Mixed Anion Control of the Partial Oxidation of Methane to Methanol on the β-PtO2 Surface.

Although the C-H bond of methane is very strong, it can be easily dissociated on the (110) surface of β-PtO2. This is because a very stable Pt-C bond is formed between the coordinatively unsaturated Pt atom and CH3 on the surface. Owing to the stable nature of the Pt-C bond, CH3 is strongly bound to the surface. When it comes to methanol synthesis from methane, the Pt-C bond has to be cleaved to form a C-O bond during the reaction process. However, this is unlikely to occur on the β-PtO2 surface: The activation energy of the process is calculated to be so large as 47.9 kcal/mol. If the surface can be modified in such a way that the ability for the C-H bond activation is maintained but the Pt-C bond is weakened, a catalyst combining the functions of C-H bond cleavage and C-O bond formation can be created. For this purpose, analyzing the orbital interactions on the surface is found to be very useful, resulting in a prediction that the Pt-C bond can be weakened by replacing the O atom trans to the C atom with a N atom. This would be a sort of process to make β-PtO2 a mixed anion compound. Density functional theory simulations of catalytic reactions on the β-PtO2 surface show that the activation energy of the rate-limiting step of methanol synthesis can be reduced to 27.7 kcal/mol by doping the surface with N.

Introduction

Methane is abundant on earth in a variety of forms, including natural gas, shale gas, coalbed methane, biogas, and methane hydrates.[1] The direct conversion of methane into a liquid chemical such as methanol, suitable for transportation and storage, is highly desirable because of its industrial importance.[2−4] In the conventional route of the industrial synthesis of methanol, methane is first reformed into syngas, a gas mixture consisting primarily of hydrogen (H2) and carbon monoxide (CO), and then converted to methanol.[5] The step of converting methane to syngas requires a Ni catalyst, and this reaction typically proceeds at a temperature of about 850 °C and a pressure of about 2.5 MPa.[6] The step of catalytically synthesizing methanol from syngas also requires high-temperature and high-pressure conditions of 250–300 °C and 5–15 MPa, respectively. ZnO/Cr2O3 was used as a catalyst in the early days, but more recently, Cu catalysts have been used in most commercial processes.[7] Owing to the high-temperature and high-pressure reaction conditions, these chemical processes are costly. The development of methods for the direct conversion of methane to methanol under mild conditions could lead to major commercial breakthroughs in the use of methane.

The reason why the conventional conversion of methane requires high-temperature and high-pressure conditions can be attributed to the fact that the dissociation energy of the C–H bond of methane is as large as 104 kcal/mol.[2] Compared with the strength of the C–H bond of other alkanes, that of methane is found to be significantly large.[2] However, the activation energy required for the dissociation of the methane’s C–H bond is very low on the surface of some late transition-metal oxides, such as IrO2, RuO2, and PdO.[8,9] In particular, the reactivity of IrO2 is remarkable because it was experimentally observed that the dissociation of the methane’s C–H bond occurs on the IrO2 (110) surface at a low temperature of 150 K.[10] However, it is to be regretted that methanol cannot be synthesized on the surface of such a metal oxide.

Weaver and co-workers carried out a thorough study on the oxidation of methane on the IrO2 (110) surface using temperature-programmed reaction spectroscopy (TPRS) and density functional theory (DFT).[11] Its TPRS spectra indicated that the activation of methane on the stoichiometric IrO2 surface results in the competition between the oxidation of methane to CO and CO2 and the recombination of the CH3 and H species. Its DFT calculations suggested that the rate-limiting step in the oxidation of methane is C–O bond formation, the activation barrier of which is in the range of 32–39 kcal/mol, almost comparable with that for the combinative generation of methane (29 kcal/mol). The high activation barrier of C–O bond formation on the IrO2 surface may be due to the strong binding of the oxygen atom to underlying surface Ir atoms. A high temperature of about 500 K is required for these reactions.

Rui and co-workers reported a bicomponent catalyst, IrO2/CuO, for the direct oxidation of methane to methanol under mild conditions.[12] In their study, the synergetic function of IrO2 for methane activation and CuO for selective oxidation was identified. They hypothesized that metal oxides with a weak metal–O (M–O) bond strength should be beneficial for C–O bond formation and methanol extraction, when employed as a cocatalyst with IrO2.

