Unraveling the Reaction Mechanism of the Reverse Water–Gas Shift Reaction over Ni/CeO₂ and CeO_2−x Catalysts

Abstract

The reverse water–gas shift (RWGS) reaction efficiently converts CO₂ to CO, with vital applications in carbon emission reduction and Fischer-Tropsch chemical production. This study used density functional theory (DFT) to investigate CO₂ adsorption and activation on CeO₂, oxygen-vacancy CeO₂ (CeO_2−x), and single-atom Ni-loaded CeO₂ (Ni/CeO₂). Adsorption energy analysis indicates that CO₂ preferentially adsorbs at the intermediate oxygen sites on CeO₂ and Ni/CeO₂, but on CeO_2−x, it preferentially adsorbs at the oxygen vacancies. Mulliken charge and band gap results indicate that CeO_2−x and Ni/CeO₂ exhibit higher activity than pure CeO₂. Density of states studies indicate that CeO₂, CeO_2−x, and Ni/CeO₂ can activate CO₂ to varying degrees; strong hybridization between Ni’s d-orbitals and CO₂’s O p-orbitals is key to Ni/CeO₂’s high activity. Mechanistically, CeO_2−x follows the RWGS redox mechanism, while Ni/CeO₂ follows the formate-associated mechanism. This work innovatively clarifies differential CO₂ adsorption-activation by vacancies and Ni in CeO₂-based catalysts, providing a theoretical basis for RWGS catalyst design and supporting low-energy carbon conversion development.

1. Introduction

CO₂, as a major component of greenhouse gases, primarily originates from the burning of fossil fuels and has caused serious climate and environmental problems [1]. In this context, controlling excessive CO₂ emissions through carbon capture, storage, and utilization (CCUS) has attracted great attention from countries around the world [2,3]. Converting the well-known greenhouse gas CO₂ into chemical fuels is a very promising approach, as it not only helps mitigate global warming but also serves as an alternative to chemical fuels [4]. In CO₂ conversion technology, catalytic hydrogenation of CO₂ is considered one of the most commercially feasible methods [5], especially by converting CO₂ into CO through the endothermic RWGS reaction. Since CO is an important chemical raw material for the synthesis of fine chemicals and fuels, converting CO₂ into CO through the RWGS reaction can obviously bring considerable economic benefits and provide a reliable solution to energy crises and environmental challenges [6,7].

However, CO₂ is a molecule with high kinetic and thermodynamic stability, as the cleavage of its C=O bonds requires a high activation barrier under ambient conditions. Under normal conditions, the cleavage of the C=O bond in CO₂ molecules requires a very high activation barrier, making the development of efficient catalysts urgently needed. A good catalyst should have a low hydrogenation activation barrier, good C=O bond cleavage ability, and the ability to dissociate hydrogen [8]. In order to obtain high-performance RWGS reaction catalysts, researchers have conducted extensive studies. Research on noble metal catalysts (such as Pt [9], Au [10], and Pd [11]) has found that they all possess suitable hydrogenation capabilities and good RWGS catalytic activity. However, noble metals are prone to sintering at high temperatures, resulting in poor stability of noble metal catalysts, high costs, and low natural abundance, which is unfavorable for their widespread application in industrial production. To reduce costs and improve the high-temperature stability of the corresponding catalysts, researchers have started studying transition metal catalysts [12]. Transition metal catalysts, especially nickel, are widely used in CO₂ hydrogenation reactions due to their advantages such as low cost and high activity at low temperatures, including CO₂ methanation, CO₂ hydrogenation to methanol or formic acid, and water–gas shift reactions [13,14]. Although nickel catalysts exhibit high hydrogenation activity, they face issues such as carbon deposition and sintering. To address these problems, the oxide supports of many RWGS catalysts have been studied, including CeO₂, Al₂O₃, SiO₂, TiO₂, and ZrO₂ [15]. CeO₂ is known for its unique redox properties because it can rapidly interconvert between Ce⁴⁺ and Ce³⁺ [16]. At the same time, Ce³⁺ ions can enhance the stability of the CeO₂ lattice, helping to prevent carbon deposition on the catalyst surface [17]. In addition, the high oxygen mobility on the surface of CeO₂ also promotes the activation and transfer of oxygen molecules, which is crucial for the catalytic process. The presence of a large number of oxygen vacancies on nickel catalysts supported on reducible oxides originates from the metal-support interaction, which facilitates the adsorption and activation of CO₂ [18,19]. Nickel catalysts supported on CeO₂ exhibit excellent catalytic performance in terms of activity, selectivity, and stability in the RWGS reaction [20]. However, most nickel catalysts exhibit high CH₄ selectivity in the hydrogenation of CO₂. Therefore, developing catalysts for the RWGS reaction that are highly active, highly selective, and low-cost remains a challenge.

