CO₂ Interaction with Cu-Based Single-Atom Alloys as Catalysts: A Computational Study Using MOPAC-PM7

Abstract

This work investigates the behavior of carbon dioxide (CO₂) near the surface of different single-atom alloys to evaluate their potential as catalysts for decarbonization processes. Specifically, 26 transition metals from the first three transition series, alloyed with three low Miller index copper supports, were considered. Adsorption energies and distances of linear CO₂, trigonal CO₂, and CO* + O* on the surfaces were calculated using the semiempirical computational method MOPAC-PM7. Additionally, activation energies were determined from previously published research. The proposed methodology is less computationally demanding than DFT studies, and results show good agreement with both experimental and simulated data. This approach provides a computationally efficient methodology for screening promising materials that convert CO₂ into valuable products, such as methane and methanol.

1. Introduction

The synthesis of methanol from carbon dioxide hydrogenation is a widely studied topic in the current literature, particularly in relation to single-atom catalysis (SAC) and the synthesis of nano-alloys as new catalytic materials. Both experimental and theoretical studies have been conducted on different classic and improved Cu-based hydrogenation catalysts, and many examples of heterogeneous catalysts with controlled designs have been proposed [1,2,3].

In this context, a thorough investigation of the interaction steps of CO₂ with the surface of transition metals is of paramount importance. The adsorption and reaction of carbon dioxide on bare transition-metal surfaces have been extensively studied, and many transition metals have been tested. Middle-late 3d metals, such as iron, cobalt, nickel, and copper, were found to adsorb/dissociate CO₂. Computational studies have further contributed to understanding the details of CO₂ interactions with metal surfaces.

In addition, transition-metal complexes have also been explored. Specifically, the reverse water–gas shift reaction (CO₂ + H₂ → CO + H₂O) has been widely employed to understand physicochemical properties of transition-metal complexes and mechanistic pathways involving CO₂ and hydrogen for the production of CH₄, CH₃OH, and CO [4].

Furthermore, the transition-metal support, whether as an alloy or nano-alloy, has also been considered within the field of SAC [5]. The nature of the interaction with the support and the character of the methanol synthesis reaction (sensitive or insensitive to the structure) have been debated for years. A recent study has at least partially clarified some of these issues in reactions involving methanol [6]. Notably, recent reviews have focused on copper-based catalysts and reactions with methanol [5,7].

Considering the multiple pathways available for CO₂ to react with hydrogen on heterogeneous catalysts, Density Functional Theory (DFT) studies have increased our understanding of these processes. The interaction of CO₂ with the catalyst surfaces in the presence of hydrogen may produce methane or methanol as final products. For instance, Nolen et al. [8] reported that CO₂ conversion via CO* (* represents adsorbed species) and hydrogenation leads to C1 products. Ni, Co, Rh, and Ru tend to promote CO/CH₄ formation, whereas Pt and Pd are more selective toward CO/CH₃OH formation. The key factor determining the selectivity between CH₃OH and CH₄ is the ability of a metal to cleave C-O bonds. Differences in selectivity arise from CO either desorbing or reacting further with hydrogen on the surface. For CH₄ formation, C-O bond dissociation is the step that determines the activation energy, a step absent in methanol synthesis.

Making use of DFT calculations, Liu et al. [9] studied the adsorption and dissociation of CO₂ on low-index surfaces of different transition metals. They reported the order of magnitude of the energy barriers for CO₂ dissociation, as well as the strength of the interaction order between the dissociative CO*, O* species with the surfaces. The authors also explored the Brønsted-Evans-Polanyi (BEP) relationship, which correlates the activation energy of a reaction ($E_a$) with its reaction enthalpy ($∆E$) as expressed in Equation (1).

$$E_a=\gamma ·∆E+\epsilon$$

(1)

Here, $\gamma$ and $\epsilon$ are parameters, adjusted with experimental or computational data. This correlation has been verified for many reactions on the same metal surface structures and has been applied to families of reactions on the same facet of metal particles [10].

Despite the extensive research on the topic, a clear understanding of CO₂ hydrogenation on transition-metal surfaces in terms of reactivity and selectivity remains elusive. Several challenges hinder the interpretation of structure-function relationships across transition-metal surfaces for CO, CH₄, and CH₃OH synthesis.

This manuscript presents the results of the enthalpies for CO₂ adsorption/activation/dissociation onto many relevant Cu-based transition-metal single-atom alloys (SAAs) obtained using the MOPAC-PM7 method [11]. MOPAC-PM7 is a semiempirical approach that enables the calculation of structural and energetic properties, such as heats of formation and crystal geometries, offering a balance between accuracy and computational efficiency.

Specifically, three low-index Miller planes (100), (110), and (111), are investigated. The calculations consider the adsorption, coordination, and chemisorption of CO₂ modeled both as a planar and a trigonal molecule located on the top of a single atom within a copper support. Considered metals include transition elements from Sc to Zn, Y to Ag, and Hf to Au. Results are presented and discussed considering the published literature. Activation energies for CO₂ dissociation to produce CO* and O* are also calculated, reported, and discussed in comparison with the available theoretical and experimental published data.

