A First-Principles Study on the Reaction Mechanisms of Electrochemical CO 2 Reduction to C 1 and C 2 Products on Cu(110)

: The mechanism of the electrochemical CO 2 reduction reaction on a Cu(110) surface has yet to be fully revealed. In this work, based on first-principles calculations, we investigate the mechanisms of the CO 2 reduction reaction to produce C 1 (including one C atom) and C 2 (including two C atoms) products on a Cu(110) surface. The results show that CH 4 and C 2 H 5 OH are the main C 1 and C 2 products on the Cu(110) surface, respectively. CH 4 is produced along the pathway CO 2 → COOH* → CO* → CHO* → CH 2 O* → CH 3 O* → CH 4 . C 2 H 5 OH is produced via the C-C coupling pathway between CO* and CH 2 O* intermediates, which is the key reaction step. This is because CO* and CH 2 O* coupling to CO-CH 2 O* has the lowest barrier among the CH x O* (x = 0–2) coupling pathways. Therefore, it is the most likely C-C coupling pathway. Further, CO-CH 2 O* is gradually hydrogenated to C 2 H 5 OH along the following pathway: CO-CH 2 O* → CHO-CH 2 O* → CHOH-CH 2 * → CH 2 OH-CH 2 * → CH 2 OH-CH 3 * → C 2 H 5 OH.


Introduction
With the increase in the atmospheric CO 2 concentration, the global climate has undergone tremendous changes, such as global warming and ocean acidification [1,2].Khalil et al. predicted that anthropogenic CO 2 levels will reach ~590 ppm in 2100, resulting in a global temperature increase of 1.9 • C [3].In particular, the temperature increase in the polar regions will be up to three times as much as other regions [4].These changes have seriously harmed the environment in which human beings live.The Paris Agreement adopted by the Intergovernmental Panel on Climate Change (IPCC) aims to reduce net levels of CO 2 in the atmosphere by 2050 [5].To solve this problem, CO 2 capture and utilization, conversion and utilization, have become focuses of research [6,7].Due to the disadvantages of CO 2 capture and utilization, such as CO 2 gas leakage and complex design, its large-scale popularization has limitations.However, CO 2 conversion and utilization has significant advantages.Photocatalysis [8], photo-electrocatalysis [9], and electrocatalysis [10] techniques have been widely used for CO 2 conversion and utilization.These techniques can not only reduce the concentration of CO 2 in the atmosphere, but also convert CO 2 into chemicals.Therefore, they have been widely concentrated on by researchers.
Photocatalysis and photo-electrocatalysis techniques refer to the conversion of solar energy into chemical energy [11,12].They are carried out in an electrolytic cell, which includes two components (i.e., anode and cathode).On the cathode side, CO 2 reduction takes place on a p-type semiconductor, such as Cu 2 O or TiO 2 ; on the anode side, water oxidation occurs on an n-type semiconductor such as F 2 O 3 .Semiconductor materials have been applied to photocatalysis and photo-electrocatalysis in CO 2 reduction reactions [13].Their electronic structures play vital roles in photochemical and photoelectrochemical processes.The semiconductor materials are composed of a filled valence band (VB) coupled with an empty conduction band (CB), which shows an electron transfer from the VB to CB under stimulation by photons.The electron transfer leads to a positive hole in the VB.
Catalysts 2024, 14, 468 2 of 16 These holes and the electrons formed on the surface of semiconductor materials can reduce the adsorbed species in the semiconductor materials [14].The suitable electrode material can reduce the activation energy of a CO 2 reduction reaction, especially CO 2 reduction to C 2 products.The reason is that the electrode material can form C 2 O 2 •− , a transition state complex, by transferring electrons in the C-C coupling process.The electrons in the d orbital of the electrode are transferred to the π* antibonding orbital of the C 2 O 2 •− intermediate, which stabilizes the C 2 O 2 •− intermediate adsorbed on the electrode surface, thus allowing the band bending reaction and reducing the activation energy of the C-C coupling process to promote the production of C 2 products [15].Although metal oxides are commonly used to study photocatalysis [16,17] and photo-electrocatalysis, their inherent properties affect the catalytic efficiency to a certain extent.For example, the wide bandgap of TiO 2 (3.2 eV) leads to low photocatalytic efficiency owing to the very limited absorption of the solar spectrum [18]; due to the self-reduction potential between CB and VB energy values, Cu 2 O in an aqueous solution has serious photocorrosion, resulting in the decrease in photocurrent density and the decrease in solar-fuel conversion efficiency [19].
To overcome this defect, various strategies have been proposed in recent years such as band gap engineering or surface coating, which can improve the catalytic efficiency of semiconductors.However, there are also some problems: it is a challenge to reduce the bandgap of TiO 2 while maintaining sufficient redox potentials at the band edge positions for a CO 2 reduction reaction; the use of a surface coating strategy to solve the photocorrosion of Cu 2 O while maintaining its long-term stability is also a challenge.
Not only that, plasmonic materials are developed by researchers as photocatalysts.For the first time, Tirumala et al. have experimentally demonstrated that dielectric Mie resonance can significantly enhance photocatalysis in semiconductor materials when illuminated by visible light.These materials, characterized by their positive permittivity and moderate to high refractive indices, represent a groundbreaking advancement in the field [20,21].Plasmonic materials with nanostructures can focus light at the nanoscale [22].Under illumination, surface plasma excitation is established when the frequency of the incident light matches the natural frequency of oscillating surface electrons on a plasma with nanostructures.The redistributing light field, excited carriers, and heat effects produced during the relaxation process of the surface plasmon can set the stage for activating the CO 2 molecule.These excited carriers (hot electrons and holes) can offer opportunities for a CO 2 reduction reaction.By adjusting the size of the plasmonic materials, the absorption of a particular wavelength of sunlight can be realized to excite more carriers [23].Generally speaking, the UV-Vis spectroscopy can be used as an in-line process analytical technology (PAT) tool for the operando characterization of nanostructures of plasmonic materials to trace the change in size of nanostructures [24].Nonetheless, the short lifetime of excited carriers is the main factor restricting the application of plasma photocatalysts.
Compared to other techniques, the electrocatalysis technique is more easy due to the simple operating device and controllable reaction conditions.So, it is favored by researchers.It can convert CO 2 into a variety of value-added chemicals, including C 1 products such as methane (CH 4 ), formic acid (HCOOH), carbon monoxide (CO), and methanol (CH 3 OH); C 2 products, such as ethylene (C 2 H 4 ), ethanol (C 2 H 5 OH), and acetic acid (CH 3 COOH); and C 3 products, such as propylene (C 3 H 6 ) and propanol (C 3 H 8 O) [25][26][27][28][29][30].Among them, C 2 products have higher energy density than C 1 products and are important raw materials in chemical synthesis [31][32][33][34][35].In addition, the selective synthesis of C 2 products involves the formation of the C-C bond, namely, C-C coupling, which is a key challenge in heterogeneous catalysis during CO 2 reduction reactions [36,37].Therefore, the electrocatalytic reduction of CO 2 to C 2 products has attracted wide attention, especially in identifying the reaction mechanism of this process.
Transition metals are often used as catalysts for CO 2 reduction reactions, especially the metal Cu.Compared with transition metals that produce hydrogenation, such as Pd [38], Fe [39] and others, Cu tends to reduce CO 2 to hydrocarbons.Moreover, Cu is a unique catalyst with selectivity for C 2 products during CO 2 reduction reactions.For example, it has been shown in experiment that both Cu(100) and Cu(110) surfaces have high Faraday efficiency for C 2 products [40][41][42].However, the CO 2 reduction products on Cu(100) and Cu(110) surfaces are different.In experiment, the Cu(100) surface mainly produces C 2 H 4 [43], while the Cu(110) surface tends to produce C 2 H 5 OH and CH 3 CHO [44].The possible reason for this difference is that the coordination numbers of Cu(100) and Cu(110) surfaces are different.Compared to the Cu (100) surface, the Cu (110) surface has a lower coordination number.Therefore, the Cu (110) surface exhibits higher catalytic activity during the process of CO 2 reduction to C 2 products [45].In theory, previous studies on the reaction mechanism of C 2 products mostly focused on the Cu(100) surface; however, few studies have focused on the Cu(110) surface [46,47].Therefore, it is necessary to systematically study the reaction mechanism of C 2 product production on a Cu(110) surface.
Currently, the study of the CO 2 reduction reaction on a Cu(110) surface has been reported.In theory, Zhang et [50].In experiment, CH 3 COOH is the main C 2 product reported by Takahashi et al. [51].It remains challenging to reveal the main C 1 and C 2 products and the C-C coupling pathway for the CO 2 reduction reaction on a Cu(110) surface.What is clear, however, is that the two intermediates in which C-C coupling occurs form relatively easier in the C 1 product pathway.
Based on first-principles calculations, we propose that CH 4 and C 2 H 5 OH are the main C 1 and C 2 products on the Cu(110) surface, respectively, during the electrocatalytic reduction of CO 2 .For CO 2 reduction to CH 4 , we find this reaction along the following pathway:

