Electrocatalytic Pathways and Efficiency of Cuprous Oxide (Cu₂O) Surfaces in CO₂ Electrochemical Reduction (CO₂ER) to Methanol: A Computational Approach

Abstract

Carbon dioxide (CO₂) can be electrochemically, thermally, and photochemically reduced into valuable products such as carbon monoxide (CO), formic acid (HCOOH), methane (CH₄), and methanol (CH₃OH), contributing to carbon footprint mitigation. Extensive research has focused on catalysts, combining experimental approaches with computational quantum mechanics to elucidate reaction mechanisms. Although computational studies face challenges due to a lack of accurate approximations, they offer valuable insights and assist in selecting suitable catalysts for specific applications. This study investigates the electrocatalytic pathways of CO₂ reduction on cuprous oxide (Cu₂O) catalysts, utilizing the computational hydrogen electrode (CHE) model based on density functional theory (DFT). The electrocatalytic performance of flat Cu₂O (100) and hexagonal Cu₂O (111) surfaces was systematically analysed, using the standard hydrogen electrode (SHE) as a reference. Key parameters, including free energy changes (ΔG), adsorption energies (E_ads), reaction mechanisms, and pathways for various intermediates were estimated. The results showed that CO₂ was reduced to CO_(g) on both Cu₂O surfaces at low energies. However, methanol (CH₃OH) production was observed preferentially on Cu₂O (111) at ΔG = −1.61 eV, whereas formic acid (HCOOH) and formaldehyde (HCOH) formation were thermodynamically unfavourable at interfacial sites. The CO₂-to-methanol conversion on Cu₂O (100) exhibited a total ΔG of −3.38 eV, indicating lower feasibility compared to Cu₂O (111) with ΔG = −5.51 eV. These findings, which are entirely based on a computational approach, highlight the superior catalytic efficiency of Cu₂O (111) for methanol synthesis. This approach also holds the potential for assessing the catalytic performance of other transition metal oxides (e.g., nickel oxide, cobalt oxide, zinc oxide, and molybdenum oxide) and their modified forms through doping or alloying with various elements.

1. Introduction

Carbon dioxide (CO₂) emission is a significant issue contributing to climate change and environmental pollution [1,2]. Consequently, carbon capture, utilization, and storage (CCUS) technologies have been widely developed and employed to reduce CO₂ emissions [3,4]. Among CO₂ utilization technologies, thermal, photochemical, and electrochemical CO₂ reductions are extensively explored for converting CO₂ into fuels and value-added chemicals. CO₂ electrochemical reduction (CO₂ER) presents a potentially sustainable and stable technique. Nonetheless, these approaches are yet to be implemented industrially due to their considerable energy consumption and low product yield.

Turning CO₂ via CO₂ER into fuels and chemicals highly depends upon the electrolytes and catalysts used [5]. Multiple products can be formed in CO₂ER, such as formic acid (HCOOH), carbon monoxide (CO), methane (CH₄), ethylene (C₂H₄), and methanol (CH₃OH) [6]. CH₃OH conversion on one side is significantly advantageous among these products due to its high market value. However, it also entails a complex reaction pathway in CO₂ER requiring six electron–proton transfers, contrary to the formation of other products, that involve only one or two electron transfers, such as HCOOH or CO [7].

CH₃OH, which is employed industrially as a solvent, pesticide, and alternative fuel source [8], can also be stored in fuel cells, offering direct and convenient internal combustion systems [9]. The demand for CH₃OH has been increasing for various hydrocarbon applications. The total output capacity of CH₃OH was recorded at over 138 billion litres from 2015 to 2020 while CH₃OH utilization increased from 40% to 60% in emerging energy applications [10]. Approximately 250,000 tons of CH₃OH are employed daily as a chemical feedstock or transportation fuel. Producing CH₃OH through CO₂ER can be cost-effective by improving the current density, reducing the system’s energy consumption using more active catalysts, and increasing the ionic conductivity of the electrolytes. Consequently, enhancing CH₃OH production via CO₂ER can have multidimensional benefits [11].

In CO₂ER, CO₂ is reduced through a redox reaction in an electrochemical cell, which yields different products at various potentials, some of the examples are provided in Equations (1)–(5), with their respective standard potentials relative to a standard hydrogen electrode (SHE) [12,13,14,15]. CH₃OH has less negative potential as compared to formic acid and carbon monoxide but requires higher electron–proton transfer, making it more challenging to achieve higher efficiency and selectivity.

$${\mathrm{C}\mathrm{O}}_2+2{\mathrm{H}}^{+}+{2\mathrm{e}}^{-}\to \mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} (-0.61 \mathrm{V})$$

(1)

$${\mathrm{C}\mathrm{O}}_2+2{\mathrm{H}}^{+}+{2\mathrm{e}}^{-}\to \mathrm{C}\mathrm{O}+{\mathrm{H}}_2\mathrm{O}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} (-0.53 \mathrm{V})$$

(2)

$${\mathrm{C}\mathrm{O}}_2+6{\mathrm{H}}^{+}+{6\mathrm{e}}^{-}\to \mathrm{C}{\mathrm{H}}_3\mathrm{O}\mathrm{H}+{\mathrm{H}}_2\mathrm{O}\hspace{1em}\hspace{1em}\hspace{1em}(-0.38 \mathrm{V})$$

(3)

$${\mathrm{C}\mathrm{O}}_2+{12\mathrm{H}}^{+}+{12\mathrm{e}}^{-}\to {\mathrm{C}}_2{\mathrm{H}}_4{+4\mathrm{H}}_2\mathrm{O}\hspace{1em}\hspace{1em}\hspace{1em}(-0.34 \mathrm{V})$$

(4)

$${\mathrm{C}\mathrm{O}}_2+8{\mathrm{H}}^{+}+{8\mathrm{e}}^{-}\to \mathrm{C}{\mathrm{H}}_4+{2\mathrm{H}}_2\mathrm{O}\hspace{1em}\hspace{1em}\hspace{1em} (-0.24 \mathrm{V})$$

(5)

CO₂ absorption in the electrolyte and adsorption/desorption at the electrode interface also involve complex reactions, thus developing an efficient system for reducing overpotential with a high methanol production rate is challenging [16,17]. Active electrocatalysts and electrolytes are necessary to improve product yield and decrease energy consumption during CO₂ER [18,19,20]. Accordingly, miscellaneous catalysts have been assessed for CO₂ conversion into different products [21,22]. Studies have found that metal oxides [23], bimetals [24], and alloys [25] are more feasible electrocatalysts than pure metals to produce fuels, hydrocarbons, and alcohol-based products through CO₂ER [26].