Numerous studies have shown that particle sizes significantly affect the selectivity of the RWGS reaction [21]. For the CO₂ hydrogenation reaction, larger nickel particles are conducive to promoting the methanation of CO₂, whereas smaller nickel particles are more favorable for the production of CO [22,23]. Improving the dispersion of nickel by reducing its loading, introducing a second metal additive to form bimetallic alloys, and activating metal-support interactions will be an effective strategy to enhance CO selectivity [24,25,26]. Wu et al. [27] studied nickel metals supported on silica with mass fractions ranging from 0.5% to 10%. Their findings indicate that different nickel loadings result in varying coverages of H species on the catalyst surface, thereby affecting the selectivity of CO and CH₄. A similar trend has also been observed in Ni/Al₂O₃, Ni/MgO, and Ni/CeO₂ catalysts, where a low Ni loading is associated with an increase in RWGS activity [28]. Christopher and others found that atomically dispersed isolated metal centers are favorable for the RWGS reaction, whereas metal clusters serve as active centers for carbon dioxide methanation [29]. DFT has become an important tool for studying the surface structure, active sites, and microscopic mechanisms of catalysts, providing a powerful method for elucidating the microscopic characteristics of catalysts [30]. Hu et al. [31] used DFT to simulate single Pt atoms loaded on TiO₂(110) and TiO₂(101), respectively, and found that single Pt loaded on TiO₂(101) exhibited a lower energy barrier for COOH intermediate formation and a more favorable redox process, thereby enhancing the CO₂ conversion rate. Yang et al. [32] found through experiments and DFT simulations that the RWGS reaction catalyzed by single-atom Re₁ loaded on TiO₂ follows the formate pathway, while the RWGS reaction catalyzed by Re₇ clusters loaded on TiO₂ follows the redox pathway. Li et al. [33] demonstrated through experiments and DFT calculations that atomically dispersed Co-N₄ centers follow a hydrogen-assisted pathway, where the intermediate COOH* desorbs and dissociates into CO, while Co nanoparticle catalysts mainly follow a direct dissociation pathway. Although some progress has been made in highly efficient RWGS reaction catalysts, the rate-determining steps and mechanisms followed in the RWGS reaction catalyzed by CeO_2−x and Ni/CeO₂ have not been fully clarified, which limits further optimization and application of the catalysts.

The purpose of this study is to develop catalysts with high activity, high selectivity, and high stability. In this study, we investigated the effects of CeO₂, CeO_2−x, and Ni/CeO₂ on CO₂ catalysis using Mulliken charges and band gaps in DFT. By analyzing the adsorption energies and geometric parameters of CO₂ on different CeO₂ surfaces, we identified the optimal adsorption sites for CO₂ on each surface. Next, to explore the influence of different CeO₂ on CO₂ orbitals, we analyzed the density of states of CO₂ on CeO₂, CeO_2−x, and Ni/CeO₂. Finally, to investigate the rate-determining steps and reaction mechanisms of CeO_2−x and Ni/CeO₂ catalyzed RWGS reactions, we conducted transition state searches. Through DFT calculations, this study provides theoretical guidance for designing efficient CeO₂-based RWGS reaction catalysts.

2. Results and Discussion

2.1. Mulliken Charges on CeO₂, CeO_2−x, and Ni/CeO₂

The Ce and O atoms in different CeO₂ and their Mulliken charges are shown in Figure 1 and

Table 1. Mulliken charges of Ce atoms and O atoms.

Atom	CeO2(111)	CeO2−x(111)	Ni/CeO2(111)
Ce1	1.599	1.746	1.600
Ce2	1.599	1.545	1.786
Ce3	1.599	1.543	1.574
O1	−0.799	−0.859	−0.801
O2	−0.799	-	−0.809
O3	−0.799	−0.859	−0.810

. As can be seen from Table 1, compared with pure CeO₂, the Mulliken charges of Ce1, O1, and O3 atoms on the CeO_2−x surface increased by 0.147 |e|, −0.06 |e|, and −0.06 |e|, respectively, after introducing oxygen vacancies. This indicates that the introduction of oxygen vacancies significantly alters the charge distribution of Ce1, O1, and O3 atoms, which is conducive to enhancing the catalytic activity of CeO₂(111). After introducing a single Ni atom, the changes in the Mulliken charges of Ce1, Ce2, and Ce3 atoms in CeO₂ are 0.001|e|, 0.187|e|, and −0.025|e|, respectively. The Mulliken charge of the Ce2 atom connected to Ni changes the most, indicating a significant transfer of charge. This indicates that the introduction of single-atom Ni significantly changes the charge distribution of Ce2 atoms, thereby helping to enhance the catalytic activity of CeO₂.

2.2. Optimal Adsorption Sites of CO₂ on CeO₂, CeO_2−x, and Ni/CeO₂

To explore the optimal adsorption sites of CO₂ on different CeO₂ surfaces, we investigated the adsorption of CO₂ on the intermediate oxygen sites, edge oxygen sites, oxygen vacancies of CeO₂ and CeO_2−x, and Ni atoms of Ni/CeO₂. The stable configurations, adsorption energies, and geometric parameters of different CO₂ molecules adsorbed on different CeO₂ surfaces are shown in Figure 2 and

Table 2. Adsorption energies and geometric parameters of CO₂ on different CeO₂ surfaces.

