J. Phys. Chem. C 2008, 112, 8643–8648
8643
CO Adsorption and Oxidation on Ceria Surfaces from DFT+U Calculations Min Huang and Stefano Fabris* INFM-CNR DEMOCRITOS Theory@Elettra group and SISSAsScuola Internazionale Superiore di Studi AVanzati Via Beirut 2-4, I-34014 Trieste, Italy ReceiVed: October 10, 2007; ReVised Manuscript ReceiVed: February 28, 2008
The limiting steps of CO oxidation catalyzed by ceria via the Mars-van Krevelen reaction mechanism are identified and investigated by means of density functional theory calculations that account for the on-site Coulomb interaction via a Hubbard term (DFT+U). We address the adsorption of CO on the (111) and (110) surfaces, and its oxidation via participation of lattice oxygen leading to vacancy formation and CO2 desorption. CO physisorbs on the (111) ceria surface (Ebind < 0.2 eV), while it chemisorbs on the more open (110) surface (Ebind > 2 eV) yielding carbonate formation and surface reduction. The DFT+U energy of CO adsorption and oxidation is studied as a function of the parameter U. This analysis demonstrates that the values of U presently used in the literature (U > 4 eV) tend to overestimate the binding energy of CO to ceria surfaces. In contrast, the energy for the complete CO oxidation reaction is effectively independent of U and in good agreement with the available experimental data. The discussion of these results in the context of temperature programmed desorption and microcalorimetry measurements allow us to suggest that lower values of U can be more appropriate for modeling redox reactions on ceria surfaces with the DFT+U method. I. Introduction Cerium dioxide (CeO2 or ceria) is widely used in catalysis as an oxygen buffer and an active support for noble metals.1 It is a critical component of the three-way catalyst in automotive emission-control systems, which simultaneously convert hydrocarbons, CO, and NOx into H2O, CO2, and N2. The enhancement in catalytic performance is due to ceria’s ability to store and release oxygen via reversible oxygen-vacancy formation and partial reduction to CeO2-x.2–8 In CO-rich atmosphere and above 550–600 K, the prevalent mechanism for CO oxidation is of the Mars-van Krevelen type that requires the adsorption of CO as an intermediate reaction state. The actual CO oxidation step involves the participation of lattice oxygen leading to CO2 desorption and surface oxygen vacancy formation. The vacancy is then sealed by molecular oxygen that reoxidizes the surface. This paper focuses on the CO adsorption and oxidation steps of this redox reaction mechanism, by studying with density functional theory (DFT) calculations the interaction between CO molecules and ceria surfaces. Both experimental investigations9,10 and theoretical studies11,12 have shown the strong surface selectivity for CO adsorption to ceria surfaces, predicting CO physisorption for the most stable (111) CeO2 surface and chemisorption for the case of more open but less abundant surfaces, like the (110) or (001) ones. The strong binding of CO to these ceria surfaces is mediated by the formation of carbonate-like complexes.13–17 A proper theoretical description of the interaction between CO and ceria surfaces is still under debate. This is due to implicit difficulties for capturing reliably the electronic structure, the adsorbate binding configuration, and the adsorption energetics with first-principles DFT-based methods. Yang et al.15 studied the interactions of CO with the (111) and (110) ceria surfaces by means of DFT calculations in the generalized gradient approximation (GGA) for the exchange and correlation potential. CO was found to physisorb on the (111) surface, while two * Corresponding author.
