Density Functional Theory Study of CO2 Hydrogenation on Transition-Metal-Doped Cu(211) Surfaces

The massive emission of CO2 has caused a series of environmental problems, including global warming, which exacerbates natural disasters and human health. Cu-based catalysts have shown great activity in the reduction of CO2, but the mechanism of CO2 activation remains ambiguous. In this work, we performed density functional theory (DFT) calculations to investigate the hydrogenation of CO2 on Cu(211)-Rh, Cu(211)-Ni, Cu(211)-Co, and Cu(211)-Ru surfaces. The doping of Rh, Ni, Co, and Ru was found to enhance CO2 hydrogenation to produce COOH. For CO2 hydrogenation to produce HCOO, Ru plays a positive role in promoting CO dissociation, while Rh, Ni, and Co increase the barriers. These results indicate that Ru is the most effective additive for CO2 reduction in Cu-based catalysts. In addition, the doping of Rh, Ni, Co, and Ru alters the electronic properties of Cu, and the activity of Cu-based catalysts was subsequently affected according to differential charge analysis. The analysis of Bader charge shows good predictions for CO2 reduction over Cu-based catalysts. This study provides some fundamental aids for the rational design of efficient and stable CO2-reducing agents to mitigate CO2 emission.


Introduction
Since the industrial revolution, the massive emission of carbon dioxide (CO 2 ) has caused a series of environmental problems and social issues. Therefore, the reduction and utilization of CO 2 have drawn great attention from scientists [1][2][3]. There are three methods for the catalytic transformation of CO 2 into value-added chemicals: thermal catalysis, electrocatalysis, and photocatalysis [4][5][6]. As one kind of inert molecule, CO 2 is thermodynamically and kinetically stable due to its high C=O bond energy (750 kJ/mol). Generally, high temperatures are required for the utilization of CO 2 [7]. The hydrogenation of CO 2 into value-added chemicals can provide a sustainable pathway for its utilization [8,9]. The problems of hydrogen storage and transportation have been not only solved, but also, the valuable carbon-based resources have been effectively utilized [10]. For the various hydrogenation products, methanol is one of the most precious chemicals and has been widely used in automobiles, national defense, biomedicine, and so on [11,12].
Among the effective catalysts for CO 2 reduction, Cu-based catalysts had been considered one of the most suitable catalysts due to their excellent catalytic activity and stability for CO 2 hydrogenation for methanol production [13,14]. Liu et al. demonstrated through DFT and experiments that Cu 0 species are active sites for CO 2 hydrogenation to methanol when Cu 4 supported on Al 2 O 3 was used as the catalyst [15]. The study by Wu et al. [16]

Adsorption of Intermediates on Cu(211)-M Surfaces
To gain fundamental insights into M (M = Rh, Ni, Co, Ru) on reactivity, the adsorption of all possible species involved in CO 2 hydrogenation was examined [35,36]. Firstly we calculated the adsorption energy and corresponding adsorption configurations of CO 2 , H 2, COOH, and HCOO on the Cu(211)-M (M = Rh, Ni, Co, Ru) surface. Table 2 lists the adsorption energies of the most stable adsorbed states on these surfaces. The corresponding adsorption configurations are presented in Figure 1. For CO 2 adsorption, the order of adsorption energy is Cu(211) < Cu(211)-Rh < Cu(211)-Ni < Cu(211)-Ru < Cu(211)-Co. For COOH adsorption, compared to that of on the pure Cu(211) surface (−1.76 eV), the adsorption energy is lowered by 0.61, 0.29, 0.59, and 0.85 eV on the Rh-, Ni-, Co-, and Ru-doped surfaces, respectively. Therefore, the addition of transition metals facilitates the formation of COOH intermediates. For HCOO adsorption, the order of adsorption energy is Cu(211)-Rh < Cu(211)-Ru < Cu(211)-Ni < Cu(211)-Co = Cu(211). For H 2 adsorption on the pure Cu(211) surface, H 2 has the strongest adsorption, with an energy of −0.30 eV, while on the Cu(211)-Co and Cu(211)-Ru surfaces, H 2 has the weakest adsorption, with an energy of −0.01 eV. Thus, H 2 adsorption is inhibited by Rh, Ni, Co, and Ru doping. To further understand the interaction between CO 2 , COOH, HCOO, and H 2 species and the surface, Bader charge analysis was introduced. It was reported that the higher the net Bader charge, the more negative adsorption energy of CO 2 [37]. A similar conclusion can be drawn in our work. As shown in Table 2, on the Cu(211) surface, the weakest adsorption of CO 2 was observed due to the lowest net Bader charge. Conversely, the strongest energy of HCOO was attributed to the highest net Bader charge.