Configuration	Eads (eV)	C=O (Å)	Interaction	Distance (Å)
1A	−0.789	1.198, 1.232	C-O1	1.405
1B	−0.776	1.186, 1.227	C-O2	1.408
2O-vacancy	−1.170	1.233, 1.249	C-Ovacancy	-
2B	−1.024	1.225, 1.241	C-O2	1.403
3A	−1.252	1.257, 1.266	C-O1	1.382
3B	−1.232	1.248, 1.256	C-O2	1.402
3C	−1.236	1.251, 1.259	C-Ni	1.810

Note: O1 and O2 represent intermediate oxygen and edge oxygen of CeO₂-based catalysts, respectively.

. As can be seen from Figure 2 and Table 2, for CO₂ adsorption on the oxygen sites in the intermediate and at the edges of CeO₂, the adsorption energies are −0.789 eV and −0.776 eV, respectively, indicating that CO₂ adsorption on the intermediate oxygen sites of CeO₂ has a higher adsorption energy and is more stable. CO₂ adsorbs on the intermediate oxygen and edge oxygen sites of CeO₂, with the longest C=O bond lengths being 1.232 and 1.227 Å, respectively. The C=O bond length is longest when CO₂ is adsorbed on the intermediate oxygen site of CeO₂, indicating that CO₂ is most easily cleaved into CO at this site, which is favorable for CO₂ conversion. CO₂ is adsorbed on the intermediate oxygen of CeO₂, and the distance between the carbon in CO₂ and the oxygen in CeO₂ is the shortest, at 1.405 Å, indicating that CO₂ adsorption at the intermediate oxygen site of CeO₂ is the most stable. For CO₂ adsorption on CeO_2−x, the adsorption energy of CO₂ at oxygen vacancies of CeO_2−x is higher than at edge oxygen sites, and the C=O bond length at the oxygen vacancies is the longest, indicating that CO₂ is more easily adsorbed and dissociated into CO at the oxygen vacancies of CeO_2−x. This is consistent with the oxygen vacancies formed in CeO₂ serving as active centers for the activation of CO₂ molecules [34]. For Ni/CeO₂, we investigated three possible sites for CO₂ adsorption: the oxygen positions in the middle of CeO₂, the edge oxygen positions, and the Ni sites. From the adsorption energy, the C=O bond length, and the distance from the carbon in CO₂ to various sites, it can be seen that CO₂ has the highest adsorption energy, the longest C=O bond length, and the shortest distance from the carbon to the site at the intermediate oxygen position on Ni/CeO₂. This indicates that the optimal adsorption site for CO₂ on Ni/CeO₂ is not on the Ni site, but on the oxygen site in the intermediate of Ni/CeO₂. This is consistent with most of the CO₂ dissociating on CeO₂ rather than on Ni [35].

2.3. Band Gaps of CeO₂, CeO_2−x, and Ni/CeO₂ Before and After CO₂ Adsorption

In order to more accurately analyze the electronic structure characteristics of CeO₂, CeO_2−x, and Ni/CeO₂, the band structures of different CeO₂ before and after CO₂ adsorption were compared, as shown in Figure 3. The reduction in the band gap decreases the energy required for electron transition from the valence band to the conduction band, which facilitates more electrons participating in surface catalytic reactions. After the introduction of oxygen vacancies or Ni loading, the band gaps of CeO_2−x and Ni/CeO₂ are reduced by 1.877 eV and 1.759 eV, respectively, compared to CeO₂. Therefore, CeO_2−x and Ni/CeO₂ exhibit higher reactivity than CeO₂. Before and after CO₂ adsorption, the band gap of CeO₂ changed by 0.05 eV, indicating that the electron distribution of CeO₂ is hardly affected by CO₂ adsorption. CeO_2−x and Ni/CeO₂ exhibit greater bandgap changes before and after CO₂ adsorption, increasing from 0.094 eV to 0.837 eV and from 0.212 eV to 0.837 eV, respectively, indicating that CeO_2−x and Ni/CeO₂ interact more strongly with CO₂ and can stably adsorb CO₂ on their surfaces.

