Methane Dissociation on the Ceria (111) Surface - The Journal of

The complete oxidation of methane into water and carbon dioxide on the (111) surface of ceria is considered within a DFT + U framework in order to gai...
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J. Phys. Chem. C 2008, 112, 17311–17318

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Methane Dissociation on the Ceria (111) Surface Daniel Knapp and Tom Ziegler* Department of Chemistry, UniVersity of Calgary, Calgary, AB T2N 1N4, Canada ReceiVed: May 6, 2008; ReVised Manuscript ReceiVed: August 21, 2008

The complete oxidation of methane into water and carbon dioxide on the (111) surface of ceria is considered within a DFT + U framework in order to gain insight into the coke-free operation of solid oxide fuel cells with ceria-containing anodes. Preferred adsorption sites and energies are determined for CHx (x ) 0, ..., 3), H, and CO, together with transition states and kinetic barriers along the complete pathway from CH4 to H2O and CO2. The results presented are in excellent agreement with existing theoretical and experimental work suggesting that ceria is more easily reduced by CO than by H2 and offer an explanation for the apparently inconsistent observations of carbon coke formation in Ni-ceria anodes and the stable, coke-free oxidation of methane in Cu-ceria anodes. 1. Introduction Solid oxide fuel cells (SOFCs) designed for the direct oxidation of methane and other hydrocarbons based on the classic nickel-yttria-stabilized-zirconia (Ni-YSZ) anode are known to be plagued by carbon coke formation which poisons the fuel cell anode catalyst.1,2 More recent anode designs based on oxide catalysts which do not tend to catalyze carbon-carbon bond formation have shown promise in eliminating coke formation. Ceria, an oxidation catalyst well-known from its use in automotive catalytic convertors,3,4 has found recent application in SOFC anodes.1,5,6 The ability of ceria to transport oxygen tosand readily release oxygen from7sits surface would seem to allow for the direct oxidation of methane without carbon poisoning. The activation of methane is an issue of longstanding interest in the catalysis community and many studies of the interaction of methane, hydrogen and carbon monoxide with ceria have been carried out.3,4 It has been found that CeO2 remains in a fluorite crystal structure upon reduction, even after the creation of a large number of oxygen vacancies.3,8 Studies have demonstrated that CO is a much better reducing agent than H2 with reduction of ceria occurring readily at temperatures as low as room temperature for CO while temperature programmed reduction with H2 shows peaks due to H2O desorption at approximately 800 and 1100 K due to the release of surface and bulk lattice oxygen respectively, with strong OH bands showing at temperatures of up to 673 K.3,9 It is important to note that the reduction is sensitive to the morphology of the sample, that surface adsorbates such as carbonates or hydroxyls may play a complicating role, and that stoichiometric, clean surfaces are much harder to reduce.4,10-13 Experimental results suggest that methane reacts with surface oxygensespecially with coordinatively unsaturated oxygen atoms at, for example, step sitessand that the dissociative adsorption of methane is inhibited if the ceria surface is first reduced. Interestingly, the oxidation of hydrocarbons, CO, and H2 appears to be complete with only traces of partial oxidation products.3,14 Many studies of the direct oxidation of methane in ceriabased solid oxide fuel cells, based on a variety of anode designs, have also been carried out and efforts in this direction date back to 1964.4 Steele et al. showed that ceria could be used to oxidize * Corresponding author. E-mail: [email protected].

methane in a SOFC in 1990,15 and the Gorte group in particular has followed up with a series of detailed studies1,6 establishing ceria as a viable anode catalyst for SOFCs. It has been argued that direct oxidation of methane on ceria is unlikely and that a good hydrocarbon cracking catalyst must also be present,16 and experimental studies of Ni-ceria-YSZ anodes would seem to support this view. The observation of identical performance in Ni-YSZ and Ni-ceria-YSZ cells suggests that CH4 reacts on Ni to form C and H2 and that the current is generated by the reaction of H2 only17,18 with ceria possibly extending the triplephase boundary by virtue of its mixed ionic and electronic conductance. On the other hand, the addition of ceria to Cu-YSZ anodes, where the dissociation of methane is strongly disfavored19 and performance is correspondingly low,1 was found to improve performance significantly.5,18,20 Further studies, comparing the reaction products of Cu-ceria-YSZ and Cu-molybdena-YSZ fuel cells with propylene as the fuel found that the fuel was converted to H2O and CO2 for ceria, and to acrolein for molybdena at low current densities, indicating that the catalytic properties of the cell are determined by the metal oxide and that copper acts primarily as a current collector.8 The role of copper as a current collector is further supported by the observation that replacing copper with gold in ceriabased anodes shows no difference in cell performance.21 The suggested mechanism for oxidation of methane and other hydrocarbons is by the Mars-van Krevelen mechanism with ceria being reduced by the fuel and then reoxidized by oxygen atoms crossing the electrolyte, and indeed Mcintosh et al. have observed improved cell performance when YSZ is first impregnated with ceriasimproving contact between ceria and the oxygen-carrying electrolytesand then with Cu in a later step.8 Improvement of the catalytic activity of ceria-based anodes has also been achieved through the addition of precious metal dopants to the ceria surface in carbon-ceria anodes, indicating that precious metals can greatly enhance the rate of C-H bond scission.22 Despite the considerable experimental work cited above, the adsorption and oxidation of methane on ceria is a process that has yet to be treated theoretically. In this paper, we consider the dissociation of methane on the (111) surface of ceria in order to gain insight into the oxidation of methane on ceria surfaces and in solid-oxide fuel cell anodes in particular. In comparing our results to solid-oxide fuel cells, it is assumed that electrons

10.1021/jp8039862 CCC: $40.75  2008 American Chemical Society Published on Web 10/15/2008