strong adsorption sites were identified for the CeO2 (110) surface. These were labeled as “Ce-bridge” and “O-bridge”, and the latter was reported to be the most stable with a binding energy of 1.88 eV.15 However, the ability of standard DFT methods to capture the Ce4+/Ce3+ valency change of the Ce ions upon reduction and due to electron localization on the Ce4f orbitals has been shown to be limited.18–20 This is particularly relevant in the case of CO adsorption since experimental studies shows that ceria surfaces undergo reduction upon adsorption.13,14,16,17 Hence, Nolan and co-workers12,21 studied the surface dependence of CO adsorption on ceria by means of DFT(GGA)+U calculations. Even though the previous GGA calculations predicted the Ce-bridge to be metastable, their DFT(GGA)+U study12 (employing U ) 5 eV) focused only on this adsorption site, predicting the reduction of two surface Ce ions and a much larger binding energy (1.95 eV) than the one calculated at the plain GGA level for the same site (0.76 eV). Hybrid DFT embedded-cluster calculations22 were instead applied to describe CO adsorption on the O-bridge site of the (110) surface. This study predicted the reduced Ce ions to be on the subsurface layer and reported a CO binding energy of 2.12 eV. In this paper we further investigate the CO adsorption and oxidation on the most stable (111) and (110) ceria surfaces by means of DFT+U calculations. Besides confirming the surface selectivity for CO adsorption on the most open ceria surfaces reported by previous GGA and DFT(GGA)+U analysis, our results show that the O-bridge site is the most stable CO adsorption site on ceria (110) also at the DFT(GGA)+U level. In terms of geometry and surface reduction, our results for CO interacting with the (110) ceria surface are in overall good agreement with those obtained with hybrid methods,22 but with relevant differences in the actual sites of electron localization due to CO chemisorption. These differences might have important consequences on the surface reactivity of ceria-based materials. Most importantly, the analysis of the CO adsorption energetics as a function of U provides evidence that the values
10.1021/jp709898r CCC: $40.75 2008 American Chemical Society Published on Web 05/16/2008
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of this parameter presently used in the literature (U ) 4–5 eV for GGA) can lead to an overestimation of the molecular binding energy to ceria when surface reduction is involved. This conclusion results from comparing our and other available DFT+U results with microcalorimetry and temperature programmed desorption (TPD) measurements. Smaller values of U ) 2–3 eV seem to be more appropriate to the description of the ceria surface redox chemistry with the DFT(GGA)+U method, in line with some recent works.23,24 II. Computational Method The calculations are based on density functional theory with the generalized gradient corrected Perdew-Burke-Ernzerhof (PBE) approximation for the exchange and correlation functional25 and were performed by using the Quantum-ESPRESSO computer package.26 The addition of a model Hubbard-U term to the DFT(GGA) energy functional27 provides a correct qualitative description of the electronic structure of both oxidized and reduced ceria surfaces.18–20 Ionic cores were represented by ultrasoft pseudopotentials,28 while the wave function and the electron density representation were described with a plane waves basis set and were limited by kinetic energies of 30 and 300 Ry, respectively. The k-point meshes employed in the calculations were generated according to the Monkhorst-Pack scheme.29 The resulting Brillouin-zone sampling used for the supercells described below was equivalent to the one obtained with (4 × 4 × 1) grids for the primitive (1 × 1) cells of the (111) and (110) surfaces. For the DFT(GGA)+U calculations, following our previous studies, we used the value of U ) 4.5 eV,20 but the dependency of the results on this parameter was checked by spanning the U values from 0 to 4.5 eV. The occupancies of the Ce f states were calculated by using the atomic projector functions determined by solving numerically the Schrödinger equation for an isolated Ce atom in the reference configuration [Xe] 4f1 5d1 6s2. Zero-point energy and entropic effects were not included in the reported adsorption energies. All the calculations were spin polarized. Further calculation details can be found elsewhere.20,30,31 The (111) ceria surface was modeled with hexagonal (2 × 2) supercell slabs consisting of 9 layers, while the (110) surface was modeled with orthorhombic (2 × 2) supercell slabs consisting of 6 layers. We used the theoretical equilibrium lattice parameter of 5.48 Å and a vacuum thickness separating the slabs of 10.7 and 11.9 Å for the (111) and (110) surfaces, respectively. Increasing the vacuum thickness to 14 and 16 Å yields changes in adsorption energies smaller than 0.01 eV. The CO molecules were adsorbed on both sides of the supercell and the atomic positions were relaxed according to the Hellmann–Feynman forces until the maximum atomic force was less than 0.02 eV/ Å. The two central atomic layers were fixed to their bulk positions. For the purpose of comparison with literature results we also adsorbed CO on the upper side only of the slabs. In this case, the dipole correction32,33 was included in order to cope with the electric field arising from the adsorption of polar molecules to ceria surfaces and only the coordinates of the atoms in the upper part of the slab were relaxed while the atoms in the lower half of the slab were constrained to their bulk positions. The adsorption energy differences between the twoside adsorption geometry and the one-side adsorption case with dipole correction were found to be less than 0.07 eV, thus providing an estimate of the error bar due to modeling CO adsorption with the chosen periodic supercells.
