Theoretical Insights into Methane CâH Bond Activation on Alkaline

Article pubs.acs.org/JPCC

Theoretical Insights into Methane C−H Bond Activation on Alkaline Metal Oxides Hassan Aljama,† Jens K. Nørskov,†,‡ and Frank Abild-Pedersen*,†,‡ †

SUNCAT Center for Interface Science and Catalysis, Department of Chemical Engineering, Stanford University, 443 Via Ortega, Stanford, California 94305, United States ‡ SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States S Supporting Information *

ABSTRACT: In this work, we investigate the role of alkaline metal oxides (AMO) (MgO, CaO, and SrO) in activating the C− H bond in methane. We use Density Functional Theory (DFT) and microkinetic modeling to study the catalytic elementary steps in breaking the C−H bond in methane and creating the methyl radical, a precursor prior to creating C2 products. We study the effects of surface geometry on the catalytic activity of AMO by examining terrace and step sites. We observe that the process of activating methane depends strongly on the structure of the AMO. When the AMO surface is doped with an alkali metal, the transition state (TS) structure has a methyl radical-like behavior, where the methyl radical interacts weakly with the AMO surface. In this case, the TS energy scales with the hydrogen binding energy. On pure AMO, the TS interacts with AMO surface oxygen as well as the metal atom on the surface, and consequently the TS energy scales with the binding energy of hydrogen and methyl. We study the activity of AMO using a mean-field microkinetic model. The results indicate that terrace sites have similar catalytic activity, with the exception of MgO(100). Step sites bind hydrogen more strongly, making them more active, and this confirms previously reported experimental results. We map the catalytic activity of AMO using a volcano plot with two descriptors: the methyl and the hydrogen binding energies, with the latter being a more significant descriptor. The microkinetic model results suggest that C−H bond dissociation is not always the rate-limiting step. At weak hydrogen binding, the reaction is limited by C−H bond activation. At strong hydrogen binding, the reaction is limited due to poisoning of the active site. We found an increase in activity of AMO as the basicity increased. Finally, the developed microkinetic model allows screening for improved catalysts using simple calculations of the hydrogen binding energy. The work of Lunsford ignited the interest in this field when it was shown that Li-doped MgO can partially oxidize methane into ethane/ethylene.3 The reaction takes place at elevated temperatures (∼1000 K) and has a selectivity of >50%. There has been much recent experimental4,5 and theoretical6−8 work on this subject. Most of the work has focused on the impact of Li-doping on MgO activity. It has been debated whether Li affects the activity directly through Li participation in breaking the C−H bond or indirectly through inducing structural modifications.3,8 Recently, it was suggested that the effect of Li-

1. INTRODUCTION The recent surge in natural gas production, fueled by the exploitation of shale gas reserves, is providing an abundant supply of methane. Tapping into this supply by converting methane into higher value chemicals can significantly impact the chemical industry by adding new supplies of raw materials. However, methane activation remains a major challenge. It is difficult to break the strong and localized C−H bond, and in the event the bond is broken, it leads to products more reactive than methane,1,2 making it a challenge to achieve desired products instead of a complete combustion. Oxidative coupling of methane offers the potential of selectively converting methane to ethane/ethylene. © XXXX American Chemical Society

Received: June 14, 2017 Published: July 17, 2017 A

DOI: 10.1021/acs.jpcc.7b05838 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. Images of the C−H bond activation step of methane on MgO(110): (a) initial state, (b) transition state, and (c) final state (green = Mg, white = H, red = O, silver = C).