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are transported from the oxygen ions into the current collector (e.g., copper) at the anode through the ceria bulk and that neutral oxygen atoms at the ceria surface are responsible for the oxidation of methane.8,21 Charge transfer is thus assumed to occur at the current collector/ceria interface. 2. Computational Method Density functional theory (DFT) calculations have been performed using the Vienna Ab initio Software Package (VASP),23-26 with projector augmented wave (PAW)27,28 potentials. All calculations are spin-polarized and have been done within the generalized gradient approximation (GGA) with the PBE exchange correlation functional.29 The DFT + U method of Dudarev30 with U ) 5 eV was used to account for localization of the cerium 4f electron in the presence of surface oxygen vacancies.31-33 Thekineticenergycutoffwassetto400eV.TheMonkhorst-Pack method34 was used to generate k-point sets with 3 × 3 × 1 k-points. Cerium and oxygen atoms were fixed in slab geometries at their bulk-truncated positions in a fluorite-type facecentered cubic lattice with a calculated bulk lattice constant of a0 ) 5.49 Å. Nine atomic layers were used in the (111) ceria slabsceria’s most stable surface35-37swith the surface represented by an oblique p(2 × 2) unit cell. The top three atomic layers of the nine layer slab were allowed to relax in all calculations. Test calculations on slabs of up to 18 atomic layers, with up to 9 layers allowed to relax showed a negligible difference of less than 0.04 eV in the energy of CH adsorption as compared to the 9 layer slabs. The slabs were separated along the z-axis, in the direction perpendicular to the surface, by a vacuum region of approximately 11 Å. The contribution of dipole interactions along the z-axis is subtracted from the total energy. Adsorbate and surface geometries were optimized until the forces had converged to less than 0.05 eV/Å. Gas phase energies were calculated in an empty unit cell at the Γ-point only with all other parameters held fixed. Transition states and reaction barriers were calculated with the nudged-elastic band method38 used to test various reaction pathways. The improved tangent estimate39 and climbing-image method40 of Henkelman et al. were used to calculate the tangent to the elastic band at each point and to search out the saddlepoint for the minimum energy path, respectively. The geometry of images along the path was optimized until the total energy of each image in the path had converged to less than 10-3 eV. 3. Results and Discussion 3.1. Ceria (111) Surface. The (111) surface of CeO2 has been shown to be the most stable of the various surfaces as well as the surface which is hardest to reduce by removal of surface oxygen atoms.11,12,35-37,41,42 Given that it is the most prevalent surface as well as being the hardest to reduce, we consider it to be a good starting point for the examination of the baseline reactivity of methane on ceria. The (111) surface exposes a plane of cerium atoms arranged in the triangular lattice of the (111) plane of a face-centered cubic structure with a plane of oxygen atoms sitting above the surface at the 3-fold hollow (3fh) positions and another plane of oxygen atoms lying beneath the cerium plane at the 3-fold filled (3ff) positions (see Figure 1). The surface atoms are only slightly perturbed from their bulk-truncated positions with a slight contraction of the distance between the first and second cerium layers by 0.02 Å. The surface oxygen layers are largely undisturbed and exhibit a contraction of less than 0.01 Å. The cerium–oxygen bond length at the surface is 2.37 Å as compared

Figure 1. Unit cell for a 9-layer ceria slab, showing the (111) surface with high-symmetry sites labeled. Small red spheres represent oxygen atoms, and the larger gray spheres represent cerium atoms.

Figure 2. Density of states for a (111) ceria slab (bottom panel) and for the same slab with a surface oxygen atom removed from each of the top and bottom layers (top panel). The zero in energy is chosen to be the Fermi level of the ceria slab.

to 2.38 Å in the underlying atomic layers. The density of states (DOS) exhibits bulklike characteristics with a valence band of oxygen 2p and cerium 5d states separated from the empty cerium 4f states by a gap of over 2 eV, and from the conduction band of cerium 5d states by a large gap of over 5 eV (see Figure 2). These results are discussed in detail elsewhere.33,35,36,41 Since the primary means of reactivity of ceria appears to be by the Mars-van Krevelen mechanism, it is important to consider the creation of oxygen vacancies on the ceria surface. In order to calculate the vacancy creation energy, an oxygen vacancy was created in each of the top and bottom surface layers of the ceria slab to improve convergence and to prevent the formation of a large dipole moment. In order to have convergence in the energy, it was necessary to use a slab containing fifteen atomic layers, with the middle three layers frozen, and the top six and bottom six layers allowed to relax. The energy of reduction Er ) E(VO¨) + E(O) - E(CeO2), where VO¨ represents the surface with one vacancy, thus obtained is 5.64 eV, and the vacancy creation energy Ev ) E(VO¨) + 1/2E(O2) E(CeO2) is 2.61 eV. Correcting for the difference between the experimental and DFT binding energies for O232,43,44 leads to a vacancy creation energy of 3.35 eV. The vacancy creation energy of 2.61 eV is in quantitative agreement with earlier work by Nolan et al.33 (whose computational method we share) and is somewhat less than what is found by Yang et al.36 using DFT with U ) 0 (Ev ) 3.39 eV) and by Fabris et al.37 using DFT + U with U ) 4.5 eV (Ev ) 4.95 eV). Experimental measurements based on the reduction of bulk CeO2 find that Ev is in the range of 4.6-5.0 eV;45 however, measurements of the reduction of dense, nanocrystalline pellets where oxygen is primarily released from grain boundaries give a vacancy creation energy of roughly