A multicomponent electrocatalyst consisting of silver/sulphur-cuprous oxide/copper (Ag/S-Cu₂O/Cu) demonstrated a CH₃OH production at a 67.4% faradic efficiency (FE) with the presence of ionic liquid in the electrolyte [27,28]. In another report, ethanol was successfully produced with a 40.8% FE employing Ag/Cu₂O electrocatalyst [29]. On the other hand, gold (Au) nanowires were reported to produce CO at 94% FE [30]. Following CO₂ saturation, potassium bicarbonate (KHCO₃) recorded excellent FE for alcohol-based products when the Ag/Cu electrodes were prepared through sputtering deposition [31].

Oxides composed of cations and anions have more diverse surface morphologies, compositions, and structures than metals [32]. The atomic arrangement and composition of oxides result in varying activities for different reaction coordinates. Consequently, product desorption primarily depends on the nature of the catalyst surface and its interaction with the electrolytes.

Several computational techniques have been applied to correlate the performance of the electrodes and electrolytes [33,34], effective sorption energies, and the effects of variables on the reaction pathways to understand the CO₂ER mechanism on the atomic scale [35,36,37,38]. Producing HCOOH directly from *OCHO hydrogenation on Cu₂O (100) surfaces has been documented with excellent accuracy [39]. Furthermore, the ideal CO₂ → *COOH → *CO → CO pathway was obtained with Cu (111) and CuO (111), where * represents the adsorption site of the catalyst [40,41].

Chu et al. demonstrated through experimental and density functional theory (DFT) calculations that ethylene (C₂H₄) was the principal product when antimony (Sb)-modified CuO catalysts were employed [42]. The hydrogenation sequence on copper single-atom alloy for carbon monoxide (CO) production follows CO₂ + * → *CO₂ → *COOH → *CO + H₂O → CO pathway [43]. Meanwhile, CH₄ follows the longer pathway CO₂ + * → *CO₂ → *COOH → *CO + H₂O → *HCO → *H₂CO → *H₃CO → CH₄ + *O, where H₃CO* can be hydrogenated into CH₃OH with additional potential [44].

Electrocatalyst facets possess a considerable influence on electrochemical reduction catalytical activities and stability [45,46]. Consequently, establishing the role of crystal facets is critical during CH₃OH activity and selectivity on catalyst surface determinations. Hence, various computational models are used to estimate the effective potentials in the gas–liquid–solid interface. The effective DFT energies, charge densities, and thermal properties, relevant to catalysts are usually determined using constant electrode potential (CEP), Grand Canonical DFT (GC-DFT), and computational hydrogen electrode (CHE) [47]. CEP normally works on the C–C coupling stage consisting of non-redox processes influenced by the applied voltage [48]. A report estimates that the predictions of the CHE model are adequate for studies involving redox reactions, HER, or OER under DFT energies. The CEP model is suitable for studying complex structures that demand the use of external potential, and it focuses on proton-coupled electron transfer (PCET) steps [49]. The CEP model considers the change in the number of electrons in the unit cell and allows fractional value as constant potential. This increases the computational cost and effort because of the need for iterative DFT calculations at each value of the applied bias. To our knowledge, the CEP has not been extensively utilized to model the CO₂ER, in contrast to the commonly employed CHE [50]. Additionally, the GC-DFT method is computationally intensive, as it accounts for the potential and surface charges of the entire system, recalculating each potential during simulations with reduced precision for free energy values.

In this study, a computational hydrogen electrode (CHE) model with a semi-hydrogen H_2(g) reference electrode and a copper-oxide catalyst (Cu₂O) with different facets are employed during the assessments. Several types of energies have been derived through density functional theory (DFT) by solving the gas–liquid–solid interface system according to the electrochemical cell standards. Primarily, product desorption depends upon the nature of the catalyst surface and electrolyte in the system. Nevertheless, other electrolytes can also be introduced with the reference H_2(g) molecule layer [51,52].

Catalyst active site selectivity can be significantly improved with computational calculations [53]. This study employed DFT, combining quantum mechanical insights with dynamic molecular simulations to provide a more comprehensive analysis to assess transition states and potential variations during CO₂ER in different coordinates. During the reactions, CO₂ as the reactant undergoes transition states yielding various products. DFT calculations utilizing the CHE model also enabled evaluations of reaction types, energy states, and density of states in the system [45,54,55].

The direct correlation of DFT energies to the actual potential (voltage) of a system using Cu₂O (111) and (100) surfaces is still unknown. These two facets of Cu₂O vary in atomic densities and atomic arrangements, which alternatively made a significant impact on selectivity and catalytic activity. Simplifying the engineering of these surfaces, understanding binding energies (how strongly intermediates attach to the surface), and the transition from non-spontaneous to spontaneous reactions for each intermediate is crucial for understanding the stability and selectivity of Cu₂O. However, these aspects have not been thoroughly reported in the literature. Additionally, the CO₂ adsorption and activation between these two surfaces are different and are not well characterized. To the best of our knowledge, this is the first instance of a detailed discussion employing DFT to examine the influence of geometrical variations on binding and adsorption-desorption phenomena from angles to length variation for each intermediate. Furthermore, understanding the mechanisms at the interface between a solid catalyst and a liquid electrolyte, where the electrolyte helps transport gas molecules to the catalyst, is challenging.

