Correlation of Methane Activation and Oxide Catalyst Reducibility and

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Correlation of Methane Activation and Oxide Catalyst Reducibility and Its Implications for Oxidative Coupling Gaurav Kumar, Sai Lap Jacky Lau, Matthew D. Krcha, and Michael J. Janik* Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States S Supporting Information *

ABSTRACT: We investigate methane activation over a range of metal-oxide surfaces. Density functional theory calculations are used to correlate the C−H bond activation energy to the surface reducibility (oxygen vacancy formation energy, work function). The correlation includes several reducible and nonreducible metal-oxides, doped CeO2, doped TiO2, ZnO, and doped MgO, and also holds for various oxidation states of TbOx, different surface facets of TiO2, and variation of Hubbard U parameter for CeO2. We find a linear correlation between the C−H activation reaction energy, ·CH3 adsorption energy, and the oxygen vacancy formation energy of pure/doped metal-oxides, making surface reducibility a descriptor for predicting catalyst activity and selectivity against further oxidation of the ·CH3 radical. KEYWORDS: metal-oxide, C−H activation, methane, oxidative coupling, vacancy formation, DFT

1. INTRODUCTION Recent advancements in fracking technology have resulted in an upsurge in the already enormous global natural gas output a vast majority of which is combusted for energy production. An alternative use for natural gas is to convert its primary component, methane, into value added products. Converting methane into ethylene and easily transportable liquids like methanol can considerably reduce its wastage and enable its usage in portable technology and as a feedstock for the chemical industry. Methane conversion processes involve breaking of the C−H bond as the first step, understanding the mechanism of which is a “Holy Grail” in catalysis.1 A Web of Science database search for “methane activation” results in more than 14 000 published articles. In search of highly active catalysts, several experimental2,3 and computational4−7 studies have examined the C−H activation process on metal-oxide catalysts. Relating the activity to intrinsic properties of the active site remains challenging. We have previously shown that the activity for methane C−H bond activation over a series of M−CeO2 systems correlates with the surface reducibility.8 Herein, we extend the correlation across a number of oxides, examining its statistical significance and error, and discussing its implications for oxidative coupling of methane (OCM). We use density functional theory (DFT) to examine C−H activation over a wide range of reducible/nonreducible metal-oxides. By relating activity and selectivity to surface electronic and structural properties, we devise descriptors for high-performance oxidation catalysts for methane. C−H activation in methane can occur via two mechanisms: formation of σ-complexes on transition metal/oxide surfaces or H-abstraction on metal oxides. Asthagiri reported that the PdO(101) surface can mediate C−H activation by forming σcomplexes on unsaturated surface Pd atoms.9−11 Electron donation and back-donation between the methane C−H © XXXX American Chemical Society

antibonding states and Pd d-states can lead to the weakening and cleavage of the C−H bond. Alternatively, on other reducible oxides like pure/doped ceria, C−H bond activation occurs through the abstraction of a H radical to bind to a surface oxygen atom, reducing a metal atom.2,8,12−15 PdO and M−CeO2 systems are active for complete catalytic combustion of methane but cannot halt the oxidation process to produce partially oxidized hydrocarbons. Materials less active for C−H dissociation, such as MgO and its multicomponent derivatives,2,16 are selective for oxidative coupling of methane but require high temperatures to activate methane. A universal tradeoff between activity and selectivity is observed for OCM, with high conversion giving low selectivity.7,17 Lunsford and coworkers have established that OCM catalysts activate methane, producing methyl radicals that then couple in the gas phase.18−20 Though this work establishes that methane activation on OCM catalysts occurs through H atom abstraction, relating the activity and selectivity to active site descriptors has been challenging. Schlögl and co-workers published a statistical review17 of OCM catalyst development efforts, though their conclusions for development of high yield catalysts resembles a recipe rather than rational active site design, with observations suggesting as to what element combinations appear to result in optimal yields. Optimal design of OCM catalysts for various reaction/reactor configurations requires greater understanding of how active site properties dictate the trade-off in activity and selectivity. Herein, we demonstrate that the C−H activation energetics on a series of oxides, spanning those considered highly reducible and irreducible, correlate with the surface reducibility. Received: November 23, 2015 Revised: January 28, 2016

