Computational screening of single-atom doped In₂O₃ catalysts for the reverse water gas shift reaction

Abstract

The reverse water gas shift (RWGS) reaction is an important method for converting carbon dioxide (CO₂) into valuable chemicals and fuels by hydrogenation. In this paper, the catalytic activity of single-atom metal-doped (M = Pt, Ir, Pd, Rh, Cu, Ni) indium oxide (c-In₂O₃) catalysts in the cubic phase for the RWGS reaction was investigated using density functional theory (DFT) calculations. This was achieved by identifying metal sites, screening oxygen vacancies, followed by further calculating the energy barriers for the direct and indirect dissociation pathways of the RWGS reaction. Our results show that the single-atom dopant in the indium oxide lattice promotes the creation of oxygen vacancies on the In₂O₃ surface, thereby facilitating the adsorption and activation of CO₂ by the oxide surface and initiating the subsequent RWGS reaction. Furthermore, we find that the oxygen vacancy (O_V) formation energy on the surface of the single-atom metal doped c-In₂O₃(111) surface can be used as a descriptor for CO₂ adsorption, and the higher the O_V formation energy, the more stable the CO₂ adsorption structure is. The Cu/In₂O₃ structure has relatively high energy barriers for both direct (1.92 eV) and indirect dissociation (2.09 eV) in the RWGS reaction, indicating its low RWGS reactivity. In contrast, the Ir/In₂O₃ and Rh/In₂O₃ structures are more conducive to the direct dissociation of CO₂ into CO, which may serve as more efficient RWGS catalysts. Furthermore, microkinetic simulations show that single atom metal doping to In₂O₃ enhances CO₂ conversion, especially under high reaction temperatures, where the formation of oxygen vacancies is the limiting factor for CO₂ reactivity on the M/In₂O₃ (M = Cu, Ir, Rh) models. Among these three single-atom catalysts, the Ir/In₂O₃ model was predicted to have the best CO₂ reactivity at reaction temperatures above 573 K.

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1 Introduction

Carbon dioxide (CO₂) is one of the major greenhouse gases responsible for global warming and climate change.^1–5 The reverse water gas shift (RWGS) reaction (CO₂ + H₂ → CO + H₂O) is an important method for the conversion of CO₂ into the more useful carbon monoxide (CO),^6,7 which is a versatile chemical intermediate for making commodity chemicals, such as methane, formic acid, hydrocarbons as liquid fuels, alcohols, and olefins, thus providing a promising alternative to the traditional fossil fuel-based chemical industry.^8–12 The RWGS reaction can also be directly coupled with CO hydrogenation to produce higher value C₂₊ products, such as ethanol (C₂H₅OH). Huang's group¹³ recently reported a dual-functional Ir₁–In₂O₃ monatomic catalyst that integrates two catalytically active centers by anchoring the monatomic Ir to the In₂O₃ support. The Ir₁–In₂O₃ catalyst can efficiently hydrogenate CO₂ in liquid with high selectivity for ethanol (>99%). This and similar approaches can not only help reduce CO₂ emission but also provide an alternative source of valuable chemicals and fuels. Therefore, the RWGS reaction can serve as a pivotal technology for transforming the abundant CO₂ resource into chemicals and hydrocarbon fuels, which is attractive for CO₂ utilization and is of significance in building an ecological system for unconventional fuels.¹⁴

Research into the RWGS reaction has been ongoing for hundreds of years, but it has gained renewed interest in recent years due to the urgent need to address climate change. However, a big challenge to this issue is the rational design of high temperature endurable RWGS catalysts with desirable CO product selectivity. The RWGS catalysts usually consist of well-dispersed metal active sites on high surface area metal oxide supports.¹⁵ In terms of metal sites, copper¹⁶ and several noble metals (Pt,¹⁷ Pd,¹⁸ Rh¹⁹) have been extensively studied. For the support, CeO₂¹⁶ is one of the most widely explored for the RWGS reaction because of its excellent redox properties.

In₂O₃ has been predicted and proven to be an excellent catalyst for CO₂ conversion, for both hydrogenation to methanol (CH₃OH) at relatively low temperature and the RWGS reaction. Ye et al.²⁰ investigated CO₂ hydrogenation on the defective In₂O₃(110) surface with a surface oxygen vacancy using periodic density functional theory (DFT) calculations. They showed that the D1 surface with the O_v1 site is thermodynamically the most stable, whereas the D4 surface with the O_v4 site is the least stable, and the CO₂ hydrogenation to methanol reaction is more favorable on the D4 surface. In our previous studies,²¹ DFT calculations and experiments demonstrated that two distinct CO₂ adsorption structures can be formed on the In₂O₃ surfaces of both the cubic and hexagonal phases, corresponding to CH₃OH and CO formations, respectively. The (104) surface of the hexagonal phase of In₂O₃ exhibits higher activity and methanol selectivity in the CO₂ hydrogenation reaction. In addition, the c-In₂O₃ catalyst mainly exposing the (110) surface was found to have good performance for the RWGS reaction. Therefore, optimizing the concentration of oxygen vacancies and improving the structure of the catalyst will be key to further increasing the activity of indium oxide.

