*3.3. H<sup>2</sup> Dissociation and H- Formation*

Recent studies have shown that ceria has the capability of catalyzing partial hydrogenation of alkynes and CO<sup>2</sup> reduction reactions [2,4,10,11]. The formation of hydride through heterolytic dissociation of H<sup>2</sup> on the CeO<sup>2</sup> surface was found to be one of the vital processes in these reactions [7–12,38]. Then, we systematically studied the dissociative adsorption of H<sup>2</sup> on both the pristine and Cu-doped CeO2(111) surfaces.

The calculated energy profiles of H<sup>2</sup> adsorption and dissociation on the CeO2(111) and Cu/CeO2(111) surfaces are shown in Figure 3. As one can see, the adsorption energy of H<sup>2</sup> on the Cu/CeO2(111) surface (0.30 eV) is 0.26 eV higher than that on the pristine CeO2(111) surface (0.04 eV), indicating that the H<sup>2</sup> molecule has a stronger interaction with the Cu/CeO2(111) surface. We further considered the homolytic and heterolytic

pathways of H<sup>2</sup> dissociation on the CeO2(111) and Cu/CeO2(111) surfaces. The homolytic dissociation produces two surface hydroxyls, while the heterolytic dissociation produces a surface hydroxyl and a hydride species [27,38]. According to our calculations, the homolytic dissociation of H<sup>2</sup> on the CeO2(111) (gray dotted line) and Cu/CeO2(111) surfaces (black dotted line) needs to overcome the energy barriers of 1.34 and 1.08 eV, respectively (see Figures 3, S4 and S5). In each transition state of the homolytic H<sup>2</sup> dissociation, one OH species and one hydrogen radical are formed on the surface firstly (Figures S4b and S5b), giving rise to rather high barrier for this process. The as-formed H radical will then migrate to the neighboring O site to form the second OH species. Moreover, on the CeO2(111) and Cu/CeO2(111) surfaces, the homolytic H<sup>2</sup> dissociation process was calculated to be exothermic by 2.41 and 3.25 eV, respectively.

**Figure 3.** Calculated energy profiles of homolytic (Homo) and heterolytic (Heter) H<sup>2</sup> dissociation on the CeO<sup>2</sup> (111) and Cu/CeO<sup>2</sup> (111) surfaces. "\*" is defined as the surface free site, and this notation is used throughout the paper.

Interestingly, our calculated results (Figures 3, S4 and S5) showed that the energy barrier for the heterolytic dissociation of H<sup>2</sup> at the Ce-O site on the Cu/CeO2(111) (red dotted line, 0.56 eV) is lower than that on the pristine CeO2(111) (pink dotted line, 0.92 eV) and they are both significantly lower than those of the homolytic dissociation. Following the transition state (Figures S4c and S5c), one OH and one hydride species are formed, and this process is endothermic by 0.77 eV at CeO2(111) and exothermic by 1 eV at Cu/CeO2(111). Notably, we found that the obvious stability of H<sup>−</sup> species on the Cu/CeO2(111) surface (Figure S5d) can be attributed to the low coordination number of Ce at the oxygen vacancy. These results clearly indicate that the Cu doping promotes the formation of oxygen vacancies, which is critical for the stabilization of hydride species. We also calculated the heterolytic dissociation of H<sup>2</sup> at the Cu-O site on the Cu/CeO2(111) surface to produce H<sup>+</sup> and Cu-H species (blue dotted line). This process needs to overcome a barrier of 0.60 eV and is exothermic by 1.20 eV.

Furthermore, we also considered the migration of hydride species to the neighboring O site to form another hydroxyl species on the two surfaces. The calculated energy barriers of the migration process on the CeO2(111) and Cu/CeO2(111) surfaces are 0.30 and 1.02 eV, respectively. The high energy barrier of the migration on the Cu/CeO2(111) surface indicates that the hydride species can be kinetically stable on this surface. In addition, we calculated the migration of the hydrogen species (Cu-H) to the neighboring O site to form

another hydroxyl species on the Cu/CeO2(111) surface, and it needs to overcome an energy barrier of 1.46 eV and is exothermic by 1.90 eV (Figure 3).