The heat of formation of metal oxides may be a good measure of M–O bond strength.[13] According to the Materials Project database,[14] the heat of formation of IrO2, or the reaction enthalpy for Ir + O2 → IrO2, is −88 kcal/mol. Since the heat of formation of PtO2 is −65 kcal/mol, Pt–O bonds are expected to be weaker than Ir–O bonds. It would be of interest to note that, in our previous study, we theoretically predicted that PtO2 is more active for the C–H bond dissociation of methane than IrO2.[15] Therefore, PtO2 may have two advantages such as the reactivity toward CH4 and weak M–O bond strength, respectively, identified for IrO2 and CuO in the bicomponent catalyst of IrO2/CuO. In this paper, we will theoretically probe the possibility of using PtO2 as a catalyst for the direct conversion of methane to methanol.

Many studies on the oxidation of methane on late transition-metal surfaces have revealed that methane is oxidized through reaction with oxygen atoms located on the catalyst surface (surface lattice oxygen atoms), after which oxygen vacancies (VO) are left behind on the surface.[11,16,17] Such a reduced metal-oxide surface can be restored to its initial state by the reoxidation of the catalyst to complete the catalytic cycle. This is the so-called Mars–van Krevelen mechanism,[18] which is often used to describe the oxidation of hydrocarbons on heterogeneous metal-oxide catalysts.[19−21]

Figure shows a catalytic cycle to be proposed for the direct conversion of methane to methanol on the surface of PtO2 in the Mars–van Krevelen mechanism. First, a pair of Pt and O atoms on the surface dissociates a C–H bond of methane, forming CH3* and OH* species on the surface, where * denotes adsorbed species. The following C–O bond formation results in CH3OH*, the desorption of which leaves an oxygen vacancy (VO) behind the surface. Finally, the VO site is replenished by an oxygen atom supplied by a gaseous N2O molecule.

Figure 1

Proposed Mars–van Krevelen-type catalytic cycle for the direct conversion of methane to methanol on the surface of PtO2. VO denotes the oxygen vacancy, which is replenished by the reaction with N2O.

As we will see, our DFT calculations indicate that the step of C–O bond formation is the rate-limiting step with a relatively large activation barrier. To lower the activation barrier and propose a more practical catalyst, we adopt the concept of mixed-anion compounds, a series of materials containing multiple anionic species in a single solid-state phase.[22,23]

In our previous study,[24] we demonstrated that it is possible to tune the height of the activation barrier for the first C–H bond cleavage reaction of methane on the IrO2 surface by replacing an oxide with a different anion. We may term this process as doping. In this study, the same strategy is employed to reduce the activation barrier of C–O bond formation on the PtO2 surface. As a result, the doping of N into PtO2 turns out to be beneficial for the synthesis of methanol from methane. In the previous study, we focused on a single elementary reaction and tried to control its activation energy. However, in this study, we focus on the entire catalytic cycle and try to optimize the catalytic reaction by controlling the activation energy of its rate-limiting step.

Theoretical Methods

Construction of a Model Structure

Experimental studies have reported the presence of three polymorphs for PtO2: α-PtO2 (hexagonal CdI2-type structure),[25,26] β-PtO2 (orthorhombic CaCl2-type structure),[25,27] and β′-PtO2 (tetragonal rutile-type structure).[28] Preceding theoretical studies using DFT on the electronic energy calculations of these three phases have established that the total energy calculated at 0 K increases in the order of β-PtO2 α-PtO2 < β′-PtO2.[29−32] The energy difference between β-PtO2 and α-PtO2 is no larger than 0.02 eV/f.u.[29,30,32] The structures of α-PtO2 and β-PtO2 are compared in the Supporting Information. Experimentally, the phase of β-PtO2 is prepared under high temperatures and high oxygen pressures;[25] β-PtO2 has been reported to be stable at high temperatures and high pressures.[28,29]

Owing to the disagreement between theory and experiment, the relative stability between α-PtO2 and β-PtO2 is still a matter of debate. The stability of the phases of PtO2 has been investigated based on first-principles methods to calculate the Gibbs free energy. In 2006, Zhuo and Sohlberg[29] reported that the α phase is thermodynamically stable at low pressures, while the β phase is stable at high pressures, whereas in 2020, Chen and Yang[31] reported that the β phase is the most stable within a wide range of temperature (0–600 K) and pressure (0–51 GPa). We ourselves performed frozen phonon calculations for the α and β phases to evaluate how large the free-energy difference is. The results are shown in the Supporting Information. Here, just briefly, the free-energy difference is no larger than 0.004 eV/f.u. in the investigated temperature range (0–1000 K). However, it is worth noting that the β phase is slightly more stable than the α phase at high temperatures where catalytic reactions may occur.

