Dissociation of Methane on La2O3 Surfaces Doped with Cu, Mg, or Zn

ARTICLE pubs.acs.org/JPCC

Dissociation of Methane on La2O3 Surfaces Doped with Cu, Mg, or Zn Bo Li and Horia Metiu* Department of Chemistry & Biochemistry, University of California, Santa Barbara, California 93106-9510, United States ABSTRACT: We use density functional theory to examine methane dissociative adsorption on La2O3 substitutionally doped with Cu, Mg, or Zn. We find that these dopants activate the surface oxygen atoms and make methane dissociation exothermic. Cu-doped lanthana is very active, but it loses oxygen too easily and the surface is likely to be reduced at the temperatures at which methane dissociates. The reduced surface has lower activity. The effect of Mg doping on methane activation is less than that of Zn. We focus, therefore, on Zndoped lanthana and calculate the activation barrier for methane dissociation. We suggest that, for dissociative adsorption, the Brønsted
Evans
Polanyi rule needs to be modified to take into account not only the binding energy of the products but also the distance between the fragments formed by dissociation. We also show that an oxygen vacancy on the Zn-doped lanthana surface adsorbs oxygen from the gas and converts it into a species that should be described as O2
. This reacts with methane and dissociates it. Our main conclusion is that Zn-doped lanthana is a much better catalyst than lanthana, for methane activation, if one can prepare it so that the Zn dopants are in the surface layer. Unfortunately, the calculations show that the Zn atom prefers to be located in the bulk (in the absence of gases) and its influence on the chemistry of the surface, when this happens, is substantially diminished.

1. INTRODUCTION Pure1
4 La2O3 and La2O3 doped with Sr,5
8 Cu,9 Zn,10Mg,11 or Fe12 have been used as catalysts for oxidative coupling of methane (OCM) to ethylene. La2O3 is used frequently to catalyze this reaction because it is very stable and is less likely to oxidize methane to CO2 and water, at the high temperatures required by the OCM reaction. So far, the high temperatures, low yields, and low selectivity make lanthana-based catalysts for OCM impractical for commercial applications. It is hoped that doping lanthana with appropriate cations may lower the temperature at which oxidative coupling occurs and increase methane conversion without harming selectivity. In a previous paper,13 we used density functional theory (DFT) to calculate the energy of oxygen-vacancy formation, ΔEv, on Cu-, Zn-, Mg-, Fe-, or Al-doped La2O3 (001) and (011) surfaces. We found that these dopants cause a very substantial lowering of ΔEv from 6.44 eV for pure La2O3(001) to 0.52, 2.01, and 2.59 eV for La2O3(001) doped with Cu, Zn, or Mg, respectively. Because the energy of oxygen-vacancy formation is a good qualitative descriptor of the oxidative power of an oxide,14
18 we examine here the ability of Cu-, Mg-, and Zndoped La2O3 surfaces to break the C
H bond in methane. Previous work18
21 has shown that some dopants facilitate the dissociative adsorption of methane because the fragments (CH3 and H) can bind strongly to the oxygen atoms activated by the presence of the dopant. These findings suggest that Cu-, Mg-, and Zn-doped La2O3 surfaces may be able to break the C
H bond in methane at lower temperatures than La2O3. In the present work, we use density functional theory to test this r 2011 American Chemical Society

suggestion. The method of computation is described in section2. Sections 3 and 4 present results on methane dissociation on Cuand Mg-doped lanthana, respectively. We find that the dissociation energy is higher (i.e., the reaction is more exothermic) on Cu-doped lanthana (CuLa2O3) than on Mg-doped lanthana (MgLa2O3). However, CuLa2O3 loses oxygen very easily and the surface is likely to be reduced at the high temperatures at which methane activation takes place. Zn-doped lanthana (ZnLa2O3) occupies the middle ground: it is more reactive than MgLa2O3, and it does not lose oxygen as readily as CuLa2O3. For this reason, we explore methane activation by Zn-doped lanthana in more detail in section 5. Sections 5.2 and 5.3 present the dissociation energies of methane on ZnLa2O3(001) and ZnLa2O3(011), respectively. The reaction is exothermic on both surfaces, and the reaction energies are surprisingly similar even though the structures of the two faces are very different. The activation energy for methane dissociation on ZnLa2O3(001) is discussed in section 5.4. We find that the activation energy for methane dissociation on ZnLa2O3 is very low (0.58 eV). We have examined two reaction pathways: one leads to H and CH3 bound to surface oxygen atoms (state A) and the other to H bound to oxygen and CH3 bound to Zn (state B). State B has a smaller binding energy than state A (binds less strongly to the surface), but the activation energy to reach B is much smaller than that for reaching A. This seems to violate the Brønsted
Evans
Polanyi Received: May 27, 2011 Revised: July 29, 2011 Published: August 03, 2011 18239

dx.doi.org/10.1021/jp2049603 | J. Phys. Chem. C 2011, 115, 18239–18246

The Journal of Physical Chemistry C

ARTICLE

(BEP) rule.22,23 This rule has been tested extensively and was found to work well for metals.24
35 Here, we suggest that, in the case of dissociative adsorption, the BEP rule needs to be modified to take into account not only the binding energy of the products but also the distance between the binding sites of the fragments. The larger this distance is, the higher the activation energy. We suggest that the pathway to state B has a lower activation energy because, in state B, the fragments are closer to each other. The fragments have a better chance to bond to the surface while the C
H bond is being stretched, and this lowers the activation energy. In section 5.5, we show that gaseous O2 adsorbs on an oxygen vacancy at the surface of ZnLa2O3(001) and it is converted into an O2
species, which reacts with methane and dissociates it to form OH and OCH3. In section 5.6, we show that all three dopants prefer to be located in the bulk. From this location, they still influence surface reactivity, but the effect is smaller than when the dopant is in the surface layer.