Metal particle size plays an important role in controlling the stability of the CO₂ hydrogenation catalysts and the distribution of the active sites, which dictate the catalytic reactivity and product selectivity. Recently, the development of single-atom catalysts (SACs) has gained significant attention due to their high activity and product selectivity towards various catalytic reactions.^22,23 For example, a recent study²⁴ shows that incorporating atomic Rh species into In₂O₃ can lead to high methanol productivity by creating oxygen vacancies for CO₂ activation. Li et al.²⁵ doped Pt atoms into In₂O₃ to form atomically dispersed Ptⁿ⁺ species, most of which are stable under operating conditions, and their results show that adding atomically dispersed Ptⁿ⁺ improves methanol selectivity, while Pt nanoparticles on In₂O₃ mainly promote the RWGS reaction. Zhu et al.²⁶ found that the Ni promotor facilitates CH₃OH synthesis from CO₂, which was mainly attributed to the low energy barrier of H₂ dissociation on the reduced surface Ni species, facilitating hydrogenation of the adsorbed CO₂ at the oxygen vacancy (O_V) site. Cannizzaro et al.²⁷ elucidated the promotional role of Ni in In₂O₃-catalyzed CO₂ hydrogenation, where three representative models have been investigated, namely (i) a single Ni atom doped In₂O₃(111) surface, (ii) a single Ni atom adsorbed on In₂O₃(111), and (iii) a small Ni₈ cluster adsorbed on In₂O₃(111). Their microkinetic simulations reveal that only the supported Ni₈ cluster can lead to high methanol selectivity, whereas single Ni atoms either doped or adsorbed on the In₂O₃ surface mainly catalyse CO formation. Qi et al.²⁸ studied monatomic systems anchored on defective metal oxide surfaces, and used the anchoring energy to screen the stability of 232 monatomic systems under vacuum and CO₂ reduction reaction conditions. They predicted that Ru/V_O–ZrO₂(111) would maintain a single atom form and show excellent catalytic performance in the RWGS reaction.

Although In₂O₃ has excellent catalytic activity and stability for CO₂ hydrogenation, CO₂ conversion is limited by the relatively low activity of indium oxide in dissociating molecular H₂. A previous study¹³ indicated that bifunctional monatomic catalysts provide an effective approach for designing complex catalysts by synergistically utilizing the unique catalytic properties of single atomic sites and the supports. In order to explore the effect of doping for In₂O₃ with monatomic metal (M/In₂O₃) on the RWGS reaction, we selected copper (Cu), nickel (Ni), palladium (Pd), rhodium (Rh), platinum (Pt) and iridium (Ir) as the dopant on the In₂O₃ surface, and investigated the RWGS activity on these catalysts using DFT calculations.

2 Computational methods

2.1 Density functional theory calculations

We perform DFT calculations using the Vienna ab initio simulation package (VASP).^29,30 The generalized gradient approximation (GGA) with the Bayesian error estimation functional including the van der Waals correlation (BEEF-vdW)³¹ was employed to account for the electron exchange and correlation in the Kohn–Sham theory. The detailed parameters used in this work are similar to those in our previous works.^21,32,33 A plane wave energy cut-off of 400 eV and the Gaussian smearing width of 0.05 eV were employed. Convergence thresholds for the energy and force were set to 10⁻⁴ eV and 0.01 eV Å⁻¹, respectively. Both the climbing image nudged elastic band (CI-NEB) method^34,35 and the dimer method³⁶ were used to find the transition states (TS), which were further confirmed through frequency analysis.

We also investigated the effect of including the Hubbard U correction to the energies of some of our calculations. For the Ni/In₂O₃ system, DFT+U calculations were further performed with an effective U_eff value of 2.4 eV (U_eff = U − J) for Ni³⁷ for CO₂ direct dissociation. The difference in the absorption energy of [bt-CO₂*] with and without adding the Hubbard U correction is 0.38 eV, but the difference in the CO₂ dissociation energy with and without adding the Hubbard U correction is very small at 0.1 eV (Fig. S5, ESI†), so we conclude that its effect on most of the energetics calculated in this work should be relatively small. Furthermore, as the Hubard U correction was not included in most previous DFT studies,^27,38–40 we also chose not to include this correction in the rest of our DFT calculations.

The c-In₂O₃(111) surface was built from the optimized primitive unit cell similar to our previous work,⁴¹ and the surface was modelled with a p(1 × 1) slab consisting of 48 In atoms and 72 O atoms distributed in three O–In–O trilayers. The supercell has a dimension of 14.44 Å × 14.44 Å × 17.99 Å. The vacuum layer thickness is 10 Å between adjacent slabs. All atomic layers are allowed to relax. The Brillouin zone is sampled using a (3 × 3 × 1) Monkhorst–Pack k-point mesh. For the Ni-doped model, spin polarization was enabled. Spin polarization was enabled by setting ISPIN to 2 in the INCAR input file, and several other related parameters were also set to their recommended values (e.g. AMIX = 0.2, BMIX = 0.0001, AMIX_MAG = 0.8, BMIX_MAG = 0.0001).

