The remarkable performance of a single iridium atom supported on hematite for methane activation: a density functional theory study

Abstract

Methane is the major component of natural gas, and it significantly contributes to global warming. In this study, we investigated methane activation on the α-Fe₂O₃(110) surface and M/α-Fe₂O₃(110) surfaces (M = Ag, Ir, Cu, or Co) using the density-functional theory (DFT) + U method. Our study shows that the Ir/α-Fe₂O₃(110) surface is a more effective catalyst for C–H bond activation than other catalyst surfaces. We have applied electron density difference (EDD), density of states (DOS), and Bader charge calculations to confirm the cooperative CH⋯O and agostic interactions between CH₄ and the Ir/α-Fe₂O₃(110) surface. To further modify the reactivity of the Ir/α-Fe₂O₃(110) surface towards methane activation, we conducted a study of the effect of oxygen vacancy (O_V) on C–H activation and CH₄ dehydrogenation. In the comparison of pristine α-Fe₂O₃(110), Ir/α-Fe₂O₃(110), and Ir/α-Fe₂O₃(110)–O_V surfaces, the Ir/α-Fe₂O₃(110)–O_V surface is the best in terms of CH₄ adsorption energy and C–H bond elongation, whereas the Ir/α-Fe₂O₃(110) surface catalyst has the lowest C–H bond activation barrier for the CH₄ molecule. The calculations indicate that the Ir/α-Fe₂O₃(110)–O_V surface could be a candidate catalyst for CH₄ dehydrogenation reactions.

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1. Introduction

Methane is the major component of natural gas and a potential clean energy carrier because of its highest H to C ratio of any fossil fuel.^1–4 With the industrial revolution, methane is considered an alternative to nonrenewable petroleum resources and plays a significant role in the energy field.^5–8 Consequently, the combustion of methane leads to 25% of the global CO₂ emission, and methane itself is a greenhouse gas, which has a relative greenhouse impact of 25 times greater than CO₂. This rise in the greenhouse gas concentration, predominantly methane in the earth's atmosphere, triggered an increase in global air pollution and surface temperature.^9,10 Hence, the methane conversion to valuable commodity chemicals near its source is essential in the industry and addresses environmental concerns.

Over the decades, various strategies, including direct and indirect routes, have been developed to use methane effectively; however, the C–H bond activation under mild conditions is challenging.^10–13 The chemical products based on direct methane conversion have received significant interest in recent decades from industry and academia due to their more energy-efficient and environmental-friendliness.^14–16 The rutile IrO₂ surface has been the subject of intensive theoretical^17–19 and experimental studies,^20–22 among the different catalysts in methane conversion owing to its remarkable reactivity. In addition, much evidence endorses this superior catalytic reactivity and intrinsic electronic characteristics of the IrO₂ surface in methane activation.²³ Besides its higher reactivity, the high cost and the natural scarcity of iridium significantly limit its further development and application.

The doping of a single metal atom in metal oxide surfaces has attracted considerable interest, as it could afford precious metal thrifting and solve the ultimate goal of designing efficient and low-cost catalysts in heterogeneous catalysis.^24–28 For example, Y. Meng et al. demonstrated that the doping of the Pd atom improved the thermodynamic stability and catalytic performance of the Cu(111) surface towards partial oxidation of methane than the single Pd atom adsorbed surface.²⁸ Similarly, Guo and coworkers²⁹ have recently shown that Rh doped Ni(111) catalyst exhibits promising performance for coke resistance in the CH₄/CO₂ reforming reaction. Besides, the density functional theory calculations by Eisenberg and Baer have demonstrated that doping of Li atom on MgO significantly eases the hydrogen abstraction reaction from methane.²⁷ Furthermore, recent studies have described the role of single metal atom dopants in Al₂O₃ and zeolites for the activity, selectivity, stability, and regeneration capability of catalysts in propane and light alkane dehydrogenation.^30–32 Previous studies have shown that the metal oxides doped with low-valence metal atoms show better catalytic activity towards methane activation than the non-doped oxides.^33–35 Compared with other metal oxides, hematite is abundant, inexpensive, and environmentally benign. It has been widely used as a catalyst and supports catalysis because of its stability and attractive physicochemical properties.^36–38 Furthermore currently researchers used iridium oxide as a catalyst for methane activation. But iridium oxide is rare earth metal oxide and it is too expensive.

