DFT Study of CO₂ Reduction Reaction to CH₃OH on Low-Index Cu Surfaces

Abstract

The electrochemical reduction of CO₂ is an efficient method to convert CO₂ waste into hydrocarbon fuels, among which methanol is the direct liquid fuel in the direct methanol fuel cells (DMFC). Copper is the most widely used catalyst for CO₂ reduction reaction (CO₂RR); the reaction is affected by the surface morphology of the copper. Here, the morphology effect and the mechanism of CO₂RR on three typical low-index Cu (100), Cu (110) and Cu (111) surfaces are studied. According to our results, Cu (110) provides the optimum surface for the CO₂RR via CO₂ → *COOH → *CO → *CHO → *CH₂O → *CH₂OH → CH₃OH pathway, where the reduction reaction of CO₂ to *COOH is the potential-determining step (PDS). This is because Cu (110) has the highest d band center, which promotes the adsorption of *COOH.

1. Introduction

Excessive use of fossil energy sources leads to large CO₂ emissions and a range of global climate problems [1,2,3]. Thus, decreasing the amount of CO₂ in the atmosphere is crucial. Carbon capture and storage and carbon conversion to hydrocarbon products have become increasingly important [4,5]. However, the capture and storage of CO₂ requires significant amounts of energy. In contrast, the direct conversion of CO₂ into various hydrocarbon fuels is less energy intensive and is a much more attractive option. To date, thermoscatalysis, photocatalysis and electrocatalysis have been explored for converting CO₂ into various C₁ hydrocarbons (CH₃OH, HCOOH, CH₄), C₂ hydrocarbons (C₂H₄, CH₃CH₂OH) and C₂₊ hydrocarbons under ambient conditions [6,7]. CH₃OH is one of the most important hydrocarbon fuels since it can be used directly as the fuel of direct methanol fuel cells (DMFC) [8,9]; significant achievements have been attained in the development of cost-effective and product-selective electrochemical CO₂ reduction reactions (CO₂RR) [10]. Though both homogeneous and heterogeneous catalysts have been widely investigated [11,12], copper-based catalysts have been considered as the best catalysts for CO₂RR [13,14]. Both Cu⁺ ion [15] and metallic Cu [16,17] are considered as the active catalytic site for CO₂RR. Nevertheless, metallic Cu provides a comparable catalytic function to that of industrial catalysts during the synthesis of methanol [18]. In addition, the CO₂RR can be significantly affected by the morphology of the copper surface [19].

For the CO₂RR to methanol, as listed in Equations (1)–(3), three typical reduction processes, including the two-electron (2e) pathway leading to the formation of CO, the four-electron (4e) pathway leading to HCHO and the six-electron (6e) pathway leading to CH₃OH, were systematically studied in this paper.

$${\mathrm{C}\mathrm{O}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}\to \mathrm{C}\mathrm{O}\left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$$

(1)

$${\mathrm{C}\mathrm{O}}_2\left(\mathrm{g}\right)+4{\mathrm{H}}^{+}+4{\mathrm{e}}^{-}\to \mathrm{H}\mathrm{C}\mathrm{H}\mathrm{O}\left(\mathrm{l}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$$

(2)

$${\mathrm{C}\mathrm{O}}_2\left(\mathrm{g}\right)+6{\mathrm{H}}^{+}+6{\mathrm{e}}^{-}\to {\mathrm{C}\mathrm{H}}_3\mathrm{O}\mathrm{H}\left(\mathrm{l}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$$

(3)

Carbon dioxide has very strong C-O bonds; as such, the dissociation of C-O bonds in carbon dioxide is not a straightforward method. The pathway including the hydrogenation of CO₂ to COOH (${\mathrm{C}\mathrm{O}}_2+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}+\mathrm{*}\to \mathrm{*}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}$) with an indirect C-O bond dissociation and a following dissociation of COOH to CO ($\mathrm{*}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}\to \mathrm{*}\mathrm{C}\mathrm{O}+{\mathrm{H}}_2\mathrm{O}$) is much more favorable than direct C-O bond dissociation [20,21]. Thus, the indirect C-O bond dissociation method was considered in the two-electron reduction pathway. To elucidate the morphology-dependent electrochemical CO₂RR, the adsorption and Gibbs free energy of the reaction via the CO₂ → *COOH → *CO → *CHO → *CH₂O → *CH₂OH → CH₃OH pathway were systematically investigated on the Cu (100), Cu (110) and Cu (111) surfaces. It was found that Cu (110) provides the best catalytic activity towards CO₂RR, and the first step of CO₂ hydrogenation to COOH is the potential-determining step (PDS), with an overpotential of 0.72 V. The method here can also be expanded to design other morphology-dependent CO₂RR catalysts.