Substitution of an In atom on the topmost layer of the c-In₂O₃(111) surface by a metal atom (Pt, Ir, Pd, Rh, Cu, Ni) is considered, and the resulting models are denoted as Pt/In₂O₃, Ir/In₂O₃, Pd/In₂O₃, Rh/In₂O₃, Cu/In₂O₃, and Ni/In₂O₃, respectively. Definitions of the formation energy of an O_V site and the adsorption energy of an adsorbate on a slab surface are similar to our previous works.^33,42 An O_V site on the defective c-In₂O₃ surface forms upon removing one O atom from the stoichiometrically perfect c-In₂O₃ surface. The formation energy of an O_V site (ΔE_f,_OSV) is calculated as the reaction energy of the thermal desorption of molecular O₂:

where E_OV–surface, E_perfect and E_O2 denote the total energies of the defective surface, perfect surface, and gas phase O₂. The adsorption energy of an adsorbate A on a slab surface S is defined as:

E_ad,A = E_total − (E_slab + E_A)

where E_total, E_slab, and E_A are the total energies of the c-In₂O₃ slab with the adsorbate, the clean c-In₂O₃ slab, and the adsorbate as a free molecule, respectively. All structures were built and visualized using the Materials Visualizer from the Materials Studio.⁴³

2.2 Microkinetic simulations

CatMAP⁴⁴ was used to simulate the reaction kinetics of the RWGS reaction under the typical reaction conditions of 450–700 K and 50 MPa. The elementary reactions considered in this model are listed in Table S8 (ESI†). Two different sites were considered. The s_site denotes the O_V site for the adsorption of various intermediates arising from CO₂ hydrogenation, and the t_site denotes the In site for hydrogen adsorption in the form of a hydride or a proton. The t_site is a “hydrogen reservoir” site, so it does not compete with other adsorbates for the s_site, which is the free site. The enthalpy and entropy of the gaseous species were calculated using the ideal gas model, while those of the surface adsorbates and the transition states were evaluated using the harmonic approximation. The degrees of rate control (DRC)^45,46 as proposed by Campbell and implemented in CatMAP were also calculated to provide further insights into the rate determining steps.

3 Results and discussion

3.1 Monatomic metal doping site

The pristine c-In₂O₃(111) surface consists of 16 In and 12 O atoms on the topmost layer, as can be seen in Fig. 1(a), on which the In and O atoms are labelled as In₁–In₁₆ and O₁–O₁₂, respectively. Fig. 1(b) shows the side view of the three-layer slab model of c-In₂O₃(111), indicating that each layer roughly consists of the O–In–O trilayers. In this study, the O on the topmost layer of the surface is considered for vacancy formation. To determine the location of the single M atom (Pt, Ir, Pd, Rh, Cu, Ni) on the doped In₂O₃(111), all the possible structures for substitution in the topmost In layer were calculated and compared for stability, as shown in Fig. 1(c) and Fig. S1 (ESI†). It can be clearly seen that the doped single metal atom at the topmost layer of c-In₂O₃(111) has several sites with the same relative energy, which have the same chemical environment and are equivalent sites due to symmetry. This indicates that the 16 In sites could be divided into 6 groups labelled by a–f, as listed in Table S1 (ESI†).

Fig. 1 (a) and (b) Top and side views of the optimized structure of the stoichiometric c-In₂O₃(111) surface; (c) Heat map of the relative energies of single metal atom (Pt, Ir, Pd, Rh, Cu, Ni) doped in six distinct In sites on the stoichiometric c-In₂O₃(111) surface; (d) Heat map of the O_V formation energy of single metal atom (Pt, Ir, Pd, Rh, Cu, Ni) doped c-In₂O₃(111) surfaces.

In addition, as shown in Table 1, the adhesive energy (ΔE_adh) was also calculated, which was defined as the binding energy of an M atom from its bulk state to a surface In vacancy (V_In) on the In₂O₃(111) slab from the following equation

ΔE_adh = E_M/In2O3 − E_M − E_VIn/In2O3

Table 1 The adhesive energy of M/In₂O₃ (M = Pt₇, Ir₇, Pd₇, Rh₁₁, Cu₇, Ni₁₁) and the cohesive energy of bulk metal

Site	Pt7	Ir7	Pd7	Rh11	Cu7	Ni11
ΔEadh/eV	−9.78	−12.84	−8.75	−10.79	−8.01	−10.11
ΔEcoh/eV	−5.39	−8.02	−4.25	−5.65	−3.23	−5.44

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E _M/In2O3 is the energy of the M/In₂O₃(111) surface, E_M is the energy of an M atom in its bulk state, and E_VIn/In2O3 is the energy of the In₂O₃(111) slab with a surface In vacancy. Our calculations show that these six metal dopants prefer to replace the surface In₇ and In₁₁ sites. Furthermore, the ΔE_adh value is much more negative than the cohesive energy (ΔE_coh) of bulk M (M = Pt, Ir, Pd, Rh, Cu, Ni), indicating strong interaction between the atomic M dopant and the In₂O₃(111) surface, which may prevent the M dopant from self-aggregation.

In addition, for Ir/In₂O₃, the possibility for the migration of the Ir dopant from the surface to the subsurface layer was also explored. The migration energy, which was defined as the energy difference between the Ir/In₂O₃ slab with the Ir dopant located at the surface and subsurface layers, for the 16 sites on the surface was found to range from −0.72 eV to 0.44 eV (Fig. S6, ESI†), indicating that some of the surface Ir dopants might migrate to the subsurface layer, although it might incur a significant energy barrier unless there was already a subsurface In vacancy.

The heat map in Fig. 1(c) shows that the c doping site has the highest relative energy for the elements involved, whereas the f doping site has the lowest relative energy for four metal elements (Pt, Ir, Pd, Rh), and the e doping site has the lowest relative energy for the remaining two metal elements (Cu, Ni). In addition, except for the f doping site, the relative energy of metal doping to the surface of c-In₂O₃(111) increases as the row in the periodic table increases.