H2 Dissociation
For the hydrogenation and activation of CO2, the dissociation of H2 is the key initial step [26]. To investigate the H2 dissociation on the catalyst surface, the activation barrier and reaction energy of H2 dissociation on the Cu(211)-Rh, Cu(211)-Ni, Cu(211)-Co, and Cu(211)-Ru surfaces were calculated and are shown in Table 3. The corresponding geometries of the initial state (IS) of H2 adsorption, transition state (TS), and final state (FS) for H2 dissociation on the pure and transition-metal-doped Cu(211) surfaces are summarized in Figure 2.

H 2 Dissociation
For the hydrogenation and activation of CO 2 , the dissociation of H 2 is the key initial step [26]. To investigate the H 2 dissociation on the catalyst surface, the activation barrier and reaction energy of H 2 dissociation on the Cu(211)-Rh, Cu(211)-Ni, Cu(211)-Co, and Cu(211)-Ru surfaces were calculated and are shown in Table 3. The corresponding geometries of the initial state (IS) of H 2 adsorption, transition state (TS), and final state (FS) for H 2 dissociation on the pure and transition-metal-doped Cu(211) surfaces are summarized in Figure 2.
As shown in Figure 2, it can be found that H 2 prefers to adsorb at the top site on these five surfaces. After the dissociation of H 2 on the Cu(211) surface, two H atoms can be adsorbed on the adjacent 3F site; for Cu(211)-Rh, Cu(211)-Ni, Cu(211)-Co, and Cu(211)-Ru surfaces, two H atoms are adsorbed on 3F and bridge. For the dissociation of H 2 , the activation energy barrier on Cu(211) is 0.44 eV, which is consistent with the previously reported literature and differs slightly from 0.09 eV [26]. Apparently, Co and Ru doping promote the H-H bond scission, and the barrier is lower by 0.25 and 0.22 eV. On the Cu(211)-Rh and Cu(211)-Ni surfaces, the dissociation of H 2 required to overcome the energy barrier is approximately 0.42 eV. Therefore, there is a slight effect on Cu(211) surface. In addition, the reaction energies of H 2 dissociation on the Cu(211)-Rh, Cu(211)-Ni, Cu(211)-Co, and Cu(211)-Ru surfaces are −0.84, −0.57, −0.86, and −1.01 eV, respectively. Therefore, the values of E r on all the surfaces suggest that the elementary step is exothermic. Tang et al. [22] reported that the existing adsorption form of H 2 is dissociative adsorption on the Ni(211) and Ga-Ni(211) surfaces. More importantly, it can also be found that H 2 is easily activated and dissociated into adsorbed H (H*). The H* is the main form of H 2 on these five surfaces.