Motivated by these analyses and to design the low-cost catalyst with the comparable catalytic performance of IrO₂(110) surface, in this work, we designed a distinct type of different single-atom doped on hematite (α-Fe₂O₃) surface. In addition, we explored its catalytic activity towards methane adsorption and activation using density functional theory calculations. Furthermore, previous studies³⁹ indicate that the presence of oxygen vacancies in the metal oxide supports enhanced the methane activation; hence we also examined the effects of a single oxygen vacancy on the hematite support for C–H activation.

2. Computational details

All the spin-polarized DFT calculations were carried out using the widely used plane wave Vienna ab initio simulation package (VASP).^40,41 The nonlocal optB88-vdW exchange–correlation functional was used in this study, which explicitly includes the effects of van der Waals forces.^42–44 The core electrons were represented by the projector augmented wave (PAW),⁴⁵ and the energy cutoff for all the calculations was set to 500 eV based on our benchmark results. The atomic positions were optimized until the total energy converged to 10⁻⁴ eV, and the atomic positions were relaxed using the quasi-Newton algorithm until the x, y, and z components of the unconstrained atomic force were smaller 2 × 10⁻² eV Å⁻¹. To treat the on-site Coulomb and exchange interaction of the strongly localized 3d electrons of metal atoms, here we employed the DFT + U mechanism. The DFT + U is a widely used method to describe transition metal-related studies and we conduct the benchmark calculation of the U value for each transition metal. Thus, one of the most common approaches to determine the appropriate values of U is to compare the calculated band gap for a set of U values with the experimental band gap.^46,47 As shown in Fig. 1S,† when the U value increases the band gap of the oxide also increase for all dopant case. The experimental band gaps are 0,⁴⁸ 2.18,⁴⁹ 2.85,⁵⁰ 1.6,⁵¹ and 1.3 eV⁵² for IrO₂, Fe₂O₃, CuO, CoO, and Ag₂O, respectively. Therefore, we use a combination of calculated U values derived from the fitting band gaps. For Ag, Cu, Ir, Co, and Fe, we use 5.0 eV, 4.0 eV, 0.0 eV, 3.0 eV, and 4.0 eV, respectively. Similar studies also use combination U vales for heteroatom systems.^53–57

As shown in Fig. 2S,† the simulated XRD pattern of the α-Fe₂O₃ bulk structure shows the strongest intensity of (104) orientation, which agrees with the experimental results.⁵⁸ However, based on our surface energy calculated results for the three dominant surface planes of hematite (α-Fe₂O₃(104, 110, and 012)), α-Fe₂O₃(110) surface with the least surface energy is the most stable one, as shown in Table 1S.† Therefore, we selected the α-Fe₂O₃(110) surface.

The geometry optimization of α-Fe₂O₃ was carried out using a Monkhorst–Pack k-points scheme of 5 × 5 × 2 and 2 × 3 × 1 for bulk and surface calculations, respectively. For the final single-point runs for calculating the electronic properties such as DOS, a mesh of 6 × 9 × 1 was used as shown in Fig. 1a. The α-Fe₂O₃ bulk structure contains iron and oxygen atoms arranged in a triangular hexagonal structure, and the calculated α-Fe₂O₃ bulk lattice parameters are (a = b = 5.0396 Å and c = 13.7494 Å) in agreement with the experimental lattice parameter values (a = b = 5.036 Å and c = 13.75 Å) and previous theoretical calculations.⁵⁹ The dopants calculated bulk lattice parameters in their bulk forms are (a = b = c = 2.953 a = b = c = 4.003, a = b = c = 3.689, a = b = c = 4.194, and a = b = c = 4.076 Å) for Fe, Ir, Cu, Co, and Ag, respectively, which is in agreement with the experimental lattice values.^60–62 The calculated chemical potential of the dopants is, −2.879, −6.575, −0.862, −2.003, and −1.809 for Fe, Ir, Cu, Co, and Ag, dopants, respectively, as shown in Table 2S.†

Fig. 1 (a) α-Fe₂O₃ lattice with an antiferromagnetic spin arrangement indicated; spin up by yellow and down spin by blue arrows at Fe sites (b) density of states of the bulk hematite (c) calculated optimum hematite (110) surface structure and (d) DOS of the α-Fe₂O₃(110) surface plane.