This study aims to predict and understand the electrocatalytic properties of CO₂ER to C₁ products (notably CH₃OH) over Cu₂O (100) and Cu₂O (111) catalysts using the CHE model by assessing the sequential hydrogenation pathways. The present study determined the changes in the reaction-free energies, adsorption energies, reaction pathways, and shortest sites for CH₃OH formation including adsorbate behaviour on these facets in detail. The hydrogen molecule was employed as the reference electrode, which maintained the proton and electron transfer values in the elementary steps and helped standardize the measurements and comparisons. The findings demonstrate that the selectivity and product yield depend on the crystallographic planes and the active sites of the catalyst.

2. Results and Discussion

2.1. Models and Molecular Activation on Cu₂O (100) and Cu₂O (111) Sites

The varying behaviours of the adsorbates following DFT calculations on cuprous oxide facets Cu₂O (100) and Cu₂O (111) are illustrated in Figure 1 and Figure 2, respectively. The change in adsorbates’ geometries before and after interaction with the catalyst are given in

Table 1. Details of CO₂ and other adsorbates geometrical variations after interaction on Cu₂O (100) and Cu₂O (111) surfaces.

Compound Name	Compound Structure	After Activation on Cu2O (100)	After Activation on Cu2O (111)
Carbon dioxide (CO2)		∠O–Cu–O = 177.645°	∠O–Cu–O = 179.895°
Formate (HCOO)		1∠H–C–O = 112.549° 2∠H–C–O = 67.422° 3∠O–C–O = 179.807°	1∠H–C–O = 101.402° 2∠H–C–O = 101.549° 3∠O–C–O = 157.048°
Carboxyl (COOH)		1∠O–C–O = 146.253° 2∠C–O-H = 106.324°	1∠O–C–O = 175.551° 2∠C–O–H = 86.745°
Carbon Monoxide (CO)		C↔ O = 1.140°	C↔ O = 1.153°
Formic Acid (HCOOH)		1∠H−O−C = 113.255° 2∠O−C−H = 104.742° 3∠H−C−O = 123.340°	1∠H−O−C = 106.827° 2∠O−C−H = 107.428° 3∠H−C−O = 125.390°
Hydroxymethylene (HCOH)		1∠H−O−C = 113.278° 2∠H−C−O = 96.812°	1∠H−O−C = 107.966° 2∠H−C−O = 101.392°
Methoxy (H3CO)		1∠H−C−O = 108.861° 2∠H−C−O = 119.843° 3∠H−C−O = 123.132°	1∠H−O−C = 108.156° 2∠H−C−O = 110.627° 3∠H−C−O = 113.182°
Methanol (CH3OH)		1∠H−C−H = 107.87° 2∠H−O−C = 108.644° 3∠O−C−H = 142.048°	1∠H−C−H = 106.152° 2∠H−O−C = 103.948° 3∠O−C−H = 106.581°

. The colours white, red, black, and orange-red were assigned to hydrogen, oxygen, carbon, and copper atoms, respectively, while the dimensions are reported in Angstrom (Å) for length, and degree for angle. The structural diversions of different adsorbates and CO₂ on the flat Cu₂O (100) and hexagonal Cu₂O (111) surfaces were determined, and the change on (100) and (111) surfaces was also discussed.

The standard molecular dimensions were confirmed through different databases, including Materials Project, PubChem, and the Crystallography Open Database (COD) [56,57,58]. Structural deviations indicate the catalytic activities of the catalyst interacting with different absorbates. The Cu-O-Cu in both Cu₂O (100) and Cu₂O (111) shows a constant angle of 109.5° after geometry optimization; however, Cu₂O (100) exhibits higher angle changes as compared to Cu₂O (111). Details in dimension changes for facets are given in Table S1 [59,60].

In the case of CO₂ER, the higher adsorption of reaction coordinates negatively impacts selectivity and efficiency towards higher electron–proton transfer for selective products, like in the case of CH₃OH production [61,62]. The higher adsorption in most of the adsorbates for Cu₂O (100) with *CO₂, *H₃CO, and *CH₃OH recorded the highest O-Cu-O angle differences with 177.519°, 173.954°, and 175.326 as shown in Figure 1. This entity possesses the capability to facilitate one or two electron–proton transfers, ultimately resulting in the formation of the carboxyl functional group (COOH) or CO_(g) through CO₂ + * → *CO₂ → *COOH→ *CO + H₂O → CO_(g) with extra energy to proceed for the reaction. The (100) surface has also less non-stoichiometric O termination, making this surface unstable during CO₂ER. The (100) surface, in this case, is reactive and prone to noticeable changes in atomic locations, bond angles, and surface shape, and can be degraded rather than proceeding with an electrochemical reduction reaction. Moreover, minimal changes on the same surface were recorded for *CO, *HCOOH, and *HCOH. The major reason for the unstable (100) surface is its low oxygen coverage with less than 0.5 monolayer (ML), with the top layer being occupied with Cu, which can move down during the reaction, and the O atomic layer taking part to activate the adsorbates for the reaction. As a result of the electronegativity difference, the O attracts the shared electrons more strongly towards H to form a polar covalent bond, compared to the Cu, which has delocalized electrons and needs additional forces to bind with H, namely temperature, pressure, and pH.

However, the Cu₂O (111) top surface has an O layer available for H exposure, making Cu atoms more stable on this surface for catalytical activity [61,62,63]. This is also validated by the positive free energy (ΔG) values and non-spontaneous reactions for *CO and *HCOH on Cu₂O (111). The higher tendency of O bonding towards Cu from various adsorbates in Cu₂O (100) can oxidize the Cu surface, leading to copper hydroxide (Cu(OH)₂) and copper carbonate (CuCO₃) formation that reduces the lifespan of the catalyst rather than alleviating the CO₂ER, which has also been witnessed in multiple research works [64]. Furthermore, the considerable CO-CO interactions induced rearrangements in the Cu₂O structure, requiring more energy to further CO conversions into HCOOH and HCOH [65,66].