doping is to expose MgO under-coordinated sites that are thought to be more active.6 In the same study, it was shown that MgO in its pure form can have appreciable activity and that the morphology can greatly impact its reactivity. Furthermore, it was reported experimentally that Li can segregate from the surface and form an oxide phase at temperatures above 700 K.9 Despite much work on the subject, there are still many open questions. There is a lack of detailed microkinetic models that covers the complete catalytic cycle. Most of the literature work focuses on the first step of breaking the C−H bond in methane. It has been assumed that C−H bond activation is the ratelimiting step; however, later steps, such as water formation, can also affect the catalyst activity. There is also little theoretical work on other AMO, such as CaO and SrO, although experimental results have shown an increase in ethane selectivity of AMO with increased basicity.10 In addition, the impact on product selectivity of different AMO facets has not been addressed in detail, although recent experiments suggested steps are likely the active sites for the reaction.6 In this work, we attempt to address some of these questions. We study the activity of different AMO facets to better understand the impact of surface geometry on methane activation. We study scaling relations between adsorbates and transitions states and use those relations as input in a microkinetic model, and we compare the catalytic activity of AMO based on the microkinetic model results.

Geometry optimizations were conducted with a quasiNewton algorithm as implemented in the Atomic Simulation Environment (ASE).15 The convergence criterion for structural optimization was a maximum force of 0.05 eV/Å per atom. Transition states were determined using the climbing imagenudged elastic band (CI-NEB) approach.16 Spin-polarization was used for all calculations involving the methyl radical, as will be discussed later in this work. To study the impact of surface geometry on AMO activity, we considered different facets: [(100), (110), (310), (211), stepped (100), stepped (110), (111) O-oct, and (111) M-Oct]. The (111) O-Oct and (111) M-Oct are well-known forms of reconstructed AMO with oxygen and metal terminations, respectively.17,18 The studied structures are shown in Figure S1. These facets resemble terrace and stepped surfaces. In addition, we examined the effects of dopants, Li, Na, and K, on a number of these surfaces. In most cases, doped-AMO is modeled by substitution of a surface metal atom. A self-consistent mean-field microkinetic model was solved using CatMap,19 where rates were determined by solving the coupled differential equations numerically using the steady-state approximation. All microkinetic calculations were carried out at 1100 K, atmospheric pressure, and CH4:O2 ratio of 3:1, similar to experimental results reported previously.6 Free energies were calculated combining the contributions from DFT calculations, ZPE, and entropy. For gas species, the entropy contribution was calculated using Shomate equations.20 Contributions for adsorbed and transition state species due to vibrational entropy were calculated using the harmonic approximation.

2. COMPUTATION METHOD All calculations were performed with The QUANTUM ESPRESSO code11 using plane-wave DFT employing Vanderbilt ultrasoft pseudopotentials.12 We have used the BEEF-vdW exchange correlation functional13 for all calculations because it has been shown to sufficiently describe the surface properties of AMO, including band gap, and at the same time provide a good description of the CH4/AMO system.14 For all calculations, a 4 × 4 × 1 Monkhorst−Pack k-point sampling was used to model the Brillouin zone. We used a periodic unit cell containing 4 atomic layers, where the top two layers, together with the adsorbates, were allowed to relax, whereas the bottom two layers were fixed in their bulk positions. Our calculations show that a (2 × 2) unit cell size can have pronounced differences in adsorption energies as compared to larger unit cells, with differences that can be as high as 0.5 eV (see Table S1 for further details). Hence, we used unit cells larger than (2 × 2) in most calculations. A vacuum of 16 Å separated successive slabs. The plane-wave cutoff and density cutoff were 500 eV and 5000 eV, respectively.

3. RESULTS AND DISCUSSION Methane activation on pristine AMO is thought to proceed via the following elementary steps:7 2CH4(g) + 4* → 2CH3* + 2H* 2CH3* → 2CH3(g) + 2*

(I) (II)

CH3(g) + CH3(g) → C2H6(g)

(III)

H* + H* → H 2O(g) + *v + *

(IV)

1/2 O2 + *v → *

(V)

where “*” refers to adsorbate on AMO surface, and “*v” refers to a surface oxygen vacancy on AMO. AMO activates the C−H bond in methane using lattice oxygen, which results in a bond dissociation, where H* adsorbs on the oxygen and CH3* adsorbs on the adjacent metal site. This is followed by B


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Figure 2. (a) Scaling relation between the final state energy (ΔEFS) and methane C−H bond activation transition state energy (ΔETS) on pure AMO surfaces [slope = 0.68, intercept = 0.57, MAE (mean absolute error) = 0.14]. Examples of the TS structure of methane activation on MgO facets: (b) (111) O-Oct and (c) (111) M-Oct. Both structures show C−H interacting with surface Mg and lattice oxygen.