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considered for a subset of calculations, without any significant impact on accuracy. Since DFT does not accurately represent the nature of highly localized states in d or f orbitals of metal oxides,27−29 we used the DFT + U method30,31 for a subset of calculations to explore how this correction alters the observed correlation. The DFT + U method introduces an on-site coulomb interaction (U term) that penalizes noninteger occupation of localized orbitals, and thus prevents the delocalization of electrons in the state to which it is applied. The introduction of a U term on the 4f orbitals of ceria and terbia motivates proper localization of electrons in reduced cerium oxide (CeO2−x) and terbium oxide (TbOx). We used a U value of 5 eV, which is consistent with values used in previous DFT studies of ceria.5,32−39 To our knowledge, there’s no previous study on the choice of U-value of terbia. Therefore, we have used a U value of 5 eV and have explained the rationale behind it and its implications in sections 3.3.1 and 3.3.2. We also evaluate the impact of a variable U value on Ce 4f states. 2.2. Surface Models. Our study involves a series of reducible and nonreducible oxides including CeO2, TbOx, TiO2, MgO, and ZnO in their pure/doped states. For all the oxides, a 2 × 2 expansion of the surface unit cell is used. The ceria(111) surface is modeled as a slab of cubic fluorite CeO2 separated by 15 Å of vacuum space in the direction perpendicular to the surface. Terbia can also take on a cubic fluorite bulk structure,40 and our TbOx models begin with the TbO2 structure and undergo a series of reductions through removal of oxygen atoms, retaining the parent fluorite lattice structure throughout. ZnO surfaces have been modeled as the most thermodynamically stable ZnO surface facets, (100), (110), and (001), of a hexagonal wurtzite bulk structure with alternating Zn and O layers along the c-axis.41 The MgO(100) and (110) surfaces are modeled as slabs of cubic halite structure,42 while TiO2 surfaces have been modeled as anatase and rutile structures.43 For CeO2, TbOx and MgO systems, mirrored surface slabs were used to minimize spurious interslab interactions. Detailed information regarding the surface facets, lattice constants, number of atomic layers, and the number of frozen layers of the surface slabs for doped CeO2, TbOx, ZnO, doped TiO2, and doped MgO is provided in Table S3. The metal oxides were “doped” by substituting one surface metal atom with a second metal dopant. For mirrored slabs, two dopants replaced the surface metal atoms, one on each side. For nonmirrored slabs, a net surface dipole moment can develop. To diminish the effect of this spurious interaction on energetics, a dipole correction was added to the calculations within the self-consistent field cycle.44,45 Terbia’s highly oxidative property is a result of its ability to be stable in multiple oxidation states (TbO2 to Tb2O3).46,47 Through TPD experiments,40 Weaver and co-workers have shown that TbO2 films retain a fluorite lattice structure even after reduction to Tb2O3. Starting from the fully oxidized TbO2 (111) surface, we calculate the oxygen vacancy formation energy of various surface and subsurface vacancies to determine the most stable TbO1.88, TbO1.75, TbO1.63, TbO1.5, and TbO1.38 surfaces. For determining the surface reducibility to correlate with C−H activation, we define the oxygen vacancy formation energy as the energy to pull out oxygen from the topmost layer. 2.3. Oxygen Vacancy Formation Energy. We use the oxygen vacancy formation energy as a computational measure of the surface reducibility. Reduced metal-oxide surfaces were optimized by removing a surface oxygen atom. For mirrored

We further demonstrate that an equivalent correlation exists for subsequent adsorption of the methyl radical formed from CH4 activation, leading to a deeper oxidation and a tradeoff between OCM activity and selectivity. As a measure of surface reducibility, we calculate the oxygen vacancy formation energy and reduced surface work function of various “reducible” and “nonreducible” metal-oxide surfaces. Our group has previously shown8 that on doped ceria systems, the C−H activation barrier depends on the reducibility of the surface. Recently Metiu and co-workers7 have shown this relation on La2O3 doped with several metal-dopants. In both the studies, the C−H bond activation energy has been related to the oxygen vacancy formation energy of the metal-oxide catalysts. In the present work, we extend the correlation to other reducible and nonreducible oxides including TbOx, doped TiO2, ZnO and doped MgO respectively. Lunsford19−21 used experimental techniques like MIESR to conclude that the conversion of methane to C2 occurs via the gas phase coupling of methyl radicals formed during C−H activation. Therefore, selectivity to C2 hydrocarbon depends on the ability (or rather inability) of the ·CH3 radical to adsorb and further oxidize on the catalyst surface. We show herein that the vacancy formation energy is also a descriptor for the ·CH3 adsorption energy, and therefore the selectivity to coupling products in OCM. The correlations between the C−H activation (activity), the ·CH3 adsorption energy (selectivity), and the oxygen vacancy formation energy (reducibility) can be useful in predicting high-performance catalyst for OCM, and enhancing C2 yield by tuning material properties accordingly. For establishing the correlation of activity with surface reducibility, we have considered various reducible and irreducible oxides. Our goal is to establish this correlation, not to provide values indicative of specific experimental systems, since the exposed structure of a polycrystalline mixed oxide will be complex. We modulate the surface reducibility, and therefore the methane activation energetics, by doping the host oxide with the other transition metals, by varying the extent of surface reduction, by varying the surface facet, and by altering the value of Hubbard U corrections in the DFT + U formulation. We perform a statistical analysis to confirm that the correlation of methane activation energetics with the surface reducibility is equivalent regardless of which of these approaches are used to modulate surface reducibility. Sources of deviation from the correlations are discussed.