It should be noted that the CeO<sup>2</sup> surface accepts two extra electrons after the hydride migration. For the Cu/CeO2(111), we found that the two electrons prefer to be localized in the 4*f* orbitals of two Ce atoms rather than in one Ce 4*f* orbital and one Cu 3*d* orbital as the former case is 0.15 eV more stable than the latter one (Figure S5h,j). This again indicates the significant role of Ce 4*f* as the "electron reservoir" [56].

To gain deeper insights into the effect of Cu doping on the formation of hydride species on the Cu/CeO2(111) surface, we calculated the partial density of states of the Ce3+ species on the two CeO<sup>2</sup> surfaces with one H being adsorbed at the O site. Note that this H can be regarded as the "co-adsorbate" of the other H in dissociative H<sup>2</sup> adsorption (Figure 4). The calculated results show that the occupied 4*f* state of the Cu/CeO2(111) with one hydroxyl lies in the higher energy than that of the CeO2(111) with one hydroxyl. So, one may expect that the Ce3+ species on the Cu/CeO2(111) with one hydroxyl can donate this electron to the second H to form a hydride species more readily than the Ce3+ species on the CeO2(111) with one hydroxyl.

**Figure 4.** Calculated partial density of states (PDOS) of the Ce3+ on the (**a**) CeO<sup>2</sup> (111) and (**b**) Cu/CeO<sup>2</sup> (111) surfaces with one H being adsorbed on O. The Fermi energy level (E*<sup>f</sup>* ) is labeled with a red dashed line. All DOS are aligned with respect to the O 2*s* orbital of a fixed bottom O atom of the surface slabs.

Previous studies reported that surface oxygen vacancies can stabilize hydride species [33,37,38]. We then calculated the formation of an extra surface oxygen vacancy on the CeO2(111) and Cu/CeO2(111) (Figure 5). It was found that the Cu/CeO2(111) gives a much smaller surface oxygen vacancy formation energy (0.59 eV) than the CeO2(111) surface (2.41 eV), suggesting that the Cu dopant can further promote the formation of the surface oxygen vacancy. The newly formed surface oxygen vacancy can reduce two Ce4+ into Ce3+ cations. This is mainly due to the fact that the calculated crystal reduction potential (Vr) [57] for Cu2+ <sup>→</sup> Cu<sup>+</sup> (−1.43 V) is higher than that for Ce4+ <sup>→</sup> Ce3+ (−1.77 V), and the coordination number of Ce around the new O<sup>V</sup> site is also reduced (Figure 5b). We also found that it is more favorable to form hydride species on such reduced Cu/CeO2(111) surface (i.e., Cu/CeO2(111)-OV) than the Cu/CeO2(111) surface (Figure 5c,d). We calculated the dissociation of H<sup>2</sup> on the Cu/CeO2(111)-O<sup>V</sup> surface (Figures 5e and S6) and found that the heterolytic dissociation of H<sup>2</sup> at the Ce-O site to produce hydride species is kinetically the most favorable one. The energy barrier of this process is 0.47 eV, which is even lower than the corresponding energy barrier on the Cu/CeO<sup>2</sup> surface (0.56 eV). This result further indicates the great ability of the Cu/CeO2(111) in generating surface hydride species.

**Figure 5.** Calculated structures (left: side view; right: top view) of the (**a**) reduced CeO<sup>2</sup> (111) with one surface oxygen vacancy and (**b**) reduced Cu/CeO<sup>2</sup> (111) with one inherent surface oxygen vacancy and an extra surface oxygen vacancy. Calculated structures (left: side view; right: top view) of a single H at the oxygen vacancy sites of the (**c**) Cu/CeO<sup>2</sup> (111) and (**d**) reduced Cu/CeO<sup>2</sup> (111)-O<sup>V</sup> surfaces. (**e**) Calculated energy profiles of homolytic (Homo) and heterolytic (Heter) H<sup>2</sup> dissociation on the Cu/CeO<sup>2</sup> (111)-O<sup>V</sup> surface. The unfilled blue circle represents the surface oxygen vacancy, and the blue circle filled with yellow represents the inherent surface oxygen vacancy on the Cu/CeO<sup>2</sup> (111). The spin density distributions are illustrated in yellow and blue, and the surface oxygen vacancy formation energies are also given.

