Methane Dissociation on Li-, Na-, K-, and Cu-Doped Flat and Stepped

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Methane Dissociation on Li‑, Na‑, K‑, and Cu-Doped Flat and Stepped CaO(001) XiaoYing Sun,† Bo Li,‡ and Horia Metiu*,† †

Department of Chemistry & Biochemistry, University of California, Santa Barbara, Santa Barbara, California 93106-9510, United States ‡ Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016, China S Supporting Information *

ABSTRACT: We report the results of density-functional theory calculations for the dissociative adsorption of methane (DAM) on CaO(001) doped with Li, Na, K, and Cu. The presence of these dopants lowers the energy of oxygen-vacancy formation, increases the energy of the DAM reaction, and lowers the activation energy for DAM. We performed the same calculations for a stepped CaO(001) surface doped with Na and found that Na prefers being located at a step and the activation energy for DAM is lower at this step than on the doped, flat surface. We propose that such trends are valid for all oxides doped with lower-valence dopants.

1. INTRODUCTION The catalytic conversion of methane to valuable chemicals is of great interest, and oxide catalysts for such reactions have been studied extensively. It is widely believed that the rate-limiting step in methane activation is breaking the C−H bond. This means that one can compare the ability of various oxide catalysts to activate methane by calculating the activation energy Ea for dissociative adsorption. The oxidative coupling of methane (OCM) to make ethylene is an example of useful methane conversion that has been studied extensively. Two excellent reviews of this subject have been published recently.1,2 The OCM reaction requires high temperature, and because of this, the oxide catalyst must be very stable to prevent the combustion of methane. This explains why MgO, CaO, La2O3, Sm2O3, etc., are the oxides used most frequently. It was also shown that alkali dopants improve the performance of these oxides. This induced us to use density functional theory to study the electronic properties of substitutionally doped CaO. We focus on lower-valence dopants (LVDs), such as alkali metals and copper, and we provide limited information on the effect of Ag, Ni, La, and Zr dopants. The presence of an LVD creates an electron deficit in the system, and this weakens the binding energy of the oxygen atoms to the oxide. In the electronic structure calculations, this electron deficit appears as a hole in the valence band, which makes the oxide a strong Lewis acid.3 The fragments formed by the dissociative adsorption of methane (i.e., H and CH3) are Lewis bases, and their binding energy to the oxygen atoms of the doped-surface is increased because of the strong Lewis acid−base3 interaction. To test whether these qualitative arguments lead to correct conclusions, we calculated the reaction energy ΔEd and the activation energy Ea for dissociative adsorption of methane (DAM). We found that © 2013 American Chemical Society

the presence of the dopants increases the DAM reaction energy and decreases the activation energy. If the surface has a step, the dopants prefer to be at the step site, and their efficiency for DAM is higher than on the doped flat surface. The issues we address are whether the hole created by doping with an LVD is localized or not and whether doping with an LVD breaks the symmetry of the oxygen atoms surrounding the dopant. We find that the energy difference between these alternatives is very small and conclude that deciding which one prevails is irrelevant to catalysis at the high temperatures required by methane activation.

2. COMPUTATIONAL METHODS The calculations reported here were performed by using periodic, spin-polarized, density-functional theory (DFT) as implemented in the Vienna ab initio program package (VASP).4−7 The electron−ion interactions are described by the projector augmented wave (PAW) method proposed by Blöchl8 and implemented by Kresse and Joubert.9 We used the PBE functional10 and a plane wave basis set with an energy cutoff of 400 eV. For the flat CaO(001) surface, we used a three-atomic-layers slab and a 15 Å vacuum region. A few calculations with six layers were performed to test that they give the same results as those using three layers. A 3 × 3 surface cell was used in most of the calculations. We also performed a few calculations with a 4 × 4 surface cell to test the influence of the cell size (i.e., the dependence of the energy of vacancy formation on vacancy concentration). Because of the large supercell we used only the Γ-point in the calculations. For the Received: January 9, 2013 Revised: March 1, 2013 Published: April 2, 2013 7114

dx.doi.org/10.1021/jp4002803 | J. Phys. Chem. C 2013, 117, 7114−7122

The Journal of Physical Chemistry C

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for CaO doped with Li, Na, K, and Cu are listed in Table 1. Doping reduces ΔEv substantially from 5.77 eV for the undoped