2. COMPUTATIONAL METHOD The calculations reported here were performed by using periodic, spin-polarized DFT as implemented in the Vienna Ab-initio Simulation Package (VASP).36
39 The electron
ion interactions are described by the projector augmented wave (PAW) method proposed by Bl€ochl40 and implemented by Kresse.41 We used the rPBE functional42 and a plane-wave basis set with an energy cutoff of 400 eV. The La2O3 slab had 10 atomic layers and a 15 Å vacuum region. A 3  3 surface cell was employed in the calculations. Only the Γ point was used in the kmesh sampling. 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 0.02 eV/Å. The dissociative adsorption energy, Edisso, is calculated from Edisso ¼ E½CH3 , H
ECH4 ðgÞ
Es where E[CH3, H] is the energy of the oxide slab with H and CH3 adsorbed on its surface, ECH4(g) is the energy of gaseous methane, and Es is the energy of the oxide slab prior to methane adsorption. The activation energy was calculated with the nudged elastic band (NEB) method.43,44 As recommended in previous work,14,45 when we calculate the reaction path, we keep the spin polarization constant (equal to that of the reactants). We impose this spin conservation because any reaction that requires a “spin flip” to reach the final state is likely to have a low rate.

3. CH4 DISSOCIATION ON CU-DOPED LA2O3(001) Doping the La2O3(001) surface with Cu reduces13 the energy of oxygen-vacancy formation from 6.44 to 0.52 eV and also causes a large rearrangement of the oxygen atoms on the surface (see Figure 1a). The lanthanum atom in the surface layer of La2O3(001), which is replaced by Cu, is coordinated with six oxygen atoms, making three shorter bonds (2.36 Å) and three longer ones (2.76 Å) (from Table 2 in ref 13). The Cu dopant is coordinated with only three oxygen atoms, two in the top layer and one in the second. The two bonds in the first layer have an equal length of 1.82 Å. The bond to the atom in the second layer is 1.86 Å long. These bonds are much shorter than the La
O bond. Note that the geometry of the CuLa2O3(001) surface is such that one surface oxygen atom, which had been bonded to the La atom that was replaced with Cu, does not make a bond

Figure 1. Dissociation of CH4 on Cu-doped La2O3(001) (CuLa2O3(001)). (a) The surface atoms in CuLa2O3(001). (b) The lowest-energy state of dissociated CH4 on CuLa2O3(001). (c) The next-lowest energy of dissociated CH4 on CuLa2O3(001). (d) The surface atoms on the reduced CuLa2O3(001); the dashed line indicates the site from which an oxygen atom was removed. (e) The lowest-energy state for the dissociated CH4 on reduced CuLa2O3(001). (d) The next-lowestenergy state for the dissociated CH4 on reduced CuLa2O3(001). Edisso is the dissociation energy, and dC
H is the bond distance of the adsorbed hydrogen atom and carbon atom in the adsorbed CH3 after CH4 dissociation (in Å).

with Cu (the dotted line in Figure 1a represents this broken bond). This under-coordinated oxygen atom is easiest to remove and is the most reactive. The Cu dopant is the only one, among those studied here, that causes a symmetry breaking in the positions of the oxygen atoms. The results for the dissociative adsorption of methane on CuLa2O3(001) are shown in Figure 1b,c. In the lowest-energy configuration (Figure 1b), CH3 binds to an oxygen atom bonded to Cu and H binds to the under-coordinated oxygen atom (whose bond to the Cu is broken). The dissociation energy Edisso is
1.96 eV, in contrast with dissociation on undoped La2O3(001), which is endothermic by 4.45 eV. We also tested whether one of the fragments might bind to the dopant. We found that CH3 can bind to the undercoordinated oxygen atom, and H to Cu (see Figure 1c), but this state has a higher energy: Edisso =
0.53 eV. These two states (Figure 1b,c) have the lowest energy among all the states we have examined. The binding energy of molecularly adsorbed methane to the surfaces examined here is very small. Because methane activation is carried out at temperatures between 500 and 800 °C (depending on the products desired), the residence time of the molecular methane on the surface is very short. For this reason, we need not calculate the binding energy of molecular CH4. Because the energy of vacancy formation on CuLa2O3(001) is very low, we suspect that the doped oxide will form oxygen vacancies at the temperatures at which methane dissociative adsorption is likely to take place. Because of this, we examined the dissociative adsorption on CuLa2O3(001) that has an oxygen vacancy on it. The easiest oxygen atom to remove is the undercoordinated one, and the structure of the reduced surface is shown in Figure 1d. We found that methane dissociative adsorption on this reduced surface is endothermic for all the product structures we have examined (see Figure 1e,f for the 18240

dx.doi.org/10.1021/jp2049603 |J. Phys. Chem. C 2011, 115, 18239–18246

The Journal of Physical Chemistry C

ARTICLE

The MgLa2O3(011) face is slightly more reactive than MgLa2O3(001), but the dissociative adsorption energy for the two final states shown in Figure 2b,d is small. It is uphill by 0.91 eV for the state shown in Figure 2c. In addition, the H-to-CH3 distances in the two states for which the dissociation is exothermic are rather large. Our qualitative conclusion is that MgLa2O3 is not a promising catalyst for CH4 activation.