We selected the doping site with the lowest relative energy for each metal in our further calculations. In addition, according to the previous studies of our group,³³ the O_V6 site (we note the slight changes in the ordering of our labels from our previous works) has the highest O_V formation energy with the highest CO₂ reactivity, so the M₇, M₈ and M₁₁ metal doping sites near the O_V6 site are also included in our calculations. The metal doping sites and oxygen vacancies can be divided into M_9/12–O_V4/7, M_9/12–O_V8/10, M₇–O_V2, M₇–O_V5, M₇–O_V6, M₈–O_V6, and M₁₁–O_V6 as shown in the heat map in Fig. 1(d) for the O_V formation energy with further details listed in Table S2 (ESI†). Overall, the O_V formation energies of the single-atom metal doped structures near the O_V6 site are higher than those of the other sites. Ir (5d⁷6s²) and Rh (4d⁸5s¹) doped single metal atoms with the same nine valence electrons have a similar O_V formation energy. In addition, the doped metal elements Pt, Ir, Pd, and Rh in the sixth and fifth rows in the periodic table have relatively higher O_V formation energies than the doped elements Cu and Ni in the fourth row.

Furthermore, we examined the stability of the oxygen vacancy on the monatomic metal doped surface. For the Ir/In₂O₃ model, when the surface O_V6 is present, the adsorption energy ΔE of another Ir atom adsorbed at the O_V6 site was calculated to be 1.13 eV from the following equation

ΔE = E_Ir–ads − E_Ir − E_Ir7–OV6

E _Ir–ads is the energy of Ir₇–O_V6 with another Ir atom adsorbed at the vacancy O_V6, E_Ir is the energy of the Ir atom in its bulk state, and E_Ir7−OV6 is the energy of the Ir₇–O_V6 structure. Thus, the presence of oxygen vacancies may not lead to the aggregation of Ir monoatoms.

3.2 Dissociative adsorption of H₂

Heterolytic dissociation of H₂ on the perfect surface results in two H adatoms adsorbed at the O₆ and In sites near the single-metal atom M site (M = Pt, Ir, Pd, Rh, Cu, Ni, In). Fig. 2 shows the potential energy for O_V formation via H₂ reduction of the M/In₂O₃ surfaces with further details given in Table S5 (ESI†). The detailed structures of Cu/In₂O₃ with the M₇ doping site and Ni/In₂O₃ with the M₁₁ doping site are shown in this figure. The resulting In–H_a and O–H_b bond lengths are 1.77 Å and 0.97 Å, respectively. Here, the first transition state [TS–2H]* has an energy barrier between 0.66 eV, and the In–H_a and O–H_b bond lengths are 2.20 Å and 1.33 Å, respectively. This is followed by hydride transfer from In–H_a to the adjacent hydroxyl group (OH_b) to form an adsorbed H₂O molecule with an energy barrier of 0.64 eV, and the In–H_a, O–H_a and O–H_b bond lengths are 1.84 Å, 1.58 and 0.98 Å, respectively.

Fig. 2 Energy profiles for O_V formation via H₂ reduction of the M/In₂O₃ surfaces. The structure with a blue border shows the Cu/In₂O₃ model with the M₇ doping site, whereas that with a red border shows the Ni/In₂O₃ model with the M₁₁ doping site. E_a1 and E_a2 are energy barriers calculated as the energy difference between the [TS–2H]* and the H₂*, and that between the [TS–H₂O]* and the 2H*.

We find that the energy barrier of H₂ dissociation ([TS–2H]*) after single-metal atom doping is lower than that on the pure indium oxide surface (E_a = 1.08 eV), and that for H₂ dissociation on the Cu/In₂O₃ structure is the lowest. However, for the transition state of water formation ([TS–H₂O]*), the energy barriers for the M/In₂O₃ structures are higher than that of c-In₂O₃(111) (E_a = 0.52 eV). Overall, Cu/In₂O₃ is the most favourable for O_V formation through H₂ dissociation considering both the energy barrier and reaction energy.

Furthermore, for O_V formation, H₂ reduction may occur at either the In–O or M–O site. For the Pt/In₂O₃ model, the energy barrier for [TS–2H]* for H₂ dissociation at the Pt and O sites is lower than that at the In and O sites by 0.50 eV, as shown in Fig. S8 (ESI†). However, since the [MH–OH]* structure is always more stable than the [InH–OH]* structure as shown in Table S9 (ESI†), the subsequent hydrogen transfer to form the oxygen vacancy becomes more difficult, as the E_a of O_V formation from the [PtH–OH]* structure is 1.57 eV, which is 0.74 eV higher than that from the [InH–OH]* structure, as shown in Fig. S8 (ESI†).

3.3 CO₂ adsorption and activation on single-atom doped In₂O₃ surfaces

We further performed Bader charge analysis for these sites, and found that the single metal atom site on the doped c-In₂O₃(111) surface underwent a change in the oxidation state after O_V formation. As shown in Table 2, on surfaces where an oxygen vacancy is present, the oxidation states of the doped metals are all reduced, with the number of electrons gained by the doped metal ranging from 0.26 electrons (Rh) to 0.47 electrons (Pt). The number of electrons gained by In on the pure c-In₂O₃(111) is 0.41 electrons. Compared to the other doped metals, Pt and Ir, which belong to the sixth row in the periodic table, gain more electrons after O_V formation. Upon O_V formation, the oxidation state of the Pt dopant is reduced by the largest amount, whereas those of the Cu and Ni dopants are reduced by much less. Thus, the ΔQ_a value can be correlated to the oxygen vacancy formation energy of the M/In₂O₃ models, consistent with the much lower oxygen vacancy formation energies of Cu and Ni than other metals.