This contribution is a follow-up to our research on SAA catalysts for decarbonization reactions. While our previous study [12] focused on H₂ adsorption and dissociation on Cu-based SAAs, the present contribution systematically investigates CO₂ adsorption, activation, and dissociation over the same set of transition metal-doped Cu surfaces. By employing an identical computational framework (MOPAC-PM7) and catalyst models, this work enables a direct comparison between H₂ and CO₂ surface chemistries. This complementary approach provides a consistent basis for understanding the initial steps of CO₂ hydrogenation and establishes a rapid pre-screening strategy for identifying promising SAA catalysts.

Although the dominant trend in the theoretical investigation of atomic-level reaction mechanisms involves sophisticated Density Functional Theory (DFT) simulations, often integrated with machine learning modeling, our approach relies on a less resource-intensive methodology (in terms of software licensing, computational power, and processing time). This allows the estimation of trends in energies and bond lengths, aiding in the engineering of catalysts for decarbonization processes.

2. Methodology

2.1. Cu Support and Me-Cu SAAs

In nanoparticles, the most frequently exposed planes correspond to low-index Miller surfaces. The particle’s morphology determines whether these surfaces are (111) in polyhedra such as octahedra and icosahedra, (100) in cubic structures, or (110) in rhombic dodecahedra, with cuboctahedra presenting both (111) and (100) facets. Single metal atoms (Me) placed on copper structures of (100), (110), and (111) planes are considered in this study to resemble single-atom catalysts based on single-atom alloys (SAAs). Me represents atoms of the first, second, and third transition rows (Sc to Zn, Y to Ag, and Hf to Au). The description of the surfaces and the procedure to replace one top Cu atom with another transition metal Me can be found in Moreno et al. [12]. For the species adsorbed on the different metal surfaces, the enthalpy is calculated as the total energy minus the sum of the standard enthalpy of the clean surface without the adsorbate and the standard formation enthalpy of the adsorbate.

2.2. Adsorption and Dissociation of CO₂

Taking into account the different approaching pathways of the CO₂ molecule to the surface and its behavior near the metals, several main steps can be identified. In all cases and for the three Cu planes, the parallel linear CO₂ proved to be preferred. The molecule approaches perpendicularly and reorients to a parallel configuration to interact with a surface metal atom through the carbon atom. The planar trigonal form of CO₂ is particularly stable on some surfaces, whereas the final CO molecule exhibits a more favorable adsorption energy on others. The steps involved, schematized in Figure 1, are:

• Step 1: Adsorption of linear CO₂ in parallel form to the surface of the top metal (named CO₂). The adsorbate is linear carbon dioxide parallel to the metal surface.
• Step 2: Adsorption of CO₂ in a planar trigonal form (120° bond angle) on top metal (named PTCO₂). The adsorbate is planar trigonal carbon dioxide.
• Step 3: Adsorption of CO* on top metal with an O* onto the nearest Cu metal. The adsorbate is CO, while the surface includes an O* bound to the nearest Cu, which varies depending on the plane.

2.3. Location of O and CO After Dissociation onto the Surface

After CO₂ dissociation, CO* and O* were generated. The location of O* was onto the nearest Cu atom to the top metal selected for CO adsorption with a metal-C bond. Therefore, the O* from the CO₂ dissociation was placed with an O-Cu bond length at a distance from the surface of 0.0 Å at the (100) plane, 0.3 Å at the (110) plane and 1.4 Å at the (111) plane.

3. Results

3.1. Steps of CO₂ Adsorption, Chemisorption, and Dissociation-Adsorption Enthalpies for SAAs on Copper Planes

Results of ΔH° obtained with MOPAC-PM7 for the three steps of CO₂ interaction with the metal surface are presented and analyzed.

Table 1. Cu(100) plane: Adsorption enthalpy (kcal/mol) and distance (Å) for transition metals reported to produce methane (italics) and methanol (bold).

Me	CO2		PTCO2		CO* + O*
	ΔH°	d	ΔH°	d	ΔH°	d
Sc	4.89784	5.0	−8.10316	4.0	−7.55428	4.0
Ti	9.56958	4.0	4.72863	3.2	−13.42578	2.8
V	0.96330	2.8	−35.38288	2.2	−19.29212	2.2
Cr	−10.7340	2.6	−77.71759	2.2	−50.70895	2.2
Mn	14.16610	4.6	10.31000	4.6	11.56396	3.4
Fe	6.38727	5.0	−17.79723	3.2	−45.49971	3.0
Co	21.98672	4.6	−0.85929	4.6	−6.99911	4.0
Ni	16.7256	3.4	7.91322	3.4	−14.90972	3.2
Cu	30.0700	2.2	32.55519	2.4	−14.83000	2.2

,

Table 2. Cu(110) plane: Adsorption enthalpy (kcal/mol) and distance (Å) for transition metals reported to produce methane (italics) and methanol (bold).