5. CH4 DISSOCIATION ON ZN-DOPED LA2O3 SURFACES

Figure 2. Structures of CH4 dissociation on Mg-doped La2O3(001) (a) and (011) (b, c, d). Edisso is the energy of dissociation adsorption in eV, and dC
H is the distance of the adsorbed hydrogen atom and carbon atom in the adsorbed CH3 after CH4 dissociation (in Å). O4 and O6 indicate the four-coordinated or six-coordinated oxygen atom, respectively.

lowest-energy product structures). These dissociation energies are fairly high, and we conclude that the reduced surface is not reactive.

4. CH4 DISSOCIATION ON MG-DOPED LA2O3 SURFACES Previous work13 has shown that doping La2O3(001) with Mg maintains the symmetry of the oxygen atoms but changes the bonding scheme. The La atom replaced by Mg had six bonds with the surrounding oxygen atoms: three are 2.36 Å long, and the other three are 2.76 Å long. The Mg dopant binds only to the three oxygen atoms located in the top oxygen layer, which form an equilateral triangle. These three bonds have equal lengths of 2.05 Å and are substantially shorter than the bonds La made with the same oxygen atoms. The other three oxygen atoms, which had been bonded to the La, are now located 3.31 Å away from the dopant; they are not bonded to Mg. The energy to make an oxygen vacancy on the surface, near Mg, is 2.59 eV for a fourcoordinated oxygen atom (O4, in the top layer) and 2.57 eV for a six-coordinated oxygen atom (O6, in the second layer). The most likely sites for dissociative adsorption of methane on MgLa2O3(001) are shown in Figure 2a. The dissociation of methane on MgLa2O3(001) is uphill by 0.34 eV. The large distance (3.32 Å) between the C atom in the CH3 fragment and the hydrogen atom in the hydroxyl formed during dissociation suggests that the activation energy for dissociating into this final state ought to be large. We base this statement on the following argument. The energy required for breaking the C
H bond in methane, in the gas phase, is very large. Stretching the C
H bond, to break it, requires quite a bit of energy and the activation energy is very large, unless fragments made start making bonds with the surface as the bond is stretched. In the dissociated state shown in Figure 2a, the distance between the fragments is large (3.32 Å), and this means that, to reach this state, we must stretch the C
H bond without the benefit of forming new bonds with the surface. The activation energy for dissociation adsorption will be high.

5.1. Introduction. Of the three dopants studied here, Zn is the most interesting. The energy of oxygen-vacancy formation for Cu-doped La2O3 is rather low. Methane is a fairly good reductant, and therefore, we suspect that Cu-doped lanthana will be reduced at the high temperature and low oxygen concentration used in OCM. Our calculations show that the reduced CuLa2O3(001) is not reactive. As a general rule, if the reaction consumes oxygen atoms from the surface layer of an oxide catalyst, a very low energy for oxygen-vacancy formation is not favorable to catalysis. To complete the catalytic cycle, the oxygen atoms removed from the surface must be replaced by oxygen atoms from the gas. The easier it is for the catalyst to lose oxygen from the surface, the harder it is to gain it back from the gas. Good oxide catalysts are those that lose oxygen easily, but not too easily. These qualitative arguments suggest that Cu doping is not the best system among those examined here. The MgLa2O3 catalyst has the opposite problem. Lanthana is a very unreactive oxide (it is used in methane coupling because it does not combust methane readily, even at the high temperatures required for OCM), and Mg does not increase its ability to bind dissociatively CH4. The ZnLa2O3 system has intermediate properties between the Cu-doped and the Mg-doped lanthana, and for this reason, we studied it in more detail. We calculated the energy of dissociative adsorption of methane on the (001) and (011) faces. In addition, we calculated the activation energy for methane dissociation by two mechanisms: one that results in the formation of OH and OCH3 (H and CH3 bound to surface oxygen atoms), and another that forms OH on the surface and a CH3 bound to Zn. Also, we show that gaseous O2 adsorbs at the oxygen-vacancy site and becomes activated so that it reacts with gas-phase methane and dissociates it. Finally, the influence from the dopant’s location on methane activation is discussed. 5.2. CH4 Dissociation on Zn-Doped La2O3(001). The surface La atom being replaced by the Zn dopant has three short bonds (2.01 Å) with the oxygen atoms in the first layer and three longer ones (3.36 Å) with the oxygen atoms in the second layer (see Table 2 in ref 13). Each group of three oxygen atoms forms an equilateral triangle. The Zn dopant binds only to the three oxygen atoms in the top surface layer and makes with them shorter bonds than La did (2.01 Å instead of 2.36 Å). These three atoms form an equilateral triangle: doping with Zn does not break the local symmetry of the O atoms in La2O3(001). The energies of oxygen-vacancy formation in ZnLa2O3(001) are 2.01 eV, for removing a four-coordinated oxygen atom (O4, in the outermost oxygen layer), and 2.52 eV, for removing a sixcoordinated oxygen atom (O6, in the second oxygen layer). These values are smaller than those for MgLa2O3 and larger than those for CuLa2O3(001). Therefore, we expect that ZnLa2O3(001) is a better oxidant than MgLa2O3 and is not reduced as easily as CuLa2O3(001). 18241