stepped CaO(001) surface, we used a six-layer slab and a large 7 × 5 surface cell. During structure optimization all ions in the unit cell were allowed to relax and no symmetry was imposed. The optimization was stopped when the force on the atoms was smaller than 0.05 eV/Å. The nudged elastic band method,11 with at least eight images, was used to find the transition state for methane dissociation. As recommended in previous work,12 the spin polarization was maintained constant along the reaction path. The energy of vacancy formation, ΔEv, is defined by 1 ΔEv = Ev + E(O2 (g)) − Es 2 Here Ev is the energy of the slab with one vacancy per supercell (in the top oxygen layer), E(O2(g)) is the energy of an O2 molecule in gas phase, and Es is the energy of the slab without a vacancy. The energy of the dissociative adsorption of methane, ΔEd, is defined by

Table 1. Various Energies Provided by DFT Calculations for Flat CaO(001) Surfaces (Doped and Undoped)a CaO ΔEd(H−Os, CH3−Os) ΔEd(H−Os, CH3−Cas) ΔEd(H−Os, CH3−Ds) Ea(H−Os, CH3−Os) ΔEv

3.42

5.77

Lidoped

Nadoped

Kdoped

Cudoped

−0.06 0.27 0.25 0.40 3.00

0.19 0.47 0.49 0.75 3.13

0.30 0.63 0.70 0.70 3.13

0.46 0.87 −0.07 0.74 3.67

ΔEd(H−Os, CH3−Os) is the energy of the dissociative adsorption of methane (DAM) when H binds to a surface oxygen atom (denoted Os) and CH3 binds to another surface oxygen atom. ΔEd(H−Os, CH3−Ds) is the energy of DAM when the methyl binds to the dopant (located in the surface layer), and the H atom forms a hydroxyl. Ea(H−Os, CH3−Os) is the activation energy for DAM when the products are CH3−Os and H−Os. ΔEv is the energy of oxygen-vacancy formation (the energy to remove one oxygen atom near the dopant to form 1/2O2 in the gas and an oxygen vacancy in the surface). All energies are in eV. a

ΔEd = E(H, CH3) − E(CH4(g)) − Es

Here E(H,CH3) is the energy of the slab with H and CH3 adsorbed on it, and E(CH4(g)) is the energy of the methane molecule in the gas phase. E(H,CH3) changes when we change the adsorption sites of the fragments. Since we are only interested in the trends caused by doping, we have not included the zero-point energies in these definitions of the reaction energies.

CaO to 3.00 eV for Li-doped CaO, 3.13 eV for Na-doped CaO, 3.13 eV for K-doped CaO, and 3.67 eV for Cu doped CaO. A similar reduction in ΔEv has been seen on other oxides doped with LVDs.13−34 We have postulated that this is a general rule: the reduction of ΔEv by lower-valence dopants in very stable oxides is very large (several electronvolts). The magnitude of ΔEv is almost independent of the chemical nature of the alkali dopant: the fact that the dopant has a lower valence than Ca seems to be a dominant factor. ΔEv for Cudoped CaO is larger by 0.54 or 0.67 eV than ΔEv for CaO doped with an alkali. We suspect that this difference exists because both CuO and Cu2O are stable, and therefore it is not proper to assume that the difference in the formal valence of Ca and Cu is equal to 1. To explore whether this assumption is reasonable, we have also calculated ΔEv for Ag-doped CaO, and this is equal to 3.20 eV, which is very close to the result obtained for CaO doped with alkali. It is interesting that all dopants whose valence is smaller than that of the cations they substitute change ΔEv by about the same amount. Dopants having a higher valence than the cation they substitute have the opposite effect. We found that ΔEv for Ladoped CaO is 6.23 eV and for Zr-doped CaO is 6.36 eV; these values are larger than ΔEv for undoped CaO, which is 5.77 eV. We have postulated that this is a general feature of highervalence dopants (HVDs) that dope irreducible oxides. These HVDs reduce the ability of the oxide to act as an oxidation catalyst through a Mars−van Krevelen mechanism. However, they may act as oxidation catalysts by adsorbing oxygen (on the dopant) and activating it.35 Reducible oxides (e.g., TiO2, CeO2) doped with HVDs behave differently because the highervalence dopants donate electrons, to reduce the cations of the host oxide, until their valence equals that of the cation they substitute.3,32 Finally, we have found that ΔEv = 4.41 eV for Ni-doped CaO which is smaller than ΔEv = 5.77 eV for undoped CaO. Ni has a fairly large effect even though Ni and Ca have the same valence, which indicates that the valence difference is not the only factor affecting ΔEv for doped oxides. The difference in the ionic size of the alkali dopants, located in the topmost surface layer, does not seem to affect the