Me	CO2		PTCO2		CO* + O*
	ΔH°	d	ΔH°	d	ΔH°	d
Sc	13.68801	4.0	−25.84055	4.4	−3.68856	4.8
Ti	−6.90095	5.0	−11.53224	5.0	−13.80164	3.2
V	3.72436	3.2	−2.74696	3.0	−4.79440	2.8
Cr	1.55321	3.2	−33.80800	3.2	8.12329	3.4
Mn	9.89776	5.0	−0.49126	5.0	−3.72793	3.6
Fe	33.19463	4.8	−1.25146	3.8	−34.06857	3.6
Co	12.82623	5.0	−13.25967	4.4	−16.75242	3.8
Ni	18.93698	4.0	−13.60804	3.8	−26.13904	3.8
Cu	14.45170	5.0	−30.94556	4.5	−4.16000	2.4

and

Table 3. Cu(111) plane: Adsorption enthalpy (kcal/mol) and distance (Å) for transition metals reported to produce methane (italics) and methanol (bold).

Me	CO2		PTCO2		CO* + O*
	ΔH°	d	ΔH°	d	ΔH°	d
Sc	−40.86935	5.0	−41.57607	4.0	−17.26000	4.2
Ti	3.16346	5.0	0.58361	4.4	−20.96325	3.8
V	3.49021	5.0	5.55048	5.0	−8.94220	3.0
Cr	6.74033	4.2	42.5768	3.8	−35.93000	3.4
Mn	5.77479	3.8	5.22000	5.0	−32.84000	3.6
Fe	−43.42453	5.0	−42.80803	5.0	−24.36000	3.4
Co	7.29243	5.0	2.01442	4.0	−22.85000	3.6
Ni	6.58655	3.6	7.68106	3.8	−25.72000	3.6
Cu	5.81126	5.0	54.73400	5.0	−22.13000	2.1

summarize data for the (100), (110), and (111) planes, respectively. All enthalpies were obtained as:

$$∆H°=∆{H°}_{total enthalpy of the model}-∆{H°}_{surface without adsorbate}-{∆H°}_{adsorbate}$$

(2)

Fe, Co, and Ru are reputed catalysts for Fischer–Tropsch synthesis. Precursors of Fe metal may be oxidized to Fe₃O₄ (magnetite), a common active phase for CO production. Carbonization due to the CO₂/H₂ reaction shifts the products to higher hydrocarbons. Catalysts based on Co promote carbon-chain growth during CO hydrogenation, leading primarily to CH₄ or CO, depending on the particular structure of the metal. In contrast, Ru-based catalysts mainly yield CH₄. Ni and Rh are also applied for CO₂ methanation, showing high activity and methane selectivity.

Transition metals such as Cu, Ag, Au, Pd, and Pt have low activity for C–O bond cleavage. Historically, they have been used for hydrogen-assisted CO₂ dissociation to produce CO and/or CH₃OH from CO₂ hydrogenation.

Adsorption of CO₂ is generally endergonic (see Table 1, Table 2 and Table 3), except for Cr-Cu(100) (−10.73 kcal/mol), Ti-Cu(110) (−6.9 kcal/mol), Sc-Cu(111) (−40.8 kcal/mol), and Fe-Cu(111) (−43.42 kcal/mol). It has been reported that CO₂ adsorption remains endergonic for Ni, Co, Rh, Ru, Pd, and Pt [13].

It is now widely accepted that the interaction CO₂–linear–molecule/transition–metal–surface is often weak physisorption. The activation steps are related to a change in CO₂ conformation (“bent”) and finally dissociation to CO*.

When PTCO₂ is analyzed, Table 1, Table 2 and Table 3 show that the reactions are mainly exothermic for Cu(100) and Cu(110) planes, except for Ti-Cu(100), Mn-Cu(100), Ni-Cu(100), Cu(100), and Mn-Cu(110). On Cu(111), PTCO₂ formation is endothermic with the exception of Sc, Mn, and Fe SAAs. For dissociated CO₂, most values indicate an exothermic reaction, but for Mn-Cu(100) and Cr-Cu(110).

Analysis of the data, considering the most exothermic and endothermic adsorption energies for first-row transition metals replacing one top Cu atom onto the different planes, reveals interesting trends. These trends can be interpreted through the lens of the Sabatier principle, which states that the most effective catalyst for a reaction has moderate bonding strength with key intermediates. Correlations in reaction energetics can be visualized using volcano plots, which provide a tool to identify both the optimal adsorption energies and the maximum achievable reaction rates, governed by a balance between competing reaction steps. When adsorption energies are too weak, bond-breaking becomes rate-limiting; conversely, if they are too strong, desorption or bond-forming steps become slow. Volcano plots imply that when multiple potential rate-limiting steps are interconnected, accelerating one step necessarily slows another [14]. Related to BEP relations are Transition State Scaling (TSS) relations, which correlate the transition state energy to the adsorption energy (often the energy of the final state) [15]. Notably, alloys may overcome volcano plots and other simple correlations [16].

Jin et al. [13] performed DFT calculations of CO₂ interaction with twenty-one transition metals, analyzing both flat and stepped surfaces of pure metals. They carefully studied the reaction pathways for CO₂ dissociation. Their results indicated that the chemisorption of bent CO₂ is supported by transition-metal surfaces, characterized by large negative adsorption energies also correlating to low dissociation barriers. The lower the electronegativity of the transition metal, the stronger the metal surface/CO₂ interaction.