2. Computational Details

Density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package [22,23]. The projector-augmented wave (PAW) method was applied to deal with the ion-electron interactions [24], and the Perdew–Burke–Ernzerhof (PBE) [25] functional within generalized gradient approximation (GGA) [26] was used to describe the exchange-correlation functional. The plane wave energy cutoff was set as 500 eV, and the Monkforst–Pack k-point mesh of 4 × 4 × 1 was employed [27]. The convergence criteria of electronic energy and forces were 1.0 × 10⁻⁵ eV and 0.02 eV/Å, respectively. A 3 × 3 slab model consisting of four Cu layers was constructed for various low-index Cu (111), Cu (110) and Cu (100) surfaces, and a vacuum of 15 Å was built to avoid any interaction between different two surfaces.

The surface energy (E_sur) of various copper surface is calculated according to Equation (4):

$$E_{sur}=(E_{slab}-{nE}_{Cu})/2A$$

(4)

where E_slab is the calculated energy of various optimized copper surface, n is the number of Cu atoms in the slab, E_Cu represents the energy of a single Cu atom in the crystal cell and A is the area of various copper surface.

The adsorption energy (E_ads) of the species adsorbed on various low-index Cu surfaces was calculated according to the Equation (5):

$$E_{ads}=E_{Cu/C}-E_C-E_{Cu}$$

(5)

where E_Cu/C, E_C and E_Cu represent the total energy of the adsorption system, the energy of adsorbed carbon species and the energy of Cu surface, respectively. A more negative value of E_ads means a more stable adsorption.

Gibbs free energy change of elementary reaction was calculated according to Equation (6):

$$∆G=∆E+∆E_{ZPE}-T∆S+∆G_{pH}+∆G_U$$

(6)

where ΔE is the change of reaction energy directly obtained from DFT total energy, ΔE_ZPE is the change of zero-point energy, T is the temperature (298.15 K), ΔS is the change of entropy and the results of ZPE and TS corrections to G are listed in Table S1. $∆G_U=-neU$, where n is the number of transferred electrons and U is the electrode potential. ΔG_pH is the correction of the H⁺ free energy by the concentration, $∆G_{pH}=k_{B}T\times \ln 10\times pH$, k_B is the Boltzmann constant and the value of pH was set to be zero for acidic condition. Zero-point energy of every CO₂RR intermediate was computed from vibrational frequencies. The vibrational modes of the adsorbate were computed explicitly, while the Cu surfaces were fixed since the vibrations of the substrate can be negligible. The entropy of thermodynamically stable species in the gas phase was taken from the National Institute of Standards and Technology (NIST) database.

3. Results and Discussion

3.1. Structures and Stability of Low-Index Cu Surfaces

As shown in

Table 1. Surface energy of Cu (111), Cu (100) and Cu (110) surface, respectively.

Surface	Cu (111)	Cu (100)	Cu (110)
Esur (J/m2)	1.77	1.91	2.04

, the surface energies of Cu (100), Cu (110) and Cu (111) are 1.91 J/m², 2.04 J/m² and 1.77 J/m², respectively. The largest difference of surface energy among the three low index Cu surfaces is only 0.27 J/m²; this means that the three typical low-index surfaces share the comparable stability and can be synthesized easily in the experiments. The closest distance between two Cu atoms (Figure 1) is 2.555 ± 0.001 Å in all the Cu surfaces; this is consistent with that in the bulk copper. These findings can be supported by the experimental synthesis performed by Gawande et al. [28] and Ghosh et al. [29].

3.2. Gibbs Free Energy Change during CO₂RR on Low-Index Cu Surfaces

Gibbs free energy changes of the elementary reaction in the CO₂RR via the CO₂ → *COOH → *CO → *CHO → *CH₂O → *CH₂OH → CH₃OH pathway were systematically investigated. Three typical products, including CO, HCHO and CH₃OH, during the electrochemical reduction of CO₂ were studied comparatively on low-index Cu (100), Cu (110) and Cu (111) surfaces. The reduction pathway via formate (HCOO) species was omitted since the formate is a ‘dead-end’ species [30]. Therefore, a proton-coupled electron transfer process that leads to the formation of O-H bond was considered in this paper [31].

All the optimized structures of CO₂RR to CO through a two-electron pathway, to HCHO through a four-electron pathway and to CH₃OH through a six-electron pathway are presented in Figure 2; the related free energy changes of elementary reaction for the electrochemical CO₂RR in presented in Figure 3. A proton-electron pair was added into the elementary step in the pathway, and the energetic levels of all the species are given at U = 0 V_RHE (RHE = reversible hydrogen electrode). The most favorable pathway is the pathway with the lowest positive change of Gibbs free energy between any two steps.