Although whether β-PtO2 exists under ambient conditions may be a moot question, in this study, we adopted the structure of β-PtO2 for a model of PtO2. This is because the CaCl2-type structure of β-PtO2 can be viewed as an orthorhombic distortion of the rutile structure,[28] and methane activation on the surface of rutile-type metal dioxides has been extensively investigated.[8−11,15,24]

The crystal structure of β-PtO2 was optimized using DFT, as implemented in Vienna ab initio simulation package (VASP) 5.4.1.[33−36] The generalized gradient approximation was adopted with the functional described by Perdew, Burke, and Ernzerhof (PBE).[37] The Kohn–Sham equations were solved with a plane-wave basis set using the projector-augmented wave method.[38,39] The cutoff energy for the plane-wave basis set was set to 500 eV. A Gaussian smearing with a width of σ = 0.05 eV for the occupation of the electronic levels was used. The convergence threshold for self-consistent field iteration was set to 1.0 × 10–6 eV. The atoms in the slab model were relaxed until the forces on all of the atoms are less than 0.03 eV/Å. The Γ-centered k-point meshes with k spacing of 2π × 0.05 Å–1 were employed for sampling the Brillouin zone. Spin-polarization calculations were performed for all of the systems.

Shannon reported the semiconductive properties of β-PtO2 based on its resistivity measurement.[27] Yang et al.[40] conducted a theoretical study using the single-shot GW (G0W0) approach, reporting a calculated band gap of 1.25 eV. They also reported that the DFT plus Hubbard U (DFT + U) method can reproduce the G0W0-calculated band gap when the effective on-site Coulomb repulsion parameter Ueff is set to 7.5 eV for Pt 5d states. Using this Ueff value, we have conducted Dudarev’s method[41] of DFT + U calculations for β-PtO2.

Figure shows the optimized bulk structure of β-PtO2. This structure is visualized using VESTA.[42] We will use this software throughout this study for visualizing structures. The optimized cell parameters of β-PtO2 are listed in the Supporting Information. They show a good agreement with those obtained in the experiment.

Figure 2

Optimized bulk structure of β-PtO2, which is viewed along the standard orientation of the crystal shape (a) and from the c axis onto the ab plane (b).

As a model for the surface of β-PtO2, the (110) and (001) surfaces have been used in previous theoretical studies.[43−46] Hu and co-workers investigated CO oxidation on PtO2 using DFT calculations, stating that (110) is the most stable surface and suitable for the modeling of the catalyst surface.[47] Using a thermodynamics approach together with DFT calculations, Jacob showed the preference for the formation of the β-PtO2 (110) surface on Pt electrodes in electrochemical environments.[48] As for rutile, the (110), (001), and (100) surfaces have been well characterized, of which the (110) is the most stable.[49] The structure of β-PtO2 can be viewed as a distorted rutile structure, and methane activation on the (110) surface of rutile-type late transition-metal dioxides has been extensively studied.[8−10] Thus, we adopted the (110) facet as a model for the surface of β-PtO2 in this study.

A slab model for the (110) surface of β-PtO2 was constructed and optimized, as shown in Figure . The created slab model has a 2 × 2 surface in the unit cell with the thickness of four O–Pt–O repeating units. The lowest two layers were fixed during the geometry optimization. A 15 Å thick vacuum layer was placed on the surface. The other calculation conditions were set to be the same as those used for the bulk calculation mentioned above.

Figure 3

Optimized slab model structure for the (110) surface of β-PtO2, which is viewed along the standard orientation of the crystal shape (a), from the c axis onto the ab plane (top view) (b), and from the a axis onto the cb plane (side view) (c). (a) and (c) are shown in a ball-and-stick model, while (b) is shown in a space-filling model. A vacuum space of 15 Å length is placed on the surface. The coordinates of the atoms in the shaded region in the side view (c) are kept fixed during optimization.

On the (110) surface of β-PtO2, one can see alternating rows of 2-fold coordinated bridging O atoms (Obr) and 5-fold coordinatively unsaturated Pt atoms (Ptcus). In methane activation, the Obr atom will abstract a H atom from methane, and the CH3 species thus generated will be adsorbed onto the Ptcus atom.