dx.doi.org/10.1021/jp2049603 |J. Phys. Chem. C 2011, 115, 18239–18246

The Journal of Physical Chemistry C

Figure 3. Structures of the dissociated CH4 on Zn-doped La2O3(001). Edisso is the energy of dissociation adsorption in eV, and dC
H is the distance of the adsorbed hydrogen atom and carbon atom in the adsorbed CH3 after CH4 dissociation (in Å). O4 and O6 indicate the four-coordinated or six-coordinated oxygen atom, respectively.

In Figure 3, we show several possible binding sites for the fragments formed by methane dissociation. In the structure having the highest binding energy (Figure 3a), the H atom and the CH3 radical are bound to the oxygen atoms neighboring the Zn dopant. These are the oxygen atoms that are easiest to remove from the surface, and the fact that they form the strongest bonds with the H and CH3 fragments confirms the idea that the energy of vacancy formation is a good qualitative descriptor of the reactivity of the oxygen atoms.46 The oxygen atoms to which the dissociation fragments are bonded are no longer bonded to the Zn atom (see the dashed line in Figure 3a). Deprived of these two bonds, the Zn atom moves toward the bulk, by 0.76 Å, and binds to one of the six-coordinated oxygen atoms in the second layer. The distance between the Zn and this oxygen atom shifts from 3.36 Å, prior to methane dissociation, to 2.18 Å. The dissociation reaction is exothermic by 0.45 eV. Figure 3b shows a structure in which the methyl radical binds to Zn and the H atom to an oxygen near the dopant. The dissociation is exothermic by 0.12 eV. The molecule ZnCH3 has been identified, in the gas phase, by electronic spectroscopy and ESR measurements.47,48 Our calculations on the gas-phase ZnCH3 give a Zn
C distance of 2.05 Å and a binding energy of
0.59 eV; the C
Zn distance in the ZnLa2O3 system is 2.2 Å. A longer bond length between the carbon and the Zn dopant is expected, because the Zn atom in ZnLa2O3 has additional bonds with the surface oxygen atoms as compared to the ZnCH3 molecule. Figure 3 shows additional structures, generated by the dissociative adsorption of methane, in which the methyl radical is

ARTICLE

bound to an oxygen in the upper layer, near the Zn, and the hydrogen is bound to an oxygen in the second layer (Figure 3c) or to the Zn (Figure 3d). In these cases, the reaction is endothermic by 0.32 and 1.14 eV, respectively. 5.3. CH4 Dissociation on Zn-Doped La2O3(011). The structure of the ZnLa2O3(011) surface was described in our previous paper.13 Zn makes three bonds with the oxygen atoms, whose length is ≈2 Å. These bonds are much shorter than the bonds of La to the same O atoms in undoped La2O3(011). The energies of oxygen-vacancy formation in Zn-doped La2O3(011) are13 2.13 eV, for an O4 atom, and 2.38 eV, for an O6 atom. Within the errors made by DFT calculations, these values are essentially the same as the ones obtained for ZnLa2O3(001). Figure 4 shows various structures of CH4 dissociated on ZnLa2O3(011). Two states (Figure 4e,f) have practically the same energy, namely,
0.45 eV (exothermic). In Figure 4f, the methyl binds to an O6 atom while the hydrogen binds to an O4 atom; in Figure 4e, the methyl and the H exchange places. The dissociation energy on ZnLa2O3(011) is practically the same as that on ZnLa2O3(001) (Figure 3a). This is not surprising, if one notes that the two faces have roughly the same surface energy, which indicates (roughly) the same degree of under-coordination. On the other hand, this same result is surprising given the substantial difference in the surface structure and in the manner in which Zn binds to oxygen atoms on these two faces. 5.4. Activation Energy for CH4 Dissociation on ZnLa2O3(001). It is widely believed that the rate-limiting step in methane activation is the breaking of the C
H bond. On oxide catalysts, breaking this bond requires high temperature. Besides making the process expensive, the high temperature hurts selectivity: the fragments formed by dissociation are reactive, and since they are formed at high temperature, they are likely to react with oxygen (from gas or from the surface) and form CO2 and water. To avoid this, we need to modify the oxide surface to lower the activation energy for breaking the C
H bond. Doping is one way of achieving this. We calculated the activation energy for the dissociative adsorption of CH4 for two pathways: one leading to the structure shown in Figure 3a and the other to the structure shown in Figure 3b. Besides being relevant to methane activation, these calculations bring out an interesting aspect in the interpretation of the Brønsted
Evans
Polanyi rule.22,23 According to the current interpretation of the BEP rule, the activation energy for the reaction leading to the products shown in Figure 3a should be lower than that leading to those shown in Figure 3b, because the products in the former have higher binding energy. Here, we argue that, for dissociative adsorption, or for fragmentation of adsorbed molecules, the BEP rules should consider two parameters: one is the binding energy of the products, and the other is the distance between the binding sites of the fragments formed by dissociation. The role of these parameters can be understood by examining the most naive “derivation” of the rules,49 which assumes that the reactants and the products can be represented by two diabatic potential energy surfaces having a parabolic form (see Figure 5). R represents the reaction coordinate along the reaction path. The blue curve in this figure is the diabatic energy surface of the reactants, and the purple curve is that of the reaction products (labeled prod. 1). The activation energy is (roughly) at the intersection of the two parabolas (E1 in the figure). Consider now a “similar” reaction, one that starts from the same reactants but yields different products (labeled prod. 2), whose potential energy surface is the yellow parabola. We put the 18242