The pristine, (defect-free) Cu₂O (111) surfaces employed in this study showed varying catalytic activities due to the dangling coordinatively unsaturated copper (CuU) atom bonds on the Cu₂O (111) surfaces, making them more catalytically active [67]. The non-polar stoichiometric oxygen-terminated surface of Cu₂O (111) exhibited more stability as shown in Figure 2a [67,68,69]. The highest structure change in O-Cu-O for Cu₂O (111) was seen for *COOH, *HCOOH, and *CH₃OH, while the least changes were recorded for *CO₂, *HCOO, and *H₃CO. The ∠O-Cu-O angle for *CH₃OH on Cu₂O (100) was recorded at 175.326° and Cu₂O (111) exhibited an angle of 169.569°. On the other hand, the Cu-O-Cu change in angle for *CH₃OH was 110.725° for Cu₂O (100) and 103.228° for Cu₂O (111). These variations in Cu₂O (111) for CH₃OH are due to flexible Cu in the catalyst and strong hydroxyl (-OH) bonding towards Cu atoms from methanol. This change is based on the structure relaxation and rearrangement of Cu and O to minimize overall energy in the final product.

The *CH₃OH shows higher adsorption in Cu₂O (100) as illustrated in Figure 1i, which entirely changes the structure of CH₃OH and makes it difficult to stabilize and detach from the surface. The change in the angle of O-C-H in CH₃OH after optimization was measured at 142.048° on Cu₂O (100), which is much higher than the (111) surface. Due to the larger angle and structural changes, CH₃OH becomes unstable on the Cu₂O (100) surface. This instability increases the likelihood that *CH₃OH will dissociate into carbon monoxide (CO) gas or methoxy (H₃CO) rather than forming CH₃OH_(l).

The standard angle of O=C=O for CO₂ is found to change from 180° to 177.645° at the Cu₂O (100) surface and to 179.895° on the Cu₂O (111) surface. The Cu₂O (100) is more reactive with less coordinated atoms, and additional unsaturated bonds interact with adsorbed CO₂ molecules leading to greater distortion in CO₂ molecules. It enhances the weakening of the C-O bond and can be slightly better for CO₂ activation than the (111) surface, with the latter consuming more energy during initial reduction. Therefore, the reaction from *CO₂ to *COOH was also determined to be more promising on the (100) surface following the free energy profile. The H stretching in *HCOO and *COOH towards Cu atoms were noted on (100) and (111) surfaces, respectively, which helps to catalytically decompose *HCOO and *COOH towards CO with the highest angle variation in H-C-O of 67.422° in *HCOO on (100) surface, and C-O-H of 86.745° in *COOH for (111) surface (see Table 1).

The CO_(g) was found to be stable on both surfaces with minor changes in length. In the case of *HCOOH, the O forming the bond with the Cu atom was found with the highest change on the (100) surface, increasing the angle from 109.514° to 104.742° for ∠O–C–H. Meanwhile, for the (111) surface, the change was observed from 109.514° to 107.428°. Therefore, the desorption of HCOOH_(l) from adsorbed *HCOOH on the (111) surface must be higher. Similarly, the variation in angle for H–C–O for *HCOH and *H₃CO computed after adsorption was 96.812° and 123.132° on the Cu₂O (100) and (111) surfaces, respectively. This phenomenon involved carbon (C) bonding from *HCOH towards Cu. In bulk, this can lead to the formation of CuCO₃ on the surface, producing H₂O molecules in the electrolyte as a by-product (see Figure 1).

Similar but less pronounced changes were observed on the Cu₂O (111) surface. This suggests that the catalytic conversion of adsorbed molecules occurs more stably without distorting the surface. Therefore, the catalytic activity for converting CO₂ to CH₃OH is more promising on Cu₂O (111) compared to Cu₂O (100).

2.2. Adsorption Energies (E_ads)

The adsorption energies (E_ads) and thermodynamic properties of the different species and catalysts evaluated in the present study were calculated at standard temperature and pressure (298 K and 1 atm) (see Tables S2–S4 in the Supplementary Materials). After geometry optimization, hydrogen gas (H₂) exhibited the lowest heat capacity of 6.99 J/K and an enthalpy of 4.57 kcal/mol, indicating that it has the lowest formation enthalpy among the substances studied [70]. On Cu₂O (100) and (111), the thermodynamic characteristics of various adsorbates revealed a precisely proportional relationship between molar masses and free energies. The E_ads obtained in this study were determined following the equations given in Supporting Information Equations (S1)–(S8). According to the results given in Figure 3, the more negative adsorption energies (E_ads) lead to higher exergonic rates (more spontaneous) and require more potential than their positive counterparts, requiring more potential to drive CO₂ reduction. Consequently, the adsorption energy is inversely related to the free energy changes during the adsorption and desorption processes.

The compounds with low molecular weight yielded less negative adsorption. The E_ads released during *CO₂ was less negative (−0.37 eV) than the E_ads of *HCOOH (−1.19 eV) on Cu₂O (100), which indicates that *CO₂→CO₂ or CO is more exergonic than *CO₂ → HCOOH. The E_ads show a good correlation with molecular activation, as discussed in the previous section. The Cu₂O (111) also documented similar results, where *CO₂ and *HCOOH recorded E_ads of −0.46 eV and −1.08 eV, respectively. The E_ads for *CH₃OH on Cu₂O (100) and Cu₂O (111) were recorded at −2.8 eV and −2.0 eV, respectively, indicating the bulk adsorption of *CH₃OH on Cu₂O (100) than Cu₂O (111). On the other hand, *CO₂ recorded the lowest E_ads, considering it is produced in the first elementary step before hydrogenation. The adsorption energies (E_ads) of *CO were found to be −0.48 eV for the (100) surface and a much lower value of −0.84 eV for the (111) surface. The adsorption energy value indicates the stability of the adsorbate on the catalyst surface where a more negative value means a stronger bond and more stable adsorption. In this case, CO molecules have a stronger interaction with Cu₂O (111) than Cu₂O (100). Furthermore, the more negative values of E_ads (stronger bond) from CO₂ activation to *CH₃OH can be explained by the increasing number of H and O atoms available in the molecular structures. A slightly higher difference in adsorption energies between *H₃CO and *CH₃OH was observed during the interaction of H from *H₃CO and C/O from *CH₃OH. Moreover, the weak van der Waals forces between hydrogen (H) and copper (Cu) or oxygen (O), combined with the strong chemical bonding of carbon (C) or oxygen (O) to copper, can lead to the formation of CuCO₃ or Cu(OH)₂. This results in the deactivation of the catalyst surface. Therefore, further investigation of the catalyst surface using bulk electrolysis or long-term chronoamperometric measurements is recommended.