Search for Transition-State Structures

To obtain the minimum energy path and the transition-state structure for each step in the catalytic cycle proposed in Figure , we performed the climbing image-nudged elastic band (CI-NEB) method,[50−52] as implemented in VASP through the VTST Tools.[53] The spring constant between adjacent NEB images was set to 5.0 eV/Å. The quasi-Newton algorithm[54] implemented in VASP was adopted for the geometry optimization of all of the NEB images. The other calculation conditions were set to be the same as those used for the bulk calculation mentioned above.

Analysis of Electronic Structures

There may be some ways to approach the electronic aspect of the catalytic activity of β-PtO2. In this study, we have made good use of a powerful band-decomposition tool called crystal orbital overlap population (COOP).[55,56] COOP can be viewed as a partial density of states for a pair of atoms weighted with the corresponding Mulliken overlap population.[57,58] COOP is plotted as a function of energy, providing a simple graphical representation as to whether the interaction between the pair of atoms exhibits a bonding character or antibonding one at a certain energy level: positive COOP values indicate bonding interactions, while negative values indicate antibonding interactions.

In this study, the COOP calculations were carried out by using the extended Hückel (eH) program of YAeHMOP,[59] as implemented in Avogadro software.[60] The standard atomic parameters used were taken from the literature,[61] as tabulated in the Supporting Information. The same k spacing as used in the DFT calculations was used. One could conduct the same calculation at the DFT level, but we performed at the eH level. This is because in our previous studies on methane activation on metal oxides,[15,24,62] we have confirmed that these two methods generally provide results with the same trend.

To identify COOP peaks, we performed a fragment molecular orbital (FMO) analysis, as implemented in YAeHMOP.[59] Since this analysis cannot directly be applied to systems with periodic boundary conditions, we cut out a cluster from the optimized slab model and performed FMO calculations for the cluster model. FMO diagrams were drawn with Viewkel.[63] The isosurfaces of eHMOs were generated using the QuantumWise Atomistix ToolKit (QuantumATK) 2019 package[64] and visualized using VESTA.

Results and Discussion

Methanol Synthesis on the Surface of β-PtO2

Figure shows the calculated energy diagram for methanol synthesis on the (110) surface of β-PtO2. For simplicity, the structures are shown in a schematic manner. Their optimized atomic coordinates are shown in the Supporting Information, and some of them will be discussed more in detail later in this paper.

Figure 4

Calculated energy diagram for methanol synthesis on the (110) surface of β-PtO2. The structures are drawn in a schematic way to help one clearly understand what is going on. The numbers shown above the black bold horizontal lines representing intermediate states are their energies (in kcal/mol), which are calculated by taking the energy of the initial state as a reference. The activation barrier of the rate-limiting step is highlighted by red. The structures are sequentially numbered in the order of their appearance in the reaction.

Let us explain what occurs on the surface in words. The first step is the adsorption of methane followed by the C–H bond dissociation reaction. The adsorption structure as well as the transition-state structure for the dissociation has already been investigated and discussed in detail in our previous publication.[15] We will touch briefly on these steps.

The adsorption energy of methane on the β-PtO2 surface is about −3.9 kcal/mol, slightly larger in magnitude than that on the Pt (111) surface (ca. −3.4 kcal/mol).[65] The activation barrier to dissociation from the molecularly adsorbed state is as low as about 0.3 kcal/mol, much smaller than that on the IrO2 (110) surface (ca. 6.8 kcal/mol).[10] Judging from the adsorption and activation energies calculated and the values from the relevant experiments, the dissociative chemisorption of methane on the β-PtO2 surface occurs readily even at low temperatures.

The rotation of the OH group, which is generated as a result of the H atom abstraction from methane by the Obr atom, will follow the dissociative chemisorption of methane. This reaction is almost thermoneutral, and its activation barrier is not large (4.7 kcal/mol). This step may be deemed a trivial step.

Let us turn to the important process of C–O bond formation, which would occur after the OH rotation. The calculated activation barrier of this step is as large as 47.9 kcal/mol. If this barrier is overcome, the release of methanol would occur with a moderate desorption barrier of about 26 kcal/mol. By and large, this desorption barrier is smaller than the energy required for methanol desorption from the active site of the typical catalysts of Fe- and Cu-exchanged zeolites.[66]

The highest energy barrier that must be overcome in the course of the reaction is the barrier to TS3, so converting 6 to 8 via 7 is likely to be the rate-limiting step. To facilitate the methanol synthesis on the β-PtO2 surface, we will try to make this energy barrier lower in the remaining part of this paper. First, we will analyze the electronic structure of 6 (or 4) to gain an insight into the amelioration of the catalyst.