2. METHODS 2.1. Electronic Structure Methods. All the electronic structure calculations were carried out using the Vienna ab initio simulation package (VASP), an ab initio total energy, and molecular dynamics program developed at the Institute of Material Physics, University of Vienna.22,23 The projector augmented-wave (PAW) method was used to represent the ion-core electron interactions.24 The valence electrons were represented by using a plane wave basis set with an energy cutoff of 450 eV. The valence configurations for all the atoms involved are given in Table S1. The Perdew−Wang (PW91) version of the generalized gradient approximation (GGA) was used to incorporate exchange and correlation energies.25 kPoint sampling was performed using the Monkhorst Pack scheme,26 and the meshes used for the various surfaces are given in Table S2. All the calculations performed were spin polarized. Forces on all atoms were minimized to 0.05 eV Å−1, which required less computational time than 0.02 eV Å−1, 1813

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ACS Catalysis slabs, a surface oxygen atom was removed from each side of the slab. For doped surfaces, the oxygen atom removed is nearestneighbor to the dopant. Even though subsurface oxygen vacancies often have lower vacancy formation energies,48 surface oxygen vacancies were examined to correlate with the reductive surface process of activating methane over surface O atoms. The vacancy formation energy for the mirrored and nonmirrored slabs is calculated as ΔEvac =

With the pseudo transition state approach, methane dissociation barriers for mirrored and nonmirrored slabs are calculated as ΔEact =

ΔEvac = E M nOxn−1 +

EO2 2

(4)

respectively, where E2H* and EH* are the energies of surface slabs with adsorbed H*, EMnOxn is the energy of the bare surface, and ECH4 and E·CH3 are the energies of isolated CH4 and ·CH3 respectively. We examined C−H bond activation on a relatively irreducible oxideMgO(100). We use a 5-atomic-layer, nonmirrored slab (Figure 1) to calculate the methane activation

(1)

− E M nOxn

(3)

2

ΔEact = E H * + E·CH3 − (E M nOxn + ECH4)

E M nOxn−2 + EO2 − E M nOxn 2

E2H * + 2E·CH3 − (E M nOxn + 2ECH4)

(2)

respectively, where EMnOxn−2 and EMnOxn−1 are the energies of the reduced unit cell, EO2 is the energy of gas-phase O2, and EMnOxn is the energy of the stoichiometric surface slab with n metal atoms, each having a valency of 2x. Since DFT overestimates the O2 binding energy,49 the vacancy formation energies cannot be directly compared with experimental values. In this study, we are examining the trends in C−H activation energy and ·CH3 adsorption energy with respect to the vacancy formation energy, and therefore, corrections to O2 binding need not be applied. 2.4. Work Functions, Φ. Work function is the minimum work required to displace an electron from the surface lattice to a point in vacuum. Therefore, work function can also be used to characterize the reductive property of a surface. Using VASP, we calculate the work function using the standard approach50 of correcting the Fermi level to a vacuum reference at the center of the vacuum region between the periodic slabs. The VASP Fermi energies and vacuum referenced energies have been provided in Table S4. The DFT calculation of work function does not directly consider the energy of the positive vacancy left behind after electron removal and therefore is not a direct analogy to an experimentally measured value for systems in which this vacancy would significantly localize. 2.5. C−H Activation Energy. On many metal-oxide surfaces, C−H activation proceeds via H-abstraction and the formation of a ·CH3 radical in the transition state. We use the “pseudo steady state approach” to approximate the methane activation barrier as the reaction energy to form a surface adsorbed H species (H*) and a gas phase ·CH3 radical. The pseudobarrier approach recognizes the existence of a BEP correlation between the activation barrier and reaction energy for the dissociation of methane to form H* and the methyl radical, and uses an effective BEP slope of 1. We have previously demonstrated the existence of this BEP correlation for doped CeO2 surfaces.8 The “late” nature of the H abstraction transition state has also been illustrated for MgO,4 La2O3,51 and VOx clusters.52 Section 3.1 validates that this correlation exists across a wide range of oxide materials by showing that the activation barrier only slightly exceeds the reaction energy on both the highly reducible CeO2 and relatively irreducible MgO surface. Here, we use low-index single crystal surfaces as our goal is to establish a correlation, and not to provide reaction energetics comparable to experimental systems. In real systems, the presence of lowenergy surface defect states can substantially change the energy landscape.53

Figure 1. (a) Initial state. (b) Transition state. (c) Final state for dissociative methane adsorption on MgO(100) surface. (d) ·CH3 adsorption. Mg is displayed as green (light), O as red (dark), H as white, and C as gray.

barrier. To isolate the transition state for CH4 (g) → ·CH3 + H*, we used the climbing image nudged elastic band method (CI-NEB).54−56 The CI-NEB method uses a series of images along the reaction path, and optimizes them while constraining along the reaction coordinate. The highest energy image is made to climb along the minimum energy path to reach the saddle point.54 The transition state was identified as the highest energy image with a force tangent to the reaction coordinate less than 0.05 eV Å−1. The transition state was confirmed by calculating the harmonic vibrational modes for the transition image and confirming the existence of a unique imaginary vibrational frequency. 1814