Figure 2 illustrates the ranges in which adsorption enthalpies correlate with improvements in CO₂ hydrogenation to methanol. Too exothermic enthalpies are related to CO dissociation and methane formation, or even C-C coupling. The figure shows the results for steps 1, 2, and 3 of the first transition metal series on the (100), (110), and (111) Cu planes. Red boxes highlight the best enthalpies for steps 1, 2, and 3 on the transition metals that produce methanol. Outside these boxes, the enthalpies are either too endothermic or too exothermic to be productive for methanol synthesis.

The selected adsorption enthalpy ranges are guided by the well-established relationship between adsorption strength and catalytic activity, commonly represented by volcano-type plots, as discussed in [14]. According to the Sabatier principle, an effective catalyst should bind key intermediates with moderate strength: strong enough to promote activation, yet weak enough to allow subsequent desorption.

3.2. Experimental Adsorption Enthalpies: Comparison with Theoretical Calculation

Experimental adsorption energy data for CO₂ onto transition metals tagged with chloride are: −163 (±66) kJ/mol for Cr, −80 (± 32) kJ/mol for Mn, −120 (±48) for Fe, −124 (±50) for Co, −137 (±55) for Ni, and −60 (±24) kJ/mol for Cu.

Single-atom catalysts have been studied as M–N–C (porphyrin)-contained structures with 3d transition metals (Me = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn), in the center of porphyrin active for the CO₂ reduction reaction (CO₂RR) using DFT. In CO₂RR, the bonding energy of the CO* intermediate plays a critical role in CO generation. The predictions follow the activity series Co > Fe > Mn > Ni > Cu, consistent with the experimental results.

The substitution of Pd with Cu/ZrO₂ increases the methanol production rate from 223 μmol g⁻¹h⁻¹ to 512 μmol g⁻¹h⁻¹ under relatively mild conditions (1.5 MPa, 260 °C) [17]. A Pd–Cu bimetallic promoting effect on the formation of methanol from CO₂ hydrogenation has been reported, assigned to the Pd–Cu SAAs formation [18]. Similarly, a Cu–Zn bimetallic solid (Cu–Zn/Al foam) produced 7.81 g methanol gCu⁻¹ h⁻¹, with 9.9% CO₂ conversion and 82.7% selectivity to methanol [19]. Continuous efforts are being made to improve the Cu/ZnO-based catalysts [20]. Moreover, the catalytic performance of bimetallic Cu_xCo_y catalysts has been found to be superior to that of monometallic catalysts [21].

Pd, Zn, and Co in bimetallic Me-Cu systems have been the most studied as SAAs. More recently, the combination of other elements of group 13 (Al, Ga, In) has added further complexity to catalyst design.

Two main challenges have hindered progress in the identification of the active site in bimetallic systems: (i) the lack of catalyst modeling frameworks, and (ii) the absence of detailed information about the geometric and electronic structures of the catalyst under realistic working conditions (so-called operando studies).

Non-copper combinations are increasingly being explored [22,23], mainly centered on indium (In) and gallium (Ga) compounds. Catalysts based on Cu-Zr and Ti supported onto zeolites have demonstrated high performance in methanol synthesis [24].

Based on Cu-ZnO-Al₂O₃ catalysts, Guil-López et al. [25] reviewed the state of the art in 2019 and reported that the use of metals, such as Pt, Rh, Au, or Pd enhances the performance of Cu-based catalysts for methanol synthesis also pointing out that such enhancement does not necessarily justifies the high costs associated with these metals, particularly due to problems in recycling and recovery. With respect to changes in basicity, the additional studies have focused on three so-called promoters: zirconium, zinc, and fluoride. Promoters such as ZrO₂, Ga₂O₃, and carbonaceous materials have shown positive effects, as well as the introduction of Ag or In₂O₃.

Pd and Au have been explored as alternatives to Cu, while bimetallic alloys combining Rh and Pt or Co and Pt have been reported as different phases to replace Cu–ZnO in CO₂ hydrogenation. Furthermore, the addition of Ni to Cu-Mn/ZrO₂ has been shown to improve the catalyst performance in CO₂ hydrogenation related to Cu-Mn/ZrO₂ [26].

Mapping the turnover frequency of CO₂ related to energetic changes in the chemisorption energies of carbon (ΔEC) and oxygen (ΔEO) reveals a volcano-shaped relationship. Cu is near the optimum, whereas Ni, Rh, Ru, Re, Fe, Pt, and Pd are on the strong-binding side, while Au and Ag fall on the weak-binding side [27].

Mn appears to act as a promoter effect in methanol synthesis with Cu/ZnO catalysts [28]. When Fe-Cu catalysts are analyzed, the catalytic activity measured at 30 bar and 200–260 °C increases for CO₂ conversion with temperature compared to Cu alone. However, methanol selectivity drops, accompanied by a marked increase in CO and CH₄ selectivity [29]. This experimental finding is in line with the results presented in Table 1, Table 2 and Table 3.

For Fe-Cu(100), the values of CO₂ adsorption, PTCO₂, and CO are 6.38727, −17.79723, and −45.49971 kcal/mol, respectively; for Fe-Cu(110), they are 33.19463, −1.25146, and −34.06857; and for Fe-Cu(111), they are −43.42453, −42.80803, and −24.36 kcal/mol, respectively. These results imply that CO adsorption on the three planes is always very strong and exothermic, thereby favoring CO dissociation into carbon and subsequently methane formation on the surface.