Figure 3. (a) Scaling relation between the hydrogen binding energy (EH) and methane C−H bond activation transition state energy ΔETS on dopedMgO with alkali metals and some under-coordinated oxygens in pure AMO [slope = 0.52, intercept = 1.64, MAE = 0.07]. Examples of TS structure on (b) Li-doped MgO(110) and (c) MgO(110) superoxide. TS shows interaction with only the lattice oxygen, making the hydrogen binding energy the descriptor.

surface (tabulated data for all energies calculated in this work are available in Table S2). Our results, seen in Figure 2a, for different facets of pure AMO, reveal a scaling between ΔEFS and ΔETS. On pristine AMO, the structure of the TS indicates interaction with the surface metal atom and lattice oxygen (examples of TS structures are shown in Figure 2b and c). This explains the need for both CH3* and H* adsorption energies as descriptors for the scaling relation. The observed energy scaling is comparable to a recently reported relation for transition metals and some transition metal oxides, where a similar TS structure was observed.21 We also do not observe a clear correlation between CH3* and H* binding energies. This is not unexpected because CH3* and H* have different adsorption sites (metal atom and lattice oxygen, respectively). We also observe that spin-polarization does not affect the conclusions made; that is, the same pathway and TS energies are observed when spin-polarization is considered. The wide range of activation barriers in Figure 2 supports the argument that surface morphology can have an appreciable impact on AMO activity.6 We also examined C−H activation barrier of methane on AMO doped with alkali metals. The dopant is introduced by substitution of a surface metal atom. Figure 3a shows the

desorption of the methyl radical to the gas phase. Ethane is formed through methyl radical recombination in the gas phase. Water is formed via a Mars−van Krevelen mechanism where two adjacent H* sites combine with lattice oxygen leaving behind an oxygen vacancy. The active site is then regenerated from oxygen gas. In this work, we only model elementary steps that take place on the catalyst surface (step III, which takes place in the gas phase, is considered barrierless). 3.1. C−H Bond Activation. In the first part of this work, we will focus mainly on the first step, activating the C−H bond in methane. A schematic of the first step is shown in Figure 1, where the initial state (IS), transition state (TS), and final state (FS) are illustrated. On pure AMO, we have calculated the energies of the FS and TS as follows: ΔE FS = ECH3*+H * − E − ECH4(g) *

(1)

ΔE TS = ECH3− H * − E − ECH4(g) *

(2)

where ECH3*+H* is the total energy of the true final state in which CH3* and H* are in the same unit cell, ECH3−H* is the total TS energy for C−H bond activation, ECH4(g) is the gasphase energy of methane, and E* is the total energy of the clean C


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The Journal of Physical Chemistry C energy of the TS as a function of the hydrogen binding energy (EH): 1 E H = E H * − E − E H2(g) * 2