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(5)

2·CH3 → C2H6

(6)

2H* → H 2O + *V

(7)

1 O2 + *V → * 2

(8)

To substantiate the pseudobarrier approach used to calculate methane activation barriers across MOx surfaces, we added the barrier for CH4 activation on MgO(100) to the BEP correlation previously reported for M-doped CeO2(111).8 Figure 1 illustrates the initial, final and the transition states for the C− H activation on the MgO(100) surface. As shown in Figure 2,

1 O2 → C2H6 + H 2O (9) 2 where * represents the catalyst surface and *v represents the catalyst surface with one oxygen vacancy. We use the C−H activation process to form gas phase ·CH3 as an indicator of catalyst activity. The initial C−H bond activation step has been shown to be rate limiting for methane catalytic combustion, methane reforming, and OCM.14,57,58 In competition with the gas phase radical coupling, ·CH3 can also adsorb to O atoms on the catalyst surface, leading to further oxidation and diminishing the C2 selectivity. We, therefore, examine ·CH3 adsorption as an indicator of selectivity, with stronger ·CH3 adsorption expected to indicate a less selective catalyst against deeper oxidation. The ·CH3 adsorption energy for mirrored and nonmirrored slabs is calculated as Overall:

ΔEads =

2CH4 +

Figure 2. Brønsted−Evans−Polanyi relationship for the abstraction of H from methane on the surface of reducible M-doped CeO2 (◆) and nonreducible MgO (■). The best fit line slope of nearly 1 (1.005, intercept 0.23 eV) implies the existence of a late transition state, and therefore, the reaction energy ΔEact can be used as a pseudoactivation barrier, in place of the actual barrier ΔEbarrier.

the barrier for methane activation (Ebarrier) for irreducible MgO and previously reported reducible doped CeO28 exhibit a Brønsted−Evans−Polanyi (BEP) relationship59−61 with the C− H activation energy (ΔEact). The BEP slope of Figure 2 is 1.005. This value being near 1 substantiates the use of the final state to approximate the transition state in considering methane activation. The intercept of 0.23 indicates a slight, constant underestimation of the activation barrier when using this pseudo barrier approach. Due to the presence of this “late” transition state, the reaction energy can be used as the pseudoactivation barrier. The existence of a linear correlation between the actual activation barrier and the reaction energy for methane activation indicates that linear correlation between the pseudobarrier (hereafter called C−H activation energy, ΔEact) and vacancy formation energy (section 3.3) will also give a linear correlation between the actual barrier and vacancy formation energies. 3.2. Correlation of C−H Bond Activation and Surface Reducibility. Figure 3 displays a correlation of the C−H bond activation of methane (ΔEact, eqs 3 and 4) and the surface reducibility (ΔEvac, eqs 1 and 2) of the CeO2(111) surface doped with transition metals, ZnO, TbOx(111), doped TiO2, and doped MgO. The data used for Figure 3 is provided in Table S5. The correlation between C−H bond activation and surface reducibility has been previously established over a range of transition metal dopants, and across low index facets for CeO25,8 and La2O3.7 Figure 3 demonstrates that a linear correlation holds across oxides ranging from those considered highly reducible (doped ceria) and relatively irreducible (MgO). The correlation coefficient R2 value is 0.88. Detailed statistical investigation of the data including 95% confidence intervals for the slope and intercept has been provided in Table S6. Though this correlation broadly holds, deviations are

E2CH3* − (E M nOxn + 2E·CH3) 2

ΔEads = ECH3* − (E M nOxn + E·CH3)

(10) (11)

respectively, where E2CH3* and ECH3* are the energies of surface slabs with adsorbed CH3*, EMnOxn is the energy of the bare surface, and E·CH3 is energy of isolated ·CH3 radical. Following H-abstraction by the surface oxygen atom, H atoms desorb as H2O to create an oxygen vacancy, which is then refilled by gas phase oxygen fed in the reaction system. H2O desorption and vacancy refilling completes the catalytic cycle, and therefore, their rate can impact catalyst turnover frequency. The oxygen vacancy formation energy can be considered as a descriptor of these processes, as H2O will desorb easily when the oxygen vacancy is more stable, and vacancy refilling will be easier if vacancy formation is less favorable. We neglect other processes that can impact product selectivity such as ethane activation. The C−H bond strength in C2H6 (422 kJ/mol) is less than CH4 (439 kJ/mol), and the C− H bond in C2H6 can further activate to form ·C2H5 which further reacts with O2 to form C2H4.4 Ethyl coupling and other oligomerization processes could form larger hydrocarbons, however, surface coupling processes have been found to be minimal,3 and therefore, the catalyst composition will have minimal effect on many of these processes.