dx.doi.org/10.1021/jp2049603 |J. Phys. Chem. C 2011, 115, 18239–18246

The Journal of Physical Chemistry C

ARTICLE

Figure 4. Structures of the dissociated CH4 on Zn-doped La2O3(011). Edisso is the energy of dissociation adsorption in eV, and dC
H is the distance of the adsorbed hydrogen atom and carbon atom in the adsorbed CH3 after CH4 dissociation (in Å). O4 and O6 indicate the four-coordinated or sixcoordinated oxygen atom, respectively.

word “similar” in quotation marks because it is difficult to find a precise definition of this term; one relies on common sense to decide if two reactions are similar. For simplicity, we assume that the distance between fragments (i.e., the value of R where the product surface has a minimum) is the same for both products. Because the products, whose potential energy is represented by the yellow curve, bind more strongly than the products represented by the purple curve, the activation energy E2 for forming the “yellow products” is smaller than that for forming the “purple products”. The lower the binding energy of the products of similar reactions, starting from the same reactants, the lower the activation energy. This is the standard interpretation of the BEP rule. The validity of the “derivation” is questionable, given the simplifications made by the model, but the rule works for a very large number of systems for which the structure of the activated complex resembles that of the products. Compare now the “purple reaction” to the “green reaction” having the potential energy surface labeled prod. 3. The prod. 3 has the same binding energy as the purple prod. 1, but the distance R3 between the fragments produced by the “green dissociation reaction” is now much larger than R2. According to the customary interpretation of the BEP, which takes into account only the binding energy, the purple and the green reactions should have the same activation energy. This is obviously not true: the activation energy E3 of the green reaction is much higher than the activation energy E1 of the purple reaction. From this crude argument, we conclude that, the further the fragments produced by the reaction are from each other, the larger the activation energy (an upper limit for the activation energy is the dissociation energy). This crude analysis tells us that, in applying the BEP rule, we must consider both the binding energy of the products and the distance between the binding sites of the dissociation products.

Figure 5. Schematic diagram of the Brønsted
Evans
Polanyi rule. Two parameters should be taken into account: dissociation energy (E) and reaction coordinate (R).

The suggestion that this distance should matter is reasonable even if we ignore this crude model and use common sense. Dissociative adsorption or the dissociation of an adsorbate takes place by stretching a bond until it breaks. The activation energy is lowered if the fragments make new bonds with the surface, as the bond to be broken is being stretched. Such new bonds are made earlier, during stretching, if the final binding sites of the fragments are close to each other. This is why, in trying to guess which of the many possible final states, for methane dissociative adsorption, will have a lower activation energy, one should consider not only the binding energy of the products (as in BEP) but also the distance between the binding sites. In the case of methane dissociation on Zn-doped La2O3(100), the products in Figure 3a have lower binding energy than those in Figure 3b, but the distance between the fragments is larger in Figure 3a than 18243

dx.doi.org/10.1021/jp2049603 |J. Phys. Chem. C 2011, 115, 18239–18246

The Journal of Physical Chemistry C

Figure 6. NEB calculation of the dissociation of methane on La2O3(001). (A) Calculation with the final structure shown in Figure 3a. (B) Calculation with the final structure shown in Figure 3b. CH4 is initially in the gas phase. The reaction coordinate is the label of the points in the NEB calculation. The left-most point is the initial state (CH4 in gas), and the right-most represents the dissociated molecule.

in Figure 3b. From NEB calculations (shown in Figure 6), it turns out that the barrier of CH4 dissociation leading to the products shown in Figure 3b is equal to 0.58 eV and is smaller than the barrier leading to the products shown in Figure 3a, which is 1.38 eV. This observation strengthens the argument that we made for above: the activation energy depends on the dissociation energy and also on the distance between the dissociated fragments. 5.5. O2 Adsorption on Oxygen Vacancies and Its Activation. We assume here that, after dissociation, the methyl will react further (probably by forming ethane and combustion products) and the hydrogen will be removed from the surface as water. It is believed that the ethylene is formed by oxidative dehydrogenation of ethane. We do not study this complex mechanism here, but concentrate on one of the issues. Water formation is likely to create oxygen vacancies, and it is believed that these are annihilated by reaction with the oxygen from the gas. We examine the latter process and show that O2 adsorbs on the oxygen vacancy on ZnLa2O3(001) and reacts with methane and dissociates it. Figure 7a shows the lowest-energy structure for the O2 molecule adsorbed on a ZnLa2O3(001) surface that has an oxygen vacancy near the Zn dopant. One of the oxygen atoms of the O2 molecule is located at the position of the oxygen atom that was removed to make the oxygen vacancy. The other atom is 2.23 Å away from the Zn atom. This is close enough to assume that an O
Zn bond is formed. The distance between the two oxygen atoms in the adsorbed O2 molecule is 1.36 Å. This is longer than the O2 bond length of the gas-phase oxygen and comparable to that of the gaseous O2
molecule (1.33 Å). The Bader charge on each O atom in the adsorbed O2 is
0.42e. This is consistent with previous calculations,13 which show that the unpaired electrons created when an oxygen vacancy is formed are localized at the vacancy site and are available for the O2 molecule to take. The adsorption energy of O2 at the vacancy site is
2.42 eV. It has been claimed50
52 that O2
is an active oxygen species for OCM, and we find that it reacts with methane, dissociating it and forming the structure shown in Figure 7b. The oxygen atom that was located in the oxygen vacancy makes a hydroxyl, and the other oxygen atom makes a methoxide bound to the Zn dopant (CH3
O
Zn). The reaction is exothermic (
1.88 eV), and the distance between the C atom in CH3 and the H atom in the hydroxyl is 3.07 Å. We have not followed the fate of these fragments because we confine ourself to studying the breaking of the C
H bond.