Electronic Structure Analysis

By looking over the whole potential energy profile associated with the reaction of converting methane to methanol on the β-PtO2 surface, one can perceive that the high activation barrier to TS3 has something to do with a substantial stabilization of the CH3 group on the surface. One can notice that there is a deep valley in the potential energy profile, the bottom of which includes structures 4, 5, and 6. The significant affinity of the Ptcus atom for CH3 can be effective in promoting the initial C–H bond dissociation of methane, but CH3 is too strongly bound to the surface to be transferred to the OH group. This is why we will analyze the Ptcus–CH3 bond to trace the origin of the strong binding and will ponder on how to reduce the strength of the interaction.

Figure a shows the COOP curve for the Ptcus–CH3 bond on the surface of structure 4. Even if one uses the structure of 6 instead, almost the same plot will be obtained. The positive and negative regions in the curve indicate bonding and antibonding interactions, respectively. A substantially high positive peak can be spotted at around E = −13.5 eV. Such a significant Pt–C bonding interaction is likely to be the cause of the strong binding of the CH3 group to the surface.

Figure 5

(a) COOP curve for the Ptcus–CH3 bond on the surface in the structure of 4. In the inset, the bond calculated is pointed by an arrow. The dotted line indicates the Fermi level. (b) FMO interaction diagram for the formation of the cluster of [Pt(CH3)O5]7– from the CH3– and [PtO5]6– fragments. The eH-calculated σPt–C and orbitals are visualized, with the isosurface value set to 0.05 e1/2/a03/2. The symmetry labels used for the orbitals of the PtO5 fragment correspond to those for square-pyramidal C4v symmetry for simplicity, though in reality the fragment structure is distorted from the square pyramid. A qualitative understanding of the generation of the fragment orbitals for [PtO5]6– is presented in the Supporting Information.

To see by what kind of orbital interaction the bonding peak is generated, let us analyze the orbital interaction on the surface. As our modus operandi,[15,24,62] the part of PtO5–CH3 is cut out from 4 to generate a cluster model and an FMO analysis is carried out for the cluster, as shown in Figure b. In the orbital interaction diagram, one can clarify how the orbitals of the cluster model can be built up from those of the fragments of CH3– and [PtO5]6–. One can see a clear correspondence between the COOP curve and the orbital interaction diagram: The positive COOP peak at around E = −13.5 eV and the negative one at around E = −9.1 eV can be assigned to the σPt–C and orbitals, respectively. Thus, the strong binding of the CH3 group to the surface can be traced back to the formation of the σPt–C orbital. Note that the energy levels in the COOP curve very precisely corresponding to those in the FMO result because both of them were calculated at the same theoretical level, namely, the eH method, where the same atomic parameters were used.

What we intend to do is to weaken the interaction between the CH3 group and the surface so that the bottom of the valley in the potential energy profile can be raised. All we may need to do is to make the stabilized σPt–C orbital destabilized. Let us see how it works, first with the eH method and then with DFT.

The σPt–C orbital originates from the bonding interaction between the n(p) orbital of CH3 and the orbital of PtO5. The n(p) orbital is primarily derived from the 2p orbital of the C atom though there is a tiny contribution from the 1s orbitals of the H atoms, while the orbital is formed by the contribution of the 2p orbital of the axial O ligand to the orbital of the Pt atom. The formation of the orbital is analyzed, as shown in Figure a. Although Viewkel does not draw any line between the orbital and the 2p orbital of the axial O ligand, it is clear from the isosurface plot for the orbital in the inset that the antibonding interaction between the a1g orbital of PtO4 and the 2p orbital is the main component of the orbital.

Figure 6

(a) FMO interaction diagram for the formation of the [PtO5]6– fragment in Figure b from the [PtO4]4– fragment and the axial O2– ligand. The eH-calculated orbital is visualized, with the isosurface value set to 0.05 e1/2/a03/2. The symmetry labels used for the orbitals of the PtO4 fragment correspond to those for square planar D symmetry for simplicity, though in reality the fragment structure is distorted from the square plane. (b) FMO diagram revised after replacing the axial O ligand with a N ligand.