Table 2 Calculated Bader charges of single-atom doped metals on three models, where Q1 denotes the positive charges for the doped metal M in the perfect M/In₂O₃ surface, Q2 denotes the positive charges for the doped metal M in the M/In₂O₃ surface with O_V, and Q3 denotes the positive charges for the doped metal M in the M/In₂O₃_O_V surface with the bt-CO₂ adsorbate

Q/|e|	Pt7	Ir7	Pd7	Rh11	Cu7	Ni11	In2O3
Q1 (M_P)	1.19	1.44	1.08	1.22	1.17	1.23	1.79
Q2 (M_OV)	0.72	1.00	0.74	0.96	0.86	0.89	1.38
Q3 (M_CO2)	0.96	1.23	0.87	1.07	0.96	1.04	1.61
ΔQa (= Q2 − Q1)	−0.47	−0.44	−0.34	−0.26	−0.31	−0.34	−0.41
ΔQb (= Q3 − Q2)	0.24	0.23	0.13	0.11	0.10	0.15	0.23

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Adsorption and activation of CO₂ at the above representative Ov sites on the M/In₂O₃ surfaces are further studied, which are important in the CO₂ hydrogenation reaction. According to our previous study on the In₂O₃ surfaces,³² sites with higher O_V formation energy tend to favour CO₂ adsorption and activation. Therefore, we focused on the adsorption of CO₂ at the M_7/8/11–O_V6 sites as shown in Table S3 and Fig. S2 (ESI†). The most stable adsorption structures of CO₂ at the single metal sites were screened. Our calculations show that doping a single metal atom on the In₂O₃ catalyst can improve CO₂ adsorption and activation. The optimized structures of the surfaces with these monatomic metal doping sites and oxygen vacancy (O_V6) sites are shown in Fig. 3(a), and our subsequent calculations on the RWGS reaction are performed on these structures.

Fig. 3 (a) Structures of single metal atom-oxygen vacancy sites (M–O_V6, M = Pt₇, Ir₇, Pd₇, Rh₁₁, Cu₇, Ni₁₁) on the M-doped c-In₂O₃(111) surfaces along with the undoped In₂O₃ surface. (b) Plot of O_V formation energies and CO₂ adsorption energies. The linear fit and the associated R² value are shown, where the undoped In₂O₃ surface and the Pt₇–O_V6 surface are considered as outliers (in the dashed red circle).

Previous studies in our group³² have revealed two different CO₂ adsorption configurations. Again, taking the Cu₇–O_V6 structure as an example, the bent CO₂ (bt-CO₂*) structure adsorbed on the surface is shown in Fig. S2 (ESI†), where the CO₂ adsorbate is distorted, resulting in an O–C–O angle of 132.7°, compared to the linear O–C–O configuration in a free CO₂ molecule. One O atom of the CO₂ adsorbate occupies the O_V6 site, whereas the C atom binds the Cu atom. The C–O bonds in the CO₂ adsorbate are elongated to 1.20 Å and 1.31 Å from those of 1.18 Å in a free CO₂ molecule. These results indicate that the CO₂ adsorbate is activated. Compared with the pure indium oxide surface, monatomic metal doping benefits CO₂ adsorption in the bt-CO₂*, and CO₂ adsorption at the Pt₇–O_V6 site is the most stable.

Bader charge analysis further shows that the doped metal site in the M/In₂O₃ structure undergoes a significant change in the oxidation state upon CO₂ adsorption in the bt-CO₂*. As shown in Table 1, the number of electrons lost from the monatomic metal after CO₂ adsorption ranges from 0.10 e to 0.24 e. Combined with the above analysis of the CO₂ adsorption energies on these structures, electron transfer from the doped metal may contribute to the strong CO₂ adsorption, and the greater the number of electrons transferred from the doped metal, the more stable the CO₂ adsorption structure is. For example, the CO₂ adsorption energy at the Cu site is −0.5 eV with ΔQ_b = 0.10 |e|, whereas that at the Pt site it is −1.46 eV with ΔQ_b = 0.24 |e|.

In addition, at these monatomic metal doping sites, the larger the O_V formation energy, the more stable the CO₂ adsorption is. As shown in Fig. 3(b), except for c-In₂O₃(111), the O_V formation energy can be approximately linearly correlated with the bt-CO₂* adsorption energy. For instance, the Cu₇–O_V6 site has the lowest O_V formation energy (2.18 eV) and its corresponding CO₂ adsorption energy (−0.5 eV) is also the least negative. From Fig. 3(b), CO₂ adsorption on all the M/In₂O₃ structures are more stable than that on the pure c-In₂O₃(111).

3.4 RWGS reaction pathway

The main mechanisms reported for the RWGS reaction are direct dissociation and indirect conversion via carboxylic acid (COOH*). The intermediate bt-CO₂* is involved in the direct dissociation pathway, which dissociates to form CO* and O*, with CO* desorption to yield CO. The second pathway occurs via CO₂* hydrogenation to form the intermediate COOH*; its C–OH bond is then broken to give CO* and OH*, followed by CO* desorption to produce CO.