3. OXYGEN-VACANCY FORMATION ON CaO(001) DOPED WITH Li, Na, K, Cu, Ag, Ni, La, AND Zr 3.1. Location of the Dopant. When doped oxides are prepared, the precursors are homogeneously mixed, and therefore one hopes that during the preparation of the doped oxide the cations of the dopant do not have a chance to segregate and form their own oxide. To ensure this, it is preferable to keep the calcination temperature as low as possible to prevent dopant motion once the solid is formed. If this is done, the dopant ought to be trapped where it was located initially and be incorporated into the lattice of the host oxide by substituting a Ca ion or as an interstitial. We study here only substitutional doping of Ca in the surface layer. At the high temperatures necessary for methane activation, it is possible that the dopant may be able to migrate from the lattice site in which it was trapped during preparation to positions of lower energy that may be in the bulk. For this reason we have calculated the energy change when the dopant is moved from the top Ca layer to the second Ca layer. These energies are 0 eV (for Li), 0.16 eV (for Na), 0.96 eV (for K), 0.13 eV (for Cu), 0.20 eV (for Ag), −0.24 eV (for Ni), 0.58 eV (for La), and −0.46 eV (for Zr). The dopants for which these numbers are positive are likely to stay in the surface layer if they happened to be placed there when the doped oxide was prepared. However, one should keep in mind that the preference for a surface site can be affected by the gases with which the surface is in contact. Moreover, at the high temperatures at which methane catalytic activation takes place, it is likely that all atoms in the surface are mobile and the composition and the morphology of the surface are changing all the time. Therefore, the models used in the calculations will provide, at best, trends rather than absolute results. 3.2. Effect of Doping on the Energy of OxygenVacancy Formation. The calculated values of the energy of oxygen-vacancy formation, ΔEv, for undoped CaO(001) and 7115



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magnitude of ΔEv. In part, this happens because the K atom, which is the largest, does not sit at the location of the Ca atom it has substituted, but moves toward the vacuum; its distance to the outermost layer of Ca atoms is 0.71 Å. Li and Na, on the other hand, are located essentially in the same plane as the calcium atoms. The distance between the alkali dopants and the neighboring oxygen atoms is 2.52, 2.54, and 2.68 Å for Li, Na, and K, respectively, while the Ca−O distance in the undoped CaO(001) is 2.42 Å. The increase of the distance for K is caused by its displacement toward the vacuum (in the direction perpendicular to the surface) away from the Ca lattice site. 3.3. Changes in the Density of States upon Doping. Some understanding of the changes in the electronic structure that occur when we make an oxygen vacancy in the doped and undoped CaO is provided by the density of states (DOS) shown in Figure 1. The results are for Na-doped CaO(001);

the Al dopant and the four oxygen atoms surrounding it. This group is imbedded in silica. We use this notation because we can think of this group as consisting of a combination of a AlO4− ion and a hole h having a +1 charge. The whole group is charge-neutral, which is indicated by the superscript 0. The experiments on this system have been summarized by several authors.36−38 EPR measurements find that the hole is localized on one of the oxygen atoms in [AlO4h]0, and this breaks the symmetry: the oxygen atom on which the hole is localized is closer to Al than the other oxygen atoms. Several calculations have shown that, if GGA-DFT is used, the hole is delocalized over the four oxygen atoms neighboring Al.39−42 Methods deemed to be more reliable than GGA-DFT43−45 find that the hole is localized. Pacchioni et al.45 have calculated the EPR spectrum and showed that their calculations (in which the hole is localized) are in reasonable agreement with the measurements. The impression has been created that the inability of GGA-DFT to capture this hole localization, and the geometry distortion created by it, is a severe shortcoming of DFT. We argue below that the energy difference between a state with a localized hole and one with a delocalized hole is very small; at the temperatures at which catalysis takes place this difference is irrelevant. This suggestion is supported by EPR experiments on [AlO4h]0 which show36−38 that the hole-localization disappears when the temperature exceeds 170 K. The activation energy for a transition from a localized hole to a delocalized one was estimated to be 0.03 eV. As a side comment we mention that [AlO4h]0 is extremely difficult to prepare.36−38 The Al-doped silica normally contains AlO4H or AlO4Li, and it takes heroic efforts to remove H and Li to make [AlO4h]0. This is expected since [AlO4h]0 is a strong Lewis acid and will readily react with Lewis bases such as H or Li.3 The situation is similar in Al-containing siliceous zeolites in which presence of AlO4 in the frame is always accompanied by positive ions in the cage so that the correct formula is AlO4H (which the counterion is a proton), not AlO4h. Finally, GGA-DFT calculations on La-doped CeO2(111) by Dr. S. Chrétien (these will be reported in detail in a separate article) show that GGA-DFT predicts two low-energy states one in which the hole is localized and another in which it is not. The energy difference between them is ∼0.03 eV (well within the error of DFT). We suggest that while this localization is of interest to theory, it is not important for catalysis. 3.4. Changes in the Density of States When a Vacancy Is Made. The DOS of CaO with an oxygen vacancy in the topmost layer in the supercell is shown in Figure 1c. The removal of an oxygen atom leaves behind two unpaired electrons that had been tied up in bonds with the removed oxygen. The DOS of the doped oxide having an oxygen vacancy near the dopant shows only one state in the gap, not two (Figure 1d). This happens because one of the unpaired electrons, formed when the oxygen vacancy is created, fills the hole present in the doped oxide. The energy gained from this hole filling is one of the reasons why it is easier to make a vacancy in the surface of an oxide doped with an LVD. We proposed that this mechanism is general for all irreducible oxides doped with an LVD.23 Reducible oxides are more complicated because the unpaired electrons can reduce the cations of the doped oxide.32