(3)

where EH* is the total energy of H* adsorbed on the clean surface and EH2(g) is the hydrogen gas-phase energy. Examples of the TS structures are shown in Figure 3b and c. In this case, we observe a methyl radical-like behavior in the TS. The CH3 in the TS does not interact with the surface, making EH the only descriptor. Calculated density of states projected onto the carbon 2p states at the TS is shown in Figure S2a, and it reveals spin polarization on the carbon in the case of Li-doped MgO(110), which is absent in the TS on pure MgO(110), shown in Figure S2b. The methyl radical behavior in Li-doped MgO has been documented in the literature.3,22,23 We examined doping many of the surfaces that in their pristine form follow the correlation shown in Figure 2a. As for the case of MgO(110), once the surfaces are doped with Li, it switches to the radical-like correlation shown in Figure 3a. This suggests a shift in the C−H activation mechanism once the surface is doped. In addition, we observe special cases where even undoped AMO follows the radical-like scaling behavior in Figure 3a. AMO superoxide (with preadsorbed oxygen), as well as stepped (211) orientations of AMO, present surfaces that geometrically do not allow the TS structure to interact with the surface metal atoms (as shown in Figure 3c for MgO superoxide). The absence of neighboring metal atoms needed to stabilize the TS in these two cases leads to a TS with radicallike behavior. Furthermore, the results shown in Figure 3a are a subset of a more universal scaling line describing broader classes of materials where CH3 in the TS has a radical-like behavior.24 3.2. Hydrogen Binding Energy and Oxygen Vacancy Formation Scaling. On the basis of the elementary steps in reactions I−V, we need three intermediate adsorbate energies (EH, Ev, and ECH3) and two TS energies (ECH3−H and EHO−H) to completely describe the reaction network. The oxygen vacancy formation energy, EO‑formation, and the TS energy required to form water, EHO−H, are given by 1 EO‐formation = E − Ev − EO2(g) * 2

(4)

E HO − H = E H 2O(g) + E + Ev − 2E H * *

(5)

Figure 4. Scaling relations between the hydrogen binding energy (EH) and the energy of oxygen vacancy formation (EO‑formation) in pure and doped AMO [slope = −1.24, intercept = −5.99, MAE = 0.13].

3.3. Microkinetic Model. We have primarily focused on the step of activating the first C−H bond in methane, a step that can take place either in a surface-mediated pathway (on pure AMO) or through a radical-like pathway (on doped AMO with alkali metal). It was recently shown that Li can phase segregate from MgO at high temperatures,9 and because it is questionable whether Li would be present on the AMO surface at OCM conditions (T > 700 K), we have focused only on pure AMO in our microkinetic analysis. Figure 5 shows the free energy diagram (FED) for the elementary steps defined in eqs I−V on MgO(110) at four

Figure 5. Free energy diagrams of 2CH4(g) + 1/2O2(g) → C2H6(g) + H2O(g) on MgO(110). In the first step, the C−H bond in CH4(g) is broken, thus creating CH3* and H*, followed by CH3 desorption to the gas phase. This step is repeated to create a second CH3(g) radical. This is followed by water formation through two adjacently adsorbed H*, which leaves an oxygen vacancy. C2H6 is formed by CH3 radical combination. In the last step, active site is regenerated by oxygen gas filling surface oxygen vacancy.

where Ev is the total energy of the clean surface with an oxygen vacancy, EO2(g) is the oxygen gas-phase energy, and EH2O(g) is the gas-phase energy of water. In previous sections, we have shown the scaling between ΔETS and EH/ΔEFS for the important methane activation step. Because the preferred adsorption site of H is ontop of a lattice oxygen, we also observe a scaling relation between EH and EO‑formation, as shown in Figure 4. Because EHO−H is calculated on the basis of Ev and EH*, which scale with each other, EHO−H can be described by the hydrogen binding energy alone. These different scaling relations help identify the number of linearly independent parameters needed to describe the rates, thus simplifying the microkinetic model. In essence, the same descriptors that we have used for scaling the TS energies, the hydrogen and methyl binding energies, are sufficient to describe the complete catalytic cycle.

different temperatures. We have explicitly assumed that the water desorption barrier is equal to the enthalpy of water in the gas phase and that the entropy in the TS structure of desorbing water is equal to the entropy of adsorbed water. This is an upper limit because molecular water is expected to have a higher entropy contribution.25 In addition, we assume a barrierless regeneration of surface vacancy sites from oxygen gas given D