Figure 1. Side view of the physisorption configuration of CO on the (111) ceria surface. The distances characterizing the adsorption geometry are marked by dashed lines and expressed in Å. Gray, red, and black spheres represent Ce, O, and C ions, respectively. For clarity, the periodic images of the CO molecules are not shown.
III. Results A. CO Physisorption on the (111) and (110) Surfaces. CO is found to weakly interact with the (111) ceria surface (Figure 1). The calculated binding energy of ≈0.2 eV is consistent with that of previous DFT(GGA) (0.17 eV15) and DFT(GGA)+U (0.26 eV12,21) analysis. We do not claim that the existing energy functionals are capable of describing accurately the adsorption energetics and binding site in this physisorption regime. We nevertheless report these data predicted by our DFT(GGA)+U calculations for the purpose of comparison with the previous literature studies. Given the weak molecule-surface interaction, only negligible structural changes result in the (111) surface upon CO adsorption. The C-O bond length is unchanged with respect to the calculated value for free CO molecule, 1.14 Å (the experimental value is 1.13 Å34). The C atom lies at 2.86 Å above the surface Ce atom so that the resulting distance between the C and the nearest surface O atoms is 3.07 Å. Further indication that there is no chemical interaction between CO and the (111) surface is inferred by the analysis of the electronic density of states (DOS) displayed in Figure 2. The total DOS of CO adsorbed on the (111) surface is compared with the DOS of the clean (111) surface and with the electron states of the free CO molecule. The analysis of the projected density of states (PDOS) of the CO adsorbate (whose atoms are labeled as C and O1), and of the surface Ce and O ions (labeled as Ce4+ and O2), indicates that the Ce ions are not reduced upon CO adsorption on this surface. A similar physisorption site for CO on top of a Ce ion is also predicted for the (110) surface. In this case, the distance between the C atom and the Ce surface atom is 2.91 Å, similar to the value for the (111) surface. In this weak adsorption configuration, surface structural changes are negligible and the CO molecular bond length remains fixed at 1.14 Å. The binding energy is ≈0.2 eV, consistent with the literature values of 0.1–0.2 eV.12,15,21,22,35 We notice that the long-range van der Waals interaction may increase the bonding strength of CO to these surface sites, but this contribution is unlikely to play an important role into the
CO Adsorption and Oxidation on Ceria Surfaces
Figure 2. Density of states for a CO molecule adsorbed on the ceria (111) surface compared with that of the clean (111) surface and with the electron states of the free CO molecule, together with the projected density of state of the CO adsorbate (C and O1) and of the nearest neighbors O and Ce surface ions (O2 and Ce4+). The solid vertical line represents the Fermi level.
Figure 3. Side view of the lowest energy configuration for CO adsorption on the O-bridge site of the (110) ceria surface. The distances characterizing the adsorption geometry are expressed in Å. The gray, red, and black spheres represent Ce, O and C ions, respectively, while the reduced Ce ions are shown in dark gray color and labeled as Ce3+. For clarity, the periodic images of the CO molecules are not shown.
surface selectivity for CO adsorption predicted by the present and by the previous DFT analysis. B. CO Chemisorption on the (110) Surface: Binding Geometry and Electronic Structure. CO is found to form strong chemical bonds with the (110) ceria surface. Two adsorption sites are identified, which we label as “Ce-bridge” and “O-bridge” following ref 15. We first characterize the changes in geometry and electronic structure due to CO adsorption on these two sites of the (110) surface and then discuss the energetics of adsorption in the context of the existing literature. 1. The Lowest-Energy O-Bridge Site for CO Adsorption. The most stable adsorption configuration (Figure 3) for a CO molecule binding the (110) surface is on the O-bridge site. The CO interaction with the (110) surface induces strong modifica-
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Figure 4. Density of states for a CO molecule adsorbed on the (110) ceria surface at the O-bridge site compared with that of the clean (110) surface, together with the projected density of state of the CO adsorbate (C and O1) and of the closest Ce ions (Ce3+ and Ce4+) and O surface ions (O2 and O3). The solid vertical line represents the Fermi level.