CO 2 Reduction to CH 4
The Gibbs free energies of the reduction of CO 2 into CH 4 are calculated, and the results are shown in Figure 1.All of the intermediates are adsorbed on the most favorable sites, and their optimized adsorption geometries are shown in the insets.In addition, the bond distances between intermediates and Cu(110) surface are shown in Figure S1 of the Supplementary Materials.It is worth noting that we only label the key intermediates in the figures in this study.In addition, the solvent molecule has been removed from the figures to clearly show the adsorption geometries.
Our calculations show the reduction of CO 2 to CH 4 along the COOH pathway on the Cu(110) surface.Previous studies have indicated that the Cu(110) surface with a coordination number of seven tends to follow the COOH pathway.In contrast, the Cu(111) surface with a coordination number of nine prefers to follow the HCOO pathway [52,53].This also proves that our calculation results can be trusted.
In Figure 1, the potential−limiting step is the formation of a COOH* intermediate on the Cu(110) surface.Because this step has the highest positive variation of Gibbs free energy of 0.66 eV among all reaction steps from CO 2 reduction to CH 4 .Our result is close to the ∆G(0.76eV) for forming COOH* on Cu(110) in the previous literature [54].Since our calculations take into account the solvent effect, the ∆G of forming COOH* on the Cu(110) surface is lower.An earlier report also suggests that the formation of COOH* is the potential-determining step on the Cu(110) surface [55], which is consistent with our calculation.For the step of COOH* → CO*, COOH* binds with H to form CO* and H 2 O(g).Since CO* is the important intermediate that participates in the CO 2 reduction reaction, we only label it in Figure 1.In Figure 1, the potential−limiting step is the formation of a COOH* intermediate on the Cu(110) surface.Because this step has the highest positive variation of Gibbs free energy of 0.66 eV among all reaction steps from CO2 reduction to CH4.Our result is close to the ∆(0.76eV) for forming COOH* on Cu(110) in the previous literature [54].Since our calculations take into account the solvent effect, the ∆ of forming COOH* on the Cu(110) surface is lower.An earlier report also suggests that the formation of COOH* is the potential-determining step on the Cu(110) surface [55], which is consistent with our calculation.For the step of COOH* → CO*, COOH* binds with H to form CO* and H2O(g).Since CO* is the important intermediate that participates in the CO2 reduction reaction, we only label it in Figure 1.
For the CO*, it may involve either desorption or hydrogenation on the Cu(110) surface.To compare which is the next possible reaction of CO*, the activation energies of CO* desorption and hydrogenation are calculated, and the results are shown in Figure S2 of the Supplementary Materials and Figure 2, respectively.The activation energy of CO* desorption is 1.31 eV; the activation energies of CO* hydrogenation to CHO* and COH*are 1.10 and 2.56 eV, respectively.Although the activation energy of CO* desorption is higher than that of the hydrogenation to COH*, it is lower than that of hydrogenation to CHO*.Therefore, CO* prefers hydrogenation rather than desorption on a Cu(110) surface.In Figure 1, the potential−limiting step is the formation of a COOH* intermediate on the Cu(110) surface.Because this step has the highest positive variation of Gibbs free energy of 0.66 eV among all reaction steps from CO2 reduction to CH4.Our result is close to the ∆(0.76eV) for forming COOH* on Cu(110) in the previous literature [54].Since our calculations take into account the solvent effect, the ∆ of forming COOH* on the Cu(110) surface is lower.An earlier report also suggests that the formation of COOH* is the potential-determining step on the Cu(110) surface [55], which is consistent with our calculation.For the step of COOH* → CO*, COOH* binds with H to form CO* and H2O(g).Since CO* is the important intermediate that participates in the CO2 reduction reaction, we only label it in Figure 1.
For the CO*, it may involve either desorption or hydrogenation on the Cu(110) surface.To compare which is the next possible reaction of CO*, the activation energies of CO* desorption and hydrogenation are calculated, and the results are shown in Figure S2 of the Supplementary Materials and Figure 2, respectively.The activation energy of CO* desorption is 1.31 eV; the activation energies of CO* hydrogenation to CHO* and COH*are 1.10 and 2.56 eV, respectively.Although the activation energy of CO* desorption is higher than that of the hydrogenation to COH*, it is lower than that of hydrogenation to CHO*.Therefore, CO* prefers hydrogenation rather than desorption on a Cu(110) surface.