Fig. 4(a) shows the energy profile for the direct dissociation of CO₂ on the M/In₂O₃ surfaces with the detailed energies given in Table S6 (ESI†). Taking the Cu/In₂O₃ structure with an O_V as an example, the bt-CO₂* structure is formed, where the C–Cu bond length is 1.95 Å, and the C–O bond length is 1.20 Å and 1.30 Å (near O_V6), respectively. Then, the C–O bond in the CO₂* adsorbate with the O atom near O_V6 breaks with an energy barrier (E_a) of 1.92 eV, whose bond length in the transition state is 1.95 Å. The CO₂ is thus reduced to CO, whereas the leaving O atom fills the O_V6. In the CO* structure, the C–Cu and C–O bond lengths are 3.73 Å and 1.14 Å, respectively, and CO desorption from the CO* adsorbed at the Cu site to give CO in the gas phase is endothermic by 0.14 eV.

Fig. 4 (a) Energy profiles for CO₂ direct dissociation on M/In₂O₃ (M = Ni, Pt, Pd, Cu, Rh, Ir). The structure with a blue border shows the Cu/In₂O₃ model with the M₇ doping site, whereas that with the red border shows a Ni/In₂O₃ model with the M₁₁ doping site. (b) Plot of CO*_P adsorption energies (E_{ads,CO*_P}) and the energy barriers (E_a) of CO₂ dissociation with the linear fit and the associated R² value is also shown, where the undoped In₂O₃ surface and the Pt₇–O_V6 surface are considered as outliers (in dashed red circles).

For the Rh/In₂O₃ structure, the C–O bond breaking in the bt-CO₂* structure to form CO* has an exothermicity of −0.77 eV and an energy barrier of 0.01 eV, where for the Ir/In₂O₃ structure, it has an exothermicity of −1.27 eV and an energy barrier of 0.08 eV. With very low energy barriers, the Rh/In₂O₃ and Ir/In₂O₃ structures are conducive to direct dissociation of CO₂. In contrast, the energy barriers of CO₂ direct dissociation for the other M/In₂O₃ models are higher than that for the c-In₂O₃ (111) (E_a = 0.32 eV), so there is a lower probability for the adsorbed bt-CO₂* to directly dissociate for these models. Doping of the monatomic metals enhances the absorption of bt-CO₂* on the In₂O₃ surface (Table S6, ESI†). The bt-CO₂* adsorption structure on the In₂O₃ surface is unstable as indicated by its positive adsorption energy of 0.13 eV, so CO₂ is either physisorbed as the ln-CO₂* structure with a slightly negative adsorption energy of −0.16 eV or adsorbed as the carb-CO₂* structure with a more negative adsorption energy of −0.36 eV. In addition, the CO generated from CO₂ dissociation may occupy the surface M–O_V site, which will become unavailable for CO₂ adsorption, thus causing catalyst poisoning. Our DFT calculations show that the CO adsorption energy on the Pt/In₂O₃ structure is the most negative (E_ads = −3.07 eV) as shown in Table S4 (ESI†), while that on the Cu/In₂O₃ structure is the least negative (E_ads = −0.71 eV). Moreover, CO adsorption on all the M/In₂O₃ structures are stronger than CO₂ adsorption, so it may hinder CO₂ adsorption on the catalyst surface for the subsequent reaction.

The energies of the CO*_P adsorption state (E_{ads,CO*_P}) for the different M/In₂O₃ structures vary greatly (Fig. 4(a) and Table S6, ESI†). Similar to the linear relationship between the oxygen vacancy formation energy and the adsorption energy of bt-CO₂*, the E_{ads,CO*_P} value also has an approximately linear relationship with the E_a value for CO₂ dissociation, and a more positive E_{ads,CO*_P} value corresponds to a higher E_a value for CO₂ dissociation, as shown in Fig. 4(b).

The indirect dissociation pathway of the RWGS reaction on the M/In₂O₃ models is further shown in Fig. 5 and Fig. S3 (ESI†). For the Cu/In₂O₃ structure, all the transition states along this reaction pathway are found as shown in Fig. 5. The bt-CO₂* first reacts with the H* adsorbed at the In site to form COOH*, which is endothermic by 1.38 eV with an energy barrier of 2.09 eV. The C–OH bond in the COOH* breaks to form CO* and OH*, which is also exothermic by −0.39 eV with an energy barrier of 0.01 eV. The C–O bond lengths in the [TS–COOH]*, [COOH]*, and [TS–CO–OH]* structures are 1.41 Å, 1.46 Å and 1.63 Å, respectively. CO desorption from the CO* adsorbed at the Cu site to give CO in the gas phase is endothermic by 0.23 eV. Thus, our calculations show that the rate-determining step along the indirect dissociation pathway of the RWGS reaction on the Cu/In₂O₃ structure is the first step for [CO₂ + H]* to [TS–COOH]*.

Fig. 5 Energy profiles for CO₂ hydrogenation to form CO via the direct and indirect dissociation pathways on the Cu/In₂O₃ model.

For the other M/In₂O₃ models, the transition states are difficult to locate, so only the relative energies of the reaction intermediates are given in Fig. S3 and Table S7 (ESI†). Furthermore, the [COOH]* structure is also not stable on these surfaces, so hydrogenation of the adsorbed CO₂* in the [CO₂ + H]* directly leads to the [CO + OH]* by breaking one of the C–O bonds. The C–O bond length of the C from CO* to the O from OH* is 2.82–3.12 Å. For these M/In₂O₃ models, the relative energies of the [CO₂ + H]* structures range from −2.90 eV (Rh/In₂O₃) to −0.06 eV (Ir/In₂O₃), whereas those of the [CO + OH]* structures range from −0.81 eV (c-In₂O₃(111)) to −3.07 eV (Ir/In₂O₃). In addition, the [CO₂ + H]* structure adsorbed on Pd/In₂O₃, Pt/In₂O₃ and Rh/In₂O₃ are very stable, which may be detrimental to the subsequent reaction of the COOH*.