2.4. Density of States of CO₂ Adsorbed on CeO₂, CeO_2−x, and Ni/CeO₂

Figure 4 shows the density of states of CO₂ adsorbed on CeO₂, CeO_2−x, and Ni/CeO₂, where the C atom refers to the carbon atom in CO₂, and O_a and O_b represent the two oxygen atoms in CO₂, respectively. From Figure 4a,d,g, it can be seen that when CO₂ is adsorbed on CeO₂, CeO_2−x, and Ni/CeO₂, the orbitals of carbon in CO₂ are different, indicating that the degree of CO₂ activation is different on CeO₂, CeO_2−x, and Ni/CeO₂. From Figure 4b,c, it can be seen that CO₂ is adsorbed on CeO₂, and the orbitals of O_a and O_b in CO₂ are the same, indicating that CeO₂ affects both oxygen atoms in CO₂ equally. Similarly, from Figure 4e,f, it can be seen that CO₂ is adsorbed on CeO_2−x, and the orbitals of O_a and O_b in CO₂ are the same, indicating that CeO_2−x affects both oxygen atoms in CO₂ equally. From Figure 4h,i, it can be seen that when CO₂ is adsorbed on Ni/CeO₂, the orbitals of O_a and O_b in CO₂ are different. This may be due to the different distances between the oxygen atoms in CO₂ and the Ni atoms, indicating that CO₂ is activated in a highly asymmetric manner. At −5 eV and 0.5 eV, the d orbitals of the Ni atoms overlap with the p orbitals of the O atoms in CO₂, indicating strong hybridization between the d orbitals of Ni and the p orbitals of the O atoms in CO₂. This fully demonstrates that the interaction between CO₂ and Ni atoms is mainly attributed to the hybridization between the d orbitals of Ni and the p orbitals of O in CO₂.

2.5. Mechanism of the RWGS Reaction Catalyzed by CeO_2−x and Ni/CeO₂

There are several mechanisms for the RWGS reaction on CeO₂-based catalysts, including the direct dissociation mechanism (redox mechanism) and the hydrogen-assisted mechanism (formate-associated mechanism and carboxylate-associated mechanism), the latter involving intermediates such as formates and carboxylates [36]. The basic steps of each mechanism of the RWGS reaction are shown in

Table 3. Basic steps involved in the RWGS mechanism.

Redox Mechanism [37,38]	Formate Mechanism [39]	Carboxylate Mechanism [40,41]
H2 + 2 * → 2H*	H2(g) + 2 * → 2H*	H2(g) + 2 * → 2H*
CO2(g) + * → CO2*	CO2(g) + * → CO2*	CO2(g) + * → CO2*
CO2* + * → CO* + O*	H* + CO2* → HCOO* + *	CO2* + H* → trans-COOH* + H*
O* + H* → OH*	HCOO* → HCO* + O*	trans-COOH* → cis-COOH*
OH* + H* → H2O* + *	HCO* → CO* + H*	cis-COOH* → COH* + O*
H2O* → * + H2O(g)	H* + O* → OH* + *	COH* + * → CO* + H*
CO* → * + CO(g)	H* + OH* → H2O* + *	H* + O* → OH* + *
	H2O* → *+ H2O(g)	H* + OH* → H2O* + *
	CO* → *+ CO(g)	H2O* → * + H2O(g)
		CO* → * + CO(g)

Note: * indicates species adsorbed on the catalyst surface.

.

2.5.1. Redox Mechanism of CeO_2−x Catalyzed RWGS Reaction

The redox mechanism of the CeO_2−x catalyzed RWGS reaction is shown in Figure 5. CO₂ adsorbs on CeO_2−x, undergoing significant deformation, indicating that CO₂ is activated, forming CO₂*. Then H₂ molecules adsorb onto CeO_2−x and are dissociated into two H* atoms. CO₂* is further activated by CeO_2−x, breaking one C=O bond in CO₂* to form TS1. Then, H*, O*, and CO* move to certain positions to form TS2. Next, one of the H* combines with O* to form OH*, while the other H* approaches OH* to form TS3, and then H* combines with OH* to form H₂O*. Finally, H₂O* and CO* desorb from CeO_2−x, forming H₂O(g) and CO(g).

As shown in

Table 4. Reaction energy barriers and reaction heats in the redox process of CeO_2−x catalyzed RWGS.

Redox Pathway	Reaction Energy Barrier ΔE/eV	Reaction Heat ΔH/eV
CO2(g) + H2(g) → CO2* + H2(g)	-	−1.12
CO2* + H2(g) → CO2* + 2H*	-	−0.32
CO2* + 2H* → CO* + O* + 2H*	1.86	−0.28
CO* + O* + 2H* → CO* + OH* + H*	1.43	0.35
CO* + OH* + H* → CO* + H2O*	0.76	0.46
CO* + H2O* → CO* + H2O(g)	-	0.81
CO* + H2O(g) → CO(g) + H2O(g)	-	1.08

Note: * indicates species adsorbed on the catalyst surface.

, in the redox mechanism of the RWGS reaction catalyzed by CeO_2−x, the total absorbed heat is greater than the total released heat, indicating that the reaction is endothermic. The reaction energy barriers required for the cleavage of the C=O bond, the formation of OH*, and the formation of H₂O* are 1.86 eV, 1.43 eV, and 0.76 eV, respectively. In the redox mechanism of the RWGS reaction catalyzed by CeO_2−x, the cleavage of the C=O bond requires the most energy, making the breaking of the C=O bond the rate-determining step in the redox mechanism of the CeO_2−x catalyzed RWGS reaction.