Methane Dissociation on Ceria 1.5-2.3 eV.45 This implies that the energy required to create a surface vacancy would be somewhat lower than that required to create a bulk vacancy and, for the relatively stable (111) surface, theoretical results suggest this difference to be on the order of 0.5 eV.37,46 Unfortunately, known errors in the DFT calculation of the O2 binding energy and a lack of experimental measurements on clean surfaces complicates the comparison between theory and experiment. While the technology developed by Fabris et al.37sin which atomic 4f projectors are replaced by Wannier-Boys functions which by construction avoid a partial overlap with the oxygen 2p states in the valence band for the purpose of calculating the Hubbard contribution to the total energy51soffers some advantages, it appears as though the vacancy creation energies calculated by this method overestimate the vacancy creation energy relative to the experimental values by as much as the results presented here and by Nolan et al.33 underestimate them. Interestingly, Herschend et al. obtain a value of Ev ∼ 3.2 eV on the (110) surface within an embedded cluster approach where electron correlation effects are accounted for within Møller–Plesset perturbation theory.32 This should be compared to the DFT + U values of Ev ) 4.42 eV (Wannier-Boys) and Ev ) 1.99 eV (atomic projectors) obtained by Fabris et al.37 and Nolan et al.42 respectively which bracket the value of Ev ∼ 3.2 eV by 1.2 eV on either side. It should be noted that within plane-wave DFT, better values for Ev might be obtained by setting U ) 0;36 however this choice leads to an unphysical delocalization of the two electrons released from the oxygen-cerium bond. We thus proceed with our method, which correctly describes the localization of the excess electronssincluding the creation of a midgap peak in the density of states (seen in the top panel of Figure 2)33,37 and the localization of the two excess electrons onto two cerium atoms directly neighboring the oxygen vacancy7,31,32swith an awareness that the vacancy creation energy is likely underestimated. 3.2. Hydrogen Abstraction. The first step in the dissociation of methane on the ceria surface is the abstraction of a hydrogen atom from the methane molecule. Of the various high-symmetry sites on the (111) surface (see Figure 1), only the 3fh site on top of the exposed oxygen atom experiences a significant interaction with CHx adsorbates. In searching for a transition state for abstraction of the first hydrogen atom, interactions between the methane molecule and the 3fh oxygen sites were examined by various pathways. In one, the carbon atom is bonded to a 3fh oxygen atom as one of the hydrogen atoms is moved to an adjacent 3fh oxygen site. This leads to a very energetic transition state (shown in the top left panel of Figure 3) with significant distortion of CH4 with a C-H bond length of 1.28 Å and a C-O bond length of 1.64 Å. Because this transition state has C-H bond breaking without simultaneous O-H bond formation, there is a high energy cost of 91 kcal/ mol (3.95 eV) to its formation. A side-on attack in which simultaneous C-O and H-O bond formation onto adjacent 3fh oxygen atoms was also examined; however, it was found that the hydrogen atom is first removed from CH4 by the rebound mechanism before CH3 is able to bond to the adjacent 3fh oxygen atom. The rebound mechanism, with a methyl radical in the gas phase leaving behind a hydrogen atom on the surface (see the top right panel of Figure 3) appears to be the most efficient means for abstraction of the first hydrogen with an energy barrier of 33 kcal/mol (1.44 eV). The methyl radical may then bind to an available 3fh oxygen site after overcoming a small energy barrier (the transition state is shown in the bottom left panel of Figure 3) of 4.8 kcal/mol (0.21 eV). This binding of CH3 to a 3fh oxygen atom is exothermic with a change in

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Figure 3. Transition states for abstraction of the first hydrogen atom from methane (top row) and for the subsequent adsorption of the methyl radical (bottom row). The top left shows the transition state that occurs when the carbon atom is bonded to a 3fh oxygen atom while one of the hydrogen atoms is transferred to an adjacent 3fh oxygen atom. The top right shows the removal of a hydrogen atom by the rebound mechanism. In the bottom left panel, the transition state for the adsorption of a methyl radical is shown, and in the bottom right panel is the transition state to the formation of methanol.

Figure 4. Energies and kinetic barriers along the methane dissociation and oxidation pathway on the (111) surface of ceria. Equilibrium states along the pathway are labeled, and all energies are relative to CH4(g) + slab.

energy of 51 kcal/mol (2.23 eV). The formation of methanol by the attachment of the radical to the same 3fh oxygen that the hydrogen atom is attached to was also examined (Figure 3, bottom right). The formation of methanol on the surface breaks the bonds between the 3fh oxygen atom, and the three neighboring cerium atoms and forms a surface vacancy with methanol departing into the gas phase. This reaction, CH3(g) + *H f CH3OH(g) + VO¨, where VO¨ is a surface oxygen vacancy and *H is an adsorbed hydrogen atom, has an activation barrier of 18 kcal/mol (0.78 eV) with no distinguishable change in the total energy from reactant to product. The energies for these and for subsequent reactions reported in this paper are shown in Figure 4. It is interesting to note that the barrier for hydrogen abstraction on the (111) surface of ceria is lower than the corresponding barriers on the planar (45 kcal/mol) surface of copper19 and larger than those on the planar (24 kcal/mol) surface of nickel.47 This observation is corroborated by experiments on SOFCs which show that Cu-ceria-YSZ anodes have much greater activity than Cu-YSZ with the catalytic behavior determined by ceria,5,8,18,20 while in contrast the addition of ceria to Ni-YSZ anodes is not seen to improve performance, nor

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Figure 5. DOS for hydrogen adsorbed at the 3fh oxygen position on the ceria slab. The reduction of one of the neighboring cerium atoms leads to the appearance of a sharp midgap peak due to the localized 4f state. The zero in energy is chosen to separate the occupied from the unoccupied states.