3.5 Microkinetic simulations

For the above-mentioned single-atom metal doped models with a low CO₂ direct dissociation energy barrier of the RWGS reaction, first principles-based microkinetic simulations were further performed to study the reaction kinetics over the Ir/In₂O₃ and Rh/In₂O₃ models. In addition, since we also obtained a complete indirect dissociation pathway for the Cu/In₂O₃ model, we also performed microkinetic simulations despite its high energy barrier. Fig. 6(a) shows the calculated turnover frequencies (TOFs) for CO₂ consumption under the typical reaction conditions of 473–673 K and 5 MPa (H₂ : CO₂ = 3 : 1). These results show that single-atom metal doping significantly enhances CO₂ reactivity over the pure In₂O₃ catalyst at above 573 K. In addition, among the above three SACs, the Ir/In₂O₃ model was predicted to have the highest TOF, which was followed by that of the Cu/In₂O₃ model, whereas the lowest TOF was predicted for the Rh/In₂O₃ model, at temperatures above 573 K, indicating that the Ir/In₂O₃ model has the best CO₂ reactivity. Although the RWGS reaction was experimentally performed under medium to high temperature conditions, we also calculated the turnover frequencies (TOFs) from 300 K to 450 K (Fig. S7, ESI†), although for the Ir/In₂O₃ model, only TOFs in the temperature range of 400–450 K could be calculated due to the convergence issue.

Fig. 6 Microkinetic simulations of the catalytic performance of M/In₂O₃ (M = Cu, Ir, Rh) SACs. (a) Plot of the calculated turnover frequencies (TOFs) for CO₂ consumption, and calculated degrees of rate control (DRCs) for CO₂ hydrogeneration over the Cu/In₂O₃ (b), Ir/In₂O₃ (c), and Rh/In₂O₃ (d) models.

Fig. 6(b) further shows the calculated degrees of rate control (DRCs) for CO₂ consumption on the Cu/In₂O₃(111) model. The DRC of the transition state for OH* hydrogenation to H₂O* ([H + OH]* → H₂O*) is the largest, suggesting that this elementary step is rate-limiting, so lowering its energy barrier will lead to higher CO₂ reactivity. On the other hand, the DRC of the transition state for bt-CO₂* hydrogenation to COOH* ([bt-CO₂ + H]* → COOH*) increases noticeably from 598 K to 673 K. Fig. 6(c) and (d) display the calculated DRC values for the CO₂ reaction rate on the Ir/In₂O₃ and Rh/In₂O₃ models, where the DRCs of the OH* intermediate and the transition state for its hydrogenation to generate the V_O site ([H + OH]* → H₂O*) are the largest, suggesting the V_O formation is the rate limiting step.

Although the potential energy profiles of the Ir/In₂O₃ and Rh/In₂O₃ models in the CO₂ direct dissociation pathway are very close, the energy barrier of the first transition state [TS–2H]* to generate the oxygen vacancy site through H₂ reduction for the Ir/In₂O₃ model is 0.31 eV lower than that of the Rh/In₂O₃ model (Fig. 2), consistent with the much higher CO₂ reactivity of the Ir/In₂O₃ model than that of the Rh/In₂O₃ model, as oxygen vacancy formation is much easier for the Ir/In₂O₃ model. In addition, the higher reactivity of the Cu/In₂O₃ model than the In₂O₃ model may be due to the fact that its CO₂ adsorption is much stronger than that on In₂O₃, although the energy barrier of CO₂ direct dissociation on the Cu/In₂O₃ model is substantial. Furthermore, as shown in Fig. S4 (ESI†), the free site coverage for the Cu/In₂O₃ model is higher than the In₂O₃ model, which should also contribute to the higher turnover frequency for the Cu/In₂O₃ model.

3.6 Discussion

In recent years, a series of metal oxide-supported SACs have been synthesized and investigated for CO₂ hydrogenation reactions.^47–49 For these catalysts, the O_V sites play a key role in stabilizing the SACs.⁵⁰ The previous study of Qi et al.²⁸ calculated the anchoring energy of transition metal single atoms (TMSA) at the O_V site, although single metal atom doped In₂O₃ was not examined. In the present work, we first investigated the thermal stability of metal doping on c-In₂O₃(111) for M = Pt, Ir, Pd, Rh, Cu, and Ni, and screened the most stable doping site from the relative energy of the doped surface, whereas the optimal active site was further determined by comparing the O_V formation energy. In addition, single metal atom doping was found to significantly enhance CO₂ adsorption on the In₂O₃ surface, and there is an approximate linear relationship between the O_V formation energy and the CO₂ adsorption energy in the bt-CO₂* structure, where a higher O_V formation energy corresponds to stronger CO₂ adsorption in this structure. This suggests that the O_V formation energy for the M/In₂O₃ models may be used as a catalyst descriptor for CO₂ conversion, so the strength of the bt-CO₂* adsorption can be determined from the O_V formation energy, and CO₂ adsorption in the bt-CO₂* structure further facilitates the subsequent dissociation and/or hydrogenation steps involved in the RWGS reaction.