The Activation Energies from CO* Hydrogenation to CH x O*
To verify the accuracy of our results, we also calculate the activation energies of steps from CO* to CH 3 O*, which are shown in Figure 2. The bond distances of the initial states, transition states, and finial states between them and the Cu(110) surface are shown in Figure S3 of the Supplementary Materials.The E a of steps from CO* to COH* and CHO* are 2.57 and 1.10 eV, respectively.The E a of steps from CHO* to CHOH* and CH 2 O* are 0.97 and 0.17 To eliminate this potential bottleneck, applying tensile strain on a Cu(110) surface is an effective strategy.Shin et al. designed a novel catalyst that uses silver (Ag) and palladium (Pd) to support Cu thin film to decrease the activation energy of steps of CO* + H* → CHO* [56].This provides a new way for us to design new catalysts.
By comparing the activation energies for the steps from CO* to CH 3 O*, we can not only prove the effectiveness of generating the CH 4 pathway, but also identify the intermediates enriched on the Cu(110) surface.These intermediates are prone to C-C coupling.So, comparing the activation energies for the steps from CO* to CH 3 O* can provide guidance for the study of a possible C-C coupling pathway.Thus, we believe that comparing the activation energies for the steps from CO* to CH 3 O* can influence the pathway of C-C coupling.