Figure 1. Density of states (DOS) of (a) CaO, (b) Na-doped CaO, (c) undoped CaO with an oxygen vacancy in the supercell, and (d) Na-doped CaO with an oxygen vacancy in the supercell. The upper panel shows the states with spin up, and the lower panel shows the states with spin down.

the DOS for the other alkali dopants is similar, and we do not show them here. A comparison of Figure 1a (DOS for CaO) to Figure 1b (DOS for Na-doped CaO) shows that doping causes the appearance of an empty state in the valence band (indicated by arrow in Figure 1b). The presence of the LVD in a surface without an oxygen vacancy causes an electron deficit (a Ca atom that formally donates two electrons has been replaced by a Na atom that formally donates one electron). This causes the presence of a hole in the valence band. This behavior is similar to that observed for La2O3 doped with LVDs.23 The presence of this hole makes the doped CaO a strong Lewis acid,3 and this will strongly affect the dissociative adsorption of methane (see section 4). The properties of the hole created by the presence of an LVD have been the subject of extensive discussions. The most widely studied example is Al-doped silica. In the discussion that follows we denote by [AlO4h]0 the group of atoms consisting of 7116



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Figure 2. Locations of the methoxide and the hydroxyl formed by methane dissociative adsorption on Na-doped CaO(001). The structures for the dissociation products for Li- and K-doped CaO are very similar. (a) This structure has the lowest energy and is denoted SOO in the text. (b) Another possible location of the fragments of dissociative adsorption of methane on Na-doped CaO(001). This structure is denoted SONa in the text. (c) Another possible location of the fragments of dissociative adsorption of methane on Na-doped CaO(001). This structure is denoted SOCa in the text.

4. METHANE DISSOCIATIVE ADSORPTION ON DOPED AND UNDOPED CaO(001) Oxygen-vacancy formation at the surface of an oxide is often used as a proxy for the reactivity of surface oxygen when the catalytic activity of various oxides is being compared. When the reaction proceeds through a Mars−van Krevelen mechanism,46−48 one assumes that oxides for which ΔEv is small are better oxidants than those having larger ΔEv. In the case of methane activation this rule means that an oxide on which it is easier to make an oxygen vacancy will bind more strongly the fragments formed by the dissociative adsorption of CH4. According to the Brønsted−Evans−Polanyi rule,49−59 we expect that the larger the energy of the dissociative-adsorption reaction, the smaller the activation energy. Since breaking the C−H bond is the rate-limiting step for methane activation, one concludes that the easier it is to make oxygen vacancies on an oxide surface, the lower the activation energy for alkane dissociation and therefore the better oxidant the doped oxide is. To test these qualitative ideas, we calculated the reaction energy ΔEd and the activation energy Ea for the dissociative adsorption of methane. For alkali-doped CaO we examined three possible final states, which differ through the location of the dissociation fragments on the surface (Figure 2). In Figure 2a the dissociation fragments (H and CH3) bind to two different oxygen atoms located near the dopant. In Figure 2b the methyl binds to the dopant and H to one of the surfaceoxygen atoms near the dopant. In Figure 2c the methyl binds to Ca and H binds to an oxygen atom near the dopant. The geometry of the final-state structures is insensitive to the nature of the dopant: the H−Os and C−Os distances are 0.99 and 1.41 Å, respectively, for all three doped surfaces. The energy of the dissociative adsorption reaction is denoted by ΔEd(H−Os, CH3−Os) where the symbols inside the parentheses indicate how the fragments bind to the surface. For example, the energy of the reaction leading to the final state shown in Figure 2b is denoted by ΔEd(H−Os, CH3−D), where D is the dopant atom, and that leading to the state shown in Figure 2c is ΔEd(H−Os, CH3−Ca). The magnitudes of these reaction energies are given in Table 1 along with the energy of the dissociative adsorption on CaO (to form H−Os and CH3−