## *3.4. Selective Hydrogenation of CO<sup>2</sup>*

To unveil the catalytic activities of the various surfaces, we then continued to study the main reaction steps of the CO2RR at CeO2(111) and Cu/CeO2(111) (Figures 6, S7 and S8). It is generally accepted that the adsorption and activation of CO<sup>2</sup> and the generation of hydride species are the key steps of the whole CO2RR [10,11,38]. As shown in Figure 6, the adsorption of CO<sup>2</sup> on the Cu/CeO2(111) surface is exothermic by 1.06 eV. In comparison, the adsorption of CO<sup>2</sup> on the CeO2(111) surface is much weaker, with an exothermic adsorption energy of 0.32 eV only. Therefore, the Cu dopant can indeed promote CO<sup>2</sup> adsorption. This is mainly attributed to the relatively high energy level of the occupied Cu 3*d* orbital which can donate its electron to the CO<sup>2</sup> molecule (Figure 1d). This is also consistent with some previous experimental observation [13]. Then we calculated the adsorption of H<sup>2</sup> and found that the adsorption of H<sup>2</sup> is weak on both the CeO2(111) and Cu/CeO2(111) surfaces with pre-adsorbed CO2, and the corresponding adsorption energies are 0.01 and 0.12 eV, respectively, which are largely close to those on the clean surfaces (Figure 3). Nevertheless, since the adsorption of CO<sup>2</sup> is stronger than that of H<sup>2</sup> on both the CeO2(111) and Cu/CeO2(111) surfaces, it is reasonable to consider the dissociative adsorption of H<sup>2</sup> on the CO<sup>2</sup> pre-covered surfaces.

Since our calculated results presented above already showed that the hydride species are kinetically and thermodynamically unstable at CeO2(111), we only considered the formation of two hydroxyl species on the CO<sup>2</sup> pre-adsorbed CeO2(111) through H<sup>2</sup> dissociation. This process needs to overcome a barrier of 0.83 eV and is exothermic by 2.67 eV (Figure 6). We found that the produced proton species has rather low activities in the hydrogenation of CO<sup>2</sup> to HCOO\* or COOH\*, with the calculated barriers being higher than 3 eV. Moreover, the COOH pathway is both thermodynamically and kinetically more favorable than the HCOO pathway on this surface.

By contrast, on the Cu/CeO2(111) surface, hydride species can be stable, and H<sup>2</sup> can readily dissociate into one hydride and one OH− species. This process needs to overcome a barrier of 0.79 eV and is exothermic by 0.55 eV. We found that the produced hydride species is quite active for CO<sup>2</sup> hydrogenation. In the HCOO pathway, the calculated barrier and reaction energy are 1.20 and 0.18 eV, respectively, while in the COOH pathway, the corresponding values are 1.34 and −1.59 eV, respectively. Although the generated COOH\* species is more stable than the HCOO\* species, the HCOO pathway is kinetically more favorable than the COOH pathway. We also studied the reaction of CO<sup>2</sup> hydrogenation by

H<sup>+</sup> to form COOH\* on the Cu/CeO2(111) surface, and the calculated barrier is extremely high (4.47 eV). These results indicate that the as-formed hydride species is crucial to the activity and selectivity of the Cu/CeO2(111) in the CO<sup>2</sup> reduction reaction.

**Figure 6.** Calculated energy profiles of the first few key steps of the CO<sup>2</sup> hydrogenation reaction on the CeO<sup>2</sup> (111) and Cu/CeO<sup>2</sup> (111) surfaces.