C-C Coupling Pathway
In exploring the pathway of CO 2 reduction to CH 4 , we find that CHO* and CH 2 O* formed by CO* hydrogenation tend to be enriched on the Cu(110) surface.The main reason for this is that compared with other reaction steps, the steps of CO* → CHO* and CO* → CH 2 O* have relatively lower activation energies.Moreover, the step of CH 2 O* → CH 3 O* requires slightly high activation energy so that CH 2 O* prefers to remain on the Cu(110) surface.Therefore, we believe that CHO* and CH 2 O* tend to be enriched on the Cu(110) surface for the C-C coupling.In addition, we also consider CO* for the C-C coupling intermediate.Not only is it a common intermediate in C-C coupling, but its coupling with another CO* is also widely studied on low-index Cu surfaces [57].
We believe that C-C coupling will likely occur between CO*, CHO*, and We calculate the Gibbs free energies for these six pathways, and the results are shown in Figure 3. ure 3.
It is worth noting that the intermediates of C-C coupling refer to intermediates that are co-adsorbed on a Cu(110) surface.The two-CO* dimerization pathway refers to the coupling between one CO* and another CO* that are co-adsorbed on a Cu(110) surface.The CO* and CHO* coupling pathway refers to the coupling of one CO* and one co-adsorbed CHO*.For this pathway, besides the reaction step of CO* and CHO* coupling being endothermic, the formation of CHO* is also endothermic.That is to say, in addition to the energy barrier required for C-C coupling to occur, it is also necessary to consider the energy barrier required to form C-C coupling intermediates.In this case, the two-CO* dimerization pathway need overcome the energy barrier of C-C coupling with 1.47 eV.However, the CO* and CHO* coupling pathway is required to overcome an energy barrier of 2.66 eV.This includes two parts: one is from CO* to CHO*, with 1.10 eV; the other is from CO* and CHO* coupling, with 1.56 eV.Comparing these two C-C coupling pathways, the two-CO* dimerization is more likely to occur because it requires overcoming a lower energy barrier.
Similar situations also occur in other C-C coupling pathways.For the CO* and CH2O* coupling pathway, the energy barrier to be overcome is 1.46 eV.This also includes two parts: one is from CO* to CH2O*, with 1.27 eV; the other is from CO* and CH2O* coupling, with 0.19 eV.For the CHO* and CH2O* coupling pathway, the energy barrier to be overcome is 3.14 eV.This includes three parts: one is from CO* to CHO*, with 1.10 eV; one is from the other CO* to CH2O*, with 1.27 eV; the last is CHO* and CH2O* coupling, with 0.77 eV.For the CHO* and CHO* coupling pathway, the energy barrier to be overcome is 4.18 eV.This includes three parts: one is from CO* to CHO*, with 1.10 eV; one is from the other CO* to CHO*, with 1.10 eV; the last one is CHO* and CHO* coupling, with 1.98 eV.For the CH2O* and CH2O* coupling pathway, the energy barrier to be overcome is 2.89 eV.It includes three parts: one is from CO* to CH2O*, with 1.For the two-CO* dimerization pathway, although the DOS peaks of C atoms in the two CO* are slightly low compared to that of the isolate CO* on the Cu(110) surface, as shown in Figure S4a, the DOS peaks of C atoms in co-adsorbed CO* on the Cu(110) surface are similar.This demonstrates that orbital overlap of the C atoms is very low in two *CO molecules, and thus there is weak interaction between co-adsorbed CO*.So, the CO* dimerization has a high activation energy.For the pathways of CHO* and CHO* coupling, CH 2 O* and CH 2 O* coupling, similar cases take place, as shown in Figure S4d and S4e, respectively.When C-C coupling occurs between the same two intermediates, the repulsion between them causes the distance between them to become larger.So, C atomic orbitals do not overlap significantly, which may be the main reason why the DOS peaks of the C atoms do not change significantly.For the CO* and CHO* coupling pathway, compared with the isolate CHO* on the Cu(110) surface, the DOS peak of the C atom of co-adsorbed CHO* is slightly changed, as shown in Figure S4b.That is to say, the interaction of co-adsorbed CHO* and CO* is weak.For CHO* and CH 2 O* coupling, the DOS peak of the C atom in isolate CHO* is similar to that of co-adsorbed CHO*; the DOS peak of the C atom in isolate CH 2 O* is similar to that of co-adsorbed CH 2 O*.This indicates that the interaction between co-adsorbed CHO* and CH 2 O* is weak.Therefore, given our analysis above, it can conclude that CO* and CH Here, in addition to thermodynamics, other possible C-C coupling pathways do exist if the effects of other factors on C-C coupling are considered, especially the reconstruction of copper electrodes under real reaction conditions.However, further theoretical study may be needed to make an accurate evaluation.CH2OH-CH3, only the reaction steps of CO-CH2O* → CHO-CH2O* and CHOH-CH2* → CH2OH-CH2* are slightly endothermic.This indicates that the process of C2H5OH production from CO-CH2O* can easily take place.This is also consistent with the observation in experiment that the oxygenated hydrocarbon products are the main products on a Cu(110) surface [44].
It is worth noting that the hydrogenation of CH2OH-CH2* is the key to determining the product selectivity on a Cu(110) surface.The reaction energy of the CH2OH-CH2* → CH2OH-CH3* step is −1.65 eV; the CH2OH-CH2* → OH* + C2H4(g) step is −1.42 eV.It is obvious that the reaction energy of the CH2OH-CH2* → CH2OH-CH3* step is lower.Thus, we believe that the CH2OH-CH2* is prone to hydrogenation to CH2OH-CH3*, which then desorbs from the Cu(110) surface to produce C2H5OH.Although it has been indicated that CHO-CH2 is the key to determine the product selectivity of a Cu catalyst, the surface morphology or crystal orientation of a Cu catalyst is not indicated [60].Additionally, the previous literature indicated that the carbon monoxide initially dimerizes and is protonated to form *(OH)C=COH on Cu(100) [61].However, the calculation of activation energy shows that COH* is difficult to form on a Cu(110) surface, so we believe that the *(OH)C=COH is not likely to occur on a Cu(110) surface.Thus, we believe that the CH 2 OH-CH 2 * is prone to hydrogenation to CH 2 OH-CH 3 *, which then desorbs from the Cu(110) surface to produce C 2 H 5 OH.Although it has been indicated that CHO-CH 2 is the key to determine the product selectivity of a Cu catalyst, the surface morphology or crystal orientation of a Cu catalyst is not indicated [60].Additionally, the previous literature indicated that the carbon monoxide initially dimerizes and is protonated to form *(OH)C=COH on Cu(100) [61].However, the calculation of activation energy shows that COH* is difficult to form on a Cu(110) surface, so we believe that the *(OH)C=COH is not likely to occur on a Cu(110) surface.
By comparing the reaction energy of the possible formation intermediates, we identify the intermediates with smaller reaction energy.So, the reaction mechanisms of generating CH 4 and C 2 H 5 OH are revealed.In other words, even if the coverage scenario of the same intermediate is increased, the reaction mechanism is still not affected.Therefore, for the same intermediate, increasing the coverage scenario can reduce the hydrogenation reaction or C-C coupling reaction energy and improve the product efficiency, but does not affect the reaction mechanism.

The Analysis of Applied Potential
Our conclusion above is obtained at a zero applied potential, representing the reaction when no external potential is applied.The applied potential is the minimum required potential on which all elementary reaction steps become exergonic [62].Therefore, the required applied potential is the potential of the potential-limiting step.We compared the production of CH 4 and C 2 H 5 OH based on the applied potential in this section.For the reduction of CO 2 to CH 4 and C 2 H 5 OH, the potential-limiting steps are the formation of COOH* with 0.66 eV.Obviously, the applied potential with −0.66 V (vs.RHE) is required to eliminate the energy barrier.The negative sign indicates a reduction reaction.The Gibbs free energies of CO 2 reduction to CH 4 and C 2 H 5 OH with an applied potential of −0.66 V (vs.RHE) are calculated, and the results are shown in Figure 6.It is worth noting that even if the applied potentials are the same for CH 4 and C 2 H 5 OH production, the Cu(110) surface prefers to produce C 2 H 5 OH.The main reason is that the Cu(110) surface is unstable under CO 2 reduction reaction conditions.This allows the morphology of the Cu(110) surface to evolve into a complex topography of the active site, which is favorable for the formation of C 2 products [63].
reaction or C-C coupling reaction energy and improve the product efficiency, but does affect the reaction mechanism.