tions in both the adsorbate and surface geometries. Two surface O ions are pulled outward from surface along the z direction by 0.38 Å, resulting in a distance of 1.35 Å between the C ion and the O surface ions (which will be referred to as O2 and O3 in the following). This strong interaction with the surface weakens the intramolecular C-O bond whose length increases to 1.22 Å (the corresponding calculated value for a noninteracting CO molecule is 1.14 Å). The vertical distance between the C atom and the surface is now 1.24 Å, significantly shorter than in the physisorption cases discussed above. These structural changes indicate the formation of strong CO/CeO2 covalent bonds and of carbonate-like ad-species. This is confirmed by the analysis of the electronic structure showing the appearance of new states correlated to the CO adsorption. In Figure 4 we compare the DOS for CO adsorption on the O-bridge (110) surface site with that of the clean (110) surface. The figure also displays the PDOS of the surface O atoms bound to the CO molecule (O2 and O3), of two surface Ce ions (Ce3+ and Ce4+), and of the adsorbate atoms (C and O1). The adsorption process leads to new states at 0.8 eV below the bottom of the valence band. These indicate the formation of covalent bonds between CO and the two surface atoms (O1 and O2) that are pulled out from the surface. Moreover, a new state appears in the band gap, at 0.3 eV above the top of the valence band. The integrated charge corresponding to this state sums to 2 electrons per CO molecule and localizes on two surface Ce ions neighboring to the carbonate, effectively changing their valency from 4+ to 3+. We note that a similar CO strong adsorption configuration was also predicted for CO on (100) ceria surface.12,21 This analysis therefore shows that CO adsorption on the (110) surface induces the formation of carbonate-like species and the reduction of the ceria surface. In order to further characterize the changes in the surface electronic properties due to CO adsorption, we have calculated the bonding charge and spin densities for the (110) O-bridge site (Figure 5). The bonding charge density (Figure 5a) clearly reveals that the charge redistribution due to adsorption involves almost exclusively the CO molecule, two surface O ions (O2 and O3) and two reduced surface Ce ions. The spin density (Figure 5b) is nonzero only on these two surface Ce3+ ions bound to the lattice O ions of the carbonate. Reduction is facilitated by the increase of these Ce-O bond lengths by 0.34 Å, resulting from the outward relaxation of the O2 and O3 atoms.
8646 J. Phys. Chem. C, Vol. 112, No. 23, 2008
Huang and Fabris TABLE 1: Calculated DFT(GGA) and DFT(GGA)+U Energies for the Binding of CO to the (111) and (110) Ceria Surfacesa GGA
GGA+U
ref 15 this work ref 12
B3LYP
this work
ref 22
U ) 5 U ) 4.5 U ) 2 (111) Ce-top
0.17
0.18
0.26
0.17
0.17
(110) Ce-top Ce-bridge O-bridge
0.18 0.56 1.88
0.16 0.27 1.47
0.21 1.95
0.19 2.04 3.71
0.18
0.10
2.20
2.12
a
Figure 5. Bonding charge density and spin densities for a CO molecule chemisorbed on the (110) ceria surface at the O-bridge site. Red and blue colors represent positive and negative values, respectively.