2.3. ΔG Profiles and Reduction Pathways of CO₂ER

The ΔG profiles of the CO_(g), HCOOH_(l), HCOH_(l), and CH₃OH_(l) products derived from DFT calculations on both surfaces are given in Figure 4. Based on the results, CO₂ activation energies on Cu₂O (100) and (111) were recorded at −0.37 eV and −0.45 eV, respectively. The data also revealed that *CO₂ reduction to *HCOO is endergonic (non-spontaneous) on both surfaces compared to *COOH. Conversely, the *CO₂ to *COOH reaction is slightly negative and exergonic (spontaneous), with a ΔG of −0.34 eV and −0.20 eV on the Cu₂O (100) and (111) surfaces, respectively.

The formation of *HCOOH from *HCOO and *COOH intermediates is exergonic, with a ΔG of −0.82 eV and −0.10 eV for Cu₂O (100) and (111), respectively. The results indicate that *COOH production and desorption are constructive in both facets. Nonetheless, HCOOH_(l) desorption needs more energy than CO_(g) production. The reaction also originated at the negative side of the energy profile, confirming CO_(g) as the primary product on both surfaces. Consequently, CO_(g) production following the *CO₂ → *COOH → *HCOOH → CO_(g) pathway is more favourable than the HCOOH_(l) pathway, according to the *CO₂ → *COOH → *HCOOH → HCOOH_(l) reaction pathway.

An experimental report also supported the findings in this study that CO_(g) production was more quantitative in primary reactions [71]. It can be proved that the *CO₂ → *COOH → *HCOOH reaction is more spontaneous than *CO₂ → *HCOO → *HCOOH. The energy differences calculated for HCOH_(l) desorption for the two pathways *CO₂ → *HCOO → *CO → *HCO → *H₂CO → HCOH_(l) and *CO₂ → *COOH → *HCOOH → *HCO → *H₂CO → H₂CO_(l), were −0.72 eV and −1.77 eV, respectively. Based on the results, the *CO₂ → *COOH pathway is more exergonic than *CO₂ → *HCOO for HCOH_(l) production on Cu₂O (100). Similarly, concerning the pathways from *HCOH onwards, the *HCOH → *H₃CO → *H₃COH → CH₃OH_(l) reaction is more favourable than the *HCOH → *H₂COH → *H₃COH → CH₃OH_(l) counterpart to yield CH₃OH_(l). The reaction pathways and changes in the reaction ΔG for all elementary steps are listed in

Table 2. The changes in the reaction ΔG for all elementary steps on Cu₂O (100) and Cu₂O (111).

Reaction	ΔG (eV) for Cu2O (100)	ΔG (eV) for Cu2O (111)
* + CO2(g) $\to$ *$\mathrm{C}{\mathrm{O}}_2$	−0.37	−0.11
*$\mathrm{C}{\mathrm{O}}_2\to \mathrm{*}\mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}$	0.22	−0.12
*$\mathrm{C}{\mathrm{O}}_2\to \mathrm{*}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}$	0.30	0.08
*$\mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}\to \mathrm{*}\mathrm{C}\mathrm{O}+{\mathrm{H}}_2\mathrm{O}$	−0.10	0.16
*$\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}\to \mathrm{*}\mathrm{C}\mathrm{O}+{\mathrm{H}}_2\mathrm{O}$	−0.43	0.43
*$\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}\to \mathrm{*}\mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}$	0.27	0.50
*$\mathrm{C}\mathrm{O}\to \mathrm{*}\mathrm{H}\mathrm{C}\mathrm{O}$	−0.14	0.23
*$\mathrm{H}\mathrm{C}\mathrm{O}\to \mathrm{*}\mathrm{H}\mathrm{C}\mathrm{O}\mathrm{H}$	0.14	0.41
*$\mathrm{H}\mathrm{C}\mathrm{O}\to \mathrm{*}{\mathrm{H}}_2\mathrm{C}\mathrm{O}$	0.003	0.29
*$\mathrm{H}\mathrm{C}\mathrm{O}\to \mathrm{*}{\mathrm{H}}_2\mathrm{C}\mathrm{O}\mathrm{H}$	0.05	0.46
*$\mathrm{H}\mathrm{C}\mathrm{O}\to \mathrm{*}{\mathrm{H}}_3\mathrm{C}\mathrm{O}$	0.86	0.63
*${\mathrm{H}}_2\mathrm{C}\mathrm{O}\mathrm{H}\to \mathrm{*}{\mathrm{H}}_2\mathrm{C}+{\mathrm{H}}_2\mathrm{O}$	0.37	−0.05
*${\mathrm{H}}_2\mathrm{C}\mathrm{O}\mathrm{H}\to \mathrm{*}{\mathrm{H}}_3\mathrm{C}\mathrm{O}\mathrm{H}$	0.60	0.45
*${\mathrm{H}}_3\mathrm{C}\mathrm{O}\mathrm{H}\to \mathrm{C}{\mathrm{H}}_3\mathrm{O}\mathrm{H}$	0.07	0.08

.