There may be some ways to destabilize the σPt–C orbital; one way to approach it is to make the orbital destabilized. As we have seen in Figure a, the antibonding interaction of the 2p orbital of the axial O atom with the a1g orbital results in the orbital; therefore, by pushing up the energy level of the 2p orbital, the resultant orbital level will also go up. But how? If we are allowed to replace the axial O atom with a more electropositive element, say N, what we want to achieve will be achieved (see Figure b). The general concept behind this has already been detailed in our previous paper.[24]

By replacing the axial O ligand with the N ligand, which is what we call doping, the energy level of the 2p manifold of the ligand is increased, and in accordance with it, the energy of the orbital level becomes higher by about 0.6 eV. In Figure , one can see that the rise of the energy of the orbital leads to the destabilization of the σPt–C orbital. Before the doping of N (Figure b), the σPt–C orbital was located at E = −13.3 eV, while after the doping (Figure ), the orbital is found at E = −12.9 eV.

Figure 7

Molecular orbitals calculated for the cluster of [Pt(CH3)NO4]8–, which is generated by replacing the axial O ligand of the [Pt(CH3)O5]7– cluster with N, decomposed into the contributions from the orbitals of the CH3– and [PtNO4]7– fragments (FMO interaction diagram). The eH-calculated and orbitals are visualized, with the isosurface value set to 0.05 e1/2/a03/2.

Methanol Synthesis on the Surface of N-Doped β-PtO2

Let us see how effective it is to dope the β-PtO2 surface with N for methanol synthesis. We constructed a slab model for DFT calculations of the surface of N-doped β-PtO2 by replacing the axial O ligand of one Ptcus atom with N. Using the same method as used to obtain Figure , we have obtained an energy diagram for methanol synthesis on the (110) surface of N-doped β-PtO2, as shown in Figure .

Figure 8

Calculated energy diagram for methanol synthesis on the (110) surface of N-doped β-PtO2. The structures are drawn in a schematic way to help one understand what is going on clearly. The numbers shown above the black bold horizontal lines representing intermediate states are their energies (in kcal/mol), which are calculated by taking the energy of the initial state as a reference. The activation barrier of the rate-limiting step is highlighted with red. The structures are numbered in accordance with those in Figure but distinguished from them using the prime symbol.

Comparing Figure with Figure , one can notice a significant difference in the height of the activation barrier to TS3 (TS3′). By introducing a N atom into the subsurface site, the activation barrier of the rate-limiting step is reduced by about 20 kcal/mol, though the effect of N doping on the other activation barriers is relatively small. As anticipated, the mixed-anion concept has been proven to be of great help in facilitating methanol synthesis on the oxide surface.

Anion doping has also been important in the field of photocatalysis, known to be a useful means of activating metal oxides such as TiO2 toward visible light responsiveness.[67−69] This is because doping metal oxides with anions that are less electronegative than oxygen provides a new energy state above the valence band formed by the 2p orbital of oxygen, narrowing the band gap.[22,70] N-doped TiO2 with a visible light absorption band can reportedly be prepared with ease.[67] A discussion about the feasibility (e.g., thermodynamic and kinetic stability) of N-doped β-PtO2 is presented in the Supporting Information. Based on it, we expect that N-doped β-PtO2 can be synthesized.

Another difference to be noted in the energy diagram between Figures and 8 is in the process of CH4 adsorption. The adsorption of CH4 onto the surface without doping is exothermic, while that onto the N-doped is endothermic. This implies that the doping of the surface with N makes the interaction between methane and the surface weaker. This is the Achilles heel of catalysts for methane: Nothing would start without methane adsorbed on the surface, but if the affinity of the surface for methane is too strong, CH3 will just be strongly bound to the surface after the C–H bond cleavage, and no subsequent reaction is likely to occur. This is especially true for IrO2, as discussed later. It would be very hard to satisfy both sides without being in a dilemma.

Comparison of the Structures with and without N Doping

Let us see how key intermediate structures vary depending on whether the surface is doped with N or not. In Figure , we make a comparison of structures in the C–H bond dissociation process. When comparing 2 and 2′, one can notice that the structural distortion of methane is larger in 2 than in 2′; for example, the C–H bond to be dissociated is longer and the H–C–H angle directed toward the surface is wider. Since the deformation is a good measure of how much the methane is activated,[71,72] the nondoped β-PtO2 surface can be regarded as more active for the C–H bond cleavage than the one doped with N. Indeed, the activation barrier for the C–H bond dissociation is larger on the N-doped than on the nondoped. Nevertheless, the activation barrier on the N-doped is about 4.5 kcal/mol at most, which is still deemed to be small when compared to that on the active catalyst of IrO2.