We finally note that the carbonate species can be easily tilted with respect to the surface normal. The energy is shown to have a very shallow minimum (lower in energy by 0.02 eV than the upright configuration) at 31°, in qualitative good agreement with previous DFT(GGA) results reporting an angle of 53° and an energy difference of 0.08 eV.15 We remark however that the structural and electronic properties described above are unaffected by the molecule being tilted in the shallow energy minimum. 2. The Metastable Ce-Bridge Site for CO Adsorption. Molecular CO can also bind to a Ce-bridge site of the ceria (110) surface. Similar to the lowest energy case discussed above, the adsorption process on the Ce-bridge metastable site involves the interactions between CO and two O and two Ce surface atoms, leading to the formation of carbonate species. In this configuration, the two surface O atoms are pulled out of the surface by up to 1.08 Å (0.9 Å for DFT15), while a total of two electrons localize on two surface Ce atoms. The molecular C-O bond increases to 1.22 Å from the free CO value of 1.14 Å. Our results are in excellent quantitative agreement with the DFT(GGA)+U ones by Nolan et al.12,21 Finally, also in this case, the CO molecule is relatively soft with respect to tilting: the energy increases by 0.14 eV for a tilt angle of 45°. C. DFT+U Energetics of CO Chemisorption: Problems and Challenges. The structural and electronic properties presented above allowed us to identify two distinct cases of CO adsorption on ceria surfaces, one involving surface reduction and strong surface and adsorbate reorganization, the other leading to little changes in the atomic and electronic properties of both the adsorbate and the support. This is clearly reflected in the calculated energetics of adsorption that distinguishes the two cases in terms of CO chemisorption and physisorption, respectively. However, the two energy regimes require separate analysis. For the physisorption case, CO does not induce surface reduction, and the DFT and DFT+U approaches predict the same energy values (Table 1), ≈0.2 eV, which agrees with the results of previous studies 0.10–0.26 eV.12,15,21,22,35 The chemisorption regime, in which CO adsorption reduces the (110) ceria surface, is more delicate. On the one hand, it is now well established that plain DFT is not adequate to capture the reduction process and the electron localization that govern the surface chemistry of ceria.23,24,30,31,37 On the other hand, even though the DFT+U approach is suitable to capture these processes, it has been shown to be rather poor in predicting the reduction energetics. In particular, all studies have shown a
All energy values are in eV. The experimental heat of adsorption measured at 300 °C is 2.27 eV.36
Figure 6. Dependency of the calculated DFT+U energetics on the value of the parameter U for the (a) reduction reaction of ceria (2CeO2 f Ce2O3 + 1/2O2); (b) adsorption of a CO molecule on the (110) ceria surface at the O-bridge site; (c) formation of a surface vacancy on the (110) surface; and (d) CO oxidation reaction mediated by lattice oxygen. The solid horizontal lines represent the available experimental data (see text).
strong linear dependency of the energy for reduction as a function of the value of the effective parameter U.20,23,24,27 Figure 6a reports the energy difference for ceria reduction (2CeO2 f Ce2O3 + 1/2O2) calculated at the DFT(GGA)+U level and corrected for the known overbinding of molecular O2 predicted by the GGA functionals. We remark that, besides being dependent on the U value, the energetics is also dependent on the specific choice of the projector functions involved into the
CO Adsorption and Oxidation on Ceria Surfaces Hubbard term added to the energy functional.20,31 Plain DFT(GGA) results overestimate the energy for reduction and provide the wrong electronic structure of reduced ceria. On the contrary, DFT(GGA)+U results yield the correct electronic structure of reduced ceria but the values of U delivering the correct position of the filled gap state and presently used in the literature (U ) 4.5–5 eV12,18–21,35–41) yield an underestimation of the reduction energy by more than 1 eV. It is therefore expected that this will be a crucial issue for describing the surface chemistry of adsorbates involving surface reduction as the present case of CO. Both DFT(GGA) and DFT(GGA)+U calculations predict the O-bridge site to be the most stable for CO adsorption (the Cebridge site being 1.2–1.7 eV higher in energy), but there are important quantitative and qualitative variations due to the different electronic structure resulting from the CO-substrate interaction. The metastable Ce-bridge adsorption site has been the subject of previous DFT(GGA)+U