Recent studies mainly focused on the RWGS activity over three major kinds of heterogeneous catalysts, including supported metal catalysts, mixed oxide catalysts, and transition metal carbides.¹⁴ Rui et al.⁵¹ used In₂O₃ powder mixed with Pd/peptide composites and then heat-treated them to remove peptides to obtain a Pd/In₂O₃ catalyst. The Pd nanoparticles on this catalyst facilitate the dissociative adsorption of hydrogen and promote the generation of oxygen vacancies. The interfacial site also enhances the adsorption and hydrogenation of CO₂. In this work, our calculations show that Pd monatomic doped In₂O₃ also favours the dissociative adsorption of hydrogen and promotes the formation of oxygen vacancies, consistent with the above experimental work. Thus, our work shows that single-atom doped In₂O₃ SAC catalysts are promising for the RWGS reaction, and further experimental studies are needed to verify our findings.

In our previous work,²¹ the c-In₂O₃(111) surface was found to favour methanol formation from CO₂ hydrogenation. In this work, we find that the Rh and Ir monatomic doped c-In₂O₃(111) models favour CO formation via the RWGS reaction, indicating that single atom doping can regulate product selectivity of CO₂ hydrogenation. Previously, Ye et al.¹³ designed a bifunctional Ir₁–In₂O₃ single-atom catalyst that can efficiently hydrogenate CO₂ in liquids with a high ethanol selectivity of >99%. Their characterization showed that isolated Ir atoms combined with adjacent oxygen vacancies to form Lewis acid–base pairs, which promoted the adsorption and activation of CO₂ to CO*. Our calculations are consistent with the above conclusion, and the energy barrier for CO₂ dissociation to generate CO over Ir/In₂O₃ is 0.24 eV lower than that over In₂O₃ (Fig. 4).

Our results expand the choice of catalysts for the RWGS reaction and increase the variety of monatomic metal doped In₂O₃ catalysts. The linear relationship between oxygen vacancy formation energy and CO₂ adsorption energy and the energy barrier of the reaction pathway show that the magnitude of oxygen vacancy formation energy is an effective descriptor for screening the SACs for their catalytic performance in the RWGS reaction. Microkinetic simulations show that the CO₂ turnover frequencies on the doped M/In₂O₃(M = Cu, Ir, Rh) models are greater than that of the pure In₂O₃, especially at reaction temperatures above 573 K, and the Ir/In₂O₃ model was predicted to have the highest CO₂ reactivity. The rate controlling step of the CO₂ hydrogenation reaction is the hydrogenation of the OH species to form H₂O, indicating that the formation of the oxygen vacancy site is the most important limiting factor for CO₂ reactivity. In the best-case scenario, these In₂O₃ SACs may be applied in both the RWGS reaction and FT synthesis, allowing for the direct conversion of CO₂ into fuels.

4 Conclusions

In summary, we have investigated the single-atom doped In₂O₃ catalysts for the RWGS reaction using DFT calculations. Our results show that over the single-atom metal doped c-In₂O₃(111) structure for M = Pt, Ir, Pd, Rh, Cu, Ni, the energy barrier for H₂ dissociation to form the [TS–2H]* structure can be considerably lower than that of pure In₂O₃ by up to 0.4 eV. These structures are thus conducive to the dissociative adsorption of H₂, promoting the generation of surface oxygen vacancies and thereby increasing CO₂ adsorption and activation over the In₂O₃ surface. Compared to pure In₂O₃, single-atom metal doping strengthens CO₂ adsorption in the bt-CO₂* structure, suggesting the SACs facilitate CO₂ adsorption and activation over the In₂O₃ catalyst. Furthermore, the O_V formation energy on the M/In₂O₃ surface may serve as an effective descriptor for CO₂ adsorption, where higher O_V formation energy results in more stable CO₂ adsorption. For the direct dissociation pathway of the RWGS reaction, the Ir/In₂O₃ and Rh/In₂O₃ structures are conducive to CO₂ direct dissociation to form CO. In contrast, the energy barriers for CO₂ direct and indirect dissociations over the Cu doped structure are much higher at 1.92 eV and 2.09 eV, respectively, suggesting that the Cu/In₂O₃ structure is the least active for CO formation via the RWGS reaction. The adsorption energies of [CO*_P] for the M/In₂O₃ models can be linearly correlated with the E_a of CO₂ direct dissociation, so the higher adsorption energy of [CO*_P] corresponds to the higher activation energy of CO₂ direct dissociation. Microkinetic simulations further confirm that single-atom metal doping to In₂O₃ greatly benefits the CO₂ conversion, especially under relatively high reaction temperatures, and the formation of the oxygen vacancy site mainly limits the CO₂ reactivity on the M/In₂O₃ (M = Cu, Ir, Rh) models. Among the three single-atom catalysts, the turnover frequency was predicted to follow the order of Ir/In₂O₃ > Cu/In₂O₃ > Rh/In₂O₃ at reaction temperatures above 573 K, indicating that the Ir/In₂O₃ structure should have the best CO₂ reactivity.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (22172188, 22293023), the Shanghai Sailing Program from the Science and Technology Commission of Shanghai Municipality (23YF1453400), the Joint Fund of the Yulin University and the Dalian National Laboratory for Clean Energy (Grant No. YLU-DNL Fund 2022001), China National Offshore Oil Corporation (KJGG-2022-12-CCUS-030402), Qinchuangyuan “Scientists + Engineers” Team Construction Program of Shaanxi Province (2023KXJ-276), and the research program from Shaanxi Beiyuan Chemical Industry Group Co., Ltd. (2023413611014).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3cp04352e

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