The calculated band gap of bulk α-Fe₂O₃ is 2.065 eV, as shown in Fig. 1b, which is within the experimental values (1.90–2.20 eV)⁶³ and similar to the previous theoretical study of 2.1 eV.⁶⁴

The adsorption energy (E_ads) of the methane on the surface was calculated as

E_ads = E_CH4+surface − E_CH4 − E_surface

where E_CH4+surface is the total energy of the catalyst on which methane is adsorbed, E_CH4 and E_surface are the energies of the CH₄ molecule in the gas phase and the catalyst surface, respectively. We used the climbing-image nudged-elastic-band (CI-NEB)⁶⁵ method to evaluate the reaction energy barrier for methane activation, which locates the transition state (TS) structure. Vibrational frequency analyses were subsequently performed to verify the imaginary vibrational mode's uniqueness, confirming the saddle point's true nature. Charge redistributions during a surface reaction and the molecule's interaction with the surface were evaluated using the Bader charges method and partial density of states (PDOS) of atoms by considering before and after the adsorption of the CH₄ molecule.

3. Results and discussion

3.1. Surface modeling

The α-Fe₂O₃(110) surface was modeled from the optimized bulk, consisting of nine atomic layers in which the bottom three atomic layers and seven atomic layers were fixed during the structural optimization and frequency calculations, respectively. A vacuum space of 15 Å was used in the z-direction to avoid the interactions between the slabs. The α-Fe₂O₃(110) surface has three types of surface oxygen atoms: two-folded coordinated, three-folded coordinated on the top layer (denoted O_2C and O_3C, respectively), and four-folded coordinated in the subsurface (denoted as O_4C). The corresponding minimum distances of three differently coordinated oxygen atoms with the nearest metal atom are 1.79, 1.92, and 2.12 Å for two-, three- and four-folded coordinated oxygen atoms, respectively. The most stable surface has been chosen based on its surface energy for methane activation, as shown in Table 1S.† The relative stability of α-Fe₂O₃(110) surface with different single metal dopants was compared by calculating formation energy as:

E_form = E_M/Fe2O3 + μ_Fe − E_Fe2O3 − μ_M

where E_M/Fe2O3M and E_M/Fe2O3 are the total electronic energies of α-Fe₂O₃(110) surface after and before doping, respectively, μ_Fe is the chemical potential of the iron atom replaced by single-atom dopants, μ_M is the chemical potential of the dopants, and M is dopant atom (Ag, Ir, Cu, or Co). The chemical potential of the single-metal atom was assumed to be the electronic energy of a single atom in the bulk phase. Single metal atom doping site and the system geometry configuration is illustrated in Fig. 4S.†

3.2. Methane adsorption

To investigate the methane's most stable adsorption site over the pristine α-Fe₂O₃(110) surface, we considered Fe top, F–O bridge, O_2C top, and O_3C top adsorption sites, as shown in Fig. 5S.† Our results indicate that CH₄ adsorb preferentially on the Fe top of α-Fe₂O₃(110) surface with an adsorption energy of −0.211 eV by coordinating one of the C–H bonds toward the surface shown in Fig. 2a. The adsorption is relatively strong compared to those of the α-Fe₂O₃(0001) surface, on which the adsorption energy is −0.1 eV. The C⋯Fe and CH⋯O distances are 2.719 and 2.480 Å, respectively; one of the C–H bond lengths of CH₄ extended to 1.109 Å from 1.097 Å (free molecule) upon the adsorption.⁶⁶

Fig. 2 Optimized structure of CH₄ adsorption on M/α-Fe₂O₃(110) surfaces: (a) α-Fe₂O₃(110), (b) Ag/α-Fe₂O₃(110), (c), Ir/α-Fe₂O₃(110), (d) Co/α-Fe₂O₃(110), (e) Cu/α-Fe₂O₃(110), and (f) Ir/α-Fe₂O₃(110)–O_V surfaces.

Further, we obtained the most stable adsorption configuration of CH₄ on different metal-doped hematite surfaces (M/α-Fe₂O₃(110)) where (M = Ag, Cu, Ir, or Co). The optimized most stable CH₄ adsorption configurations on M/α-Fe₂O₃(110) surface are shown in Fig. 2, 6S and 7S of ESI† showing the other less stable structures. The calculated adsorption energies, selective bond lengths, and distances of CH₄ adsorption on M/α-Fe₂O₃(110) surfaces (M = Ag, Ir, Co, or Cu) are listed in Table 1. The CH₄ on the Ir/α-Fe₂O₃(110) surface has the largest adsorption energy and most extended C–H bond length compared to the other considered single-metal doped systems and the pristine surface. The C–H bond length is elongated to 1.146 Å from 1.097 Å (free molecule), indicating that the C–H has been significantly activated. Furthermore, the CH⋯O and C⋯Ir distances (2.364 and 1.918 Å, respectively) are much shorter than those single-metal doped systems and the pristine surface due to the more vital interaction between CH₄ and Ir/α-Fe₂O₃(110) surface.