It can then be deduced that the surface of the Cu₂O (111) shows higher exposure to O atoms than C atoms compared to those of the Cu₂O (100) surfaces during its crystallographic oxygen orientation, which enhances the chances of hydrogenation to proceed further and form CH₃OH. Consequently, the two surfaces show different energy profiles. At a laboratory scale, the crystallographic planes of Cu₂O (100) and (111) can be synthesized via wet chemical reductions, electrodeposition, anodization, and solvothermal synthesis [45], and can be used as electrocatalysts for CO₂ER. The products, such as H₂CO_(l) from *H₂CO or *H₂COH, and CO_(g) from *CO, obtained with Cu₂O (100), were slightly more spontaneous than Cu₂O (111). Nevertheless, among the CO₂ reduction to CH₃OH pathways evaluated in this study, the *CO₂ → *COOH → *HCOOH → *HCO → *HCOH → *H₂COH → *H₃COH → CH₃OH_(l) reaction with Cu₂O (111) shows the shortest pathway, as shown in Figure 5. The reaction involving Cu₂O (100) required an additional 0.90 eV to produce CH₃OH, determined from *H₃COH adsorption according to DFT energy calculations and ZPE profiles.

The (100) surfaces exhibited energy profiles closer to positive values, with minor deviations in adsorbates. In contrast, the Cu₂O (111) surface remained on the negative side of the energy profile, showing a more significant energy difference from *HCOOH to *HCO compared to the Cu₂O (100) facet. This shows that the Cu₂O (111) surface has higher catalytic activity and reaction rates. Based on calculations, the total ΔG needed to reduce *CO₂ to CH₃OH with Cu₂O (100) and (111) was approximately −3.14 eV and −5.72 eV, respectively. Negative values of ΔG indicate that the reaction is spontaneous and energetically favourable. Consequently, this makes the Cu₂O (111) surface a more viable choice for the electroreduction of CO₂ to CH₃OH.

Detailed reactions are documented in Supplementary Materials Equations (S9)–(S21), while the direct conversion of adsorbate from its latest reaction coordinates and possible reduction pathways are illustrated in Figure 6. *CO₂ is adsorbed on the surface and proceeded towards CH₃OH_(l) with multiple electron–proton transfer via hydrogenation. The CO_(g) in this case can be produced from adsorbed *HCOO or *COOH, which remain adsorbed on the catalyst surface and are then converted into *HCOOH via hydrogenation, where HCOOH_(l) is easily produced. The *HCO generated after the removal of the hydroxide anions is converted into H₂CO_(l) or *HCOH which can then proceed to produce CH₃OH and CH₄. Understanding the energy pathways for these products can help predict the applied potential needed at the laboratory scale for feasible CO₂ER into value-added products. Based on the elementary phases and activation energies, the ΔG for the catalyst Cu₂O (100), in descending, order are: *H₃CO < *H₃COH < *H₂C < *COOH < *HCOOH < *HCOH < *CH₃OH(l) < *H₂COH < *H₂CO < *CO < *HCO < *CO₂. Meanwhile, the ΔG for the catalyst Cu₂O (111) are: *H₃CO < *HCOOH < *H₂COH< *H₃COH < *CO < *HCO < *H₂CO < *HCOH < *COOH < *CH₃OH(l) < *H₂C < *HCOO < *CO₂.

The data showed that *H₃CO interactions consumed the most energy, while *CO₂ interactions required the least energy in both cuprous oxides. The total energy required to reduce *CO₂ to *CO through the *COOH pathway is −0.5 eV employing Cu₂O (100), while Cu₂O (111) recorded a value of 0.4 eV. The results indicated that Cu₂O (100) is superior to Cu₂O (111) for CO_(g) and bicarbonate production. Nonetheless, the oxide is unsuitable for transforming CO_(g) to CH₃OH_(l) due to the higher potential required.

The formation of CH₃OH exhibits sluggish reaction rates, as it involves six electron transfers through various intermediates. In contrast, products such as formate or CO require less electron transfer and have higher reaction rates. Additionally, catalysts tend to decline in activity over time, further reducing reaction rates. Our results demonstrate that the extensive pathway for CH₃OH formation leads to low reaction rates from *CO₂ to CH₃OH (Figure 5 and Figure 6).

These reaction pathways suggest that CO₂ER to CH₃OH needs a longer reaction pathway requiring higher overpotentials than formate or CO. Consequently, based on our findings, the Cu₂O (100) surface is not effective for long reactions due to surface reconstruction, unlike the more stable Cu₂O (111) (Figure 2a). Nonetheless, doping or complexing Cu₂O with single-atom catalysts (SACs) could enhance reaction stability and increase reaction rates for CH₃OH formation, as supported by previous reports [72,73,74,75,76].

On the other hand, a straightforward and favourable reaction pathway from CO₂ to CH₃OH is proposed using Equations (6)–(9). In this pathway, an oxygen atom from either the Cu₂O (100) or Cu₂O (111) surface adsorbs onto the carbon atom of CO₂, forming a carboxyl (COOH) radical. This radical then reacts with hydrogen/protons to produce formic acid (HCOOH). As previously discussed, the carbon atom in formic acid has a higher affinity for the Cu₂O (111) surface, especially when an exposed oxygen atom is present. This interaction promotes the formation of methanol (CH₃OH).

$$\mathrm{C}{\mathrm{O}}_2+{\mathrm{e}}^{-}\to \mathrm{C}{\mathrm{O}}_2^{\mathrm{*}}$$

(6)

$$\mathrm{C}{\mathrm{O}}_2^{\mathrm{*}}+{\mathrm{H}}^{+}\to \mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}$$

(7)

$$\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}+{\mathrm{e}}^{-}+{\mathrm{H}}^{+}\to {\mathrm{H}}^{\mathrm{*}}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}$$