CO 2 Activation
The activation of CO 2 is a key step in many catalytic reactions [38,39]. Therefore, it is very important to study the mechanism of CO 2 activation. For CO 2 activation, H-assisted dissociation via carboxyl (COOH) and formate (HCOO) intermediates have been taken into consideration on the Cu(211)-Rh, Cu(211)-Ni, Cu(211)-Co, and Cu(211)-Ru surfaces. The activation barriers and the reaction energies for CO 2 activation on the pure and M-doped Cu(211)(M = Rh, Ni, Co, and Ru) surfaces are summarized in Tables 4 and 5.  As shown in Figure 3, in the initial state, the V-type adsorbed CO 2 molecules and H atoms were coadsorbed on the surface of the catalyst. CO 2 was adsorbed on the 4F active site, and H preferred to adsorb at the 3F site. When the reaction occurred, H moved to the O atom to form COOH, and COOH adsorbed on the 4F site. From Table 4, the activation barrier of CO 2 hydrogenation is in the order Cu(211)-Ru < Cu(211)-Ni < Cu(211)-Rh < Cu(211)-Co < Cu(211). Thus, Co, Rh, Ni, and Ru doping promotes O-H bond formation and lowers the barrier by 0.81, 0.86, 0.88, and 0.95 eV, respectively. In addition, the reaction energy of CO 2 activation all are exothermic by 0.40 eV on the M-doped Cu(211)(M = Rh, Ni, Co, and Ru) surfaces. The above analysis, it clearly shows that Co, Rh, Ni, and Ru doping promotes CO 2 activation to form COOH.  In the initial state, CO2 is adsorbed on the 4F active site and H prefers to adsorb at 3F site. When the reaction occurred, H moved to the C atom to form HCOO and HCOO adsorbed on the bridge site, as shown in Figure 4. From Table 5, compared to the pure Cu(211) [26] surface (0.74 eV), the activity of CO2 activation to HCOO is higher on the Cu (211)-Ru (0.30 eV). Conversely, the C-H bond formation is inhibited by the Rh/Ni/Co doping, with the barrier being raised to 2.55, 2.35, and 0.87 eV, respectively. In addition, the reaction energy of CO2 activation is exothermic on the M-doped Cu(211)(M = Rh, Ni, Co, and Ru) surfaces. In summary, this is different from the formation of COOH-only Ru additive promotes the production of HCOO. Figure 5 it clearly shows that CO2 hydrogenation to COOH is more plausible on the Cu(211)-Rh, Cu(211)-Ni, and Cu(211)-Co surfaces, while CO2 hydrogenation to HCOO is more preferable on the Cu(211)-Ru surface.  In the initial state, CO 2 is adsorbed on the 4F active site and H prefers to adsorb at 3F site. When the reaction occurred, H moved to the C atom to form HCOO and HCOO adsorbed on the bridge site, as shown in Figure 4. From Table 5, compared to the pure Cu(211) [26] surface (0.74 eV), the activity of CO 2 activation to HCOO is higher on the Cu (211)-Ru (0.30 eV). Conversely, the C-H bond formation is inhibited by the Rh/Ni/Co doping, with the barrier being raised to 2.55, 2.35, and 0.87 eV, respectively. In addition, the reaction energy of CO 2 activation is exothermic on the M-doped Cu(211)(M = Rh, Ni, Co, and Ru) surfaces. In summary, this is different from the formation of COOHonly Ru additive promotes the production of HCOO. Figure 5 it clearly shows that CO 2 hydrogenation to COOH is more plausible on the Cu(211)-Rh, Cu(211)-Ni, and Cu(211)-Co surfaces, while CO 2 hydrogenation to HCOO is more preferable on the Cu(211)-Ru surface.  In the initial state, CO2 is adsorbed on the 4F active site and H prefers to adsorb at 3F site. When the reaction occurred, H moved to the C atom to form HCOO and HCOO adsorbed on the bridge site, as shown in Figure 4. From Table 5, compared to the pure Cu(211) [26] surface (0.74 eV), the activity of CO2 activation to HCOO is higher on the Cu (211)-Ru (0.30 eV). Conversely, the C-H bond formation is inhibited by the Rh/Ni/Co doping, with the barrier being raised to 2.55, 2.35, and 0.87 eV, respectively. In addition, the reaction energy of CO2 activation is exothermic on the M-doped Cu(211)(M = Rh, Ni, Co, and Ru) surfaces. In summary, this is different from the formation of COOH-only Ru additive promotes the production of HCOO. Figure 5 it clearly shows that CO2 hydrogenation to COOH is more plausible on the Cu(211)-Rh, Cu(211)-Ni, and Cu(211)-Co surfaces, while CO2 hydrogenation to HCOO is more preferable on the Cu(211)-Ru surface.

Electronic Structure Analysis
Generally, the catalytic performance is attributed to the electronic properties [28,40,41]. The addition of a small number of additives could change the morphology of the catalyst or modify the electronic properties of the active phase metal Cu. To visualize the electronic interaction between M (M = Rh, Ni, Co, and Ru) and Cu surfaces, the differential charge density distribution of the M/Co systems is shown in Figure 6. The results showed that the doping of Rh, Ni, Co, and Ru modified the electronic properties of Cu and therefore affected the activity of Cu-based catalysts. The charge transfer between Co surfaces and M-doped surfaces was quantified using Bader charge analysis, which is listed in Table 1. The results show that the localized electron is transferred from the Cu surface to Rh, Ni, and Ru atoms, which is attributed to the fact that Rh, Ni, and Ru are more electronegative than Cu. In contrast, the localized electron is transferred from the Co atom to the Cu surface because of the lower electronegativity of Co.