Table 1 Calculated adsorption energies (E_ads in eV), C–H bond lengths (d_C–H in Å), H to surface oxygen distance (d_CH⋯O in Å), C to nearest metal atom distances (d_C⋯M in Å), activation barriers (E_a in eV), and reaction energies (ΔE in eV) for CH₄ activation on different catalyst surfaces

Surface	Eads	dC–H	dCH⋯O	dC⋯M	Ea	ΔE	Reference
Free CH4 molecule	—	1.097	—	—	—	—	This study
α-Fe2O3(110)	−0.216	1.109	2.480	2.719	0.819	0.358	This study
Ag/α-Fe2O3(110)	−0.178	1.100	2.729	3.398	—	—	This study
Ir/α-Fe2O3(110)	−0.395	1.146	2.364	1.918	0.439	0.300	This study
Co/α-Fe2O3(110)	−0.235	1.099	2.701	3.797	—	—	This study
Cu/α-Fe2O3(110)	−0.227	1.100	3.018	3.377	—	—	This study
Ir/α-Fe2O3(110)–OV	−0.590	1.182	2.805	1.794	0.585	−0.590	This study
IrO2(110)	−0.41	1.16	2.11	—	0.300	−1.090	19
Pd/CeO2(111)	−0.19	—	—	—	1.140	—	35
Pd/Cu(111)	−0.20	—	—	—	1.460	0.940	28
IrO2/TiO2(110)	−0.74	1.15	2.24	—	0.290	−1.080	68

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Among the considered different single metal-doped α-Fe₂O₃(110) surfaces, Ir single atom doped α-Fe₂O₃(110) surface (Ir/α-Fe₂O₃(110)) has the CH₄ adsorption energy of −0.395 eV. As shown in Table 1, M/α-Fe₂O₃(110) surface (M = Ir) has the best results in C–H bond elongation, interaction, and CH₄ adsorption energy. The C–H bond elongation on Ir/α-Fe₂O₃(110) surface has a similar value to with IrO₂(110) surface catalyst, i.e., 1.15 Å. Researchers agreed that IrO₂(110) surface catalyst has a remarkable performance for CH₄ activation.^67,68 Hence Ir/α-Fe₂O₃(110) surface catalyst has nearly similar activity to the IrO₂(110) surface in terms of C–H bond elongation. As a result, this catalyst will be one of the promising and economically feasible catalysts for CH₄ activation. Therefore, we selected the Ir/α-Fe₂O₃(110) surface catalyst for further study.

As the Ir/α-Fe₂O₃(110) surface exhibits enhanced catalytic activity toward CH₄ adsorption among the others, we further considered the presence of single oxygen vacancy on the Ir/α-Fe₂O₃(110) surface (Ir/α-Fe₂O₃(110)–O_V) and investigated the reactivity towards CH₄ activation. The oxygen vacancy formation energy O_V was calculated using the following equation:

where E_Ir/Fe2O3+OV is the total energy of the surface with a single oxygen vacancy, E_sur is the electronic energy of the pure surface, and E_O2 is the total energy of the oxygen molecule in the gas phase. We calculated the O_V formation energy from the M/α-Fe₂O₃(110) surfaces by pulling out one oxygen atom from the top surface of the structure. From our study, the O_V formation energies of the twofold coordinated and threefold oxygen atoms from the top layer of the pristine α-Fe₂O₃(110) surface were 2.76 and 2.93 eV, respectively, similar to the previous study.³⁹ Similarly, O_V formation energy of the twofold coordinated and threefold coordinated oxygen atoms from the top layer of the Ir/α-Fe₂O₃(110) surface was considered. However, the structure became unstable when we created the twofold coordinated oxygen atom defect from Ir/α-Fe₂O₃(110) surface. The O_V formation energy of the threefold coordinated oxygen atoms from the top layer of the Ir/α-Fe₂O₃(110) surface was 2.55 eV. As a result, we used threefold coordinated oxygen vacancies to investigate the effect of oxygen vacancies on CH₄ adsorption; a similar method was applied in a previous study.⁶⁹