(8)

$${\mathrm{H}}^{\mathrm{*}}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}+{\mathrm{e}}^{-}+{\mathrm{H}}^{+}\to \mathrm{C}{\mathrm{H}}_3\mathrm{O}\mathrm{H}$$

(9)

According to the results presented in this work, CO desorption from *HCOO is achievable by applying extra potential, following the trends of energy activation. This process breaks the C-O bonds, converting *HCOO to CO from metal oxide sites. Alternatively, *COOH will lead to *CO production via O-H removal in the form of water. *OCHO production on metal sites is also possible from oxide formation. Initially, metals are converted to metal oxides, which can directly produce HCOOH_(l). Cu₂O, being a metal oxide, provides the highest yield of HCOOH_(l) [77]. H₂CO_(l) can be obtained through a four-electron reduction process: *HCOOH → *HCO + H₂O → *H₂CO → H₂CO_(l). Similarly, sequential protonation of *HCOOH → *HCO + H₂O → *H₂CO → *H₃CO → *H₃COH → CH₃OH_(l) produces CH₃OH_(l). However, these pathways depend on the relative hydrogenation stability of the catalyst [78,79].

Several studies have verified the synthesis of the octahedron (111), hexagonal (111), and dodecahedral (110) crystal facets with six, eight, and twelve crystal planes from cubic Cu₂O (100) through X-ray diffraction (XRD) analysis [80,81]. Although most reports focused on performance without considering the effects on electronic energies, the free energy values documented in this study are comparable with other reported computational studies as shown in

Table 3. Comparison of free energies calculated for cuprous oxide (Cu₂O) using DFT.

Adsorbate	Adsorbent	Free Energy (eV)	Reference
*$\mathrm{C}{\mathrm{O}}_2$	Cu2O (100)	−0.37	This work
	Cu2O (111)	−0.11
*HCOO	Cu2O (100)	0.22	This work
	Cu2O (111)	−0.12
*COOH	Cu2O (100)	0.30	This work
	Cu2O (111)	0.08
*CO	Cu2O (111)	−0.10	This work
	Cu2O (100)	0.16
*HCOOH	Cu2O (111)	0.27	This work
	Cu2O (100)	0.50
*CO2	Cu2O (111)	−0.09	[82]
$\mathrm{*}\mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}$		−0.14
$\mathrm{*}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}$		0.35
*$\mathrm{C}\mathrm{O}$		−0.50
$\mathrm{*}\mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}$		−0.40
CO2	Cu2O (111)	0.00	[83]
$\mathrm{*}\mathrm{C}\mathrm{O}$		−0.50
$\mathrm{*}\mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}$		−0.01
*CO2	Cu2O (111)	−0.13	[84]
$\mathrm{*}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}$		−0.12
$\mathrm{*}\mathrm{C}\mathrm{O}$		−0.65
CO2	Cu2O	0.00	[85]
$\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}$		0.10
$\mathrm{C}\mathrm{O}$		−1.00
$\mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}$		−0.50

.

Furthermore, the correlation of the respective energies offers various avenues for material selection. For example, nanosized Cu₂O particles were developed and enclosed within cubic Cu₂O (100) and Cu₂O (111) octahedron structures utilizing the hydrothermal method [86]. The study reported 35.4% as the highest FE, achieved with the octahedron Cu₂O (111) structure, while 26.2% FE was achieved by the cubic Cu₂O (100) for alcohol base products [86]. In another study, CO₂ was reduced to methane with 66.57% FE on the exposed surfaces of Cu nanostructure with predominant (111) orientation [87]. A facet-regulating experiment yielded Cu₂O (111) nanocatalysts. The substance was produced via the reductant-controlled method and achieved 74.1% FE for ethylene (C₂H₄) [88]. Performance comparison of various products between Cu₂O (100) and Cu₂O (111) from different literatures is presented in

Table 4. CO₂ER products and performance over cuprous oxide (Cu₂O).

Material	Product	% Faradic Efficiency	References
Cu2O (100)	CH3OH	26.20	[86]
Cu2O (111)	CH3OH	35.7
Cu2O (100)	CO	20
Cu2O (111)	CO	40
Cu2O (100)	C2H4	38	[45]
Cu2O (111)	C2H4	45
Cu2O (111)	CH3OH	29.1	[89]
Cu2O (100)	C2H4	30.1	[90]
Cu2O (111)	C2H4	44.9
Cu2O (111)/Cu2O (100)	C2H4	57.8

.

Research on the same material found that the tetrahedral Cu₂O (111) crystal lattice was favourable for CH₃OH selectivity when modified from Cu₂O (100). Other studies indicated that the highest CO_(g) FE was achieved with cubic Cu₂O (100) [91,92], supporting the findings of this study. The literature also noted that CH₃OH production with Cu₂O (111) was optimal due to its defect-free nature, which offers more adsorption sites and surface oxygen availability. At 140 K, the surfaces could form a mixed layer of methoxy, formaldehyde, and other CH-containing species [93]. The active CH-bond breaking properties of the structure also enable the catalyst to convert CO₂ to CH₃OH [94]. Conclusively, the surface of Cu₂O (111) possesses exceptional structural and electrical characteristics, making it efficient for the selective electrochemical reduction of CO₂ to CH₃OH [93]. These attributes include the availability of adsorption sites, surface oxygen, and the capacity to stimulate crucial reaction steps. Additionally, doping other elements with different orientations and ratios on copper and copper oxides could lead to varied results [95].

3. Model and Computational Details

The DFT calculations in the current study were performed using the DMol³ in Materials Studio (MS 20.1). The selection of DFT calculations, utilizing a transition from a single crystal to an amorphous system, aligns well with the parameters employed in this study. DFT has been widely reported in numerous research studies for its high quality and accuracy, particularly when analysing different molecules across a broad range of crystal systems [96,97,98]. The evaluations were conducted in a generalized gradient approximation (GGA) as an exchange-correlation function according to the Perdew–Burke–Ernzerh (PBE) scheme. The calculations were performed on (3 × 3 × 3) Cu₂O (100) and Cu₂O (111) surfaces, a 3.71 Å lattice constant, a 2 × 3 surface slab, and a 20 Å thick vacuum slab perpendicular z-direction to avoid periodic interaction between periodic images.