ARTICLE

Figure 7. (a) The structure of O2 from the gas phase adsorbed in the oxygen vacancy on Zn-doped La2O3(001). The blue spheres indicate the O2 molecule adsorbed from the gas phase. (b) The structure of the dissociated methane molecule at the adsorbed gas-phase O2 molecule in the vacancy.

5.6. Dopant Position: At the Surface or in the Bulk? When one makes doped oxide catalysts, one is not certain that the dopant is located in the surface layer, as assumed here. For this reason, we examined whether the dopants prefer to be located in the surface layer or in the bulk and whether they have any effect on surface chemistry if they are in the bulk. The energy when the dopant is in the fourth cation layer (4.34 Å away from the surface layer) is lower than when the dopant is in the surface layer, by 0.30, 0.74, and 0.61 eV, for Cu, Mg, and Zn, respectively. The dopant does affect the reactivity of the surface oxygen atoms even when it is in the fourth layer, but its effect is less pronounced than when it is in the surface layer. For example, the energy of making an oxygen vacancy when a Zn dopant is in the fourth layer is higher by 1.01 eV than when Zn is in the surface layer. The vacancy formation energy in this case is still much smaller than that of undoped lanthana. The energy of the dissociative adsorption of CH4 increases by 0.36 eV, when the Zn atom is in the fourth layer as compared to when Zn is in the surface layer. This too is lower than in the case of undoped lanthanum oxide. Moreover, the distance between the H and CH3 fragments increases to 4.07 Å. According to the BEP rules, the activation energy for methane dissociative adsorption will be larger than when the Zn dopant is in the outermost layer. For the dopants examined here, both energy and entropy favor the presence of the dopants in the bulk. This reduces substantially, but not completely, the efficiency of the dopant with regard to oxidation and methane dissociation. However, thermodynamic equilibrium is reached during preparation only if the temperature is sufficiently high to ensure dopant mobility. Furthermore, during preparation, the catalyst is in contact with gases (oxygen, or Ar, or N2), and this may favor the segregation of the dopants on the surface. This segregation may also be favored by contact with the reactants during steady-state catalysis. To increase the chance of making doped oxides with dopants in the surface layer, one should avoid high temperature during preparation and try to make very small nanoparticles.

6. CONCLUSIONS In this work, we have examined the chemical properties of systems in which the dopant is located in the outermost layer of the surface. It is very difficult to perform experiments to prove without a doubt that such compounds have been prepared. One could take two extreme views on this question. One view is that what matters is the dopant distribution when the reaction is 18244

dx.doi.org/10.1021/jp2049603 |J. Phys. Chem. C 2011, 115, 18239–18246

The Journal of Physical Chemistry C performed at steady state. Assuming that the temperature is high enough to give the dopants enough mobility, their spatial distribution in the material will also reach a steady state. If the energy of a dopant in the outermost layer is lowered by the presence of gases and adsorbates, then the dopant distribution will reach a steady state with a substantial dopant concentration in the surface layer. If the interaction with the gases does not favor surface segregation and the dopants have enough mobility, then the dopants examined here will be mostly located in the bulk. The other extreme view is that the temperature at which synthesis took place and the reaction temperature are such that the dopants have no mobility. In this case, they are frozen at the sites where they were trapped during catalyst synthesis. If this is the case, one can increase the chance of having dopants in the surface layer by making the doped-oxide particles as small as possible. For most of the experiments that have aimed at making doped oxide catalysts, XRD measurements show that, at low dopant concentration, the dopant makes a solid solution with the host oxide. In this case, the doped oxide has the same structure as the host, but with a slightly changed lattice constant. This indicates the presence of the dopant in the bulk but does not exclude its presence in the surface layer. The XPS measurements are surface-sensitive, and in most preparations, they detect the dopant in an ionic state. One would like to think that these dopants are in the surface region since XPS is surface-sensitive. However, it is conceivable that the dopant makes very small oxide clusters supported on the surface of the host oxide. The catalytic activity of such small clusters is different from that of large ones, and their XPS spectrum is ionic. Thus, XPS is not a good tool for deciding between these two alternatives. It is, however, useful in ruling out the segregation of the dopant to form neutral metal clusters. The most useful surface probe, in this situation, is surface chemistry. One should compare the catalytic activity of the presumed doped catalyst to that of supported dopant
oxide clusters and to those of supported metallic dopant clusters. The latter two catalysts must be prepared intentionally, with the purpose of showing that they have a different catalytic activity than the presumed doped oxide. Given all these uncertainties, we believe that the present calculations should be viewed as a means for improving our chances of finding good, doped-oxide catalysts, rather than firm predictions. We have found that, for the dopants examined here, the doped lanthana is more reactive than the undoped one. We find that the ease with which one can make oxygen vacancies correlates with the reactivity of the surface toward methane dissociation. This is consistent with our previous work.13,46 If a doped oxide is used as an oxidation catalyst by a Mars
van Krevelen mechanism, then one should seek a dopant that makes it easy to make oxygen vacancies, but not too easy. Informally, we call this a moderation principle. The point is that, if the oxygen is very easy to remove, then it is a very good oxidant, but not a good oxidation catalyst, since it is difficult to put the oxygen back. Cudoped lanthanum oxide is an example of this. The oxygen is so easy to remove that it is likely to be lost at a temperature lower than that of methane activation. This means that, under reaction conditions, the catalyst is reduced; our calculations show that the reduced CuLa2O3 does not break the C
H bond efficiently. Mg-doped lanthana is not as active in breaking the C
H bond as is Zn-doped lanthana. For this reason, we examined the latter