In the same case, different adsorption sites were considered on the Ir/α-Fe₂O₃(110)–O_V surface, and each selected configuration was optimized to find a stable structure. The calculated adsorption energy for the different adsorption sites and selected geometry parameters are given in Fig. 8S.† As it has seen in Fig. 2f, it is the most stable CH₄ adsorption site on the Ir/α-Fe₂O₃(110)–O_V surface with the adsorption energy of −0.590 eV, which is much larger than that of other surfaces considered in this study. In the process of adsorption, the elongation of the activated C–H bond of CH₄ on the Ir/α-Fe₂O₃(110)–O_V surface (1.182 Å) was the greatest compared to that on other surfaces. Recent study³⁹ also indicates that oxygen vacancy enhanced the C–H bond activation in doped metal oxides. Ir/α-Fe₂O₃(110)–O_V surface increased the C–H bond length by 0.085 Å compared to the gaseous methane C–H bond length. The CH⋯O and C⋯Ir distances on the Ir/α-Fe₂O₃(110)–O_V surface are 2.805 and 1.794 Å, respectively. Compared to Ir/α-Fe₂O₃(110) surface, the CH⋯O distance becomes longer, whereas the C⋯Ir distance is shorter, indicating that the agostic interaction increases, whereas the CH⋯O interaction decreases in the case of CH₄ adsorption on Ir/α-Fe₂O₃(110)–O_V surface. The methane molecule's C–H bond elongation on the Ir/α-Fe₂O₃(110) and Ir/α-Fe₂O₃(110)–O_V surfaces was due to the CH⋯O and agostic interactions between C–H of CH₄ and surfaces.

3.3. Electronic structure analysis

For a detailed comparison of the electronic behavior of Ir/α-Fe₂O₃(110) and Ir/α-Fe₂O₃(110)–O_V surfaces upon CH₄ adsorption; we plotted EDD and the DOS distributions for the most stable adsorption configurations. Fig. 3 shows the EDD contours of CH₄ adsorption on Ir/α-Fe₂O₃(110) and Ir/α-Fe₂O₃(110)–O_V surfaces with two different cutting planes (C–H⋯Ir and C–H⋯O_cus). As shown in Fig. 3a and b, electron accumulation between one C–H bond of methane and Ir atom on Ir/α-Fe₂O₃(110) and Ir/α-Fe₂O₃(110)–O_V surfaces were observed, which indicates the existence of agostic interaction between methane and surface. Further, as shown in Fig. 3c and d, it could be observed the electron accumulation between one of the H(C) and surface oxygen atoms on both Ir/α-Fe₂O₃(110) and Ir/α-Fe₂O₃(110)–O_V surfaces, indicating the presence of CH⋯O hydrogen bond between methane and the surface. The agostic interaction will make the electron transfer from methane to the surface, whereas CH⋯O hydrogen bonding causes the electron transfer from the surface to methane. Therefore, these two cooperative interactions between methane and the surface result in great methane adsorption energy on the Ir/α-Fe₂O₃(110) surface.^19,71 The strong interaction between methane and surface results in significant C–H bond elongation, indicating that CH₄ has significantly been activated on the Ir/α-Fe₂O₃(110) surface and Ir/α-Fe₂O₃(110)–O_V surfaces, as illustrated in Fig. 3. To understand the effect of the van der Waals force on methane adsorption, we calculated the methane adsorption energy without considering the van der Waals force correction. As shown in Table 3S,† on the surfaces of α-Fe₂O₃(110), Ir/α-Fe₂O₃(110), and Ir/α-Fe₂O₃(110)–O_V, the contribution of van der Waals force to methane adsorption is −0.17, −0.22, −0.32 eV, respectively. It is like the results of the literature.^70,71

Fig. 3 2-D plots of the calculated electron density difference (EDD) for the CH₄ adsorption. (a) C–H⋯Ir coplanar on Ir/Fe₂O₃(110) surface, (b) C–H⋯Ir coplanar on Ir/Fe₂O₃(110)–O_V surface, (c) C–H⋯O coplanar on Ir/Fe₂O₃(110) surface and (d) C–H⋯O coplanar on Ir/Fe₂O₃(110)–O_V surface. The red and blue lines represent the increasing and decreasing electron densities, respectively. The isovalue is 0.002 ebohr⁻³.