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volcano corresponds to intermediate hydrogen coverage, and in the limit of full surface coverage or negligible hydrogen coverage, the catalyst is inactive. We have modeled the activity of terrace sites using the following facets: (100), (111) M-Oct, (111) O-Oct, and (110). Results indicate that MgO(100), not shown in Figure 6, has negligible activity. This is entirely due to the high methane activation energy barrier (2.96 eV). The three other terrace sites show activity similar to that of TOFs in the order of 10−5 per active surface site. On MgO, reported activation barriers in the literature were calculated on different surface sites; however, the results in Figure 6 indicate that the type of terrace site is not very important because they mostly show similar activity, with the exception of MgO(100). We also find that MgO(100) and MgO(110) stepped surfaces have higher activity as compared to their respective terrace site. A number of previous studies examined the impact of steps on the C−H activation step.26,27 In these studies, they only considered the first step of activation of the C−H bond in methane. Reference 6 found that under-coordinated sites account for the MgO activity because loss of step sites shown by TEM correlated with an observed drop in catalytic activity. The trend found in our results is in agreement with these experimental observations. We also show results of CaO and SrO on the volcano in Figure 6. For comparison purposes, we only show the (110) facet. The activity map shows that SrO has the highest activity and that MgO has the lowest. This work does not address the question of selectivity, but experimental results have shown that CaO and SrO have better selectivity as compared to MgO. However, under OCM conditions, SrO is found to form a surface hydroxide that is unable to activate methane and thus irrelevant for OCM catalysis.10 Experimentally, MgO is observed to show activity at the beginning of the catalytic cycle; however, changes in morphology by losing active stepped sites through the unavoidable water formation lead to loss of catalytic activity.6 An alternative to further improve the current available catalysts is by activating the terrace sites. Transition metal doping of MgO/CaO might achieve this. Transition metal doping of MgO using Fe was found experimentally to improve the catalytic activity of MgO.28 The volcano plots developed in this work present a simple and efficient method for screening a wide number of new candidates to guide in experimental testing. 3.4. Adsorbate Stability on MgO Surface. The acid− base nature of the AMO surface is likely one of the critical reasons why AMO can partially oxidize methane. In a nonreduced oxide state, the surface metal and lattice oxygen in AMO retain a favorable charge configuration. As discussed in ref 29, when either CH3/H is adsorbed on the surface, the surface is in an unfavorable state as compared to when both species are present on the surface due to the chemical compensation effect. In addition, the adsorbed CH3 and H configuration becomes less stable as a function of distance between the adsorbates in the unit cell as shown in Figure S4. The stability is seen to increase gradually, and in the limit where CH3* and H* are in separate unit cells, the surface is less stable by 2.45 eV (on MgO(110)) as compared to the true final state. This further shows the additional stability retained by AMO when CH3* and H* are on adjacent sites. In principle, adsorbed CH3 could decompose further via a neighboring oxygen site, as shown in Figure S5. However, this

the high exothermic nature of the reaction step. The combination of two methyl radicals in the gas phase to form ethane is also assumed barrierless. Although gas-phase chemistry will dictate the rate of radical combination, this assumption does not impact the understanding of the role of the catalyst surface on the reaction mechanism. We also assume that the diffusion of H* in the water formation step is insignificant. On MgO(110), for example, the diffusion barrier for H* between adjacent surface sites is 0.6 eV, which is much less than other barriers in the process. Hence, only the barrier for two hydrogens on adjacent oxygens to create water by leaving an oxygen vacancy is considered. As seen in Figure 5, at 0 K, the reaction rate is limited by the CH3* desorption energy (2.59 eV). As the temperature increases, the C−H bond activation of methane becomes more dominant (2.07 eV at 1000 K). However, it appears that the water formation barrier (2.19 eV at 1000 K) is the more significant barrier at high temperatures. This shows that methane activation is not always the rate-limiting step in this process. These FEDs provide an important insight into the relative role of each elementary step; however, a full microkinetic model is needed to get a quantitative analysis of different surfaces and their reactivity. Figure 6 shows the results of the microkinetic model for pristine AMO at 1100 K and atmospheric pressure. For clarity,