The Analysis of Applied Potential
Our conclusion above is obtained at a zero applied potential, representing the re tion when no external potential is applied.The applied potential is the minimum requi potential on which all elementary reaction steps become exergonic [62].Therefore, the quired applied potential is the potential of the potential-limiting step.We compared production of CH4 and C2H5OH based on the applied potential in this section.For reduction of CO2 to CH4 and C2H5OH, the potential-limiting steps are the formation COOH* with 0.66 eV.Obviously, the applied potential with −0.66 V (vs.RHE) is requi to eliminate the energy barrier.The negative sign indicates a reduction reaction.The Gi free energies of CO2 reduction to CH4 and C2H5OH with an applied potential of −0.6 (vs.RHE) are calculated, and the results are shown in Figure 6.It is worth noting that e if the applied potentials are the same for CH4 and C2H5OH production, the Cu(110) sur prefers to produce C2H5OH.The main reason is that the Cu(110) surface is unstable un CO2 reduction reaction conditions.This allows the morphology of the Cu(110) surfac evolve into a complex topography of the active site, which is favorable for the forma of C2 products [63].In addition, the Gibbs free energies of CO 2 reduction to CH 3 OH and C 2 H 4 with an applied potential of −0.66 V (vs.RHE) are also calculated, and the results are shown in Figure S6 of the Supplementary Materials.For CO 2 reduction to CH 3 OH, the steps (* + CO 2 (g)→ COOH* and CH 3 O* → CH 3 OH*) are a positive variation of Gibbs free energies.Thus, the step of * + CO 2 (g)→ COOH* is the potential-limiting step for CH 3 OH production, which is consistent with CH 4 production.Thus, the applied potential of CO 2 reduction to CH 4 and CH 3 OH is the same.A similar situation occurs in CO 2 reduction to C 2 H 4 .Although C-C coupling is an important reaction step, the step of * + CO 2 (g)→ COOH* is the potential-limiting step for C 2 H 4 and C 2 H 5 OH production.

Computation Details
The calculations are performed within the framework of density functional theory as implemented in the Vienna Ab initio Simulation Package (VASP) [64,65].The Kohn-Sham wave functions are expanded in a plane wave basis set with a cut-off energy of 550 eV.The projector-augmented wave (PAW) method and Perdew-Burke-Ernzerhof (PBE) potential for the exchange-correlation function are used [66].Eleven-layer slab model with a surface periodicity of 3 × 5 is used to describe the Cu(110) surface, as shown in Figure 7.The two bottommost layers of the model system are fixed to the optimized bulk parameters, and the rest are fully relaxed during geometry optimization.The convergence criteria for energy and force are set to 1 × 10 −4 eV and 0.01 eV/Å, respectively.The thickness of the vacuum layer is ~15 Å, which is set to avoid interaction between slabs.The Monkhorst-Pack k-point mesh is 2 × 2 × 1.The calculated lattice constant of Cu is 3.61 Å [67], which agrees with the experimental value of 3.62 Å [68,69].Dipole corrections are applied.We use an empirical dispersion correction (D3) for the van der Waals contributions [70].The transition state (TS) is obtained using the climbing-image nudged elastic band (CI-NEB) method [71] by using 5 images, including the initial and final states, during the transition state search.This is verified by obtaining only one imaginary frequency at each TS configuration [72,73].In this study, we only analyze the thermodynamic trend of the CO 2 reduction reaction according to the transition states reported in [74].Additional computational details are provided in the Supplementary Information.In addition, the Gibbs free energies of CO2 reduction to CH3OH and C2H4 with an applied potential of −0.66 V (vs.RHE) are also calculated, and the results are shown in Figure S6 of the Supplementary Materials.For CO2 reduction to CH3OH, the steps (* + CO2(g)→ COOH* and CH3O* → CH3OH*) are a positive variation of Gibbs free energies.Thus, the step of * + CO2(g)→ COOH* is the potential-limiting step for CH3OH production, which is consistent with CH4 production.Thus, the applied potential of CO2 reduction to CH4 and CH3OH is the same.A similar situation occurs in CO2 reduction to C2H4.Although C-C coupling is an important reaction step, the step of * + CO2(g)→ COOH* is the potential-limiting step for C2H4 and C2H5OH production.

Computation Details
The calculations are performed within the framework of density functional theory as implemented in the Vienna Ab initio Simulation Package (VASP) [64,65].The Kohn-Sham wave functions are expanded in a plane wave basis set with a cut-off energy of 550 eV.The projector-augmented wave (PAW) method and Perdew-Burke-Ernzerhof (PBE) potential for the exchange-correlation function are used [66].Eleven-layer slab model with a surface periodicity of 3 × 5 is used to describe the Cu(110) surface, as shown in Figure 7.The two bottommost layers of the model system are fixed to the optimized bulk parameters, and the rest are fully relaxed during geometry optimization.The convergence criteria for energy and force are set to 1 × 10 −4 eV and 0.01 eV/Å, respectively.The thickness of the vacuum layer is ~15 Å, which is set to avoid interaction between slabs.The Monkhorst-Pack k-point mesh is 2 × 2 × 1.The calculated lattice constant of Cu is 3.61 Å [67], which agrees with the experimental value of 3.62 Å [68,69].Dipole corrections are applied.We use an empirical dispersion correction (D3) for the van der Waals contributions [70].The transition state (TS) is obtained using the climbing-image nudged elastic band (CI-NEB) method [71] by using 5 images, including the initial and final states, during the transition state search.This is verified by obtaining only one imaginary frequency at each TS configuration [72,73].In this study, we only analyze the thermodynamic trend of the CO2 reduction reaction according to the transition states reported in [74].Additional computational details are provided in the Supplementary Information.The Gibbs free energy of each elementary step is defined as where ∆ is the reaction energy of each elementary step calculated from DFT total energies.∆ and ∆ are the zero point energy (ZPE) difference and the reaction entropy The Gibbs free energy of each elementary step is defined as where ∆E is the reaction energy of each elementary step calculated from DFT total energies.∆E ZPE and ∆S are the zero point energy (ZPE) difference and the reaction entropy change between the two states of the reaction step.In this work, the temperature is 298.15K and pressure is 1 atm.E ZPE is expressed as the following equation: where vibrational frequency (v i ) is calculated using a method from [75], and only the surface-adsorbed species are allowed to shift during the calculation.The adsorption energy (E ads ) of an intermediate on Cu(110) is defined as where E X * and E * are the total energies of the surfaces with and without the adsorbed intermediates.The E X is the energy of an intermediate, which can be defined as the sum of The step with the highest positive variation of Gibbs free energy is the potentiallimiting step.During an external applied potential (U) in the reaction, the chemical potential of each elementary step changes by eU. e is the electronic charge transferred in each elementary step.The relative energy is obtained by the Gibbs free energy difference between the initial state and the final state of each elementary step [77,78].The activation energy (E a ) of the reaction step is defined as where E TS and E IS are the energy of the transition state and initial state of the reaction step.The proton-electron pairs during the CO 2 reduction reaction can be written as follows [79]: where the chemical potential of proton-electron pairs can be treated as half the energy of hydrogen.Since the CO 2 reduction reaction occurs in a solvated environment, we only consider a single solvent water molecule to reduce the cost of calculation.Thus, an explicit water molecule is included in the computational model to account for the role of solvation.Although the solvation effect can be represented in terms of a single water molecule, it can be inaccurate and lead to errors.However, Luo et al. reported that even if a full solvation model is considered during the CO 2 reduction reaction on low-index Cu surfaces, the results are similar or slightly different from those of a single-water-molecule model.This also shows the rationality of our use of a single-water-molecule model [80].