#### **4. Conclusions**

In conclusion, we systematically studied the hydride formation and its reaction with CO<sup>2</sup> on the pristine and Cu-doped CeO2(111) surfaces. The calculated results showed that the hydride species are thermodynamically and kinetically unstable on the pristine CeO2(111) surface, and the adsorption of CO<sup>2</sup> on this surface is rather weak. In contrast, kinetically stable hydride species can be effectively produced by heterolytic H<sup>2</sup> dissociation on the Cu/CeO2(111) surface with inherent oxygen vacancies. We also found that the Cu dopant promotes the formation of oxygen vacancies, which is favorable for the generation of hydride species. Moreover, the Cu dopant also promotes the adsorption of CO2, and the hydrogenation of CO<sup>2</sup> to HCOO\* can be significantly facilitated by the hydride species on the Cu/CeO2(111) surface, showing that the doping of Cu significantly improves the activity and selectivity of the CeO2(111) toward the hydrogenation of CO<sup>2</sup> to methanol. Our findings may guide the rational design of efficient ceria and Cu based catalysts for CO<sup>2</sup> reduction reactions.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/10 .3390/catal12090963/s1, Tables S1 and S2: Calculated lattice constants of bulk ceria by using different plane wave kinetic energy cutoff and different *k*-point mesh densities. Table S3: Calculated Bader charges of the Cu2+ of CuO and the Cu1+ of Cu2O. Table S4: Calculated Bader charges of the Cu and Ce species and their nearby O; calculated Cu-O and Ce-O bond distances, and the electrostatic interaction energies (ECu+Ce) between the Cu and Ce and their nearby species on the Cu/CeO<sup>2</sup> (111) and the Cu/CeO<sup>2</sup> (111) surface with H being adsorbed at the O site; calculated Cu coordinate numbers on the Cu/CeO<sup>2</sup> (111) and the Cu/CeO<sup>2</sup> (111) surface with H being adsorbed at the O site. Figure S1: Calculated density of states (DOS) of the Cu/CeO<sup>2</sup> (111) surface with H being adsorbed at the Cu site. Figure S2: Calculated structures of Cu/CeO<sup>2</sup> (111) and Cu/CeO<sup>2</sup> (111) with adsorbed H which gives to the localized electron at different site. Figure S3: Calculated density of states (DOS) of the Cu/CeO<sup>2</sup> (111) surface with H being adsorbed at the O site. Figure S4: Calculated structures

of H<sup>2</sup> adsorption and dissociation on the CeO<sup>2</sup> (111) surface. Figure S5: Calculated structures of H<sup>2</sup> adsorption and dissociation on the Cu/CeO<sup>2</sup> (111) surface. Figure S6: Calculated structures of H<sup>2</sup> adsorption and dissociation on the Cu/CeO<sup>2</sup> (111)-O<sup>V</sup> surface. Crystal Reduction Potential (Vr). Figure S7: Calculated structures of CO<sup>2</sup> hydrogenation on the CeO<sup>2</sup> (111) surface. Figure S8: Calculated structures of CO<sup>2</sup> hydrogenation on the Cu/CeO<sup>2</sup> (111) surface. References [27,38,57] are cited in the Supplementary Materials.

**Author Contributions:** Conceptualization, X.-P.W. and X.-Q.G.; methodology, H.-H.L. and Z.-Q.W.; software, H.-H.L. and Z.-Q.W.; validation, Z.-Q.W.; formal analysis, Z.-Q.W., X.-P.W. and X.-Q.G.; investigation, Z.-Q.W.; resources, X.-Q.G.; data curation, H.-H.L. and Z.-Q.W.; writing—original draft preparation, Z.-Q.W.; writing—review and editing, X.-P.W. and X.-Q.G.; visualization, Z.-Q.W.; supervision, X.-P.W., P.H. and X.-Q.G.; project administration, X.-Q.G.; funding acquisition, X.-P.W., P.H. and X.-Q.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Key R&D Program of China (2018YFA0208602) and National Nature Science Foundation of China (21825301, 22003016, 92045303, 92145302) and Shanghai Sailing Program (21YF1409400) and China Postdoctoral Science Foundation (2020M671020).

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

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