Vanadium has also been reported to positively impact the performance of Cu in methanol formation [30].

For Cr at low temperatures (200 °C), the highest selectivity of CH₃OH was about 65% over a Cr containing catalyst in a ternary system Cu-Zn-M (M = Cr, Ce, Zr, Al). The catalytic activity followed the order Cu-Zn-Cr > Cu-Zn-Ce > Cu-Zn-Zr > Cu-Zn-Al. The effect of Cr appears to be a decrease in the activation energy for CO₂ hydrogenation to methanol [31].

Sc has been proposed to weaken CO adsorption on cuprous oxide [32]. According to Table 1, Sc-Cu(100) shows an enthalpy of −7.55 kcal/mol compared with −14.83 kcal/mol for Cu(100), and Sc-Cu(110) shows an enthalpy of −3.68 kcal/mol versus −22.13 kcal/mol for Cu(110). On the Cu(111) plane, however, CO* adsorption is stronger on Sc than on Cu. These results suggest that Sc weakens the bond of CO on the Cu(100) and Cu(110) planes, but not on the Cu(111) plane.

Cr exhibits a strong CO* enthalpy, and therefore a decrease in methanol selectivity is expected (Table 1, Table 2 and Table 3). The adsorption enthalpy of PTCO₂ is highly exothermic on Cr-Cu(100) and Cr-Cu(110), as is the CO adsorption enthalpy mainly in Cr-Cu(100) and Cr-Cu(111) planes, whereas adsorption on Cr-Cu(110) is endothermic.

Doped clusters of Sc, Ti and V show strong CO₂ adsorption energies and low activation barriers for CO₂ dissociation [33].

In relation to the BEP correlation, Jin et al. [13] reported that reactions with lower activation barriers are also more thermodynamically favored. In bulk structures, CO₂ is physisorbed on the transition metals Cu, Ag, and Au on Pt(100) and Pd(100) planes. Conversely, on most other low-index transition-metal surfaces, CO₂ binds in a bent chemisorbed conformation. Among these, Fe(110), Ru(0001), and Os(0001) exhibit the highest CO₂ activation ability, outperforming Co(0001), Rh(111), Ir(111), Pd(111) and Pt(111), as well as Fe(100), Ni(100), Ni(110), Rh(100) and Ir(100). These bulk structures, however, are not directly comparable to the ones presented here because they are not single-atom structures.

In

Table 4. Enthalpy in kcal/mol for the second transition metal series (metals reported to produce methane and methanol are shown in italics and bold, respectively).

Plane	Me	CO2	PTCO2	CO* + O*
Cu(100)	Y	6.00067	−4.40583	3.66590
	Zr	21.32832	−10.07016	0.87439
	Nb	−5.28348	−44.08292	−27.19978
	Mo	13.08228	−26.94095	−68.72859
	Tc	11.37201	−45.48374	−58.57822
	Ru	5.32557	−1.15209	−49.62116
	Rh	9.54267	−24.6929	−0.59087
	Pd	9.61048	−13.01723	−47.00411
	Ag	20.4636	13.91353	7.82874
Cu(110)	Y	1.80229	4.01576	−1.18328
	Zr	9.44701	−19.47125	−6.05139
	Nb	2.59794	−21.60109	−43.50735
	Mo	14.71084	−22.18712	−38.62922
	Tc	18.55889	−8.0892	−65.97756
	Ru	34.40000	4.1549	−20.26374
	Rh	10.2416	−26.93517	−25.48125
	Pd	9.94144	−9.9348	8.24446
	Ag	21.49096	0.09983	27.98198
Cu(111)	Y	7.12495	9.28449	−10.93000
	Zr	−6.32489	−37.16269	−7.31900
	Nb	−2.50540	−6.42815	−23.85000
	Mo	33.03000	−4.99593	−45.31800
	Tc	3.50358	5.75857	−30.49000
	Ru	6.71872	1.21696	−8.52000
	Rh	9.54267	−4.26266	−24.63000
	Pd	12.93000	−1.59572	−11.19000
	Ag	18.65564	14.89826	−3.14000

and

Table 5. Enthalpy in kcal/mol for the third transition metal series (metals reported to produce methanol are shown in bold).

Plane	Me	CO2	PTCO2	CO* + O*
Cu(100)	Hf	2.97040	−7.96494	−21.54552
	Ta	16.84030	−14.26203	18.69278
	W	−48.19035	−124.81293	−91.90000
	Re	26.11895	−2.37555	−37.42898
	Os	6.14981	−87.63182	−85.11845
	Ir	8.90338	4.71384	5.33263
	Pt	6.12972	−13.39889	−12.85069
	Au	11.73403	8.61909	12.43616
Cu(110)	Hf	6.27203	−16.23070	−11.64951
	Ta	8.26843	6.17666	4.17751
	W	−65.94314	−136.67727	−98.54812
	Re	6.49586	−16.20013	−38.58503
	Os	−14.12122	−104.50903	−104.37843
	IR	7.52142	−0.58796	9.41234
	Pt	7.51840	−12.03282	−10.89288
	Au	11.95869	−1.85644	17.97276
Cu(111)	Hf	36.52649	14.88995	28.08000
	Ta	−7.96623	0.97302	−11.10000
	W	36.28768	2.18887	−63.64000
	Re	3.17000	2.24077	−55.56000
	Os	3.70766	−45.91067	−38.28000
	IR	9.58215	5.06851	11.63000
	Pt	1.82632	−6.93147	−4.01100
	Au	6.98999	5.80774	3.00000