The vacuum slab was constructed consisting of three atomic layers, where the top layer of Cu₂O was kept relaxed during geometry optimization and the bottom two layers were kept fixed. For all intermediate adsorptions, a top hollow site with perpendicular orientation was consistently employed as the model configuration. The intermediates and stable compounds were placed between hollow sites of Cu and O to see the possible interaction of molecules towards catalyst sites. To observe potential interactions between the π-electrons of various adsorbates with the d-orbitals of Cu atoms, and coordination of oxygen lone pairs with Cu sites, a perpendicular orientation was selected. This configuration provides multiple Cu atoms for coordination, promoting the stabilization of intermediates through chemical bonding. Furthermore, the presence of surface oxygen atoms on Cu₂O can contribute to hydrogen bonding or polar interactions, potentially facilitating the hydrogenation pathway.

In this study, the spin moment under regular crystals was restricted, while geometry optimization for free molecules was marked as unrestricted. Ideal unit cells were obtained by employing cartesian coordinates. In the present study, all electrons were selected for core treatment. A double numerical plus d-functions (DND) numerical basis set at a 4.4 basis file was employed due to significant atomic mass. The gamma k-point set was used during electronic calculations, which aided orbital determinations. Geometry optimization in this study was performed at the lowest observed binding energy.

According to the CHE model, the standard hydrogen electrode (SHE) is used to measure the redox potential, which is based on reversible hydrogen redox reaction and can be written as Equations (10) and (11) [99].

$${\mathrm{H}}_2\to 2{\mathrm{H}}^{+}+{2\mathrm{e}}^{-}$$

(10)

$${\mathrm{H}}_{\left(\mathrm{a}\mathrm{q}\right)}^{+}+{\mathrm{e}}^{-}\leftrightharpoons {\displaystyle \frac{1}{2}}{\mathrm{H}}_{2\left(\mathrm{g}\right)}$$

(11)

The electrode potential in this relation is computed by subtracting the experimental value of the absolute standard hydrogen electrode potential from the calculated potential of any other reference electrode potential. On the contrary, if the SHE itself is used as a reference electrode, then the potential of this SHE is added to the value of the working electrode and species reacting with that electrode. Hence, following the same calculations, the free energy values for all intermediates determined through DFT were added from the hydrogen energies relevant to the balanced e reactions in this study (given in Supplementary Materials from Equations (S9)–(S21)). The oxidation–reduction in the current study was determined according to Equations (12)–(14):

$${\displaystyle \frac{1}{2}}{\mathrm{O}}_2+\mathrm{\ast }\to {\mathrm{O}}^{\mathrm{*}}$$

(12)

$${\mathrm{O}}^{\mathrm{*}}+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}\to {\mathrm{H}\mathrm{O}}^{\mathrm{*}}$$

(13)

$${\mathrm{H}\mathrm{O}}^{\mathrm{*}}+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}\to {\mathrm{H}}_2\mathrm{O}+\mathrm{\ast }$$

(14)

where * denotes the catalyst site.

The same method was used for all adsorbates and intermediates adsorption and activation on Cu₂O surfaces having different facets. The SHE was employed to compare catalyst sites and various species participating in CO₂ activation to CH₃OH desorption post-foundation. For all reaction coordinates, the parameters employed for the calculation were based on ${\mathrm{H}}^{+}+{\mathrm{e}}^{-}$ transfer at standard potential (pH 7, 1 bar pressure, and 298 K temperature) as given in Equations (8)–(10). The free energy of hydrogen was first optimized using DFT and used for further calculations, including free energy profiles and adsorption energies (E_ads).

E_ads were determined following Equation (15). The Gibbs free energy (ΔG) of all elementary steps involved was computed utilizing chemical reactions based on (${\mathrm{H}}^{+}+{\mathrm{e}}^{-}$) transfer on the adsorbed CO₂ hydrogenation. A detailed reaction adsorption energy list for all species is presented in Supplementary Information Equations (S1)–(S8) [54]:

$$E_{ads}=E_{slab+ads}^{total}-E_{iso-slab }-E_{iso-ads}$$

(15)

where slab represents the unit cells with Cu₂O (100) and Cu₂O (111) catalysts, iso-slab denotes the isolated slab system, and ads indicates adsorption.

4. Conclusions

In this study, density functional theory (DFT) calculations were employed to predict and understand the electrocatalytic properties of CO₂ electroreduction (CO₂ER) to C₁ products over Cu₂O (100) and Cu₂O (111) catalysts using the computational hydrogen electrode (CHE) model. The study focused on the performance of CO₂ER towards CH₃OH production on different facets of Cu₂O. The results showed that carbon monoxide (CO) formation was favoured during the initial reduction of CO₂ on both crystallographic planes. However, the Cu₂O (111) surface, with its protrusions, exhibited higher catalytic activity and selectivity for methanol (CH₎ compared to Cu₂O (100). The production of CH₃OH on Cu₂O (111) was more exergonic than on Cu₂O (100). Both Cu₂O (100) and Cu₂O (111) surfaces demonstrated similar tendencies to produce CO at low potentials during the decoupling of carbon from adsorbed *CO₂. Theoretically, the small Cu₂O cubic structure has a higher active surface area for CO selectivity than cupric oxide (CuO) and demonstrated stability in catalysis during CO production. These findings are consistent with data reported in other studies. The study demonstrated that crystallographic orientation affects adsorbates and desorption paths in CO₂ER. The analysis of the free energies of adsorption and desorption indicated that the reaction proceeded through CO₂ activation, leading to the formation of CH₃OH. This computational approach can help screen potential electrocatalysts and understand reaction pathways to achieve desired value-added products like CH₃OH. Further experimental validation at the laboratory scale is essential to confirm these findings.