Conclusions
In summary, based on first-principles calculations, we find that the C 1 and C 2 products of CO 2 reduction on a Cu(110) surface are CH

Supplementary Materials:
The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/catal14070468/s1, Figure S1: The optimized adsorption geometries of the intermediates in Figure 1

4 .
For reduction to C 2 H 5 OH, a C-C coupling pathway is required, which is a crucial reaction step.The energy barriers of C-C coupling among CH x O* (x = 0-2) are systematically compared.The results show that the CO* and CH 2 O* coupling to CO-CH 2 O* is the most likely C-C coupling pathway with the lowest energy barrier.Then, C 2 H 5 OH is produced along the following pathway: CO-CH 2 O* → CHO-CH 2 O* → CHOH-CH 2 * → CH 2 OH-CH 2 * → CH 2 OH-CH 3 * → C 2 H 5 OH.This study provides theoretical guidance for further investigating more C 2+ products on a Cu(110) surface.

Catalysts 2024 , 16 Figure 1 .
Figure 1.Gibbs free energy diagram for CO2 reduction to CH4 on the Cu(110) surface.The energy of [* + CO2(g) + 4H2(g)] is set as a reference.X* represents species X adsorbed on the Cu(110) surface.The optimized adsorption geometries of key intermediates are shown in the insets.Cu: yellow, C: brown, O: red, H: white.

Figure 1 .
Figure 1.Gibbs free energy diagram for CO 2 reduction to CH 4 on the Cu(110) surface.The energy of [* + CO 2 (g) + 4H 2 (g)] is set as a reference.X* represents species X adsorbed on the Cu(110) surface.The optimized adsorption geometries of key intermediates are shown in the insets.Cu: yellow, C: brown, O: red, H: white.For the CO*, it may involve either desorption or hydrogenation on the Cu(110) surface.To compare which is the next possible reaction of CO*, the activation energies of CO* desorption and hydrogenation are calculated, and the results are shown in FigureS2of the Supplementary Materials and Figure2, respectively.The activation energy of CO* desorption is 1.31 eV; the activation energies of CO* hydrogenation to CHO* and COH*are 1.10 and 2.56 eV, respectively.Although the activation energy of CO* desorption is higher than that of the hydrogenation to COH*, it is lower than that of hydrogenation to CHO*.Therefore, CO* prefers hydrogenation rather than desorption on a Cu(110) surface.

Figure 1 .
Figure 1.Gibbs free energy diagram for CO2 reduction to CH4 on the Cu(110) surface.The energy of [* + CO2(g) + 4H2(g)] is set as a reference.X* represents species X adsorbed on the Cu(110) surface.The optimized adsorption geometries of key intermediates are shown in the insets.Cu: yellow, C: brown, O: red, H: white.

Figure 2 .
Figure 2. A schematic potential energy diagram from CO* hydrogenation to CH 3 O* on the Cu(110) surface.The optimized adsorption geometries of the initial states, transition states, and finial states are shown in the insets.Cu: yellow, C: brown, O: red, H: white.For the hydrogenation of CO*, we find that H prefers to bond with C atoms of intermediates rather than O atoms.For example, for the steps of CO* → COH* and CO* → CHO*, the reaction energies are 1.28 and 0.26 eV, respectively.For the steps of CHO* → eV, respectively.The E a of steps from CH 2 O* to CH 2 OH* and CH 3 O* are 0.86 and 0.68 eV, respectively.Obviously, the activation energies of steps from CO* to CHO*, CH 2 O*, and CH 3 O* are lower than those from CO* to COH*, CHOH*, and CH 2 OH*, respectively.This indicates that CO* hydrogenation to CH 3 O* prefers to be along the following pathway: CO* → CHO* → CH 2 O* → CH 3 O*.Given our analysis above, we can conclude that CO 2 reduction to CH 4 along the following pathway: CO 2 → COOH* → CO* → CHO* → CH 2 O* → CH 3 O* → CH 4 .The step of CO* + H* → CHO* has relative high activation energy among the efficient pathway of the hydrogenation of CO* to CH 3 O*, i.e., the steps of CO* + H* → CHO*, CHO* + H* → CH 2 O*, and CH 2 O* + H* → CH 3 O*.In addition to forming COOH*, this could possibly be the other potential bottleneck in the reaction of CO 2 reduction to CH 4 .