, the data for SAAs with metals of the second and third transition rows are summarized. Relatively low activation energy values (~0.75 eV) were found for Fe, Ru, Co, Ni, Rh, and Ir metals, as well as their corresponding based SAAs. Pure Pd, Pt, and Cu metals, and Ru, Co, Ni, Rh, Ir, and Cu-based SAAs, exhibit activation energies ranging from 0.76 to 1.50 eV. In contrast, high values of activation energy (~1.51 eV) were obtained for pure Au and Ag metals, and for Pd, Pt, and Cu-based alloys.

Ko et al. [34] reported a BEP correlation for the sequential CO₂ transformations: first from linear to bent or planar trigonal, followed by a transition from planar trigonal to dissociated. Some studies omit the calculation of the activation energy from linear to bent conformation, only reporting the activation energy for dissociation. Bent CO₂ has been reported to be approximately 10 kcal/mol less stable than the linear molecule, depending on the particular metal [35].

The linear geometry of CO₂ gas molecules turns into a chemically active bent conformation with an activation energy of 4.6 kcal/mol for Rh. Generally, this step is considered non-activated onto metal surfaces [25,36].

Hu et al. [37] reported a comprehensive selectivity analysis of CO₂ hydrogenation. Mo and W exhibit both thermodynamic and kinetic instability under CO₂-containing atmospheres at high temperatures, which precludes their direct application. As shown in Table 5, the adsorption enthalpies of CO₂ and CO for W-Cu(100) and W-Cu(110) are the most exothermic of all the transition metals considered in this study.

Au/ZrO₂ is a highly active catalyst for the reverse water–gas shift reaction (production of CO and H₂O), but not for methanol synthesis. According to MOPAC-PM7 results, all steps are endothermic, leading tothe lowest selectivity to methanol. Cu/ZrO₂ and Ag/ZrO₂ present similar selectivities to methanol [38].

Table 6. Activation energy in kcal/mol for CO₂ dissociation to CO* + O* on transition metals (metals reported to produce methane and methanol are shown in italics and bold, respectively).

Me	Cu(100)	Cu(110)	Cu(111)
Sc	19.82357	21.83374	14.77660
Ti	16.77039	16.57494	23.75180
V	13.71989	21.25872	19.10185
Cr	−2.61685	27.97591	5.068200
Mn	29.76505	21.81327	6.67500
Fe	0.09195	6.03614	11.08460
Co	20.11226	15.04054	11.86980
Ni	15.99874	10.15949	10.37740
Cu	16.04020	21.58800	12.24000
Y	25.65806	23.13649	18.06820
Zr	24.20648	20.60507	19.94592
Nb	9.60791	1.12797	11.34980
Mo	−11.98706	3.66460	0.18644
Tc	−6.70887	−10.55653	7.89700
Ru	−2.05120	13.21465	19.32140
Rh	23.44454	10.50155	10.94420
Pd	−0.69033	28.03891	17.93300
Ag	27.82274	38.30242	22.11900
Hf	12.54812	17.69405	38.35340
Ta	33.47204	25.92410	17.97980
W	−24.03620	−27.49322	−9.34100
Re	4.28873	3.68758	−5.13940
Os	−20.50979	−30.52498	3.84620
Ir	26.52476	28.64621	29.79940
Pt	17.06944	18.08750	21.66608
Au	30.21860	33.09763	25.31180

shows the results of applying the BEP relation to obtain the activation energies for CO₂ dissociation calculated using Equation (3), obtained from [34]:

$$E_a=\left(0.52·{∆H}_{CO*+O*}/26.03+1.03\right)·26.03$$

(3)

The CO₂ dissociation seems to be non-activated on several transition-metal planes, particularly from the second and third rows (Mo, Tc, Ru, W, and Os). The data may be classified into three groups:

• Group A—Activation energy lower than 10 kcal/mol: Cr-Cu(111), Mn-Cu(111), Fe-Cu(100), Fe-Cu(110), Nb-Cu(100), Nb-Cu(110), Mo-Cu (all planes), Tc-Cu (all planes), Cu-Ru(100), Pd-Cu(100), W-Cu (all planes), Re-Cu (all planes), and Os-Cu (all planes).
• Group B—Activation energy higher than 25 kcal/mol: Cu-Ag(110), Cu-Pd(110), Cu-Hf(111), Ta-Cu(110), Ta-Cu(111), Ir-Cu (all planes), Au-Cu(110), and Au-Cu(100).
• Group C—Activation energy between 10 and 25 kcal/mol: all other cases not included in Groups A and B.

For a total of 78 activation energy data, 33 correspond to Groups A and B, while the remaining 45 fall within Group C.