As shown in Figure 3, the free energy change of CO₂RR in the three pathways has a similar trend; the first step reaction of carbon dioxide has the largest energy barrier and determines the activity of the overall carbon dioxide conversion, including CO₂RR to CO, HCHO and CH₃OH [32]. Thus, the hydrogenation of CO₂ to *COOH is considered as the PDS for the whole reduction processes. Moreover, Cu (110) provides the best catalytic activity among the three low-index Cu surfaces, since the energy barrier of the PDS is only 0.72 eV, which is 0.17 eV and 0.50 eV lower than that on Cu (111) and Cu (100), respectively. Specifically, for the reaction of CO₂ to CO via the two-electron pathway, the hydrogenation of *COOH to *CO takes place via a proton-electron transfer step on the three low-index Cu surfaces; the reduction reaction of *COOH to *CO is energy favorable since it is an exothermic reaction. Moreover, CO can desorb much easier on Cu (110) than on both Cu (100) and Cu (111) surfaces, since the CO desorptions on both Cu (100) and Cu (111) surface must overcome a larger energy barrier. For the reaction of CO₂ to HCHO via the four-electron pathway, the reaction follows the two-electron pathway except for the CO desorption process. The hydrogenation of *CO to *CHO in the four-electron pathway is slightly easier than the CO₂ hydrogenation to *COOH step, and the energy barriers for *CO reduction to *CHO are 0.38 eV on Cu (110), 0.81 eV on Cu (100) and 0.85 eV on Cu (111). Cu (110) still provides the best catalytic activity for the reduction reaction of CO to C₁ chemicals. The reduction of *CHO to *HCHO is an exothermic process on various low-index Cu surfaces, and the *HCHO can desorb spontaneously since the free energy change for HCHO desorption is exothermic and the adsorption energy (

Table 2. The adsorption energy of various intermediate species on Cu (111), Cu (100) and Cu (110), respectively.

Surface	Eads/eV
	*COOH	*CO	*CHO	*CH2O	*CH2OH
Cu (111)	−1.59	−0.68	−1.22	−0.02	−0.92
Cu (100)	−1.86	−0.80	−1.40	−0.17	−1.10
Cu (110)	−2.04	−0.54	−1.59	−0.32	−1.20

) is very low. The reduction of CO₂RR to CH₃OH via the six-electron pathway shares the same procedures with that in the four-electron pathway for the initial four electrons. The hydrogenation of adsorbed *HCHO to *CH₂OH is an endothermic process on various low-index Cu surfaces; as such, the three low-index Cu surfaces share similar activity for this step. The energy barriers are 0.17 eV on Cu (110), 0.07 eV on Cu (111) and 0.07 eV on Cu (100). The reduction of *CH₂OH to methanol is a spontaneous reaction on all the low-index Cu surfaces.

3.3. Adsorption of Various Intermediates

The adsorption of various intermediates were studied further. It was found that the C atom of every intermediate is always bound to Cu atom for the three low-index Cu surfaces; this is consistent with previous findings [33,34]. As shown in Table 2, the largest adsorption energy for *COOH can be obtained among all the intermediates, and the values are −2.04 eV on Cu (110), −1.86 eV Cu (100) and −1.59 eV on Cu (111). Charge density difference (Figure 4) accounts for the strongest *COOH adsorption on Cu (110), since more electrons transfer from Cu (110) to adsorbed *COOH than that which can be observed on Cu (111) and Cu (100). Furthermore, the d band center of Cu (110), as shown in Figure 5, is −2.84 eV; this is 0.11 eV and 0.52 eV closer to the Fermi level than that of both Cu (111) and Cu (100), respectively. In addition, Cu (110) shows the highest peak of d band near the Fermi level when compared with Cu (111) and Cu (100). This can account for the largest adsorption energy for the COOH adsorbed on Cu (110) among the three low-index surfaces.

*COOH can be further reduced to the adsorbed *CO according to the CO₂RR mechanism. As shown in Figure 2, CO* prefers to adsorb at the top site of both Cu (111) and Cu (100), with adsorption energy of −0.68 eV and −0.80 eV, respectively. This is consistent with the rule that the closer the d band center to the Fermi level, the stronger adsorption energy for the adsorbate. However, the adsorption energy of CO is only −0.54 eV on Cu (110), which is not consistent with the d band center rule. The reason may lie in the fact that CO prefers to adsorb at the bridge position of Cu (110) instead of the top site on Cu (111) and Cu (100).

The adsorption of CHO and CH₂OH is similar with that of COOH. The adsorption energies of every species were stronger on Cu (110) than that on either Cu (111) or Cu (100), which follows the d band center rule. The adsorption of HCHO on various Cu surfaces is very weak. It is only −0.32 eV on Cu (110) and −0.17 eV on Cu (100). However, it is close to 0 on the Cu (111) surface. This may be related to the maximized electron localization of the HCHO molecule.

4. Conclusions

DFT calculations were performed to understand the CO₂RR via the two-electron pathway to CO, the four-electron pathway to HCHO and the six-electron pathway to CH₃OH. Our results show that the initial activation of carbon dioxide is the PDS and that this determines the activity of the overall carbon dioxide conversion. Moreover, Cu (110) provides the best catalytic activity among the three low-index surfaces, since the energy barrier in the PDS is only 0.72 eV; this is 0.17 eV and 0.50 eV lower than that on Cu (111) and Cu (100), respectively. Furthermore, the d band center of Cu (110) is −2.84 eV; this is 0.11 eV and 0.52 eV closer to the Fermi level than that of both Cu (111) and Cu (100), respectively. Based on these observations, we propose that the Cu (110) surface can be a promising catalyst for the efficient and selective reduction of CO₂RR to CH₃OH. As such, this method can be used to design other catalysts used for CO₂RR.