Figure 6. Isosurface of charge density at 0.5 e/Å3, graphed from states within the energy range of the midgap peak in the DOS. The charge density has the 8-fold symmetry of a 4f orbital. Oxygen atoms are red; the darker gray spheres represent cerium atoms. All three-dimensional isosurface plots in this paper are generated by Visual Molecular Dynamics (VMD).48

prevent coking at higher temperatures.17,18 Both the experimental and theoretical results suggest that nickel is more active than ceria which is in turn more active than copper in the dissociation of methane at the SOFC anode. 3.3. Hydrogen Adsorption. Hydrogen adsorbs at 0.97 Å above the 3fh oxygen position, with no discernible attraction to any of the other high symmetry sites on the (111) surface. The adsorption of hydrogen leads to reduction of one of the three neighboring cerium atoms, with a lengthening of the respective cerium-oxygen bond by 0.26 Å from 2.37 to 2.63 Å. The other two cerium-oxygen bond lengths are increased by a shorter length of 0.20 Å from 2.37 to 2.57 Å and the oxygen atom moves 0.41 Å out from the surface. The reduction of one of the three neighboring cerium atoms shows up as a sharp midgap peak with a width of only 6 meV in the f projected density of states (Figure 5). An analysis of the charge density (Figure 6) and the density of states in the energy range of this peak show that this state is due to one electron localized on the one cerium atom of the three that is furthest from the 3fh oxygen atom. The adsorption energy for hydrogen is 78 kcal/mol (3.37 eV). These results are in excellent agreement with those of Vicario et al.49 who used the DFT + U (U ) 4 eV) method with localized Wannier-Boys projectors37 rather than atomic projectors. They find that the O-H bond length is 0.97 Å and that the cerium-oxygen bond lengths increase by 0.19 and 0.26 Å

Knapp and Ziegler

Figure 7. Density of states for hydrogen adsorbed at the 3fh oxygen position in a smaller p(1 × 2) unit cell. In this case, the reduction of one of the neighboring cerium atoms leads to the appearance of a double peak structure from the tight-binding band of localized 4f states in a linear chain of Ce3+ ions.

for the unreduced and reduced cerium atoms, respectively. They further report an adsorption energy of 82 kcal/mol. One minor difference in their results is that the midgap peak in the density of states is broader in their calculation. Calculations based on their unit cell, which has half the area of the one used here, show that the sharp single peak splits into a broader double peak structure (see Figure 7). This double peak structure arises from the interaction between reduced cerium atoms in adjacent unit cells which form a quasi-1D infinite chain of nearest neighbors with a tight-binding bandwidth (or peak-to-peak distance in the DOS) of 0.27 eV.52 It is interesting to find such close correspondence in the energetics and geometry for hydrogen adsorption given the discrepancy in the values calculated for oxygen vacancy creation by the two different methods for projection of the plane-wave Bloch states on to a local atomic basis as discussed above. 3.4. Methyl Adsorption and Dissociation. Methyl is most strongly adsorbed at the 3fh oxygen position (see Figure 8) with an adsorption energy of 52 kcal/mol (2.26 eV). There is a local minimum with the carbon atom sitting 3.19 Å above the 1f position with a very small adsorption energy of 2.8 kcal/mol (0.12 eV) that is likely due to a weak ionic attraction between the three hydrogen atoms and the three neighboring 3fh oxygen atoms. As in the case of hydrogen adsorption, one of the three cerium atoms neighboring the 3fh oxygen atom is reduced and the bond length between this cerium atom and the oxygen atom is increased by 0.25 Å from 2.37 to 2.62 Å. The other cerium-oxygen bond lengths are increased by 0.19-0.20 Å from 2.37 to 2.56-7 Å. The oxygen-carbon bond length is 1.43 Å, and the 3fh oxygen atom is pulled up an additional 0.39 Å to 1.17 Å above the cerium plane. The density of states (not shown) shows a sharp midgap peak, due to the localization of an electron into the 4f state on the reduced cerium atom. Methyl can dissociate on the ceria surface by transferring a hydrogen atom across a cerium atom to an adjacent 3fh oxygen atom. At the transition state, the two oxygen atoms are 3.59 Å apart, 0.29 Å closer than at equilibrium, and the C-H and O-H distances are 1.54 and 1.22 Å, respectively. The transition state has an energy barrier of 30 kcal/mol (1.30 eV) to the dissociation of methyl into coadsorbed methylene and hydrogen, an endothermic reaction requiring 12 kcal/mol (0.52 eV). 3.5. Methylene Adsorption and Dissociation. Methylene also adsorbs at the 3fh oxygen position but is tilted toward one of the neighboring cerium atoms (see Figure 8) with a carbon-cerium 2 distance of 2.86 Å. The adsorption energy is

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Figure 8. Adsorption geometries (on the left) and transition states (on the right) for the dissociation of hydrogen from CHx (x ) 3, 2, 1) on the (111) surface of ceria. Cerium atoms are labeled for clarity; see text for details.

76 kcal/mol (3.31 eV). The carbon-oxygen bond length of 1.30 Å is 0.13 Å shorter than for *CH3. The three neighouring cerium atoms have cerium-oxygen bond lengths of 2.71 (Ce2), 2.74 (Ce1), and 2.68 (Ce3) Å (relative to 2.37 Å at equilibrium), and the 3fh oxygen atom sits 1.40 Å away from the cerium plane, almost double the clean surface value of 0.78 Å. The shortening of the carbon-oxygen bond and the lengthening of the cerium-oxygen bonds suggests that the cerium-oxygen bonds are being gradually weakened as the carbon-oxygen bond is strengthened. The density of states for adsorbed methylene, shown in the top panel of Figure 9 has an interesting structure with three separate midgap peaks, two of which are occupied, between the valence band and the unoccupied band of 4f states. Examination of the projected density of states for the three cerium atoms neighboring the oxygen-adsorbate complex shows that of the two atoms furthest from the carbon atom (labeled Ce1 and Ce3 in the inset of Figure 9) one is reduced with a sharp peak containing one 4f electron and the other is not. The cerium atom closest to the carbon atom (labeled Ce2) has two occupied 4f peaks and one sharp unoccupied 4f peak, followed by a broader peak of unoccupied 4f states. The projected density of states for the carbon, 3fh oxygen, and hydrogen atoms shows that these 4f peaks from Ce2 lie at the same energy levels as those of the carbon and 3fh oxygen 2p states, with one electron shared among the three atoms and that the hydrogen atoms have no states at these levels. Note that the broad peak in the projected density of state for oxygen seen from -2 to -4 eV is due to interaction of the oxygen 2p states with the delocalized 4d band in the ceria slab. A graph of the charge density in the energy range of the occupied midgap peaks, along with the electron localization function (ELF), is shown in Figure 10. The shape of the charge density isosurface suggests that the occupied 2p orbitals of the carbon and oxygen atoms are bonding with the localized 4f states of Ce2. The electron localization function shows regions of localization due

Figure 9. DOS for the ceria slab with adsorbed CH2. (CH2 Ads) (111) slab with nine atomic layers and adsorbed CH2. (Ce1, 2, and 3) Projected DOS for each of the three cerium atoms neighboring the oxygen-adsorbate complex, as labeled in the inset. (C, 3fh O, H) Projected DOS for the carbon, 3fh oxygen, and hydrogen atoms. Note that the y-axis scale is varied from plot to plot for clarity.