Several factors correlate with the catalyst selectivity. In this manuscript, the reduced transition metal is analyzed, but the final activity depends on the active phase and its chemical nature, the active metal and metal particle size, the nature and properties of the support, and the presence of promoters (e.g., alkali metals).

If only the CO₂-SAA interaction is analyzed, the main differences among the transition metals with activity to methane and to methanol can be presented by plane and by species on the surface. In general, both experimental and theoretical results indicate that CO₂ adsorption is endothermic, as expected, except for Fe-Cu(111). The adsorption enthalpy falls within +5 to +35 kcal/mol. When the PTCO₂ is considered, Fe-Cu(111) again exhibits a strong exothermic adsorption for the species, while other planes range from near +55 to −7 kcal/mol for Cu(111), from −31 to near +5 kcal/mol for Cu(110), and from near +33 to −14 kcal/mol for Cu(100).

The largest differences are found in the adsorption enthalpy of CO* + O*. Fe-Cu presents the most exothermic adsorption enthalpy for case of CO* for all planes, except on (100,) where Ru shows the most exothermic adsorption enthalpy for CO.

The set of transition metals reported to promote methane formation follows a decreasing order of exothermicity in adsorption enthalpy in the frame of MOPAC-PM7 for SAAs:

• For Cu(100): Ru > Fe > Ni > Co > Rh
• For Cu(110): Fe > Ni > Rh > Ru > Co
• For Cu(111): Rh > Ni > Fe > Co > Ru

The group of transition metals reported to produce methanol has the following decreasing order of exothermicity in adsorption enthalpy in the frame of MOPAC-PM7 for SAAs:

• For Cu(100): Pd > Cu > Pt > Ag > Au
• For Cu(110): Pt > Cu > Pd > Au > Ag
• For Cu(111): Cu > Pd > Pt > Ag > Au

Table 7. Comparison of adsorption enthalpies for different geometries of CO₂ and CO for transition metals reported to produce methane (italics) and methanol (bold).

Plane	Me	CO2	PTCO2	CO* + O*
Cu(100)	Fe	6.38727	−17.79723	−45.49971
	Co	21.98672	−0.85929	−6.99911
	Ni	16.7256	7.91322	−14.90972
	Ru	5.32557	−1.15209	−49.62116
	Rh	9.54267	−24.6929	−0.59087
	Pd	9.61048	−13.01723	−47.00411
	Ag	20.46360	13.91353	7.82874
	Pt	6.12972	−13.39889	−12.85069
	Au	11.73403	8.61909	12.43616
	Cu	30.07000	32.55519	−14.83000
Cu(110)	Fe	33.19463	−1.25146	−34.06857
	Co	12.82623	−13.25967	−16.75242
	Ni	18.93698	−13.60804	−26.13904
	Ru	34.40000	4.15490	−20.26374
	Rh	10.24160	−26.93517	−25.48125
	Pd	9.94144	−9.93480	8.24446
	Ag	21.49096	0.09983	27.98198
	Pt	7.51840	−12.03282	−10.89288
	Au	11.95869	−1.85644	17.97276
	Cu	14.45170	−30.94556	−4.16000
Cu(111)	Fe	−43.42453	−42.80803	−24.36000
	Co	7.29243	2.01442	−22.85000
	Ni	6.58655	7.68106	−25.72000
	Ru	6.71872	1.21696	−8.52000
	Rh	9.54267	−4.26266	−24.63000
	Pd	12.93000	−1.59572	−11.19000
	Ag	18.65564	14.89826	−3.14000
	Pt	1.82632	−6.93147	−4.01100
	Au	6.98999	5.80774	3.00000
	Cu	5.81126	54.73400	−22.13000

summarizes the differences between the group of transition metals that favor methane (italics) and methanol (bold), related to CO₂ adsorption and dissociation.

From the trends obtained with the theoretical calculations, it is evident that SAAs related to methanol synthesis exhibit more endothermic enthalpies for planar CO₂ than those linked to methane and CO production, especially at the (110) and (111) planes. The most endothermic adsorption for PTCO₂ is observed for bare Cu(100) and Cu(111). The literature reports that the most exothermic the adsorption of CO*, the most likely the formation of methane through CO dissociation. The calculated activation energies for CO₂ dissociation (Table 7) range from 12 to 22 kcal/mol for bare Cu planes. Values of activation energy for Pt alloys fall within this range, while for Pd alloys they vary from non-activated to nearly 28 kcal/mol. For Ag and Au alloys, the activation energies lie between 22 and 40 kcal/mol. In contrast, alloys involving transition metals correlated with CH₄/CO production show lower activation energies: from 0 to near +24 kcal/mol in the case of Rh, but generally between +6 and +16 kcal/mol.

3.3. Distances

Although only the adsorption enthalpies of the species involved with the considered SAAs have been analyzed so far, the equilibrium distances between the species and the surfaces provide additional insights. The corresponding data are provided as Supplementary Material (see Tables S1–S3).