Os). Other binding configurations have higher energy, and we do not discuss them here. The dissociative adsorption on CaO(001) is very endoergic, ΔEd(H−Os, CH3Os) = 3.42 eV (Table 1). The presence of alkali-metal dopants reduces this energy considerably (Table 1). While the numerical values are subject to the well-known uncertainties in the accuracy of DFT, the trend is unmistakable: the presence of the dopant lowers the reaction energy very substantially. One reason for this is the assistance from a strong Lewis acid−base interaction. Both dissociation fragments are Lewis bases (H and CH3 are electron donors), and the doped surface is a strong Lewis acid (electron acceptor). A substantial energy is gained in the dissociative adsorption reaction because the fragments donate electronic charge to fill the hole created by doping. We have postulated that this is a general feature for all oxide surfaces doped with lower-valence dopants.3 Note also that ΔEd on Li-doped CaO is less than ΔEd for Na-doped CaO, which in turn is less than ΔEd for K-doped CaO. The ionization energy of the atoms of the dopant vary in the order Li > Na > K. This suggest that the oxide doped with an atom that is less willing to donate an electron will bind the dissociation fragments (which are electron donors) more strongly. Given the ambiguous nature of the valence of the Cu dopant (which could be mono or divalent), we discuss it separately. It is obvious that Cu-doped CaO acts differently than alkali-doped CaO. The lowest energy for the dissociative adsorption on Cudoped CaO is −0.07 eV, for the final state in which CH3 binds to Cu and H binds to an oxygen atom in the surface (near Cu). This is the least favorable final state for alkali-doped CaO.

5. ACTIVATION ENERGY FOR METHANE DISSOCIATIVE ADSORPTION The nudged elastic band (NEB) method11,60−62 has been used to calculate the activation energy for the dissociative adsorption reaction that results in the formation of H−Os and CH3−Os on the doped surfaces. The energies along the reaction coordinates are shown in Figure 3. The activation energies are given in Table 1. We discuss first the results shown in Figure 3b for the reaction path on the Na-doped CaO. The NEB graphs start 7117



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are being stretched simultaneously. The geometry of the system in the state 4 on the NEB curve (Figure 3b) is shown in Figure 4a: the C−H bond is broken and a hydroxyl is formed; the CH3 radical is yet to form a bond with the surface. To do this, the CH3 group moves quite a distance so that the C atom can bind to an oxygen atom in the surface. The energies corresponding to the geometries representing this motion are those between 4 and 8 (in Figure 3b). In Figure 4b we show the geometry corresponding to point 6, and in Figure 4c the geometry corresponding to point 8. Once CH3 is close to its final resting place the energy drops sharply as the C−Os bond is formed. A similar evolution is seen for Li-doped and for K-doped CaO (Figures 3a and 3c, respectively), except that the two peaks are not as well formed as in the case of the Na-doped system. The main point is that there are two stages in the dissociation: the C−H bond is first stretched and broken to make a hydroxyl, followed by the large displacement of CH3 to find an O atom to bind to. The NEB for Cu-doped CaO is different: it has the “normal” one-barrier shape. As seen from Figures 4a and 4b, while the OH bond is formed during the reaction, the CH3 radical is fairly far from both H and the surface. Its geometry is almost planar, which is the structure of CH3 in the gas phase. This suggests that it would not take much energy to move CH3 into the gas once the C−H bond is broken. The results of NEB calculations for the barrier opposing the formation of gas-phase CH3 and a hydroxyl are shown in Figure 5. The activation energy is essentially the same as the one for the formation of H−Os and CH3−Os. This is consistent with experimental observations on similar systems, which have shown that gas-phase radicals are present during the oxidative coupling of methane.1,2,63−65