studies that used a value of U ) 5 eV and predicted a CO binding energy to the surface of 1.95 eV.12 Our result for this adsorption configuration (obtained with U ) 4.5 eV) is 2.04 eV, in very good agreement with the reported value, but the binding energy calculated for the most stable O-bridge site results to be unrealistically large, 3.71 eV (Table 1). Similar large values (3.01 eV) have been predicted by Nolan et al. with DFT(GGA)+U calculations using U ) 5 eV for the CO adsorption on the (001) ceria surface.12 The binding energy calculated with hybrid DFT functionals on a relaxed cluster modeling the (110) surface is much smaller, 2.12 eV22 (Table 1) and is in good agreement with the experimental heat of CO adsorption measured by microcalorimetry at 300 °C, 2.27 eV.36 Incidentally, even though the electronic structure predicted by plain DFT(GGA) calculations is wrong, the corresponding binding energy of 1.5–1.9 eV is not too far from the experiment. It becomes therefore evident that the values of U presently used in the literature and giving the correct position of the filled gap state in reduced ceria (U ) 4–5 eV), besides underestimating the reduction energy, can also yield a large overestimation of the CO binding energy to ceria surfaces. Since the two problems have the same physical origin, i.e. the reduction of Ce ions, one possibility for improvement could be the use of maximally localized Wannier functions as projector in the Hubbard term of the energy functional. We have shown that this specific choice for the projector functions makes the calculated DFT(GGA)+U energetics independent of the parameter U and recovers the plain GGA values.20,31 But despite this improvement and the nice property of being U-independent, the DFT(GGA)+U energy of reduction calculated with the Wannier functions does not reproduce the available experimental data with the precision necessary to predict the redox surface chemistry of ceria-based materials. A more pragmatic approach, probably more appropriate to the study of these complex systems, can be identified by analyzing the dependency of the energy for CO adsorption on the value of U plotted in Figure 6b: the same slope dE/dU is predicted for both the ceria reduction (-0.64) and the CO adsorption (-0.61) processes. The linear deviation of the DFT+U energetics from its DFT reference is therefore determined almost exclusively by the electron localization process, while it is weakly affected by differences in the local structural and chemical environment. This is further confirmed by the energy for vacancy formation on the (110) surface, displayed in Figure 6c. Also in this case, the energy depends on U with very similar slope of the cases discussed above (-0.59). Because
J. Phys. Chem. C, Vol. 112, No. 23, 2008 8647 of this similarity, it can be expected that the value of U that gives the reduction energetics experimentally observed would also transfer to the other cases of surface vacancy formation and binding of reducing adsorbates. In particular, the energy for reduction (CeO2 f Ce2O3) calculated with all the DFT(GGA)+U implementations intersects the available experimental values42 (solid horizontal lines in Figure 6a) for values of U between 2 and 3 eV.20,23,24,37 Indeed, the CO binding energy calculated with U ) 2 is 2.2 eV (Table 1), in very good agreement with the value obtained with hybrid functionals (2.12 eV22) and with the experimental heat of adsorption, 2.27 eV.36 We remark once again that the DFT+U results obtained with a specific value of the U parameter are intrinsically associated with the projector functions used in the DFT+U functional. Moreover, exceedingly small values of U would affect the degree of localization of the excess electrons on the Ce f states. In this respect, the value of U ) 2 eV should be considered as a lower bound. This is evident from the calculated occupancies of the Ce-f states being 0.91, 0.96, and 0.98 electrons resulting from U ) 2, 3, and 4 eV, correspondingly, and from the linear dependency of the CO adsorption energy in this U range (Figure 6). All this discussion on the linear dependency of the DFT+U energetics and on the choice of the optimal value of U is however irrelevant for the description of CO oxidation step in the Mars-van Krevelen reaction mechanism. In fact, while the precise value of the CO adsorption energy will be important for resolving issues like the preferential adsorption in the presence of supported metal nanoparticles, for what concerns the reaction on the oxide substrate, all that matters is the strong chemisorption of CO on open ceria surfaces. This determines the initial state of the oxidation reaction, which in the specific case of the (110) surface corresponds to the CO molecule bound to the O-bridge site