2.5.2. Formate Association Mechanism of CeO_2−x Catalyzed RWGS Reaction

As shown in Figure 6, in the formate-associated mechanism of the RWGS reaction catalyzed by CeO_2−x, the initial adsorption states of CO₂ and H₂ are consistent with the redox pathway. CO₂ adsorbs on CeO_2−x, forming CO₂*. H₂ adsorbs on CeO_2−x and dissociates into two H*. One of the H* approaches the C in CO₂* to form TS1, H* combines with CO₂* to form HCOO*, and then HCOO* is cleaved into HCO* and O* to form TS2. H*, O*, and HCO* move to certain positions to form TS3. Then HCO* is cleaved into CO* and H*. CO*, H*, and O* move to certain positions to form TS4. O* and H* form OH*, OH* and H* approach each other to form TS5, and OH* combines with H* to form H₂O*. Finally, H₂O* and CO* desorb from CeO_2−x, forming H₂O(g) and CO(g).

As shown in

Table 5. Reaction energy barriers and reaction enthalpies in the formate-mechanism of the RWGS reaction catalyzed by CeO_2−x.

Formate Pathway	Reaction Energy Barrier ΔE/eV	Reaction Heat ΔH/eV
CO2(g) + H2(g) → CO2* + H2(g)	-	−1.12
CO2* + H2(g) → CO2* + 2H*	-	−0.32
CO2* + 2H* → HCOO* + H*	0.72	−0.09
HCOO* + H* → HCO* + O* + H*	1.93	−0.18
HCO* + O* + H* → CO* + O* + 2H*	1.58	−0.16
CO* + O* + 2H* → CO* + OH* + H*	1.42	0.35
CO* + OH* + H* → CO* + H2O*	0.76	0.46
CO* + H2O* → CO* + H2O(g)	-	0.81
CO* + H2O(g) → CO(g) + H2O(g)	-	1.08

Note: * indicates species adsorbed on the catalyst surface.

, in the formate-association mechanism of the RWGS reaction catalyzed by CeO_2−x, the total heat absorbed is greater than the total heat released, making this an endothermic reaction. The reaction energy barriers required for the formation of HCOO*, HCO*, CO*, OH*, and H₂O* are 0.72 eV, 1.93 eV, 1.58 eV, 1.42 eV, and 0.76 eV, respectively. In the formate-association mechanism for reverse water–gas shift catalyzed by CeO_2−x, the energy required for the decomposition of HCOO* into HCO* is the highest. Therefore, the decomposition of HCOO* is the rate-determining step in the formate-associated mechanism of the RWGS reaction catalyzed by CeO_2−x.

2.5.3. Carboxylate Association Mechanism of CeO_2−x Catalyzed RWGS Reaction

As shown in Figure 7, in the carboxylate-associated mechanism of CeO_2−x catalyzed RWGS reaction, the initial adsorption states of CO₂ and H₂ are consistent with the redox pathway. After CO₂ and H₂ molecules are adsorbed and activated on CeO_2−x, H₂ is dissociated into two H* atoms, one of which combines with CO₂* to form trans-COOH*, after which trans-COOH* moves with H* to form TS2. Then one oxygen atom in trans-COOH* rotates by a certain angle, forming cis-COOH. cis-COOH* and H* move, forming TS3, then one O atom in cis-COOH* cleaves, forming COH* and O*. COH* rotates by a certain angle to form TS4, after which the H in COH* cleaves to form CO* and H*. At this moment, O* approaches one of the H* atoms to form TS5, O* combines with H* to form OH*, then OH* moves with another H* to form TS6, and OH* combines with H* to form H₂O*. Finally, H₂O* and CO* desorb from CeO_2−x, forming H₂O(g) and CO(g).

As shown in

Table 6. Reaction energy barriers and reaction enthalpies in the carboxylate association mechanism of CeO_2−x catalyzed RWGS reaction.

Carboxylate Pathway	Reaction Energy Barrier ΔE/eV	Reaction Heat ΔH/eV
CO2(g) + H2(g) → CO2* + H2(g)	-	−1.12
CO2* + H2(g) → CO2* + 2H*	-	−0.32
CO2* + 2H* → trans-COOH* + H*	1.96	0.52
trans-COOH* + H* → cis-COOH* + H*	0.56	0.12
cis-COOH* + H* → COH* + O* + H*	0.88	−0.35
COH* + O* + H* → CO* + O* + 2H*	1.46	−0.42
CO* + O* + 2H* → CO* + OH* + H*	1.42	0.35
CO* + OH* + H* → CO* + H2O*	0.66	0.42
CO* + H2O* → CO* + H2O(g)	-	0.81
CO* + H2O(g) → CO(g) + H2O(g)	-	1.08

Note: * indicates species adsorbed on the catalyst surface.