ARTICLE

in more detail. We found that the activity of ZnLa2O3(001) is comparable to that of ZnLa2O3(011), even though the fact that the structures of the two faces are very different. We believe that this happens because the two faces have almost the same surface energy, hence the same degree of undercoordination (roughly, the surface energy is the energy to cut bonds to form the surface; the higher the surface energy, the higher the undercoordination). We calculated the activation energy for methane dissociative adsorption on ZnLa2O3(001) for two final states, which differ through the location of the adsorbed H and CH3 fragments formed by dissociation. They are state A, in which both fragments are bound to oxygen, and state B, in which one fragment is bound to oxygen and the other to Zn. The binding energy of state A is lower than that of B. The conventional interpretation of the Brønsted
Evans
Polanyi (BEP) rule would suggest that the activation energy to product A should be lower than that for forming B. However, in state B, the fragments are closer to each other than in state A. Therefore, they are better able to make bonds with the surface as the C
H bond is being stretched to dissociate CH4. We argue that this distance needs to be taken into account when applying BEP rules. The calculations show that the activation energy to reach state B is lower than that for reaching state A, despite the fact that A binds more strongly. In this example, the shorter distance prevails over the higher binding energy. We are in the process of examining other examples to determine whether this observation is accidental or systematic. Finally, we examined the interaction of the gas-phase O2 with the reduced ZnLa2O3(001) surface (reduced means that oxygen vacancies are present). O2 adsorbs in the electron-rich vacancy site and acquires electrons from it. The bond length of this adsorbed O2 is longer than that of gas-phase O2 and comparable to that of gas-phase O2
. This species reacts with CH4 and dissociates it.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We gratefully acknowledge support from the Air Force Office of Scientific Research (Grant FAA9550-06-1-0167) and the Department of Energy (Grant DE-FG02-89ER140048). Computing resources at UCSB have been suported, in part, by the National Science Foundation under Grant No. CHE 0321368. 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 No. DE-AC02-06CH11357. ’ REFERENCES (1) Campbell, K. D.; Zhang, H.; Lunsford, J. H. J. Phys. Chem. 1988, 92, 750. (2) DeBoy, J. M.; Hicks, R. F. Ind. Eng. Chem. Res. 1988, 27, 1577. (3) Hutchings, G. J.; Scurrell, M. S.; Woodhouse, J. R. Catal. Today 1989, 4, 371. (4) Squire, G. D.; Luc, H.; Puxley, D. C. Appl. Catal., A 1994, 108, 261. (5) Xu, M.; Lunsford, J. H. Catal. Lett. 1991, 11, 295. (6) Deboy, J. M.; Hicks, R. F. J. Catal. 1988, 113, 517. (7) Choudhary, V. R.; Mulla, S. A. R.; Rane, V. H. J. Chem. Technol. Biotechnol. 1998, 71, 167. 18245