Figure 3 .
Figure 3. Schematic potential energy diagrams for (a) two-CO* dimerization, (b) CO* and CHO* coupling, (c) CO* and CH 2 O* coupling, (d) CHO* and CH 2 O* coupling, (e) CHO* and CHO* coupling, and (f) CH 2 O* and CH 2 O* coupling on the Cu(110) surface.The optimized adsorption geometries of initial states, transition states, and finial states are shown in the insets.Cu: yellow, C: brown, O: red, H: white.It is worth noting that the intermediates of C-C coupling refer to intermediates that are co-adsorbed on a Cu(110) surface.The two-CO* dimerization pathway refers to the coupling between one CO* and another CO* that are co-adsorbed on a Cu(110) surface.The CO* and CHO* coupling pathway refers to the coupling of one CO* and one co-adsorbed CHO*.For this pathway, besides the reaction step of CO* and CHO* coupling being endothermic, the formation of CHO* is also endothermic.That is to say, in addition to the energy barrier required for C-C coupling to occur, it is also necessary to consider the energy barrier required to form C-C coupling intermediates.In this case, the two-CO* dimerization pathway need overcome the energy barrier of C-C coupling with 1.47 eV.However, the CO* and CHO* coupling pathway is required to overcome an energy barrier of 2.66 eV.This includes two parts: one is from CO* to CHO*, with 1.10 eV; the other is from CO* and CHO* coupling, with 1.56 eV.Comparing these two C-C coupling pathways, the two-CO* dimerization is more likely to occur because it requires overcoming a lower energy barrier.
27 eV; one is from the other CO* to CH2O*, with 1.27 eV; the last one is CH2O* and CH2O* coupling, with 0.35 eV.By comparing the energy barriers of these six C-C coupling pathways, we find that the energy barrier of CO* and CH2O* coupling to form CO-CH2O * is the lowest with 1.46 eV.It is worth noting that the two-CO* dimerization pathway (1.47 eV) has a similar energy barrier with coupling of CO* and CH2O* (1.46 eV).To compare which of these two C-C coupling pathways is the most likely, the adsorption energies of CO-CO* and CO-CH2O* intermediates are calculated to evaluate the adsorption strengths of them on a Cu(110) surface.The   of the CO-CO* intermediate is −1.93 eV; the   of the CO-CH2O* intermediate is −0.28 eV.Obviously, the adsorption energy of the CO-CH2O* intermediate on a Cu(110) surface is more positive.This indicates that the adsorption strength of the CO-CH2O* intermediate to Cu(110) is stronger.It will make the CO-CH2O* intermediate occupy more active sites, thus weakening the adsorption strength of CO-CO* on a Cu(110) surface.Therefore, even though two-CO* dimerization has a similar energy barrier to CO* and CH2O* coupling, CO* and CH2O* coupling is the most likely C-C coupling pathway on a Cu(110) surface.As we know, the geometric and electronic structures of intermediates play significant roles in the process of C-C coupling.The density of states (DOSs) of six C-C coupling pathways are calculated.The result for the CO* and CH2O* coupling pathway, i.e., the most likely C-C coupling pathway, is shown in Figure 4a.Other results of DOS for C-C coupling pathways are shown in Figure S4 of the Supplementary Materials.

Figure 4 .
Figure 4. (a) The DOSs of C atoms in the adsorbed intermediates for the CO* and CH 2 O* coupling pathway on the Cu(110) surface.(b) Diagrams of the difference in charge densities of CO-CH 2 O* on the Cu(110) surface by an isosurface of 0.002 eV/Å.Yellow represents an electron-accumulation region and blue represents an electron-loss region.∆ρ = ρ(X * ) − ρ( * ) − ρ(X).
For the CO* and CH 2 O* coupling pathway, the C atoms of CO* and CH 2 O* are adsorbed on the Cu(110) surface, respectively.Compared with the DOS peak of the C atom in isolated CO*, the DOS peak of the C atom in co-adsorbed CO* on the Cu(110) surface decreases; compared with the DOS peak of the C atom in isolated CH 2 O*, the DOS peak of the C atom in co-adsorbed CH 2 O* on the Cu(110) surface also decreases.So, compared with the isolate species on the Cu(110) surface, the DOS peaks of co-adsorbed CO* and CH 2 O* distinctly change, as shown in Figure 4a.The reason for this is the orbital overlap of C atoms in co-adsorbed CO* and CH 2 O*.This indicates a strong interaction between CO* and CH 2 O*.Therefore, the CO* and CH 2 O* coupling has a low activation energy.
2 O* is the most likely C-C coupling pathway on the Cu(110) surface.The previous literature suggested that CO* and CH* coupling is a possible C-C coupling pathway on a Cu(110) surface, and CH* formation along the pathway CO* → CHO* → CHOH* → CH* [48].In the literature, CHO* tends to be hydrogenated to CHOH* adsorbed on a Cu(110) surface rather than CH 2 O(g) desorbed from the surface.It is worth noting that the adsorption of CH 2 O* on a Cu(110) surface is completely ignored.Besides the hydrogenation in CHO* to CHOH* and CH 2 O(g) mentioned in the literature, the adsorbed CH 2 O(g) must also be considered.We calculated the reaction energy of the CHO* → CH 2 O* step to compare with the CHO* → CHOH* step, and the results are shown in Figure 1.The result shows that, comparing the CHO* → CHOH* and CHO* → CH 2 O(g) steps, the reaction energy of the CHO* → CH 2 O* step is the lowest.Thus, CHO* prefers hydrogenation to CH 2 O* adsorbed on a Cu(110) surface rather than CHOH*.Thus, the CH* formed along the pathway CHO* → CHOH* → CH* is a challenge.The differences in charge densities of C-C coupling intermediates are calculated and the results are shown in Figure 4b and Figure S5 in the Supplementary Materials, which have been widely used to analyze the interactions between an intermediate and catalyst surface and stability of intermediate on a Cu surface [58,59].For six C-C coupling intermediates, the electron overlap area around Cu atoms is the most large when the CO-CH 2 O* intermediate is adsorbed on the Cu(110) surface.It reveals that the interaction between the CO-CH 2 O* intermediate and Cu(110) surface is the strongest among six C-C coupling intermediates.Because the stronger interaction between the intermediate and the Cu surface, the higher stability of intermediate.Thus, we believe that the CO-CH 2 O* intermediate is the most stable on the Cu(110) surface.This supports that CO* and CH 2 O* coupling is the most likely C-C coupling pathway.
. C 2 H 5 OH Production Pathway Now that we know that the CO* and CH 2 O* coupling to CO-CH 2 O* is the most likely C-C coupling pathway, we explore C 2 products from there.We calculate the Gibbs free energies to produce CH 3 CH 2 OH, i.e., C 2 H 5 OH, and the results are shown in Figure 5.In Figure 5, C 2 H 5 OH is produced along the following pathway: CO-CH 2 O* → CHO-CH 2 O* → CHOH-CH 2 * → CH 2 OH-CH 2 * → CH 2 OH-CH 3 * → C 2 H 5 OH.From CO-CH 2 O* → CH 2 OH-CH 3 , only the reaction steps of CO-CH 2 O* → CHO-CH 2 O* and CHOH-CH 2 * → CH 2 OH-CH 2 * are slightly endothermic.This indicates that the process of C 2 H 5 OH production from CO-CH 2 O* can easily take place.This is also consistent with the observation in experiment that the oxygenated hydrocarbon products are the main products on a Cu(110) surface[44].