Electronic Structure Analysis
Generally, the catalytic performance is attributed to the electronic properties [28,40,41]. The addition of a small number of additives could change the morphology of the catalyst or modify the electronic properties of the active phase metal Cu. To visualize the electronic interaction between M (M = Rh, Ni, Co, and Ru) and Cu surfaces, the differential charge density distribution of the M/Co systems is shown in Figure 6. The results showed that the doping of Rh, Ni, Co, and Ru modified the electronic properties of Cu and therefore affected the activity of Cu-based catalysts. The charge transfer between Co surfaces and M-doped surfaces was quantified using Bader charge analysis, which is listed in Table 1. The results show that the localized electron is transferred from the Cu surface to Rh, Ni, and Ru atoms, which is attributed to the fact that Rh, Ni, and Ru are more electronegative than Cu. In contrast, the localized electron is transferred from the Co atom to the Cu surface because of the lower electronegativity of Co.

Electronic Structure Analysis
Generally, the catalytic performance is attributed to the electronic properties [28,40,41]. The addition of a small number of additives could change the morphology of the catalyst or modify the electronic properties of the active phase metal Cu. To visualize the electronic interaction between M (M = Rh, Ni, Co, and Ru) and Cu surfaces, the differential charge density distribution of the M/Co systems is shown in Figure 6. The results showed that the doping of Rh, Ni, Co, and Ru modified the electronic properties of Cu and therefore affected the activity of Cu-based catalysts. The charge transfer between Co surfaces and M-doped surfaces was quantified using Bader charge analysis, which is listed in Table 1. The results show that the localized electron is transferred from the Cu surface to Rh, Ni, and Ru atoms, which is attributed to the fact that Rh, Ni, and Ru are more electronegative than Cu. In contrast, the localized electron is transferred from the Co atom to the Cu surface because of the lower electronegativity of Co.  Exploring CO 2 reduction on catalysts is a very complicated and comprehensive work, and we attempt to find descriptors that can predict activation energy in this part. Based on the computed energy data on the pure and M-doped Cu(211) surfaces (M = Rh, Ni, Co, and Ru), we examined the Brønsted-Evans-Polanyi (BEP) [42], which is the most successful example of the relationship between the associated activation barrier and reaction energy. In the previous studies, Chen et al. [41] found that the reaction energy can be a descriptor for the CO activation on different χ-Fe 5 C 2 catalyst surfaces. Gong et al. [37] reported that there is a linear relationship between the CO activation barrier and reaction energy on the pure and M-doped Fe(100) surfaces (M = Cr/Mn/Co/Ni/Cu). Firstly, we analyze the relationship between the activation barrier and the reaction energy of CO 2 hydrogenation to COOH and HCOO on these five doped surfaces. The correlation is shown in Figure 7; it can be found that the reaction energy of CO 2 reduction does not give a good description of the CO 2 activation barrier for the different transition metal dopants' Cu(211) surfaces. In addition, Chen et al. [41] suggested that the corresponding linear relation is slightly poor between the activation barrier and the reaction energy for CO dissociation on the different χ-Fe 5 C 2 surfaces. Exploring CO2 reduction on catalysts is a very complicated and comprehensive work, and we attempt to find descriptors that can predict activation energy in this part. Based on the computed energy data on the pure and M-doped Cu(211) surfaces (M = Rh, Ni, Co, and Ru), we examined the Brønsted-Evans-Polanyi (BEP) [42], which is the most successful example of the relationship between the associated activation barrier and reaction energy. In the previous studies, Chen et al. [41] found that the reaction energy can be a descriptor for the CO activation on different χ-Fe5C2 catalyst surfaces. Gong et al. [37] reported that there is a linear relationship between the CO activation barrier and reaction energy on the pure and M-doped Fe(100) surfaces (M = Cr/Mn/Co/Ni/Cu). Firstly, we analyze the relationship between the activation barrier and the reaction energy of CO2 hydrogenation to COOH and HCOO on these five doped surfaces. The correlation is shown in Figure 7; it can be found that the reaction energy of CO2 reduction does not give a good description of the CO2 activation barrier for the different transition metal dopants' Cu(211) surfaces. In addition, Chen et al. [41] suggested that the corresponding linear relation is slightly poor between the activation barrier and the reaction energy for CO dissociation on the different χ-Fe5C2 surfaces. In order to gain insight into the underlying mechanism of electronic effects introduced by transition metals for CO2 reduction, the Bader analysis is employed. Figure 8 shows that the charges of the involved surface Cu and doped metal atoms follow a nearly linear relation with the CO2 activation barrier. Obviously, different transition metal dopants' Cu surfaces have different abilities to donate electrons for the CO2 activation. Therefore, the atomic charge of the involved surface and doped metal atoms for the CO2 activation is suggested as a dominant factor to describe the CO2 activation on the different Cubased catalyst surfaces. Therefore, we could predict the reactivity of CO2 reduction on the Cu surfaces with these correlations.  In order to gain insight into the underlying mechanism of electronic effects introduced by transition metals for CO 2 reduction, the Bader analysis is employed. Figure 8 shows that the charges of the involved surface Cu and doped metal atoms follow a nearly linear relation with the CO 2 activation barrier. Obviously, different transition metal dopants' Cu surfaces have different abilities to donate electrons for the CO 2 activation. Therefore, the atomic charge of the involved surface and doped metal atoms for the CO 2 activation is suggested as a dominant factor to describe the CO 2 activation on the different Cu-based catalyst surfaces. Therefore, we could predict the reactivity of CO 2 reduction on the Cu surfaces with these correlations. Exploring CO2 reduction on catalysts is a very complicated and comprehensive work, and we attempt to find descriptors that can predict activation energy in this part. Based on the computed energy data on the pure and M-doped Cu(211) surfaces (M = Rh, Ni, Co, and Ru), we examined the Brønsted-Evans-Polanyi (BEP) [42], which is the most successful example of the relationship between the associated activation barrier and reaction energy. In the previous studies, Chen et al. [41] found that the reaction energy can be a descriptor for the CO activation on different χ-Fe5C2 catalyst surfaces. Gong et al. [37] reported that there is a linear relationship between the CO activation barrier and reaction energy on the pure and M-doped Fe(100) surfaces (M = Cr/Mn/Co/Ni/Cu). Firstly, we analyze the relationship between the activation barrier and the reaction energy of CO2 hydrogenation to COOH and HCOO on these five doped surfaces. The correlation is shown in Figure 7; it can be found that the reaction energy of CO2 reduction does not give a good description of the CO2 activation barrier for the different transition metal dopants' Cu(211) surfaces. In addition, Chen et al. [41] suggested that the corresponding linear relation is slightly poor between the activation barrier and the reaction energy for CO dissociation on the different χ-Fe5C2 surfaces. In order to gain insight into the underlying mechanism of electronic effects introduced by transition metals for CO2 reduction, the Bader analysis is employed. Figure 8 shows that the charges of the involved surface Cu and doped metal atoms follow a nearly linear relation with the CO2 activation barrier. Obviously, different transition metal dopants' Cu surfaces have different abilities to donate electrons for the CO2 activation. Therefore, the atomic charge of the involved surface and doped metal atoms for the CO2 activation is suggested as a dominant factor to describe the CO2 activation on the different Cubased catalyst surfaces. Therefore, we could predict the reactivity of CO2 reduction on the Cu surfaces with these correlations.  As mentioned above, Ru has been shown to be the most effective additive for CO 2 hydrogenation in Cu-based catalysts. It can be argued that Ru additives can improve the catalytic activity of copper-based catalysts in several ways. First, electron transfer has been reported to be essential for reactant adsorption, which in turn affects the activity of reactants [43]. Ru alters the electronic properties of Cu, thus influencing the charge of surface reactants. Moreover, Ru is an effective catalyst for CO 2 hydrogenation [44]. Wesselbaum et al. suggested that a single Ru-triphos catalyst could improve the hydrogenation of CO 2 to methanol via the direct route [45]. Thus, the addition of Ru facilitates the conversion of CO 2 .