dx.doi.org/10.1021/jp2049603 |J. Phys. Chem. C 2011, 115, 18239–18246

The Journal of Physical Chemistry C (8) Gonzalez-Cortes, S. L.; Orozco, J.; Moronta, D.; Fontal, B.; Imbert, F. E. React. Kinet. Catal. Lett. 2000, 69, 145. (9) Au, C. T.; Hu, Y. H.; Wan, H. L. Catal. Lett. 1996, 36, 159. (10) Borchert, H.; Baerns, M. J. Catal. 1997, 168, 315. (11) Choudhary, V. R.; Mulla, S. A. R.; Rane, V. H. J. Chem. Technol. Biotechnol. 1998, 72, 125. (12) Sekine, Y.; Tanaka, K.; Matsukata, M.; Kikuchi, E. Energy Fuels 2009, 23, 613. (13) Li, B.; Metiu, H. J. Phys. Chem. C 2010, 114, 12234. (14) Kim, H. Y.; Lee, H. M.; Pala, R. G. S.; Shapovalov, V.; Metiu, H. J. Phys. Chem. C 2008, 112, 12398. (15) Nolan, M.; Verdugo, V. S.; Metiu, H. Surf. Sci. 2008, 602, 2734. (16) Shapovalov, V.; Metiu, H. J. Catal. 2007, 245, 205. (17) Chretien, S.; Metiu, H. Catal. Lett. 2006, 107, 143. (18) Tang, W.; Hu, Z. P.; Wang, M. J.; Stucky, G. D.; Metiu, H.; McFarland, E. W. J. Catal. 2010, 273, 125. (19) Kim, H. Y.; Lee, H. M.; Pala, R. G. S.; Metiu, H. J. Phys. Chem. C 2009, 113, 16083. (20) Mayernick, A. D.; Janik, M. J. J. Phys. Chem. C 2008, 112, 14955–14964. (21) Mayernick, A. D.; Janik, M. J. J. Catal. 2011, 278, 16. (22) Brønsted, J. N. Chem. Rev. 1928, 5, 231. (23) Evans, M. G.; Polanyi, M. Trans. Faraday Soc. 1938, 34, 11. (24) Pallassana, V.; Neurock, M. J. Catal. 2000, 191, 301. (25) Logadottir, A.; Rod, T.; Nørskov, J.; Hammer, B.; Dahl, S.; Jacobsen, C. J. Catal. 2001, 197, 229. (26) Liu, Z.; Hu, P. J. Chem. Phys. 2001, 114, 8244. (27) Nørskov, J. K.; Bligaard, T.; Logadottir, A.; Bahn, S.; Hansen, L. B.; Bollinger, M.; Bengaard, H.; Hammer, B.; Sljivancanin, Z.; Mavrikakis, M.; Xu, Y.; Dahl, S.; Jacobsen, C. J. H. J. Catal. 2002, 209, 275. (28) Michaelides, A.; Liu, Z.; Zhang, C.; Alavi, A.; King, D.; Hu, P. J. Am. Chem. Soc. 2003, 125, 3704. (29) Falsig, H.; Hvolbæk, B.; Kristensen, I.; Jiang, T.; Bligaard, T.; Christensen, C.; Nørskov, J. Angew. Chem., Int. Ed. 2008, 120, 4913. (30) Wang, S.; Temel, B.; Shen, J.; Jones, G.; Grabow, L.; Studt, F.; Bligaard, T.; Abild-Pedersen, F.; Christensen, C.; Nørskov, J. Catal. Lett. 2011, 141, 370. (31) Studt, F.; Abild-Pedersen, F.; Hansen, H.; Man, I.; Rossmeisl, J.; Bligaard, T. ChemCatChem 2010, 2, 98. (32) Bligaard, T.; Norskov, J.; Dahl, S.; Matthiesen, J.; Christensen, C.; Sehested, J. J. Catal. 2004, 224, 206. (33) Barteau, M. A. Catal. Lett. 1991, 8, 175. (34) Hammer, B. Surf. Sci. 2000, 459, 323. (35) Gajdos, M.; Hafner, J.; Eichler, A. J. Phys.: Condens. Matter 2006, 18, 41. (36) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 47, 558. (37) Kresse, G.; Hafner, J. Phys. Rev. B 1994, 49, 14251. (38) Kresse, G.; Furthm€uller, J. Comput. Mater. Sci. 1996, 6, 15. (39) Kresse, G.; Furthm€uller, J. Phys. Rev. B 1996, 54, 11169. (40) Bl€ochl, P. E. Phys. Rev. B 1994, 50, 17953. (41) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758. (42) Hammer, B.; Hansen, L. B.; Nørskov, J. K. Phys. Rev. B 1999, 59, 7413. (43) Henkelman, G.; Johannesson, G.; Jonsson, H. In Progess in Theoretical Chemistry and Physics; Schwartz, S. D., Ed.; Kluwer Academic: Dordrecht, The Netherlands, 2000; pp 269
300. (44) Jonsson, H; Mills, G; Jacobsen, K. W. In Classical and Quantum Dynamics in Condensed Phase Simulation; Berne, B. J., Cicotti, G., Coker, D. F., Eds.; World Scientific Publishing: Singapore, 1998; pp 385
404. (45) Chretien, S.; Metiu, H. J. Chem. Phys. 2008, 129, 074705. (46) Pala, R. G. S.; Metiu, H. J. Phys. Chem. C 2007, 111, 8617. (47) Cerny, T. M.; Tan, X. Q.; Williamson, J. M.; Robles, E. S. J.; Ellis, A. M.; Miller, T. A. J. Chem. Phys. 1993, 99, 9376. (48) McKinley, A. J.; Karakyriakos, E.; Knight, L. B.; Babb, R.; Williams, A. J. Phys. Chem. A 2000, 104, 3528. (49) Masel, R. Chemical Kinetics and Catalysis; Wiley-Interscience: New York, 2001.

ARTICLE

(50) Louis, C.; Lin Chang, T.; Kermarec, M.; Le Vana, T.; Michel Tatibou€et, J.; Chea, M. Catal. Today 1992, 283. (51) Dubois, J.-L.; Cameron, C. J. Appl. Catal. 1990, 67, 49. (52) Biela nski, A.; Haber, J. Oxygen in Catalysis; Marcel Dekker Inc.: New York, 1991.

18246

dx.doi.org/10.1021/jp2049603 |J. Phys. Chem. C 2011, 115, 18239–18246