3. RESULTS AND DISCUSSIONS 3.1. Pseudoactivation Barrier Approach Validation. The activity for methane activation can be described using the activation barrier for the initial H3C−H bond activation. Tedious barrier calculations can be avoided by using C−H bond activation reaction energy as the pseudoactivation barrier. 1815

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oxide in the correlation of Figure 3 is subject to the choice of U correction on metal atom d or f states. Though the specific location for a certain composition is difficult to conclude precisely, we show here that the correlation itself is independent of the use of U correction. Figure 4 (diamonds) represents the correlation between the C−H activation energy (ΔEact) and the surface reducibility

Figure 3. C−H activation energy (ΔEact) is correlated with the oxygen vacancy formation energy (ΔEvac). The solid line represents the best linear fit to the data, ΔEact = 0.5694ΔEvac + 0.0814.

significant (mean absolute error = 0.36 eV, maximum absolute error = 1.51 eV). Causes of deviations are discussed in section 3.7. Figure 3 shows a few oxides that have both negative “activation barriers” and oxygen vacancy formation energies. The pseudobarrier approach is clearly unreliable when it predicts negative barriers, and these systems would be expected to show effectively barrierless methane activation in full transition state searches. However, the negative oxygen vacancy formation energies show that these models represent an unstable, overoxidized state and are used only to show the wide range of the correlation presented. No periodic trend in oxygen vacancy formation energy was observed within the doped MgO system with regard to the dopants used. For Li-doped MgO, the energy barrier for H abstraction has been experimentally reported as 80−160 kJ mol−1.62,63 Using the B3LYP functional for cluster and periodic models, and considering Li+O·‑ as the active site, Schlögl and co-workers have reported the DFT calculated energy barrier for H abstraction as 12 ± 6 kJ mol−1.4 Our DFT calculated reaction energy of H-abstraction on Li doped on MgO (100) is 48 kJ mol−1. The difference between these experimental and computational values highlight the impact of surface model/ facet used and the difficulty in replicating the experimental values from complex structures of mixed oxides. Both O vacancy and methane activation are processes that reduce the surface, and specific “trap states” associated with defects or nonidealized structures may be more reducible than we observe using single crystal models. This discussion reinforces the intention of the work hereinMgO and its doping are used to add a range of reducibility to Figure 3, and we have made no attempt for our model of Li−MgO to match the likely active site in experimental Li−MgO catalysts. Instead, the correlation in Figure 3 suggests that if such a model were created, the reducibility of the active site would predict well the methane activation energy. 3.3. Subcorrelations of Methane Activation with Surface Reducibility. 3.3.1. Varying Surface Reducibility Using Ce f-State U-Value. The inability of DFT to correctly represent the localized metal-oxide state necessitates the use of a U correction. The “proper” U value to represent surface catalytic processes such as methane activation is unknown. On the CeO2(111) surface, there is a considerable difference (∼1 eV) between ΔEvac at U = 0 and 6 eV. The exact position of an

Figure 4. C−H activation reaction energy plotted against the oxygen vacancy formation energy, the correlation for which holds when varying the U value for Ce in CeO2 (◆), the surface facets for TiO2 (■), and the oxidation state for TbOx (●). Other data included in the overall correlation is also shown (+).

(ΔEvac) at various Ce f U values ranging from 0 to 6 eV. Even though “standard” DFT (U = 0) may not be sufficient to quantitatively predict the reaction energies for oxides involving d and f block elements, the C−H activation still follows the linear trend with the vacancy formation energy ΔEvac. The C− H activation energy data for this subcorrelation lies within the 95% CI of the overall correlation, statistical details of which can be found in Table S6. This suggests that the two correlations are statistically equivalent. A considerable number of studies5,32−39 have established the U value for Ce in CeO2 to be ∼5 eV; however, the existence of the qualitative trend irrespective of the used U value is an important result we speculate to be transferable to other oxides involving d and f block elements. 3.3.2. Varying the Surface Facet and the Active Oxygen in TiO2. Most catalyst surfaces are not perfect single crystals, but expose different surface facets. TiO2 can exist in anatase and rutile phase with surfaces that expose both bridging (Obrg) as well as in surface plane (Oip) oxygen atoms. Figure 4 (squares) includes data that correlates the C−H activation energy (ΔEact) and the surface reducibility (ΔEvac) on various anatase and rutile TiO2 surfaces with different active oxygens. C−H activation data on TiO2 surfaces also remain within the 95% CI of the overall correlation; the statistical details are provided in Table S6. Staying within the TiO2 surface family, we observe a large variation (2.00 to 5.49 eV) in the surface reducibility (ΔEvac) for different facets and active oxygen. This variation in the reducibility is equally reflected in the corresponding C−H activation energies (ΔEact). Unlike previous studies that consider vacancy formation energies for TiO2,64−66 we have not used any U correction on Ti d states. U corrected values for the vacancy formation energies will be different, however, similar to the CeO2 U correction subcorrelation in section 1816