Figure 3. Reaction path calculated by the NEB method for dissociative adsorption of methane on CaO(001) doped with (a) Li, (b) Na, (c) K, and (d) Cu. In the final state the system consists of a hydroxyl and a methoxide formed with the oxygen atoms near the dopant.

from methane in the gas phase and the doped surface (the lefthand side of the graph) and end with a structure of the type shown in Figure 2a (which is H−Os, CH3−Os). In most cases, in such calculations one expects that there is one maximum along the reaction path, a steep ascent to it from the reactants state, and a steep descent to the product state. The graph in Figure 3b is different: there are distinct peaks with a depression between them. During the ascent to the first peak (labeled 4 in Figure 3b), methane approaches the surface and a hydrogen atom in a C−H bond stretches toward a surface oxygen which moves toward this H atom to form a bond. The sharp increase in energy, to reach point 4, occurs because two strong bonds (the Os bond to the surface and the C−H bond in methane)

Figure 4. Structure of methane at points along the reaction coordinate in the case of methane dissociative adsorption on Na-doped CaO: (a) point 4, (b) point 6, and (c) point 8 (see Figure 3b for point numbering). Point 4 corresponds to the first peak in the NEB graph in Figure 3b. 7118



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Figure 5. NEB calculation of the barrier for the dissociation of CH4 on Na-doped CaO with the formation of a hydroxyl and a CH3 radical in the gas.

6. METHANE DISSOCIATION ON STEPPED CaO(001) Because the atoms at a step are undercoordinated (as compared to the same kind of atoms located in a flat surface), we expect

Figure 7. Final state in the dissociative adsorption of methane at a step.

Figure 6. The monoatomic step used in the calculations. Various lattice sites at and near the step are numbered so that we can refer to them in the text. The figure shows one of the final configurations produced by methane dissociation.

them to be more reactive. For this reason we performed exploratory calculations to determine whether the dopant has lower energy if it is located at the step and to find the energy of dissociative adsorption of methane at various step sites. The step is shown in Figure 6. The only dopant we have considered is Na. We examined various possible positions of the dopant and found that the lowest-energy position corresponds to dopant in the step (see Figure 6). The energy for all other dopant positions is higher by at least 0.3 eV. Therefore, if the

Figure 8. Reaction path for the dissociative adsorption of methane at the step with a final state in which CH3 is bound to oxygen atom 5 and H is bound to oxygen atom 1 (for the labeling of the atoms see Figure 6). The structure of the final state is shown in Figure 7.

Table 2. Dissociation Energy of CH4, ΔEd (in eV), on Na-Doped, Stepped CaO(001)a ΔEd(H−O, CH3−O) H site CH3 site ΔEd ΔEd

1 2 0.23

1 3 −0.01

1 4 −0.87

stepped CaO(001) 1 5 5 1 0.13 −0.18 flat Na-doped CaO(001)

0.19

H−O and CH3−D

H−O and CH3−Ca

1 6 −0.06

1 7 −0.04

0.49

0.47

a The numbering of the sites is defined in Figure 6. For example, the dissociative adsorption energy to a final state in which the H atom binds to the oxygen atom 1 and the CH3 radical binds to the oxygen atom 4 is −0.87 eV. The dissociation energy to form H−O and CH3−O on flat CaO(001) is also included for comparison.

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Figure 9. (a) Geometry of the system in the first transition state along the reaction path for the dissociative adsorption of CH4 at the step. (b) The second transition state along the reaction path for methane dissociative adsorption at the step.

smaller than the activation energy for Na-doped CaO(001) surface which is 0.75 eV. The reaction path has two peaks, and we show the structure of the system at these peaks (the two transition states) in Figure 9. The first transition state (Figure 9a) entails the formation of an H−O bond, with an oxygen atom in the step, and the stretching of the H−C bond. In the second transition state, the CH3 radical rotates so that it can make a bond with an oxygen atom on the terrace. The fact that the CH3 radical at the transition state is planar and is fairly far from the surface suggests that the radical can easily move into the vacuum.