Figure 6. Turnover frequency (TOF) of CH3(g) on pristine AMO from the microkinetic model at T = 1100 K, P = 1 atm, and CH4/O2 = 3/1. When the hydrogen binding energy is weak, the surface is limited by C−H bond activation, and at stronger hydrogen binding energies, the active surface sites are poisoned by hydrogen.

only select sites are shown in Figure 6; however, all data are tabulated in Table S2. For pure AMO, the volcano is shown as a function of EH and ECH3, and the latter energy is defined as ECH3 = ECH3* − E − ECH4(g) + 0.5E H2(g) (6) * where ECH3* is the total energy of adsorbed CH3. Spinpolarization was found to stabilize CH3* binding energy by 0.2 eV in some cases. The volcano plot in Figure 6 shows EH has a more pronounced impact on the catalyst activity. At weak hydrogen binding energy, the surface is inactive due to high C− H bond activation. At strong hydrogen binding energy, the active site is poisoned by hydrogen. This is also shown nicely in the hydrogen coverage plot (Figure S3) where the peak of the E



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ACKNOWLEDGMENTS We gratefully acknowledge the support from the U.S. Department of Energy, Office of Basic Energy Sciences, to the SUNCAT Center for Interface Science and Catalysis. H.A. was also supported by Aramco Services Co. through the Advanced Degree Program.

leads to a significant destabilization following similar electron structure arguments as described above. The activation barrier for this reaction step is calculated to be 2.57 eV, an unsurmountable barrier at relevant process conditions. As shown in the FED in Figure 5, at high temperature, desorption barriers are small. Thus, further CH3 activation on the surface is unfavorable as compared to CH3 desorption (for MgO(110), CH4 activation at 1000 K requires 2.04 eV; however, CH3* desorption requires only 0.87 eV). This explains why AMO works well as a high temperature OCM catalyst. The process conditions lead to a final state where methyl rather desorbs than decomposes further.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b05838.

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REFERENCES

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4. CONCLUSION In this work, we have examined C−H bond activation in methane on different surface facets of AMO. For clean AMO, we find the CH3−H TS to be stabilized by the surface through the lattice oxygen and metal atoms, and hence the energy of the TS scales with the methyl and hydrogen binding energies. For doped AMO with alkali metals, the TS geometry has a radicallike behavior, where CH3 in the TS interacts weakly with the surface, and the hydrogen binding energy is therefore a sufficient descriptor for the energy of the TS. There are few exceptions to this, such as AMO(211) and AMO(110) superoxide where the TS follows the behavior of dopedAMO, and this is entirely due to constraints set by the surface geometry. We have identified energy scaling relations between adsorbates and TS in the reaction network, thus reducing the number of independent energy variables to only the hydrogen and methyl binding energies. These relations were used as an input to our microkinetic model. MgO terrace sites, with the exception of MgO(100), were found to have a similar catalytic activity. Among MgO sites, stepped surfaces were found to be the most active. Our results also show that C−H bond activation is not always the rate-limiting step, as regeneration of active surface sites via water formation can be significant. Our MgO comparison with other AMO (CaO and SrO) indicates potential room for improvement by using the other AMOs. However, SrO does not retain its pure oxide phase at the extreme OCM conditions. Hence, improvement on MgO/CaO is needed to have a viable OCM catalyst. The volcano plot developed in this work allows for the screening of many potential candidates using simple calculations.

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Details on calculation results for binding energies and activation barriers, and projected density of states (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Frank Abild-Pedersen: 0000-0002-1911-074X Notes

The authors declare no competing financial interest. F


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Theoretical Insights into Methane CâH Bond Activation on Alkaline

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