Figure 10. Charge density and ELF for CH2 adsorption. The charge density, on the left, is plotted at an isovalue of 0.10 e/Å3 from wave functions in the energy range -0.185 f 0 eV encompassing the occupied midgap peaks of the DOS shown in the top panel of Figure 9. The ELF is shown along a plane defined by the positions of the C, O, and Ce atoms.

to covalent bonding between the carbon and oxygen atoms and between the carbon and cerium atoms. It can thus be argued that the tilting of the carbon-oxygen bond toward one of the neighboring cerium atoms is due to bonding of the 2p orbital of carbon with the 4f orbital on the partially reduced Ce atom. The lowest barrier to the dissociation of one of the hydrogen atoms from CH2 to an adjacent 3fh oxygen atom is found by moving a hydrogen atom to another of the 3fh oxygen atoms connected to Ce2. The energy barrier along this pathway is 14 kcal/mol (0.62 eV). The associated transition state pulls the CH2-O complex away from the far cerium atoms and stretches the Ce1-O and Ce3-O distances to 3.14 and 3.07 Å, respectively. While the 3fh oxygen atom is pulled away from

17316 J. Phys. Chem. C, Vol. 112, No. 44, 2008 the ceria plane to a height of 1.81 Å, the Ce2-O distance is only increased by 0.01 Å. The carbon-hydrogen bond length is stretched to 1.31 Å at the transition state, with the hydrogen-adjacent oxygen distance shortening to 1.44 Å. The adjacent 3fh oxygen atom is lifted up from the cerium plane by 0.25 Å to 1.03 Å as it rises to meet the transferred hydrogen atom. The overall reaction *CH2 + 2*H f *CH + 3*H is endothermic by 5.1 kcal/mol (0.22 eV). The desorption of formaldehyde, which creates a surface oxygen vacancy, was also considered, but the reaction *CH2 + 2*H f CH2(g) + VO¨ + 2*H is endothermic by 19 kcal/mol (0.76 eV) and is less likely to occur. 3.6. Methylidine Adsorption and Dissociation. The adsorption of methylidine echoes that of methylene. CH is adsorbed at the 3fh oxygen position, with the carbon atom sitting above the surface between the 3fh oxygen atom and the neighboring cerium atom Ce1 (see Figure 8). The adsorption energy is 107 kcal/mol (4.63 eV). The carbon-cerium distance, C-Ce1, is 2.59Å,0.25Åcloserthanthatformethylene.Thecarbon-hydrogen bond length is 1.13 Å, and the carbon-oxygen bond length is 1.27 Å, continuing the trend of shortening the C-O bond as the number of hydrogen atoms decreases. The cerium-oxygen bond lengths are 2.68, 2.78, and 2.88 Å for Ce3, Ce2, and Ce1, respectively. The bond length of 2.68 Å for O-Ce3 matches that for methylene above, but the other two cerium-oxygen bonds are longer by 0.14 Å for the cerium atom closest to the adsorbate (Ce1 for *CH and Ce2 for *CH2) and 0.07 Å for the other far cerium atom (Ce2 for *CH and Ce1 for *CH2). The oxygen atom sits 1.52 Å above the cerium plane, relative to 1.40 Å for methylene and 0.78 Å for the clean surface. In the case of *CH, the changes in the various bond lengths suggest stronger carbon-oxygen and carbon-cerium bonds and weaker cerium-oxygen bonds. The carbon-cerium interaction can be seen in the density of states for adsorbed CH (see Figure 11) in which there is a peak at -0.38 eV shared by the Ce1, C, 3fh O, and H atoms which contains two electrons. No such peak was seen for H in the projected density of states for *CH2 (see Figure 9 for comparison). In contrast to *CH2 where the carbon 2p orbital interacting with the near cerium atom is orthogonal to the sp orbitals binding the two hydrogen atoms, the single hydrogen atom in the CH adsorbate is in line with the C-Ce bond. This change in symmetry brings the hydrogen atom into the highest occupied orbital of the O-C-Ce1 complex, adds an extra electron to the energy band of the first midgap peak, and increases the strength of the C-Ce1 bond. As seen in Figure 12, the charge density plotted over the energy range of the midgap peaks shows this overlap with the hydrogen atom, and the ELF shows a higher degree of localization between the carbon and cerium atoms than in the case of CH2 (see Figure 10). Methylidine is most easily dissociated by transfer of a hydrogen atom to an adjacent 3fh oxygen atom. Whereas the transition state in methylene was due to breaking of the C-H bond, the stronger C-Ce bond in the case of methylidine makes the breaking of the C-Ce bondswhich allows the hydrogen atom to approach the adjacent 3fh O atomsthe limiting step in the dissociation reaction. The transition state has a C-Ce1 separation of 3.15 Å, an increase of 0.56 Å over the C-Ce1 bond length for *CH. The Ce1-O bond length of 2.87 Å is unchanged from its value at equilibrium, but the oxygen atom is pulled away from the surface to a height of 1.62 Å and the Ce3-O and Ce2-O bond lengths are increased by approximately 0.1 Å to 2.78 and 2.90 Å, respectively, as a result. The energy barrier of 21 kcal/mol (0.89 eV) to the dissociation

Knapp and Ziegler

Figure 11. DOS for the ceria slab with adsorbed CH. (CH Ads) (111) slab with nine atomic layers and adsorbed *CH. (Ce1, 2, 3) Projected DOS for each of the three cerium atoms neighboring the oxygen-adsorbate complex, as labeled in the inset. (C, O, H) Projected DOS for the carbon, 3fh oxygen, and hydrogen atoms. Note that the y-axis scale is varied from plot to plot for clarity.