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ACS Catalysis 3.3.1, the vacancy formation energy for TiO2 facets would be expected to follow the qualitative linear trend with the C−H activation energy. 3.3.3. Varying the Oxidation State through the O Vacancy Concentration in TbOx(111). Tb oxide exhibits multiple oxidation states depending on the oxygen chemical potential of the surrounding environment. To find the most stable TbOx surface structure at various oxidation states, we remove surface and subsurface oxygen atoms from different layers iteratively from a stoichiometric TbO2(111) surface. The details of the calculations relating to the TbOx surfaces including the locations of the oxygen vacancies in the most stable TbOx configurations are provided in Table S7. Figure 4 (circles) includes the correlation between the C−H activation energy (ΔEact) and the surface reducibility (ΔEvac) at various oxidation levels in TbOx. C−H activation data on TbOx also remain within the 95% CI of the overall correlation, the statistical details being provided in Table S6. TbO2 (extreme left in Figure 4) is highly reducible, and therefore, facilitates activation of methane. As the oxidation state is lowered from Tb4+ to Tb3+, the surface becomes less reducible. Through successive vacancy formations, when the TbO2 structure reaches the Tb2O3 stoichiometry (extreme right in Figure 4), the oxidative property is diminished considerably. Further removal of oxygen atoms from Tb2O3 forces some Tb atoms to a Tb2+ state, which is highly unfavorable. As Figure 4 shows, the vacancy level manipulation in TbOx provides data points at the extremes of highly reducible and irreducible, following a statistically equivalent correlation to that observed when changing the oxide host, metal dopant, and U correction. The results from TbOx are extremely encouraging toward the prospect of rational design of catalysts by tuning their oxidative property. Tb2O3.25 is extremely favorable toward activating methane (left end of Figure 4) while Tb2O3 exhibits low activity toward it (right end of Figure 4). The active form of the catalyst may not be stoichiometric, as the oxygen pressure can cause oscillation about the different oxidation states. However, we again show that the correlation is independent of the oxidation state, or the oxygen pressure. The implication of this result for oxidative coupling of methane is discussed in section 3.6. 3.4. Correlation of C−H Activation with Work Function Φ. In previous sections, we have shown that the C−H bond activation in methane correlates with the reducibility of the catalyst surface. We used the oxygen vacancy formation energy as a descriptor for the reducibility, and thereby for the C−H activation. The work function of the reduced surface, Φ, is another measure of the surface reducibility. For oxygen vacancy formation, surface reducibility is a measure of the propensity of the surface to incorporate the “leftover” electrons due to oxygen removal. Reducibility may, therefore, also be measured as the energy required for removal of an electron from the oxygen vacant surface. We calculated the work function of the oxygen vacant surface to use as a descriptor for surface reducibility. In Figure 5, which represents the correlation between the C−H activation energy with the work function, we observe similar correlation as with the oxygen vacancy formation energy in metal-oxide systems. However, both the correlations are not exactly similar due to the inherent difference in the nature of their reductive processes. For the oxygen vacancy formation energy, we examine the 2e− reduction process, while the work function

Figure 5. C−H activation energy (ΔEact) is correlated with the work function (Φ) of the oxygen vacant surface. The solid line represents the best linear fit to the data, with R2 = 0.82, ΔEact = −1.2307Φ + 6.8857.

calculation involves the removal of only one e− from the HOMO of the oxide surface. The correlation of C−H activation energy with work function, Φ has an R2 value of 0.81, mean absolute error = 0.55 eV, and maximum absolute error = 1.65 eV. Oxygen vacancy formation energy acts as a better descriptor for the surface reducibility than this work function, since the correlation with the former has a comparatively higher R2 value (0.88) and lower mean and maximum error (0.36 and 1.51 eV respectively). We speculate that oxygen vacancy formation serves as a better descriptor because it encompasses more information than the work function, providing some indication of the M−O bond strength and structural reorganization upon reduction that also impacts the methane activation energy. 3.5. Density of States. In reducible oxides like doped ceria, metal atoms (Ce or dopant) get reduced by accepting the two electrons left after the removal of surface oxygen, into a localized d or f orbital. Using density of states and orbital imaging, it was explicitly shown that the “extra” electrons occupied the localized d or f states of the dopant or the nearest host cerium atoms.5 We also find similar reduction of the dopant/metal atom upon H abstraction from methane, establishing that C−H activation reduces the oxide surface, and oxygen vacancy formation can be used as a descriptor for this process.8 For the relatively irreducible oxide MgO, total and partial densities of states (Figure 6) reveal that the reduction results in a delocalization of the additional electron throughout the MgO surface. The density of states for intact MgO surface (Figure 6a) shows no filled orbital between the valence band and the conduction band. Upon H-abstraction (Figure 6b), the electron from the hydrogen occupies a gap state. The partial densities of states for nearest neighbor and next nearest neighbor Mg reveal that unlike the localized states found in Ceria, the electrons are delocalized over the all the surface Mg atoms (Figure 6c and d). Oxygen removal from reducible oxides like CeO2 leads to localized Ce f states,8 whereas removal of oxygen from nonreducible oxide MgO gives trapped electrons localized to form an f center.67 3.6. Implications on Oxidative Coupling of Methane (OCM). We have already observed a correlation between surface reducibility and C−H bond activation, which is a descriptor for the overall activity of a catalyst for methane 1817