, in the carboxylate-associated mechanism of the CeO_2−x catalyzed RWGS reaction, the total absorbed heat is greater than the total released heat, indicating that the reaction is endothermic. The reaction energy barriers required for the formation of trans-COOH*, cis-COOH*, COH*, CO*, OH*, and H₂O* are 1.96 eV, 0.56 eV, 0.88 eV, 1.46 eV, 1.42 eV, and 0.66 eV, respectively. In the carboxylate-associated mechanism of reverse water–gas shift catalyzed by CeO_2−x, the formation of COOH* requires the most energy. Therefore, the formation of COOH* is the rate-determining step in the carboxylate association mechanism of the reverse water–gas shift reaction catalyzed by CeO_2−x.

As shown in Figure 8, the energies required for the rate-determining steps in the redox pathway, formate-associated pathway, and carboxylate-associated mechanism of CeO_2−x catalyzed RWGS reaction are 1.86 eV, 1.93 eV, and 1.96 eV, respectively. The rate-determining step of the redox mechanism requires the least energy, so the most favorable reaction mechanism for CeO_2−x catalyzed RWGS reaction is the redox pathway, indicating that CeO_2−x catalyzed RWGS reaction follows a redox mechanism. This is consistent with the findings of Liu et al. [35] that the direct oxidative decomposition of carbon dioxide at oxygen vacancies on CeO₂ catalysts is considered the main reaction mechanism of the RWGS.

2.5.4. Redox Mechanisms of the Ni/CeO₂ Catalyzed RWGS Reaction

As shown in Figure 9, in the redox mechanism of the RWGS reaction catalyzed by Ni/CeO₂, CO₂ adsorbs on Ni/CeO₂ and undergoes significant distortion, indicating that CO₂* is activated. H₂ molecules adsorbed onto Ni atoms are directly cleaved into two H*, indicating the excellent H₂ dissociation and activation capability of Ni-based catalysts. Then CO₂* decomposes into CO* and O*, forming TS1.O* and H* move positions to form TS2. Then, O* combines with H* to form OH*. OH* and H* move a certain distance to form TS3. Then OH* combines with H* to form H₂O*. Finally, CO* and H₂O* absorb a certain amount of heat, desorb from Ni/CeO₂, and form CO(g) and H₂O(g).

As shown in

Table 7. Reaction energy barriers and reaction heats in the Ni/CeO₂ catalyzed RWGS redox process.

Redox Pathway	Reaction Energy Barrier ΔE/eV	Reaction Heat ΔH/eV
CO2(g) + H2(g) → CO2* + H2(g)	-	−1.17
CO2* + H2(g) → CO2* + 2H*	-	−0.36
CO2* + 2H* → CO*+O* + 2H*	1.78	−0.26
CO* + O* + 2H* → CO* + OH* + H*	1.37	0.34
CO* + OH* + H* → CO* + H2O*	0.62	0.41
CO* + H2O* → CO* + H2O(g)	-	0.76
CO* + H2O(g) → CO(g) + H2O(g)	-	1.03

Note: * indicates species adsorbed on the catalyst surface.

, in the redox mechanism of the Ni/CeO₂ catalyzed RWGS reaction, the total endothermic energy is greater than the total exothermic energy, indicating that the reaction is endothermic. The energy required to break the C=O bond is 1.78 eV, which is the highest energy needed; therefore, the breaking of the C=O bond is the rate-determining step in the redox mechanism of the Ni/CeO₂ catalyzed RWGS reaction.

2.5.5. Formate Association Mechanism of Ni/CeO₂ Catalyzed RWGS Reaction

As shown in Figure 10, the initial adsorption states of CO₂ and H₂ in the formate association mechanism are consistent with those in the redox pathway. CO₂ adsorbed on Ni/CeO₂ undergoes deformation, and H₂ molecules adsorbed on Ni atoms are directly dissociated into two H*. H* approaches the carbon atom in CO₂* to form TS1. Next, H* combines with CO₂* to form HCOO*. HCOO* absorbs a certain amount of energy, causing the C=O bond to break into HCO* and O*, forming TS2. HCO* twists at a certain angle to form TS3. Next, the C-H bond in HCO* breaks, forming CO* and H*. O* and H* move a certain distance to form TS4. When the distance between O* and one of the H* atoms is sufficiently close, O* combines with H* to form OH*, which twists at a certain angle to form TS5. Then OH* combines with another H* to form H₂O*. Finally, CO* and H₂O* absorb a certain amount of heat, desorb from Ni/CeO₂, and form CO(g) and H₂O(g).

As shown in

Table 8. Reaction energy barriers and reaction heats in the formate-associated mechanism of the Ni/CeO₂ catalyzed RWGS reaction.

Formate Pathway	Reaction Energy Barrier ΔE/eV	Reaction Heat ΔH/eV
CO2(g) + H2(g) → CO2* + H2(g)	-	−1.17
CO2* + H2(g) → CO2* + 2H*	-	−0.36
CO2* + 2H* → HCOO* + H*	0.63	−0.11
HCOO* + H* → HCO* + O* + H*	1.57	−0.21
HCO* + O* + H* → CO* + O* + 2H*	1.29	−0.18
CO* + O* + 2H* → CO* + OH* +H*	1.37	0.34
CO* + OH* + H* → CO* + H2O*	0.62	0.41
CO* + H2O* → CO* + H2O(g)	-	0.76
CO* + H2O(g) → CO(g) + H2O(g)	-	1.03

Note: * indicates species adsorbed on the catalyst surface.