Fig. 4 shows the DOS of the CH₄ molecule before and after adsorbed on α-Fe₂O₃(110), Ir/α-Fe₂O₃(110), and Ir/α-Fe₂O₃(110)–O_V surfaces. The DOS plot of the free CH₄ molecule shows there are two peaks located at around −5.1 and −12.6 eV, which belong to the t₂ and a₁ states of CH₄ σ hybridization states, respectively. After adsorption, both states shift to lower energy regions, and the t₂ state becomes much broad. The order of amplitude of shift and broadening is α-Fe₂O₃(110) > Ir/α-Fe₂O₃(110) > Ir/α-Fe₂O₃(110)–O_V, related to adsorption energy. The interaction of CH₄ with Ir/α-Fe₂O₃(110)–O_V is the strongest, resulting in the most extensive degree of state energy downshift and broadening. The Bader charge calculation found that 0.034, 0.143, and 0.145 net electrons/charges were transferred from the CH₄ molecule to α-Fe₂O₃(110), Ir/α-Fe₂O₃(110), and Ir/α-Fe₂O₃(110)–O_V surfaces, respectively. The last two have large electrons transfer from methane to the surface, indicating that the agostic interactions are large, which causes the great C–H activation.

Fig. 4 The density of states of CH₄: free molecule (red line), on α-Fe₂O₃(110) (blue line), Ir/α-Fe₂O₃(110) surfaces (cyan line), and Ir/α-Fe₂O₃(110)–O_V surfaces (green line), respectively. The upper and lower panels represent spin up and spin down, respectively.

3.4. Methane activation

The activation of the first C–H bond is the critical and the rate-limiting step in methane conversion on most catalysts. In this work, we predominantly calculated the first dehydrogenation of CH₄ over α-Fe₂O₃(110), Ir/α-Fe₂O₃(110), and Ir/α-Fe₂O₃(110)–O_V surfaces. The calculated energy barrier and reaction energy profile for CH₄ activation over these three catalysts are illustrated in Fig. 5, and the structure of the initial state transition state (TS), and intermediate state (dis-CH₄) are given in Fig. 6. As shown in Fig. 5, the dehydrogenation barrier of the CH₄ molecule on the α-Fe₂O₃(110) surface is the largest with 0.819 eV, and the reaction energy is endothermic by 0.358 eV. The dehydrogenation barrier of the CH₄ molecule on the Ir/α-Fe₂O₃(110) surface is lowest at 0.439 eV, and reaction energy is slightly endothermic at 0.297 eV. However, the adsorption energy is −0.395 eV, smaller than the reaction barrier. Although the C–H activation barrier on Ir/α-Fe₂O₃(110)–O_V surface is 0.585 eV, which is slightly higher than that on Ir/α-Fe₂O₃(110) surface, it has larger desorption energy making the CH₄ activation reaction on the Ir/α-Fe₂O₃(110)–O_V surface can occur through a mediated mechanism and at a lower temperature. In addition, the CH₄ reaction on Ir/α-Fe₂O₃(110)–O_V surface is exothermic by 0.585 eV. Though the CH₄ adsorption energy and its C–H activation barrier over Ir/α-Fe₂O₃(110)–O_V surface compete with each other, the activation of the adsorbent on the catalyst could be proceeded by adapting the suitable reaction conditions or introducing Lewis–Brønsted acid site pairs in the catalyst.^72,73 Lercher et al. recently proposed the Lewis–Brønsted acid mechanism, in which the Lewis–Brønsted acid site pair dehydrogenates alkanes via a bifunctional mechanism that is more active than the isolated Lewis and Brønsted acid sites.⁷³ The first C–H bond activation on Ir/α-Fe₂O₃(110)–O_V surface is higher than pure IrO₂(110), and IrO₂/TiO₂(110) surfaces but much smaller compared to Pd/Cu(111) and Pd/CeO₂(111) surfaces, as shown in Table 1. After activation, the C–H bond length of the Ir/α-Fe₂O₃(110)–O_V surface is the longest, but the activation energy is higher than that of the pristine IrO₂(110) and IrO₂/TiO₂(110) surfaces. It may be due to the weaker CH⋯O hydrogen bonding since the CH⋯O distance on the Ir/α-Fe₂O₃(110)–O_V surface is longer than on the other surfaces. Likewise, the reaction energy for CH₄ activation on Ir/α-Fe₂O₃(110)–O_V surface is slightly less exothermic compared on IrO₂(110) and IrO₂/TiO₂(110) surfaces but much exothermic than on Pd/Cu(111) surface. Although compared with IrO₂(110) and IrO₂/TiO₂(110) surfaces, Ir/α-Fe₂O₃(110)–O_V surface is slightly less favorable thermodynamically and kinetically for CH₄ activation. However, this catalyst uses a relatively small amount of expensive Ir, and the activation energy is still quite low, making it a viable candidate for CH₄ activation both thermodynamically and kinetically.

