancy on the surface to provide a site for the dissociated S, which is a 1 Ovac site in the reaction step 2. The pristine CuO surface, for example, has one oxygen vacancy and a different terminology from the pristine CuO surface in the earlier section. Figure 12 provides DFT energy diagrams of COS desulfurization into CO2 and S in the three surface environments. The corresponding relaxed configuration for each step is provided in the Supplemental Information. The DFT calculation predicts that C-S bond dissociation from CO-S requires a high energy barrier of 227.0 kJ/mol with an exothermicity of 55.6 kJ/mol on the pristine CuO(111). Although this initial step is exothermic, the large kinetic barrier would hinder CO-S bond cleavage on the pristine surface. The next step, step 3, was predicted to be endothermic with a high energy barrier of 264.9 kJ/mol to form CO2. Overall, the desulfurization mechanism requires large energies to be activated on the pristine surface, which does not agree with the experimentally observed high performance of CuO at low temperatures. On the defect surface, the COS dissociation step needs to overcome a high-energy barrier of 238.4 kJ/mol with even higher exothermicity (167.7 kJ/mol). DFT predicts that the high reaction barrier (227.0 kJ/mol) for step 3 to form CO2, which is similar to the pristine CuO(111) surface, does provide low endothermicity (34.9 kJ/mol). [PERSON] et al. also explored the desulfurization mechanisms on CuO(111) surface with surface defects [38]. The reported COS* adsorption energy was 136.23 kJ/mol on an oxygen vacancy introduced on a CuO(111) surface. The large adsorption energy is approximately five times larger than the reported COS* adsorption energy in this study. The large difference stems from the formation of COS-O*, which was defined as COS* in the earlier work by [PERSON] et al. Such formation requires additional energy to remove the C-Obond to allow COS* to leave from the COS-O*. Lastly, both sulfur and oxygen vacancies were introduced on the surface to investigate the cooperative effects of surface sulfur and surface oxygen on the desulfurization mechanism. The DFT simulation predicts that step1 would be a barrierless reaction with the reverse barrier of 107.1 kJ/mol when introducing both a sulfur surface atom and an oxygen vacancy. Hence, COS* readily undergoes CO-S bond breaking as soon as COS(g) adsorbs on the surface due to the negligible barrier. In contrast to the effects on CO-S bond breaking, the presence of surface sulfur and oxygen vacancy does not have significant impacts on CO\({}_{2}\) formation because DFT predicts still a high reaction barrier (231.4 kJ/mol) with 214.1 kJ/mol endothermicity. Although the second step requires a large kinetic barrier in the presence of oxygen vacancy and a surface sulfur atom, such a surface environment potentially accelerates the desulfurization rate.