By comparing the SAA including transition metals of the first, second, and third series on low Miller index planes of Cu, several observations can be drawn:

• A general trend in Me-C bond lengths is observed for the three Cu planes: the length of Me-CO* bond is shorter than the length of the Me-PTCO₂ bond. Additionally, the length of the Me- PTCO₂ bond is shorter than that of the Me-CO₂ bond, as expected.
• For the first transition metal series, the shortest bond is the Cu-Cu(111)-CO* (2.1 Å). For the second transition metal series, the shortest bond is the Ru-Cu(100)-CO* bond (1.2 Å). For the third transition metal series, the shorter bond is Os-Cu(100)-CO* (1.8 Å). It is interesting that Ru and Os both are both from group 8 (6 and 7 d electrons respectively).
• The energetic minimum and the resulting size is dependent of several factors: the Z of the transition metal, the energetics of the metal HOMO and LUMO, the size and orientation of the d orbitals involved considering the geometry of the interaction, the number of d electrons and the repulsive–attractive balance for the COx-metal interaction. There is no easy pathway to find a trend, because the size of the transition metal in the SAAs, orbital orientations, and energetic and geometric disposition of the plane surface, change the nature of the interaction. Sometimes, larger bond Me-C length does not imply less energy, and a shorter Me-C bond is not necessarily related to a more exothermic enthalpy.
• Very few metal atoms adsorb linear CO₂ at bond lengths shorter than 3.0 Å. Looking at the second transition metal row, only Tc-C in Tc-Cu(100) is 2.6 Å, whereas considering the third row, only Ta-W onto Cu(100) achieves 2.8 Å. Considering the PTCO₂, Ta, W, Re, Os, and Pt present shorter bond lengths than 3.0 Å in SAAs onto Cu(100), whereas only Pt shows this kind of feature for the metal-carbon bond at the Cu(110). The trend is inverted with CO*. Many SAAs adsorb CO at a Me-C bond length shorter than 3.0 Å, mainly for SAAs onto Cu(100) and Cu(110). Pd presents a bond length Pd-CO* shorter than 2.5 Å onto the three planes whereas the Ru-C bond length is shorter than 1.5 Å for Ru-Cu(100) and Ru-Cu(111).

3.4. A Discussion of H₂ and CO₂ Adsorption in Different Geometries-CO₂ Dissociation

In a previous work [12], we showed that MOPAC-PM7 is a valuable tool for studying H₂ adsorption on Cu-based SAAs. The best transition metals for methanol synthesis, based on H₂ adsorption, were found to be Ti, V, Cr, Nb, Tc, Ag, Os, Ir, Pt, and Cu for the three planes, and Au and Ta for the (100) and (110) planes. H₂ adsorption on Pd-Cu was found to be highly exothermic and stable on the top metal for the three planes (ranging from −11.9 kcal/mol to nearly −28 kcal/mol). For CO₂, the best transition metals found in this work were Cu, Pd, Pt, Ag, and Au. These computational findings using MOPAC-PM7 are consistent with the experimental observations.

4. Conclusions and Future Work

Using semiempirical software, the obtained results support and correlate with the experimentally reported trends the CO₂ hydrogenation to produce methanol and, additionally, methane, in terms of adsorption enthalpies of different conformations of CO₂, the adsorption enthalpy of CO* and the activation energies for the CO₂ dissociation at different Cu-based SAAs.

The best transition-metals for Cu-based SACs in methanol synthesis were found to be Cu, Pd, Pt, Ag, and Au, with adsorption enthalpies ranging from +20 to −20 kcal/mol. In contrast, the transition metals most favorable for methane production (Fe, Co, Ni, Ru, Rh) presented adsorption enthalpies from +33 to nearly −50 kcal/mol. Activation energies for CO₂ dissociation were calculated using BEP correlations and discussed taking into account reports of experimental results. Overall, MOPAC-PM7 proves to be a useful tool to understand the adsorption and dissociation of CO₂ on Cu-based transition metal alloys, and the proposed methodology is considered practical for providing meaningful insights for the preliminary screening of promising catalysts for decarbonization processes in an inexpensive manner.

Further investigation of the most promising SAA systems identified in this study could be pursued through higher-level computational approaches, such as DFT calculations, including adsorption energy refinement, transition-state analysis, and reaction pathway exploration. In parallel, experimental validation could be conducted via the synthesis of the selected alloys, followed by catalytic testing under relevant reaction conditions to assess their performance in CO₂ hydrogenation.

Future work will focus on elucidating the mechanism of such decarbonization reactions based on previous studies. Specifically, it has been proposed that CO₂ hydrogenation to methanol proceeds via three main reaction steps: (i) direct CO₂-to-methanol conversion, (ii) reverse water–gas shift (RWGS), and (iii) CO hydrogenation to methanol. The prevailing view suggests that methanol is primarily generated from CO₂, while CO is converted to CO₂ via the water–gas shift (WGS) reaction [39]. In contrast, methane formation has been reported to occur via two pathways: (i) CO₂ reduction to CO and subsequent hydrogenation to CH₄, and (ii) routes involving carbonate and formate as intermediates [40,41]. Additionally, future work will address the co-adsorption of H₂ and CO₂ on the most promising SAA surfaces identified in this study, including the calculation of co-adsorption energies and H₂ dissociation barriers, which are critical for understanding the complete hydrogenation pathway [42,43].