Figure 5 .
Figure 5. Gibbs free energy diagram for the production of C2H5OH on the Cu(110) surface.The optimized adsorption geometries of key intermediates are shown in the insets.Cu: yellow, C: brown, O: red, H: white.

Figure 5 .
Figure 5. Gibbs free energy diagram for the production of C 2 H 5 OH on the Cu(110) surface.The optimized adsorption geometries of key intermediates are shown in the insets.Cu: yellow, C: brown, O: red, H: white.It is worth noting that the hydrogenation of CH 2 OH-CH 2 * is the key to determining the product selectivity on a Cu(110) surface.The reaction energy of the CH 2 OH-CH 2 * → CH 2 OH-CH 3 * step is −1.65 eV; the CH 2 OH-CH 2 * → OH* + C 2 H 4 (g) step is −1.42 eV.It is obvious that the reaction energy of the CH 2 OH-CH 2 * → CH 2 OH-CH 3 * step is lower.Thus, we believe that the CH 2 OH-CH 2 * is prone to hydrogenation to CH 2 OH-CH 3 *, which then desorbs from the Cu(110) surface to produce C 2 H 5 OH.Although it has been indicated that CHO-CH 2 is the key to determine the product selectivity of a Cu catalyst, the surface morphology or crystal orientation of a Cu catalyst is not indicated[60].Additionally, the previous literature indicated that the carbon monoxide initially dimerizes and is protonated to form *(OH)C=COH on Cu(100)[61].However, the calculation of activation energy shows that COH* is difficult to form on a Cu(110) surface, so we believe that the *(OH)C=COH is not likely to occur on a Cu(110) surface.By comparing the reaction energy of the possible formation intermediates, we identify the intermediates with smaller reaction energy.So, the reaction mechanisms of generating CH 4 and C 2 H 5 OH are revealed.In other words, even if the coverage scenario of the same intermediate is increased, the reaction mechanism is still not affected.Therefore, for the same intermediate, increasing the coverage scenario can reduce the hydrogenation reaction or C-C coupling reaction energy and improve the product efficiency, but does not affect the reaction mechanism.

Figure 6 .
Figure 6.Gibbs free energy diagrams for CO 2 reduction to (a) CH 4 and (b) C 2 H 5 OH on Cu(110) surface with applied potentials of 0 V and −0.66 V versus RHE.

Figure 6 .
Figure 6.Gibbs free energy diagrams for CO2 reduction to (a) CH4 and (b) C2H5OH on Cu(110) surface with applied potentials of 0 V and −0.66 V versus RHE.

Figure 7 .
Figure 7.The (a) top view and (b) side views of the Cu(110) surface.Cu: yellow.

Figure 7 .
Figure 7.The (a) top view and (b) side views of the Cu(110) surface.Cu: yellow.
4 and C 2 H 5 OH, respectively.CH 4 is produced via the CO 2 → COOH* → CO* → CHO* → CH 2 O* → CH 3 O* → CH 4 pathway.C 2 H 5 OH is produced through CO* and CH 2 O* coupling to the CO-CH 2 O* pathway.This is because this pathway has the lowest activation energy among the C-C coupling pathways between CH x O* (x = 0-2).Then, C 2 H 5 OH is produced along the following pathway: CO-CH 2 O* → CHO-CH 2 O* → CHOH-CH 2 * → CH 2 OH-CH 2 * → CH 2 OH-CH 3 * → C 2 H 5 OH.Our results provide theoretical guidance for further understanding of the mechanism of C 2 production on a Cu(110) surface.
and the bonding distances between them and the Cu(110) surface are shown; Figure S2: Schematic potential energy diagram for CO* desorption from Cu(110) surface; Figure S3: The optimized adsorption geometries of initial states, transition states, and finial states involved in CO* reduction to CH 3 O* in Figure 2 and the bonding distances between them and the Cu(110) surface are also shown; Figure S4: Density of states (DOS) plots of C atoms of adsorbed intermediates in (a) two-CO*; (b) CO* and CHO*; (c) CHO* and CH 2 O*; (d) CHO* and CHO*; and (e) CH 2 O* and CH 2 O* pathways on Cu(110) surface; Figure S5: Diagrams of difference in charge densities of (a) CO-CO*; (b) CO-CHO*; (c) CHO-CH 2 O*; (d) CHO-CHO*; and (e) CH 2 O-CH 2 O* on Cu(110) surface; Figure S6: Gibbs free energy diagrams for CO 2 reduction to (a) CH 3 OH and (b) C 2 H 4 on the Cu(110) surface with applied potentials of 0 V and −0.66 V versus RHE.References [81-87] are cited in the supplementary materials.Author Contributions: Conceptualization, Y.X.; methodology, Y.X. and L.Z.; validation, Y.X.; data curation, Y.X.; writing-original draft preparation, Y.X.; writing-review and editing, Y.X.; visualization, Y.X.All authors have read and agreed to the published version of the manuscript.Funding: This research received no external funding.
al. reported that CH 3 OH is the main C 1 product on a Cu(110) surface and that CO* and CH 2 * coupling to CO-CH 2 * is the key to forming C 2+ products [48].Kuo et al. showed that CO* and CH* are high-concentration C 1 intermediates during the CO 2 electrochemical reduction to CH 4 on a Cu(110) surface.These are the possible C-C coupling species for C 2+ product formation [49].Bagger et al. showed that acetaldehyde is the main C 2 product on Cu(110) surfaces in theory E C , E O , and E H of the intermediate.The E C , E O , and E H are referenced to the energies of CO 2 , H 2 , and the difference between H 2 O and H 2 , respectively.By this definition, more positive E ads means stronger binding.Our calculation method is consistent with that of Dong et al. [76].