position of the dopant is controlled by thermodynamics (rather than the kinetics of doped-oxide formation), most of the dopants in the surface will be located at the step edge. Several binding sites for the dissociation fragments (CH3 and H) were examined. The dissociation energies are given in Table 2. The energy of dissociative adsorption resulting in fragments that bind to the oxygen atoms 1 and 4 is −0.87 eV (exoergic). Dissociative adsorption to this final state is more exoergic than on a flat, doped CaO surface. However, the distance between the carbon atom in CH3 and the hydrogen atom in the hydroxyl, in this final state, is very large (i.e., 4.95 Å). When this is the case, we expect the activation energy to be large because the C−H bond is stretched without simultaneously forming bonds with the final resting place. This propensity rule is useful for avoiding calculating Ea for some of the final states. On the basis of this argument, we conjecture that the activation energy for the dissociative adsorption reaction that results in fragments bound to the oxygen atoms 1 and 4 (which are far from each other) is larger than the activation energies of the reaction with the following bonding sites for the fragments: H bound to the oxygen atom 1 and CH3 bound to the oxygen atom 3. The conclusion reached by using this rule is in direct conflict with the Brønsted−Evans−Polanyi rule which states that the reaction having the highest binding energy for products has the lowest activation energy. However, we caution that these qualitative arguments need to be verified by calculations in the future. Because of these considerations, we calculated the activation energy only for the dissociation resulting in CH3 bound to the oxygen atom 5 and H bound to oxygen atom 1 (see Figure 7 for the final state structure and Figure 8 for the NEB results). The activation energy is equal to 0.43 eV. This is substantially

7. DISCUSSION AND CONCLUSIONS The O−Ca bond in CaO is very strong, and this makes it unsuitable for oxidation catalysis by a Mars−van Krevelen mechanism. Doping with LVDs lowers the energy of oxygenvacancy formation and activates the oxygen atoms near the dopant, causing them to bind H and CH3 much more strongly than they do on the undoped CaO. The CH3 radical desorbs and initiates reactions that lead to ethane formation, which is in agreement with the experiments1,2,63−65 All dopants studied here lower, substantially, the activation energy for dissociative adsorption of methane, with Li being the most effective. The LVDs act by creating a hole in the valence band that makes the doped-oxide surface a Lewis acid. The presence of the hole increases substantially the binding energy of a Lewis base (e.g., H or CH3) to the surface, and therefore it increases the energy of dissociative adsorption of methane. We have seen similar behavior on La2O3 doped with LVDs,23,33 and we have postulated that this behavior is general: it is valid for any oxide surface doped with any LVD dopant. 7120