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Figure 6. Total DOS plotted versus energy (referenced to Fermi level) for (a) an intact MgO (100) surface, (b) H-adsorbed MgO (100) surface. Partial DOS plotted versus energy (referenced to Fermi level) for (c) Mg atom on the intact surface, and (d) Mg atom nearest to the H-adsorbed oxygen.

conversion. However, once the C−H bond is activated, the methyl radical can undergo subsequent oxidation to form a multitude of products. The desired products in the coupling of methane are C2 hydrocarbons, the selectivity to which relies on the catalyst’s inability to adsorb the methyl radical, which can lead to further oxidation to CO or CO2. Therefore, the ·CH3 adsorption energy can describe the methane selectivity to C2 hydrocarbons during the OCM process. Figure 7 shows a linear correlation between the C−H activation energy and the ·CH3 adsorption energy; surfaces that more readily activate the C−H bond also more strongly bind the resulting radical. Therefore, it can be deduced that activity and selectivity during the coupling of methane are inversely correlated. Since ·CH3 adsorption is a similar process to Habstraction, both of which effect a 1 e− reduction of the surface, the selectivity for OCM is also described by surface reducibility. Figure 8 illustrates the overall correlation between activity, C2 selectivity and the surface reducibility of the metal-oxide catalysts. Catalysts with high surface reducibility (doped ceria and TbO2) favor C−H activation, and therefore exhibit high activity toward methane conversion. However, they also facilitate ·CH3 adsorption leading to low selectivity toward C2 hydrocarbons. These materials would be effective as combustion catalysts, but their usage in OCM would result in poor C2 yield. Conversely, catalysts with low surface reducibility (doped MgO and Tb2O3) do not favor C−H activation, and therefore exhibit low activity toward methane conversion. However, they

Figure 7. Correlation between the C−H activation reaction energy (ΔEact) and the ·CH3 adsorption energy (ΔEads).

do not facilitate ·CH3 adsorption, which allows coupling in the gas phase resulting in high selectivity toward C2 hydrocarbons. Despite having high selectivity, these catalysts are not ideal for OCM owing to their low activity, and therefore low C2 yield. As discussed in section 3.3.2, oxygen pressure affects the oxidation state of TbOx. At low oxygen pressure, the catalyst surface may oscillate about Tb2O3 and be selective but less active for OCM. Conversely, at high oxygen pressure, it may 1818

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Figure 9. Highlight of data points with significant deviations from the linear correlation of methane activation and surface reducibility: rutile TiO2(110) with in plane oxygen, Oip as the surface active site (◆), Lidoped MgO(100) (■), Ga-doped MgO(100) (●), and Ge-doped MgO(100) (▲). Blue symbols represent methane dissociative adsorption activation barriers, and red symbols represent the negative of CH3 radical adsorption energies.

Figure 8. Overall correlation of oxygen vacancy formation energy (ΔEvac) with C−H bond activation reaction energy, ΔEact (◆), and the negative of ·CH3 adsorption energy, ΔEads (■). Oxides which favor C−H bond activation also adsorb ·CH3 favorably, and therefore an inverse correlation between activity and selectivity is observed. The reducible oxides on the far left of the plot favor C−H activation but exhibit low coupling selectivity due to favorable ·CH3 adsorption. The irreducible oxides on the far right exhibit the opposite characteristics.

energetics (diamonds) appear to the left of the correlation. The surface will be less active and more selective, than suggested by its oxygen vacancy formation energy. More generally, surfaces that show significant reconstruction that differs between vacancy formation and H/CH3 adsorption will show deviation from the overall linear correlation. The squares represent the C−H activation reaction energy and the ·CH3 adsorption energy for Li-doped MgO. Here, one Li atom replaces one surface Mg atom creating a Li+ O− configuration. A one electron reduction of this surface (C−H activation or ·CH3 adsorption) is highly favorable, as the intact surface has an F+ center. A two electron reduction by the creation of an oxygen vacancy is less favorable. As a result, the data points (squares) shift toward the right due to higher vacancy formation energy (two electron reduction) of this LiMgO model relative to its one electron H· or ·CH3 adsorption. This suggests this surface will be more active (and less selective) than suggested by its oxygen vacancy formation energy. To generalize, surfaces where 1e− and 2e− reduction energetics involve significantly different electronic states will demonstrate substantial deviations from the overall linear correlation. The deviation arising from the contrast between a one electron and a two electrons reduction is also observed in the C−H activation reaction energy and the ·CH3 adsorption energy data for Ga-doped MgO (circles) and Ge-doped MgO (triangles). Ga prefers a one electron reduction from a 3+ state to a 2+ state allowing for C−H activation or ·CH3 adsorption. These surfaces exhibit a higher oxygen vacancy formation energy than expected by the linear correlation due to the less favorable two electron reduction, shifting the data to the right of the linear correlation. Conversely, Ge prefers a two electron reduction from a 4+ state to a 2+ state, and therefore exhibits a relatively lower oxygen vacancy formation energy when compared to the one electron C−H activation and ·CH3 adsorption processes. This shifts the data toward the left of the linear correlation. The previous examples show that differences in structural rearrangement or one/two electron reduction states can cause materials to deviate from the presented linear correlation. The