Figure 9

C–H bond dissociation reaction of methane on the (110) surface of β-PtO2 (a) and that doped with N (b). The initial (2 or 2′), transition (3 or 3′), and final (4 or 4′) states are shown. These structures are numbered in accordance with those in Figures and 8. Selected distances are shown in Å. The corresponding part of the potential energy diagram is shown below the structures, with the energy in the unit of kcal/mol referenced to that of the initial state (2 or 2′).

When comparing 4 and 4′ in Figure , the C–Pt bond is longer on the N-doped than on the nondoped. This is indicative of the weakening of the bond as a result of the replacement of the axial O atom with a N atom, the result measuring up to our expectation.

Let us move on to a comparison of structures in the C–O bond formation (see Figure ). At a first glance, the difference in geometry between the two looks very small. However, the difference in energetics is significant.

Figure 10

C–O bond formation reaction on the (110) surface of β-PtO2 (a) and that doped with N (b). The initial (6 or 6′), transition (7 or 7′), and final (8 or 8′) states are shown. These structures are numbered in accordance with those in Figures and 8. Selected distances are shown in Å. The corresponding part of the potential energy diagram is shown below the structures, with the energy in the unit of kcal/mol referenced to that of the initial state (6 or 6′).

In the transition states (7 and 7′), the carbon atom has a trigonal planar geometry, which is specific to the methyl radical. If we assume that the instability of the system associated with methyl radical formation is comparable between the two, the difference in the activation energy can be attributed to the difference in the energy of the initial state.

It may also be important to note that the length of the Pt–N bond is shortened during the transition from state 6′ to state 7′. In the nondoped system, there is also shrinkage of the corresponding Pt–O bond; however, the extent to which the bond is shortened is larger for the N-doped than for the nondoped. The destabilization associated with the cleavage of the Pt–C bond may be compensated somewhat by the strengthening of the Pt–N bond. This also seems conducive to the lowering of the activation barrier in the N-doped.

Replenishment of the Oxygen Vacancy

Let us complete the catalytic cycle shown in Figure . Up to this point, we have simulated steps 1–4. Owing to the very high activation barrier of 47.9 kcal/mol for the C–O bond formation on the nondoped β-PtO2 surface, methanol synthesis on the β-PtO2 surface is unlikely to occur. However, when β-PtO2 is doped with N, the activation barrier for the C–O bond formation is reduced to 27.7 kcal/mol, but the effects on the other activation barriers are less significant. Thus, methanol synthesis may occur on the doped surface, leaving an oxygen vacancy (VO) behind.

The reduced VO site can be reoxidized by N2O, resulting in gas-phase N2 and restoring the lattice oxygen atom.[73] This process was simulated using the CI-NEB method for the N-doped surface, as shown in Figure . This figure indicates that the activation barrier associated with the regeneration of the catalyst is not high compared to that of the C–O bond formation. As such, the catalytic cycle can successfully be completed.

Figure 11

Calculated energy diagram for the reoxidation of the N-doped β-PtO2 surface with an oxygen vacancy (VO) by N2O: first, the adsorption of N2O occurs and then the N–O bond is dissociated with N2 released. The numbers shown above the black bold horizontal lines representing intermediate states are their energies (in kcal/mol), which are calculated by taking the energy of the initial state as a reference. Selected distances are shown in Å.

Although the activity of the Ptcus atom is crucial for the catalytic mechanism, the Ptcus atoms are not necessarily oxidized preferentially in the reoxidation of the catalyst. This is because the reduced VO site is more easily oxidized: the surface state where one Ptcus atom is oxidized with the VO site left is higher in energy by about 2.5 eV than the one where the VO site is oxidized.