, in the formate-associated mechanism of the Ni/CeO₂ catalyzed RWGS reaction, the absorbed heat is greater than the released heat, making this an endothermic reaction. The reaction energy barriers required for the formation of HCOO*, HCO*, CO*, OH*, and H₂O* are 0.63 eV, 1.57 eV, 1.29 eV, 1.37 eV, and 0.62 eV, respectively. In the Ni/CeO₂ catalyzed RWGS reaction via the formate-associated pathway, the energy required for HCOO* to decompose into HCO* is the highest, making the decomposition of HCOO* the rate-determining step in the formate-associated mechanism of the Ni/CeO₂ catalyzed RWGS reaction.

2.5.6. Carboxylate Association Mechanism of Ni/CeO₂ Catalyzed RWGS Reaction

As shown in Figure 11, after the CO₂ and H₂ molecules are adsorbed and activated, CO₂* approaches one of the H*, forming TS1. CO₂* combines with H* to form trans-COOH*, and one O in trans-COOH* twists by a certain angle to form TS2. When the O in trans-COOH* twists to a certain angle, it forms cis-COOH*. Then, the C=O bond in cis-COOH elongates, forming TS3. When the C=O bond in cis-COOH is stretched to a certain distance, it breaks, forming COH* and O*. Subsequently, COH* is cleaved into CO* and H*, forming TS4. O* approaches one of the H* atoms, forming TS5. When the distance between O* and H* is close enough, OH* is formed. OH* twists at a certain angle to approach another H*, forming TS6. OH* combines with H* to form H₂O*. Finally, CO* and H₂O* absorb a certain amount of heat and desorb from Ni/CeO₂, forming CO(g) and H₂O(g).

As shown in

Table 9. Carboxylate Association Mechanisms of Ni/CeO₂ Catalyzed RWGS Reaction.

Carboxylate Pathway	Reaction Energy Barrier ΔE/eV	Reaction Heat ΔH/eV
CO2(g) + H2(g) ⟶ CO2* + H2(g)	-	−1.17
CO2* + H2(g) ⟶ CO2* + 2H*	-	−0.36
CO2* + 2H* ⟶ trans-COOH* + H*	1.85	0.56
trans-COOH* + H* ⟶ cis-COOH* + H*	0.42	0.08
cis-COOH* + H* ⟶ COH* + O* + H*	0.76	−0.36
COH* + O* + H* ⟶ CO* + O* + 2H*	1.39	−0.43
CO* + O* + 2H* ⟶ CO* + OH* + H*	1.37	0.34
CO* + OH* + H* ⟶ CO* + H2O*	0.62	0.41
CO* + H2O* ⟶ CO* + H2O(g)	-	0.76
CO* + H2O(g) ⟶ CO(g) + H2O(g)	-	1.03

Note: * indicates species adsorbed on the catalyst surface.

, in the carboxylate associative mechanism of the RWGS reaction catalyzed by Ni/CeO₂, the absorbed heat is greater than the released heat, making the reaction endothermic. The reaction energy barrier required for the formation of trans-COOH* is 1.85 eV, which is the highest energy needed in the carboxylate association mechanism of the RWGS reaction catalyzed by Ni/CeO₂. Therefore, the formation of COOH* is the rate-determining step in the carboxylate association mechanism of the RWGS reaction catalyzed by Ni/CeO₂.

As can be seen from Figure 12, the energy required for the rate-determining steps of the redox mechanism, formate-associated mechanism, and carboxylate-associated mechanism of Ni/CeO₂ catalyzed RWGS reaction are 1.78 eV, 1.57 eV, and 1.85 eV, respectively. In the Ni/CeO₂ catalyzed RWGS reaction, the rate-determining step along the formate mechanism requires the least energy. Therefore, the most favorable reaction mechanism in the Ni/CeO₂ catalyzed RWGS reaction is the formate mechanism, indicating that single-atom Ni-loaded CeO₂ catalyzes the RWGS reaction following the formate-association mechanism. This is consistent with Yu et al. [42], who found that CO mainly originates from the decomposition of formate species.

3. Calculation Details

All density functional calculations were performed using the DMol3 module of Materials Studio [43]. The exchange-correlation function used the generalized gradient approximation (GGA) and the Perdew-Burke-Ernzerhof (PBE) equation [44]. The core is treated with DFT semi-core pseudopotentials (DSPP) for self-consistent field calculations. The atomic orbital basis set is based on the double numerical plus polarization (DNP) basis set. The integrations of the Brillouin zone were described using a 2 × 2 × 1 k-point grid according to the Monkhorst-Pack method. The convergence tolerance of geometric optimization and property calculation were 1 × 10⁻⁵ Ha for the tolerance of energy, 0.002 Ha/Å for maximum force, 0.005 Å for maximum displacement and 1.0 × 10⁻⁶ Ha for self-consistent field (SCF) tolerance. Studies have shown that the PBE functional can be used to obtain accurate structural information in calculations involving transition metals and transition metal oxides [45,46]. The transition state of the reaction was determined using the full LST/QST method [47].