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MgO-Based Catalysts for the Oxidative Coupling of Methane. Catal. Rev.Sci. Eng. 2011, 53, 424−514. (3) Metiu, H.; Chrétien, S.; Hu, Z.; Li, B.; Sun, X. Chemistry of Lewis Acid-Base Pairs on Oxide Surfaces. J. Phys. Chem. C 2012, 116, 10439−10450. (4) Kresse, G.; Hafner, J. Ab-Initio Molecular-Dynamics for LiquidMetals. Phys. Rev. B 1993, 47, 558−561. (5) Kresse, G.; Hafner, J. Ab-Initio Molecular Dynamics Simulation of the Liquid-Metal Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B 1994, 49, 14251−14269. (6) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (7) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169−11186. (8) Blöchl, P. E. Projector Augmented-Wave Method. Phy. Rev. B 1994, 50, 17953−17979. (9) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758− 1775. (10) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (11) Henkelman, G.; Johannesson, G.; Jonsson, H. Methods for Finding Saddle Points and Minimum Energy Paths. In Progress in Theoretical Chemistry and Physics; Schwartz, S. D., Ed.; Kluwer Academic: Dordrecht, 2000; pp 269−300. (12) Chrétien, S.; Metiu, H. O2 Evolution on a Clean Partially Reduced Rutile TiO2(110) Surface and on the Same Surface Precovered with Au1 and Au2: The Importance of Spin Conservation. J. Chem. Phys. 2008, 129, 0747705. (13) Chrétien, S.; Metiu, H. Density Functional Study of the CO Oxidation on a Doped Rutile TiO2(110): Effect of Ionic Au in Catalysis. Catal. Lett. 2006, 107, 143−147. (14) Shapovalov, V.; Metiu, H. Catalysis by Doped Oxides: CO Oxidation by AuxCe1‑xO2. J. Catal. 2007, 245, 205−214. (15) Pala, R. G. S.; Metiu, H. Modification of the Oxidative Power of ZnO(1 0 1̅ 0) Surface by Substituting Some Surface Zn Atoms with Other Metals. J. Phys. Chem. C 2007, 111, 8617−8622. (16) Yang, Z.; Luo, G.; Lu, Z.; Hermansson, K. Oxygen Vacancy Formation Energy in Pd-Doped Ceria: A DFT + U Study. J. Chem. Phys. 2007, 127, 074704. (17) Nolan, M.; Soto Verdugo, V.; Metiu, H. Vacancy Formation and CO Adsorption on Gold-Doped Ceria Surfaces. Surf. Sci. 2008, 602, 2734−2742. (18) Nolan, M. Healing of Oxygen Vacancies on Reduced Surfaces of Gold-Doped Ceria. J. Chem. Phys. 2009, 130, 144702. (19) Yeriskin, I.; Nolan, M. Effect of La Doping on CO Adsorption at Ceria Surfaces. J. Chem. Phys. 2009, 131, 244702. (20) Camellone, M. F.; Fabris, S. Reaction Mechanisms for the CO Oxidation on Au/CeO2 Catalysts: Activity of Substitutional Au3+/Au+ Cations and Deactivation of Supported Au+ Adatoms. J. Am. Chem. Soc. 2009, 131, 10473−10483. (21) Yang, Z. X.; He, B. L.; Lu, Z. S.; Hermansson, K. Physisorbed, Chemisorbed, and Oxidized CO on Highly Active Cu-CeO2(111). J. Phys. Chem. C 2010, 114, 4486−4494. (22) Roldan, A.; Boronat, M.; Corma, A.; Illas, F. Theoretical Confirmation of the Enhanced Facility to Increase Oxygen Vacancy Concentration in TiO2 by Iron Doping. J. Phys. Chem. C 2010, 114, 6511−6517. (23) Li, B.; Metiu, H. DFT Studies of Oxygen Vacancies on Undoped and Doped La2O3 Surfaces. J. Phys. Chem. C 2010, 114, 12234−12244. (24) Szabova, L.; Camellone, M. F.; Huang, M.; Matolin, V.; Fabris, S. Thermodynamic, Electronic and Structural Properties of Cu/CeO2 Surfaces and Interfaces from First-Principles DFT + U Calculations. J. Chem. Phys. 2010, 133, 234705. (25) Wang, X. Q.; Shen, M. Q.; Wang, J.; Fabris, S. Enhanced Oxygen Buffering by Substitutional and Interstitial Ni Point Defects in

It is very difficult to compare these calculations to the experiments in part because we are never quite certain that the prepared catalysts are doped oxides with the dopant in the surface layer. In addition, calculations on other systems show that a Lewis base adsorbed on the surface of an oxide doped with an LVD will tend to cancel the effect the dopant has on the chemistry of the surface.31 In other words, if a hydroxyl is present on a surface doped with an LVD (e.g., Li-doped CaO), the chemistry of that surface (e.g., the energy to make an oxygen vacancy, its ability to bind CH3) is closer to that of the undoped oxide (e.g., CaO) than to that of the doped oxide (e.g., Li-doped CaO). This chemical compensation effect takes place, roughly, because the adsorption of a Lewis base, such as H, fills the hole created by the LVD. The extent to which the surface is compensated by hydroxyls is not known experimentally. Finally, at the high temperatures used in methane activation, it is possible that the model used in the calculations is unstable: the dopant may leave its site and travel on the surface.1,2 Nevertheless, numerous experiments show that oxides doped with LVDs are more effective for alkane activation than the undoped oxides. This is in agreement with the trends described here. Exploratory calculations of the chemistry at a step on the CaO(001) surface doped with Na show that the step is more active than the flat surface. The dopants prefer to be located at the step edge and the energy of dissociative adsorption reaction increases, while the activation energy decreases (as compared to the doped surface without steps).

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ASSOCIATED CONTENT

* Supporting Information S

Animation (.avi file) showing the reaction of methane with the doped oxide. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel 805-893-2256; fax 805-893-4120; e-mail metiu@chem. ucsb.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support was supplied by the National Science Foundation (EFRI-1038234) and the Air Force Office of Scientific Research (FA9550-12-1-0147). We acknowledge support from the Center for Scientific Computing at the California NanoSystems Institute and the UCSB Materials Research Laboratory (an NSF MRSEC, DMR-1121053) funded in part by NSF CNS-0960316 and Hewlett-Packard. Use of the Center for Nanoscale Materials was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract DE-AC02-06CH11357.

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REFERENCES

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Methane Dissociation on Li-, Na-, K-, and Cu-Doped Flat and Stepped

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