Fig. 5 Potential energy profile of CH₄ activation on α-Fe₂O₃(110) (red dash line), Ir/α-Fe₂O₃(110) (green dash line), and Ir/α-Fe₂O₃(110)–O_V surfaces (blue dash line).

Fig. 6 Side view of initial, transition, and intermediate states of CH₄ oxidation on α-Fe₂O₃(110), Ir/α-Fe₂O₃(110), and Ir/α-Fe₂O₃(110)–O_V surfaces.

To examine the relationship between activation barriers (E_a) and adsorption energies (E_ads) for C–H dissociation of methane on α-Fe₂O₃(110), Ir/α-Fe₂O₃(110), and Ir/α-Fe₂O₃(110)–O_V surfaces, we found that they have no linear relationship, as shown in Fig. 3S.† The bond lengths for C–H activation on α-Fe₂O₃(110), Ir/α-Fe₂O₃(110), and Ir/α-Fe₂O₃(110)–O_V surfaces are 1.408, 1.312, and 1.147 Å, respectively. It indicates that the C–H activation exists in late transition on the α-Fe₂O₃(110) surface, and early transition state on Ir/α-Fe₂O₃(110)–O_V surface, resulting in no linear relationship between adsorption energy and activation barrier.

Previous studies have shown that IrO₂ has excellent catalytic activity for methane dehydrogenation.^74,75 But methane is completely oxidized to CO₂ and H₂O.^76,77 In this study, we only considered a single metal doping and a single oxygen vacancy which is very active for methane adsorption. Cheng et al. studied the adsorption and dissociation of methane on ferric oxide oxygen carriers and they found that the activation barrier of C–H decreased when the surface oxygen vacancy concentration was increased from 0%–2.67%.⁷⁸ In the future, we will further investigate whether increasing the concentration of dopants and oxygen vacancies can further improve catalytic activity.

4. Conclusions

In this study, the DFT + U method calculations were performed to study the C–H bond activation of CH₄ molecules on the surfaces of pristine α-Fe₂O₃(110) and doped α-Fe₂O₃(110) with single-atom (Ag, Ir, Co, or Cu). From calculation results, we found that the Ir/α-Fe₂O₃(110) surface has considerable interaction with CH₄ molecules compared to other considered single-atom doped surfaces. Furthermore, we investigated the activation of CH₄ on the Ir/α-Fe₂O₃(110) surface with oxygen vacancy. EDD, DOS, and Bader charge analyses show that the co-existence of CH⋯O hydrogen bonding and agostic interactions between methane and surfaces results in large adsorption energies of −0.395 and −0.590 eV on Ir/α-Fe₂O₃(110) and Ir/α-Fe₂O₃(110)–O_V surfaces, respectively, and significantly elongated the length of one C–H bond on methane. Although the C–H activation barrier on Ir/α-Fe₂O₃(110)–O_V surface is slightly higher than that on Ir/α-Fe₂O₃(110) surface, it has larger desorption energy making the CH₄ activation reaction on the Ir/α-Fe₂O₃(110)–O_V surface can occur through a mediated mechanism and at a lower temperature. The calculation indicates that the first dehydrogenation of the CH₄ molecule on the Ir/α-Fe₂O₃(110)–O_V surface is thermodynamically and kinetically favorable.

Conflicts of interest

The authors declare that there is no conflict of interest.

Acknowledgements

The authors gratefully acknowledge the financial support for this work from the Ministry of Science and Technology, Taiwan (MOST 110-2113-M-011-002-MY3). The authors are also grateful to the National Center for High-Performance Computing, Taiwan, for donating computer time and facilities.

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Footnote

† Electronic supplementary information (ESI) available: Tables 1S–3S, Fig. 1S–8S, and POSCAR files of the initial, intermediate, and final products. See https://doi.org/10.1039/d2ra03585e

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