The definition of adsorption energy in this article is shown in Equation (1):

E_ads = E_{adsorbate-catalyst} − E_adsorbate − E_catalyst

(1)

E_{adsorbate-catalyst} represents the total energy of the adsorbate and the catalyst when the adsorbate is stable on the catalyst surface, while E_adsorbate and E_catalyst represent the total energy of the adsorbate and the catalyst, respectively.

The energy required to move from reactant to transition state on a catalyst in this paper is shown in Equation (2):

ΔE = E_TS − E_R

(2)

where ΔE represents the energy required for the reactants to the transition state, and E_R represents the energy of the reactants adsorbed on the catalyst. E_TS represents the energy of the transition state adsorbed on the catalyst.

All catalyst models use a periodic 3 × 3 supercell representation with six layers and 20 Å of vacuum to avoid interactions between periodic images. The bottom four atomic layers are fixed, while the top two layers and the adsorbates are fully relaxed without any constraints. The CeO₂(111) surface is the first stable surface of CeO₂, while the CeO₂(110) surface is its second stable surface. Therefore, we chose the CeO₂(111) surface for our study. An oxygen atom is removed from the outermost CeO₂ layer to form an oxygen vacancy CeO_2−x(111). A Ni atom is loaded onto the CeO₂, forming Ni/CeO₂. The front and top views of the structural models of CeO₂, CeO_2−x, and Ni/CeO₂ are shown in Figure 13 and Figure 14.

4. Conclusions

This study employed DFT to systematically investigate the RWGS reaction over three CeO₂-based catalysts: pure CeO₂, CeO_2−x, and Ni/CeO₂, with key findings summarized as follows: First, regarding CO₂ adsorption sites: DFT calculations revealed that CO₂ is more easily adsorbed at the intermediate oxygen sites of CeO₂ and Ni/CeO₂, while it preferentially binds to the oxygen vacancies of CeO_2−x. Second, on catalytic activity: Through Mulliken charge analysis and band gap calculations, the catalytic activities of the three catalysts were compared. The results indicated that CeO_2−x and Ni/CeO₂ exhibit significantly higher activity than pure CeO₂. For Ni/CeO₂, the enhanced activity is closely related to the electronic interaction between Ni and the CeO₂ support, which modulates the electronic structure of active sites and promotes CO₂ activation. Third, regarding the CO₂ activation mechanism: the activation mechanisms of different CeO₂-based catalysts were revealed using density of states analysis. The study found that all three catalysts can activate CO₂ to varying degrees; notably, there is strong hybridization between the d orbitals of Ni and the p orbitals of oxygen in CO₂ in Ni/CeO₂, which serves as the core electronic driving force for the high activation efficiency of Ni/CeO₂. Fourth, regarding the RWGS reaction mechanism and rate-determining steps: the study further explored the reaction mechanisms of CeO_2−x and Ni/CeO₂ in catalytic RWGS reactions, as well as the rate-determining steps of each mechanism. The results show that for RWGS reactions catalyzed by these two catalysts: the rate-determining step of the redox mechanism is the breaking of the C=O bond; the rate-determining step of the formate mechanism is the decomposition of HCOO*; and the rate-determining step of the carboxylate mechanism is the formation of COOH*. Finally, regarding the dominant mechanism of the catalyst: key studies on the mechanisms of CeO_2−x and Ni/CeO₂ confirmed that CeO_2−x catalyzes the RWGS reaction through the redox mechanism, while Ni/CeO₂ follows a mechanism related to formate. This clear understanding of the dominant mechanisms provides a precise theoretical basis for the design and optimization of CeO_2−x and Ni/CeO₂ catalysts in RWGS applications.

Although this study conducted an in-depth investigation of the RWGS reaction on CeO₂, CeO_2−x, and Ni/CeO₂ using DFT calculations, certain challenges still exist. Traditional DFT methods have obvious limitations when dealing with strongly correlated systems, and they cannot fully account for defect sites commonly present in actual catalytic systems (such as multiple oxygen vacancies and surface hydroxyl groups) as well as dynamic structural evolution processes (such as catalyst surface reconstruction). These limitations may lead to discrepancies between theoretical predictions and experimental results. To address these issues, it is recommended that future research focus on the following directions: constructing a closed-loop research paradigm of computational design–machine learning optimization–experimental validation, integrating theoretical predictions with experimental verification to improve the reliability of catalyst design, and establishing standardized multi-source databases, integrating experimental data (such as catalytic activity and structural characterization) with simulation data (such as DFT-calculated adsorption energies and electronic structures), to facilitate data sharing and cross-validation.