The first step of the catalysis, namely, the reduction of the catalytically active site, shown in Figure , is accompanied by an energy change of −6.93 kcal/mol. The second step, namely, the reoxidation of the catalyst, shown in Figure , is accompanied by an energy change of −25.8 kcal/mol. Thus, the overall energy change for the reaction of CH4 + N2O → CH3OH + N2 is −32.7 kcal/mol. Using the standard thermodynamic data,[74] one can obtain a change in the enthalpy of ca. −50.7 kcal/mol for this reaction. There seemingly is a discrepancy. However, one should note that the change in the total electronic energy calculated at 0 K with DFT cannot directly be compared with the enthalpy change observed in the experiment. This is because the zero-point energy coming from zero-point oscillations and the temperature-dependent vibrational energy are not taken into account.[75] Also, the density functional used may be critical for the results. A preceding PBE study for this reaction provided the overall energy change of about −38 kcal/mol,[76] which is consistent with our result. Could one use a hybrid functional, the energy difference would get closer to the experimental enthalpy difference, but there would still be a deviation of about 10 kcal/mol from the experimental value.[77]

Comparison with IrO2

In our recent work on IrO2,[24] we discussed a similar idea of controlling reactivity by anion doping, but the physical insights provided in this paper for β-PtO2 cannot be drawn from the work on IrO2. However, since the oxidation of methane on the surface of IrO2 has been well studied experimentally,[8−11] IrO2 may serve as a bridge to link our predictive theoretical study on β-PtO2 with the experiment.

We calculated the activation energy of the C–O bond formation reaction on the (110) surface of IrO2 using the same method as used for the calculations of the β-PtO2 surface above. As shown in Figure , the activation energy of the C–O bond formation reaction on the IrO2 surface is as high as 60.6 kcal/mol. This value is larger than that on the β-PtO2 surface by about 13 kcal/mol. This is likely because of the fact that the Ir–C bond is stronger than the Pt–C bond.

Figure 12

Calculated energy diagram for the C–O bond formation reaction on the (110) surfaces of IrO2 (blue) and N-doped IrO2 (orange). The numbers shown above the bold horizontal lines representing intermediate states are their energies (in kcal/mol), which are calculated by taking the energy of the initial state as a reference. Side views of the structures for the initial, transition, and final states are also shown.

To confirm the difference in the bond strength between Ir–C and Pt–C, we calculated the binding energy of CH3 to the surface, defined as follows:where denotes the energy of the whole system where CH3 is adsorbed on the surface, like the initial structure in Figure . Esurf and , respectively, denote the energies of the surface slab and CH3 calculated separately by maintaining the geometry as it was in the adsorbed state. The CH3-binding energies on the IrO2 and β-PtO2 surfaces were calculated to be 3.2 and 2.4 eV, respectively. Indeed, the Ir–C bond was found to be stronger than the Pt–C bond.

By replacing the O atom in the axial position of the Ir atom with a N atom in the IrO2 surface, the activation barrier is reduced by about 22 kcal/mol (see Figure ). The amount of decrease in activation energy caused by N doping is almost the same as that on the β-PtO2 surface. The original activation energy of the C–O bond formation reaction on the IrO2 surface is so high that we have to conclude that the activation energy is indeed lowered by doping the surface with N but is still higher than that on the N-doped β-PtO2 surface.

Conclusions

There is no report of methane being converted to methanol by the IrO2 catalyst, but there is an experimental report that methane is converted to methanol by the IrO2/CuO catalyst. The concept of the present study is to replace the roles of IrO2 and CuO in the IrO2/CuO catalyst by a single oxide. Based on the strength of the metal–oxygen bond in the oxide, we have proposed a catalyst of β-PtO2. In our previous work regarding the C–H bond activation of methane on oxide surfaces, we actually made a theoretical prediction that β-PtO2 would be more active than IrO2. However, we did not predict anything about what occurs after the C–H bond is cleaved. In the present study, we have theoretically investigated whether a useful product of methane partial oxidation, i.e., methanol, can be formed on the surface of β-PtO2 on the basis of the Mars–van Krevelen mechanism. Unfortunately, the activation barrier for the C–O bond formation process is so large, calculated to be 47.9 kcal/mol, that we have to conclude that this reaction is unlikely to occur. However, we never know when to give up, so we have made good use of techniques of orbital interaction analysis, such as COOP and FMO, to find out the origin of the very high activation energy. The strong Pt–C bond has been found to be the cause. The results of the orbital interaction analysis have suggested that the Pt–C bond can be destabilized by replacing the O atom in the axial position of the Pt atom with another element that has a lower electronegativity than O. To verify this, we have created a surface model in which the O atom is replaced with a N atom and calculated the energy profile of methanol synthesis. As a result, the activation energy of the rate-limiting step, the C–O bond formation process, has been greatly reduced to 27.7 kcal/mol. The magnitude of the activation barriers for the other stages of the reaction has hardly been affected, and it has been shown that the regeneration of the catalyst with N2O can also occur with a relatively small activation energy.