Figure 12. Charge density and ELF for CH adsorption. The charge density, on the left, is plotted at an isovalue of 0.10 e/Å3 from wave functions in the energy range -0.4 f 0 eV encompassing the occupied midgap peaks of the DOS shown in the top panel of Figure 11. The ELF is shown along a plane shared by the C, O, H, and Ce1 atoms.

of *CH is higher than that for *CH2 by 6.2 kcal/mol. Interestingly, the formation of the carbon monoxide fragment breaks the remaining cerium-oxygen bonds and CO spontaneously desorbs into the gas phase leaving behind an oxygen vacancy. The resulting reaction, CH + 3*H f CO(g) + VO¨ + 4*H, is exothermic and releases 24 kcal/mol (1.04 eV). 3.7. Formation of Carbon Monoxide and Dioxide by Surface Reduction. The adsorption of carbon on the (111) ceria surface leads to the spontaneous desorption of carbon monoxide and the creation of an associated surface oxygen vacancy regardless of the high symmetry site chosen as the starting position for the adsorbed carbon atom. From the gas phase, carbon monoxide thus formed can be adsorbed and further reduce the ceria surface by binding with another surface oxygen

Methane Dissociation on Ceria

Figure 13. Transition state for the reaction CO(g) + CeO2 + VO¨.

atom to form carbon dioxide. Carbon monoxide is weakly adsorbed at the 1f position, 2.85 Å above a cerium atom, with the C-O bond length barely changing from 1.13 to 1.14 Å. The small adsorption energy of 4.1 kcal/mol (0.18 eV) is in excellent agreement with the energy of 3.9 kcal/mol reported in a U ) 0 DFT study of CO adsorption on ceria.13 The lack of a strong interaction leading to reduction of a cerium atom is responsible for the correspondence in the energies derived from the U ) 0 and the U ) 5 eV calculations. Interaction with a neighboring 3fh oxygen atom can lead to the oxidation of carbon monoxide, and the transition state for this process is shown in Figure 13. At the transition state the 3fh oxygen atom is pulled 0.28 Å up to 1.06 Å above the cerium surface and the distances to the three neighboring cerium atoms are lengthened from 2.37 to 2.49, 2.49, and 2.58 Å. The longest 3fh O-Ce bond is associated with the cerium atom closest to the CO molecule. Lengthening of the 3fh O-Ce bond has been shown to correspond to reduction of the associated cerium atom for all of the adsorbates discussed above, and it is likely that the cerium atom in this transition state is at least partly reduced by interaction with the carbon atom and by weakening of the 3fh O-C bond. The carbon-cerium distance is 2.53 Å, which is shorter than the cerium-carbon bond for the CH adsorbate where a significant cerium-carbon interaction was seen to exist in the density of states and the electron localization function. The 3fh O-C bond length at the transition state is 1.59 Å, and the associated energy barrier to the formation of CO2 from adsorbed *CO is 12 kcal/mol (0.53 eV), in good agreement with the experimental value of 14-16 kcal/mol reported by Aneggi et al.11 The overall change in energy for the exothermic reaction CO(g) + VO¨ + 4*H f CO2(g) + 2VO¨ + 4*H is -15 kcal/mol (-0.65 eV), only slightly larger than the value of -13 kcal/ mol (-0.56) eV obtained by Nolan et al.44 3.8. Water Formation. Water can be formed on the (111) surface of ceria by the joining of neighboring OH groups on the ceria surface. The bonding of two hydrogen atoms to a single 3fh oxygen atom breaks the oxygen-cerium bonds and leads to the desorption of water from the surface. This vacancy creating process is extremely expensive, requiring 53 kcal/mol (2.29 eV). Given that the number of O-H bonds does not change and given that an oxygen vacancy is created in the process, it is not surprising that the reaction 2*H f H2O(g) + VO¨ is highly endothermic. This result is in good agreement with the energy of 56 kcal/mol (2.45 eV) reported by Watkins et al.50 in a DFT + U study of the hydrogen cycle on the (111) surface of ceria and is in qualitative agreement with the experimental observations that ceria surfaces are much harder to reduce with H2 than with CO and that strong OH bands persist at temperatures of up to 673 K.3 It should be noted that there is a saddle point in the minimum energy path where one of the hydrogen atoms is transferred from one oxygen atom to the other in the creation of water (see Figures 4 and 14), but the energy

J. Phys. Chem. C, Vol. 112, No. 44, 2008 17317

Figure 14. Formation of water on ceria starts from hydrogen atoms adsorbed on adjacent 3fh oxygen atoms (left) and proceeds by transfer of a hydrogen atom from one 3fh oxygen to its neighbor (right).