characterized above. The final state is an oxidized CO2 in the gas phase and a ceria surface with an oxygen vacancy. Recent TPD experiments show that the activation temperature for CO oxidation on ceria nanopowders is 550–600 K.10 A Boltzmann analysis performed by considering an attempt rate of 1013 and a reaction rate of 1 ms or less at these temperatures predicts activation energies of 1.8–2.1 eV (horizontal lines in Figure 6d). The calculated energy difference between final and initial states (1.7–1.8 eV) is in good agreement with this estimate and, most importantly, it is effectively independent of the U value (Figure 6d). The final step of the redox Mars-van Krevelen reaction involves vacancy sealing by molecular O2 and surface reoxidation, a process which we have described in a separate study.41 IV. Conclusions The CO adsorption and oxidation on the (111) and (110) ceria surfaces have been described on the basis of DFT(GGA)+U calculations. The overall Mars-van Krevelen reaction displays a strong surface selectivity controlled by the CO adsorption step. CO physisorbs on the most stable (111) surface while it strongly chemisorbs on more open ceria surfaces, like the (110). In this case, we have presented a comprehensive description of the active sites, focusing particularly on the lowest energy configuration, labeled as “O-bridge”. The adsorption leads to significant structural changes of both the CO molecule and the (110) surface and to the formation of surface carbonate species. Most importantly, the process results in reduction of the substrate through the Ce4+/Ce3+ change of valency of two surface Ce ions neighboring the carbonate via charge localization on their f states, thus leading to the appearance of a gap state in the electronic structure.
8648 J. Phys. Chem. C, Vol. 112, No. 23, 2008 The analysis of the energetics of CO adsorption predicted by the DFT+U methods reveals its strong dependency on the value of the parameter U. Admittedly, several studies have shown that there is no unique optimal value of U that allows one to capture all the electronic and structural properties of ceria, as well as the energetics of reduction,23,24 the latter one being, in our opinion, the most severe problem. This points to the importance of performing more reliable calculations using, for example, hybrid functionals. These are computationally very demanding, but the results obtained for selected and relevant cases can be used to identify values of the U parameter in DFT+U methods delivering acceptable precision in the calculated properties, a strategy recently followed for example in ref 24. These benchmarking calculations become particularly relevant since our results show that reduction processes as different as oxygen vacancy formation and CO adsorption yield very similar slopes in the calculated DFT+U reduction energetics. Hence the overall suitable values of U identified for the simplest case of ceria bulk reduction can be expected to transfer also to more complex chemical and structural local environments. The analysis of the CO adsorption energetics as a function of U provides evidence that the values of this parameter presently used in the literature (U ) 4–5 eV for GGA) can lead to severe overestimation of molecular binding energy to ceria when surface reduction is involved. Our results suggest that values of U ) 2–3 eV can be more appropriate to the description of the surface chemistry of ceria with the DFT(GGA)+U method, in line with some recent works.23,24 We conclude by showing that, since the (110) ceria surface is reduced by CO adsorption, both the calculated DFT(GGA) and DFT(GGA)+U energetics of the actual oxidation step, leading to CO2 desorption and oxygen vacancy formation on the (110) surface, turn out to be in good agreement with TPD experiments. These considerations can be expected to be relevant for the modeling of a wider class of redox surface reactions. Acknowledgment. We are grateful to Stefano Baroni, Stefano de Gironcoli, Friedrich Esch, and Gabriele Balducci for useful discussions. Calculations have been made possible by the SISSA-CINECA scientific agreement and by the allocation of computer resources from INFM Progetto Calcolo Parallelo. Graphics have been generated with the XCRYSDEN computer program.43 References and Notes (1) Trovarelli, A., Ed.; Catalysis by Ceria and Related Materials; Imperial College Press: London, 2002. (2) Trovarelli, A. Catal. ReV.-Sci. Eng. 1996, 38, 439. (3) Skorodumova, N. V.; Simak, S. I.; Lundqvist, B. I.; Abrikosov, I. A.; Johansson, B. Phys. ReV. Lett. 2002, 89, 166601. (4) Harrison, B.; Diwell, A. F.; Hallett, C. Platinum Met. ReV. 1988, 32, 73. (5) Oh, S. H.; Eickel, C. C. J. Catal. 1988, 112, 543.
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