oscillate about TbO2 and be highly active but less selective. Therefore, for some oxides, changing the reaction conditions can also be an effective way to tune reducibility, and the overall yield during OCM. The correlation between activity, selectivity, and reducibility in Figure 8 is only a qualitative one; it should not be used to quantify the exact C2 yield for any catalyst. OCM catalysis suffers from an intrinsic trade-off between C−H activation energy and ·CH3 adsorption energy. Since the OCM process involves removal and refilling of oxygen atoms from the lattice, a high-performance catalyst is also expected to have an optimum value for oxygen vacancy energy to have a high turnover frequency. 3.7. Physical Origins of the Deviations from the Linear Correlation. In previous sections, we explained the theoretical basis for the correlations between C−H activation reaction energy, ·CH3 adsorption energy and reducibility (namely oxygen vacancy formation energy). Though the correlations hold well over a wide-range of oxides, the mean absolute error is significant, suggesting the correlation alone does not capture all of the relevant physics that dictate how surface properties impact methane activation energetics. We now select four surfaces, their data highlighted in Figure 9, with appreciable deviation and explain the physical origins of their deviations. For all four surfaces, the C−H activation reaction energy correlates strongly with the ·CH3 adsorption energy, reinforcing that both processes are similar. The C−H activation energy and ·CH3 adsorption energy, however, deviate from their expected value correlating with their oxygen vacancy formation energies. The diamonds in Figure 9 represent the C−H activation reaction energy and the ·CH3 adsorption energy for rutile (110) with the in surface plane oxygen (Oip) being the surface active site. For this surface, vacancy formation removing Oip results in significant surface reconstruction, with the bridging oxygen moving to a position between the bridging and in-plane site. This surface reconstruction stabilizes the vacant surface, thereby lowering the vacancy formation energy. The reconstruction stabilization for the vacancy does not occur when adsorbing H or ·CH3, and, therefore, the surface 1819

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inherent self-interaction error that casts doubt on the absolute energetic values from these DFT methods, however, does not clearly contribute to these deviations. As shown in section 3.3.1, the application of Hubbard U corrections does not cause deviations from the linear trend; these corrections instead shift the position of a material along the linear correlation. This suggests that the energy involved in reducing the surface, either through O vacancy formation or H/CH3 adsorption, is equally effected by the self-interaction error or U correction. Despite these deviations, the correlation between C−H activation reaction energy, ·CH3 adsorption energy and the oxygen vacancy formation energy holds broadly across several pure/doped metal-oxides with a wide range of reducibility.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge support from the National Science Foundation DMREF Grant no. 1436206.

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REFERENCES

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4. CONCLUSIONS Methane activation was investigated over a range of reducible and nonreducible catalysts. Electronic structure calculations were used to relate C−H activation energy (measure of activity) and ·CH3 adsorption energy (measure of selectivity against ·CH3 adsorption) with the surface reducibility of metaloxide catalysts. The existence of a linear correlation between activity, selectivity and surface reducibility shows that surface reducibility can be used as a descriptor for methane activation and conversion to C2, and that there is an inherent trade-off in activity and selectivity against further oxidation of the ·CH3 radical. Despite the reliability of the linear correlation across materials with large differences in reducibility, considerable error suggests the use of reducibility as a descriptor is limited to a broad analysis across materials. Low surface reducibility (high vacancy formation energy) leads to low C−H activity and higher selectivity. Conversely, a catalyst with high surface reducibility (low vacancy formation energy) exhibits higher activity and lower selectivity, and may also be limited by oxygen vacancy refilling. In this regard, catalysts which can take multiple oxidation states, like TbOx, may allow for tuning the activity/selectivity trade-off by varying the reaction oxygen atmosphere. One of the limitations of DFT is that the cell size has to be small in order to make the calculations computationally tractable. This limits the choice of dopant concentration in the surface structures. Further studies will vary the dopant concentration, and will include several surface facets. The correlation presented here is a step toward high-throughput DFT screening of catalysts for high-yield OCM process. Further models to relate experimentally observed yields to computationally calculated reaction energies need to be developed.

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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/acscatal.5b02657. Supplementary information includes Tables S1−S7 as described in the text, which include valence electron configurations for each atom, details on the structure of surface models used (lattice constants, number of layers, k-point sampling, figures of surface structures and vacancy configurations in TbOx structures, and tables of data included in figures within the main paper (PDF) 1820

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