continues to rise after the saddle point as H2O escapes into the gas phase and leaves behind a surface vacancy. In SOFC anodes based on Ni-ceria, there is evidence that H2 is burned on ceria after the dissociation of CH4 on the nickel surface.17,18 With this in mind, the adsorption energy for H2 was also calculated53 and found to be 51 kcal/mol (2.22 eV), only slightly smaller than the adsorption energy for H2O. These results suggest that H2 would be readily adsorbed on ceria and that the desorption of hydrogen from surface 3fh oxygen atoms as either water or molecular hydrogen will be strongly discouraged in the absence of a vacancy-filling mechanism. 4. Conclusions The dissociation of methane on the (111) surface of ceria to carbon dioxide and adsorbed hydrogen is exothermic, generating 43 kcal/mol. The generation of methanol on the surface by the dissociation of methane and the creation of an oxygen vacancy is not competitive with the adsorption of methyl and hydrogen requiring an additional 50 kcal/mol. All adsorbates interact most strongly with the 3fh oxygen atoms and the adsorption leads to the reduction of one of the neighboring Ce4+ ions. Partial reduction of a second Ce4+ ion was also found to occur in *CH2 and *CH by the formation of a covalent bond between the 2p and sp orbitals of carbon and the 4f orbitals of the nearby cerium ion. Interestingly, the adsorption of carbon on the (111) surface of ceria leads to the spontaneous desorption of carbon monoxide and the creation of a surface oxygen vacancy regardless of the high symmetry site chosen as the starting point for the calculation. In agreement with earlier calculations,13 CO was found to adsorb weakly at the 1f position on the (111) surface. Interaction of gas phase CO with surface oxygen atoms can lead to the formation of carbon dioxide and an oxygen vacancy, with an energy barrier of 12 kcal/mol, in good agreement with experimental measurements of 14-16 kcal/mol.11 Desorption of the four dissociated hydrogen atoms into the gas phase as either H2 or H2O is highly endothermic, costing up to 103 kcal/mol in energy, and is unlikely to occur in the absence of high temperatures or pressure gradients. This observation agrees with the results of earlier calculations of the hydrogen cycle on ceria (111) by Watkins et al.50 and with experimental observations that ceria is more easily reduced by CO than by H2, with strong OH bands persisting on the surface at high temperatures of up to 673 K.3 While this result might seem to be inconsistent with the stable operation of SOFCs based on Cu-ceria-YSZ anodes, it must be remembered that the generation of water will be driven by an oxygen concentration gradient which will in turn drive an oxygen ion current through the electrolyte from the cathode to the anode and replenish the surface oxygen vacancies left behind by the departure of water and carbon dioxide.

17318 J. Phys. Chem. C, Vol. 112, No. 44, 2008 From the perspective of SOFCs, the results presented here demonstrate that methane can be dissociated on the (111) surface of ceria without leading to the adsorption of carbon and the subsequent formation of carbon cokes. Transition state barriers were calculated for all steps in the dissociation of methane and, with a barrier of 33 kcal/mol, the abstraction of the first hydrogen atom is shown to be a rate-limiting step. That this energy barrier lies between those of 24 kcal/mol on nickel (111) surfaces47 and of 45 kcal/mol on copper (111) surfaces19 suggests that nickel is more active than ceria, which is in turn more active than copper in the dissociation of methane. These results help to explain experimental observations that suggest that nickel is responsible for dissociating methane into carbon and H2 in Ni-ceria-YSZ anodes17,18 and that it is ceria that drives the catalytic behavior of Cu-ceria-YSZ anodes5,8,18,20 in the complete oxidation of methane into carbon dioxide and water. References and Notes (1) McIntosh, S.; Gorte, R. J. Chem. ReV. 2004, 104, 4845. (2) Helveg, S.; Lo´pez-Cartes, C.; Sehested, J.; Hansen, P. L.; Clausen, B. S.; Rostrup-Nielsen, J. R.; Abild-Pedersen, F.; Nørskov, J. K. Nature 2004, 427, 426–429. (3) Trovarelli, A. Catal. ReV.sSci. Eng. 1996, 38, 439–520. (4) Catalysis by Ceria and Related Materials; Trovarelli, A., Ed; Imperial College Press: London, UK, 2002; Vol. 2. (5) Park, S.; Vohs, J. M.; Gorte, R. J. Nature 2000, 404, 265–267. (6) Gorte, R. J.; Kim, H.; Vohs, J. M. J. Power Sources 2002, 106, 10–15. (7) Skorodumova, N. V.; Simak, S. I.; Lundqvist, B. I.; Abrikosov, I. A.; Johansson, B. Phys. ReV. Lett. 2002, 89, 166601. (8) McIntosh, S.; Vohs, J. M.; Gorte, R. J. Electrochim. Acta 2002, 47, 3815–3821. (9) Perrichon, V.; Laachir, A.; Bergeret, G.; Fre´ty, R.; Tournayan, L.; Touret, O. J. Chem. Soc. Faraday Trans. 1994, 90, 773–781. (10) Overbury, S. H.; Mullins, D. R. Ceria Surfaces and Films for Model Catalytic Studies Using Surface Analysis Techniques. In Catalysis by Ceria and Related Materials; Trovarelli, A., Ed.; Imperial College Press: London, UK, 2002; Vol 2, pp 311-341. (11) Aneggi, E.; Llorca, J.; Boaro, M.; Trovarelli, A. J. Catal. 2005, 234, 88–95. (12) Zhou, K.; Wang, X.; Sun, X.; Peng, Q.; Li, Y. J. Catal. 2005, 229, 206–212. (13) Yang, Z.; Woo, T. K.; Hermansson, K. Chem. Phys. Lett. 2004, 396, 384–392. (14) Primet, M.; Garbowski, E. Fundamentals and Applications of Ceria in Combustion Reactions. In Catalysis by Ceria and Related Materials; Trovarelli, A., Ed; Imperial College Press: London, UK, 2002; Vol. 2, pp 407-429. (15) Steele, B. C. H.; Middleton, P. H.; Rudkin, R. A. Solid State Ionics 1990, 40-41, 388–393. (16) Mogensen, M. Ceria-Based Electrodes. In Catalysis by Ceria and Related Materials; Trovarelli, A., Ed; Imperial College Press: London, UK, 2002; Vol 2, pp 453-481. (17) Murray, E. P.; Tsai, T.; Barnett, S. A. Nature 1999, 400, 649. (18) Park, S.; Craciun, R.; Vohs, J. M.; Gorte, R. J. J. Electrochem. Soc. 1999, 146, 3603–3605. (19) Galea, N. M.; Knapp, D.; Ziegler, T. J. Catal. 2007, 247, 20–33. (20) Craciun, R.; Park, S.; Gorte, R. J.; Vohs, J. M.; Wang, C.; Worrell, W. L. J. Electrochem. Soc. 1999, 146, 4019–4022. (21) Lu, C.; Worrell, W. L.; Vohs, J. M.; Gorte, R. J. J. Electrochem. Soc. 2003, 150, A1357–A1359. (22) McIntosh, S.; Vohs, J. M.; Gorte, R. J. Electrochem. Solid-State Lett. 2003, 6, A240–A243. (23) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 48, 13115–13118. (24) Kresse, G.; Hafner, J. Phys. ReV. B 1994, 49, 14251–14269. (25) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15–50. (26) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169–11186. (27) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953–17979. (28) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758–1775. (29) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865–3868.