Model
In order to study the CO 2 hydrogenation reaction mechanism using doped metals on the Cu-based catalysts, we selected a p(2×4) Cu(211) periodic model with three layers, which included 72 Cu atoms. There were different adsorption sites on the surface of Cu(211), including top (T), bridge (B), three-fold (3F), and four-fold (4F) sites, which are shown in Figure 9. Additionally, there was no interaction between the periodically repeated models. The vacuum layer was set to 15 Å. During the calculations, the adsorbates and top two layers were relaxed, and the remaining bottom layers were fixed in their bulk positions. As shown in Figure 9, the substitution model was used, in which the local surface Cu sites are replaced by Rh, Ni, Co, and Ru. The formula for formation energy is as follows [22]: where E sub is the substitution energy of the Cu(211)-M surface; E Cu(211) and E Cu(211)-M are the total energies of Cu(211) and Cu(211)-M surfaces, respectively. E Cu and E M are the total energies of single Cu and promoter atoms (including Rh, Ni, Co, and Ru). According to this definition, it is indicated that the negative E f value suggests that the formation process is exothermic and preferable.
Molecules 2023, 27, x FOR PEER REVIEW 9 of 13 As mentioned above, Ru has been shown to be the most effective additive for CO2 hydrogenation in Cu-based catalysts. It can be argued that Ru additives can improve the catalytic activity of copper-based catalysts in several ways. First, electron transfer has been reported to be essential for reactant adsorption, which in turn affects the activity of reactants [43]. Ru alters the electronic properties of Cu, thus influencing the charge of surface reactants. Moreover, Ru is an effective catalyst for CO2 hydrogenation [44]. Wesselbaum et al. suggested that a single Ru-triphos catalyst could improve the hydrogenation of CO2 to methanol via the direct route [45]. Thus, the addition of Ru facilitates the conversion of CO2.

Model
In order to study the CO2 hydrogenation reaction mechanism using doped metals on the Cu-based catalysts, we selected a p(2×4) Cu(211) periodic model with three layers, which included 72 Cu atoms. There were different adsorption sites on the surface of Cu(211), including top (T), bridge (B), three-fold (3F), and four-fold (4F) sites, which are shown in Figure 9. Additionally, there was no interaction between the periodically repeated models. The vacuum layer was set to 15 Å. During the calculations, the adsorbates and top two layers were relaxed, and the remaining bottom layers were fixed in their bulk positions. As shown in Figure 9, the substitution model was used, in which the local surface Cu sites are replaced by Rh, Ni, Co, and Ru. The formula for formation energy is as follows [22]: where Esub is the substitution energy of the Cu(211)-M surface; ECu(211) and ECu(211)-M are the total energies of Cu(211) and Cu(211)-M surfaces, respectively. ECu and EM are the total energies of single Cu and promoter atoms (including Rh, Ni, Co, and Ru). According to this definition, it is indicated that the negative Ef value suggests that the formation process is exothermic and preferable.

Calculation Method
The VASP (Vienna Ab-initio Simulation Package) software (version 5.4.4) developed by the University of Vienna Hafner was used to study the adsorption energies and activation energies of the CO 2 hydrogenation [46,47]. The generalized gradient approximation (GGA) method with Perdew-Burke-Ernzerhof (PBE) was used as the exchange-correlation energy. [48] The plane wave basis set was set to 400 eV. When the total energy converges to 10 −5 eV and the force is less than 0.03 eV/Å, the geometry optimization is thought to be converged. A 3 × 2 × 1 k-point sampling in the surface Brillouin zone was used for all calculations. We tested the parameters including k-point grids and cutoff energy (see Table 6) for convergence accuracy using COOH adsorption on a Cu(211)-Ru surface as an example, and the results showed energy differences in the range of 0.01-0.04 eV. The CI-NEB (climbing image-nudged elastic band) [49,50] was performed to confirm the transition state structure. When atomic force is less than 0.05 eV/Å, the transition state would be converged. In addition, the vibrational frequencies were introduced to verify the transition states with only one imaginary frequency. The adsorption energy (E ads ) of adsorbates is defined as: here, E adsorbate/slab , E slab , and E adsorbate are the total energies of the slab with the adsorbate, the slab surface, and the free adsorbate, respectively. It is indicated that the more negative the value of E sub , the stronger the adsorption. The activation barrier (E a ) and reaction energy (E r ) are defined as: here, E IS , E TS , and E FS are the total energy of the initial, transition, and final states.

Conclusions
In this work, the effects of transition metal doping on Cu(211) surfaces for CO 2 hydrogenation were investigated using the density functional theory method. It is revealed that the doping of Rh, Ni, Co, and Ru doping enhances the dissociation of H 2 and the hydrogenation of CO 2 to COOH. For the hydrogenation of CO 2 to HCOO, Ru shows a positive role in promoting the formation of HCOO, while the doping of Rh, Ni, and Co leads to an increase in the energy barrier. Therefore, the doping of Ru is the most effective for the reduction of CO 2 . Differential charge analysis showed that the doping of Rh, Ni, Co, and Ru alters the electronic properties of Cu, which in turn influences the activity of Cu-based catalysts for CO 2 reduction. Bader charge as a descriptor was introduced in CO 2 activation on various Cu(211) surfaces. According to the calculations, there is a good relationship between the atomic charges of the involved surface Cu and M (M = Rh, Ni, Co, and Ru) atoms and the activation barriers for CO 2 activation. With these correlations, the performance of different Cu-based catalysts could be reasonably and accurately predicted.