Knapp and Ziegler (30) Dudarev, S. L. Phys. ReV. B 1998, 57, 1505–1509. (31) Esch, F.; Fabris, S.; Zhou, L.; Montini, T.; Africh, C.; Fornasiero, P.; Comelli, G.; Rosei, R. Science 2005, 309, 752–755. (32) Herschend, B.; Baudin, M.; Hermansson, K. Surf. Sci. 2005, 599, 173–186. (33) Nolan, M.; Girgoleit, S.; Sayle, D. C.; Parker, S. C.; Watson, G. W. Surf. Sci. 2005, 576, 217–229. (34) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188–5192. (35) Skorodumova, N. V.; Baudin, M.; Hermansson, K. Phys. ReV. B 2004, 69, 075401. (36) Yang, Z.; Woo, T. K.; Baudin, B.; Micael; Hermansson, K. J. Chem. Phys. 2004, 120, 7741–7749. (37) Fabris, S.; Vicario, G.; Balducci, G.; de Gironcoli, S.; Baroni, S. J. Phys. Chem. B 2005, 109, 22860–22867. (38) Jo´nsson, H.; Mills, G.; Jacobsen, K. W. Nudged elastic band method for finding minimum energy paths of transitions. Classical and Quantum Dynamics in Condensed Matter Phase Simulations, Singapore, 1998; pp 385-404. (39) Henkelman, G.; Jo´nsson, H. J. Chem. Phys. 2000, 113, 9978. (40) Henkelman, G.; Uberuaga, B. P.; Jo´nsson, H. J. Chem. Phys. 2000, 133, 9901. (41) Jiang, Y.; Adams, J. B.; van Schilfgaarde, M. J. Chem. Phys. 2005, 123, 064701. (42) Nolan, M.; Fearon, J. E.; Watson, G. W. Solid State Ionics 2006, 177, 3069–3074. (43) Patton, D. C.; Porezag, D. V.; Pederson, M. R. Phys. ReV. B 1997, 55, 7454–7459. (44) Nolan, M.; Parker, S. C.; Watson, W. Graeme Phys. Chem. Chem. Phys. 2006, 8, 216–218. (45) Chiang, Y.-M.; Lavik, E.; Blom, D. Nanostruct. Mater. 1997, 9, 633–642. (46) Yang, Z.; Woo, T. K.; Hermansson, K. J. Chem. Phys. 2006, 124, 224704. (47) Bengaard, H. S.; Nørskov, J. K.; Sehested, J.; Clausen, B. S.; Nielsen, L. P.; Molenbroek, A. M.; Rostrup-Nielsen, J. R. J. Catal. 2002, 209, 365–384. (48) Humphrey, W.; Dalke, A.; Schulten, K. J. Mol. Graph. 1996, 14, 33–38. (49) Vicario, G.; Balducci, G.; Fabris, S.; de Gironcoli, S.; Baroni, S. J. Phys. Chem. B 2006, 110, 19380–19385. (50) Watkins, M. B.; Foster, A. S.; Shluger, A. L. J. Phys. Chem. C 2007, 111, 15337–15341. (51) In the VASP implementation of DFT+ U, atomic orbitals are used to project the plane-wave Bloch states onto a basis of local cerium 4f states in order to calculate the on-site Coulomb repulsion in the Hubbard contribution to the total energy. One weakness of this projection is that it can lead to a partial occupancy of the cerium 4f states due to overlap of the atomic 4f projectors with the oxygen 2p states in the valence band. This partial occupancy will be penalized by the Hubbard term and, interestingly, ends up favoring reduced ceria. As has been pointed out by Watkins et al.,50 this comes about because Ce3+ has a larger atomic radius than Ce4+. This reduces the overlap between the atomic 4f projectors and the oxygen 2p states in the valence band for Ce3+ and, therefore, lowers the on-site Coulomb repulsion penalty. The reduced CeO2-x state is thus penalized less than the pure CeO2 state by this overlap and is consequently stabilized relative to the unreduced state. This stabilization lowers the vacancy creation energy and is the main source of the discrepancy between the two DFT + U approaches. (52) A similar structure is seen in the density of states for the p(2 × 2) unit cell on the (111) surface with one 3fh oxygen vacancy. In this case, two cerium atoms are reduced, creating a linear chain of Ce3+ ions, and, as expected a double peak structure is seen in the density of states. However, a very small gap appears in the middle of the double peak (not shown) which is not seen in the case of hydrogen adsorption. The appearance of this tiny gap is due to the fact that the Ce-Ce bond length alternates along the infinite chain between 4.0 and 3.7 Å in a p(2 × 2) unit cell, disrupting the periodicity seen in the p(1 × 2) unit cell used for hydrogen adsorption. That is, the double peak comes from the tight-binding band along a chain of Ce3+ ions approximately 3.7-4 Å apart, and the gap comes from the fact that the true periodicity is every two Ce3+ ions, or 7.7 Å. (53) A much higher value of 107 kcal/mol (4.65 eV) has been reported for the same process by Watkins et al.50 A private communication with the author has revealed that this discrepancy is due to a minor error in the reference energy used for H2(g).

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