Au

Nov 14, 2008 - The direct synthesis of hydrogen peroxide on Pd and Pd/Au catalysts was investigated with first-principle DFT methods for periodic ...
0 downloads 0 Views 201KB Size
J. Phys. Chem. C 2008, 112, 19501–19505

19501

Theoretical Study of the Direct Synthesis of H2O2 on Pd and Pd/Au Surfaces Aleksandar Staykov,† Takashi Kamachi,† Tatsumi Ishihara,‡ and Kazunari Yoshizawa*,† Institute for Materials Chemistry and Engineering, Department of Applied Chemistry, Faculty of Engineering, Kyushu UniVersity, Fukuoka 819-0395, Japan ReceiVed: April 7, 2008; ReVised Manuscript ReceiVed: October 20, 2008

The direct synthesis of hydrogen peroxide on Pd and Pd/Au catalysts was investigated with first-principle DFT methods for periodic two-dimensional surfaces. A two-step reaction mechanism was proposed starting from a superoxo precursor state of the dioxygen molecule on Pd surface and its subsequent reaction with two hydrogen atoms situated over neighboring 3-fold positions. A competitive reaction of dioxygen dissociation leading to the nonselective formation of water was found. We have shown that the presence of surface gold atoms blocks this dissociation and increases the selectivity toward the main product, H2O2, which explains the experimentally reported data. 1. Introduction Oxidation is a key process that can be used to functionalize molecules using selective partial oxidation or to remove pollutants using nonselective, total oxidation. Molecular oxygen is the preferred oxidant but up to date remarkably few processes are operating using it. Many processes use bulky stoichiometric oxygen donors which exhibit poor atom efficiency.1-3 From the green chemistry perspective, H2O2 is the next most preferred oxidant with widespread application in many large-scale processes as bleaching and disinfecting because water is the byproduct after oxygen donation. The direct synthesis of H2O2 is an important industrial process, which recently gains significant interest of many experimental groups.4-11 The research is addressed toward the discovery and the improvement of catalysts, which can significantly reduce the production costs. Its usage in the fine chemical industry is the reason for its low consumption.12 Hydrogen peroxide is industrially produced by the sequential hydrogenation and oxidation of an alkyl anthraquinone.13 This process is economically viable only on relatively large scale which is in contradiction with the industrial requirements of small amounts of H2O2 at a time. Hence the development of new, efficient, and smaller scale manufacturing processes for the synthesis of H2O2 is of significant commercial interest. The industrial realization of the direct synthesis of hydrogen peroxide from O2 and H2 would be highly beneficial as a small scale synthesis.12 It is reported that Pd catalyst is highly active in the direct synthesis of H2O2 from H2 and O2.6,14,15 Au catalyst is also active in this direct synthesis of H2O2 although it is of low selectivity.12,16,17 It was shown that the addition of Pd to Au is an effective way for increasing the H2O2 formation rate.18 The direct synthesis of H2O2 occurs in the explosive regime of the gases and it is considered dangerous for commercial use.19 Significant experimental efforts are directed to the optimization of the catalyst in order to lead the reaction below the explosive regime. Successful experimental results are reported on the base * To whom correspondence should be addressed. E-mail: kazunari@ ms.ifoc.kyushu-u.ac.jp. Telephone: +81-92-802-2529. Fax: +81-92-8022528. † Institute for Materials Chemistry and Engineering, Kyushu University. ‡ Department of Applied Chemistry, Faculty of Engineering, Kyushu University.

of Pd-Au catalysts.5,9,15,18 Another important issue is the selectivity of the catalyst. The conditions suitable for the synthesis of H2O2 are the same leading to its dissociation to oxygen and water or to the nonselective formation of water. The demand of improving the catalytic selectivity and reaction conditions of the direct synthesis of hydrogen peroxide leads to a large number of experimental data on the basis of the experimental design.5-12,14-17 The selectivity of the catalyst, its regeneration, and the reaction rates strongly depend on its structure and methods of preparation.5,7 Several experimental papers have been published comparing the selectivity and the reaction rate with the Au/Pd ratio on the surface.5,7 The results differ depending on the calcination of the catalyst and the solution medium in which the reaction takes place. In general, the reaction rate is lowest for Au surfaces, followed by Pd-Au, and higher for Pd surfaces. The selectivity is lowest for Au, followed by Pd, and highest for Pd-Au surfaces.5,7,12 A few theoretical investigations were performed concerning the mechanism of the reaction and the dissociations of H2 and O2 on Pd surface.20-22 The energies of adsorption and dissociation of H2 and O2 over small Pd clusters were reported recently, as well as, the activation energy of atomic hydrogen‘s migration on the surface. Honkala et al.21 performed a more detailed study of the O2 dissociation on Pd surface and, as a result, two of the three experimentally estimated precursor states were determined.21,23,24 The theoretically determined precursor states of the oxygen molecule over Pd(111) surface are a top-bridge-top superoxo species and a top-3-fold site-bridge peroxo species.21 In the supeoxo state the two oxygen atoms are equivalent and are situated at the same distance from the surface while in the peroxo state the molecule is tilted toward the bridge site. This is a stable chemisorbtion state. An electron from the Pd surface migrates to the π/ orbital of the oxygen molecule. The π/ orbital overlaps with the d-orbitals of Pd and, as a result, significant electron density is found between the surface and the molecule, which explains the stability of the state. The superoxo precursor state is the starting geometry for the oxygen dissociation with the lowest activation energy.21 The dissociation should be minimized for the high selectivity of the catalyst because water can be formed only as a result of the oxygen-oxygen bond cleavage. A large number of dissociation and formation reactions are supposed to take place on the Pd surface, making the theoretical

10.1021/jp803021n CCC: $40.75  2008 American Chemical Society Published on Web 11/14/2008

19502 J. Phys. Chem. C, Vol. 112, No. 49, 2008

Staykov et al. CHART 1

Figure 1. Pd and Pd/Au supercells used in the CASTEP simulations.

estimation of the correct mechanism a difficult task.11,22 Some of those reactions consist of two steps mechanisms including intermediate species. A theoretical study was performed in order to determine the optimal conditions for the synthesis of hydrogen peroxide on metal catalysts.22 The main conclusion was that the peroxide is formed rather as a result of the interaction of molecular oxygen ands atomic hydrogen than the interaction of two hydroxyl radicals. However that research was not based on first-principal methods and did not provide a reaction mechanism. The aim of our study is to give a full first-principle treatment of the direct interaction of hydrogen and oxygen on Pd(111) surface to propose a reaction mechanism and to explain the high selectivity of the Pd/Au catalysts. 2. Computational Methods All calculations were performed with the CASTEP software package.25 Plane wave basis functions with spin polarization and the Perdew, Burke, Erzenhof gradient corrected functional (PBE-GGA) were used.26 The transition state search was performed with the linear and quadratic synchronous transit (LST/QST) complete search. The spin state was not optimized during the SCF procedure in order to avoid high spin states of the metal surface. The geometry optimizations and the transition state searches were performed with coarse accuracy (2 × 2 × 1K points) in order to save computational efforts. Calculations with medium accuracy (3 × 3 × 2K points) were performed for some of the structures but significant differences were not observed. The calculations were performed on a super unit cell containing two layers of nine metal atoms each, as shown in Figure 1. We have simulated a surface by including 10 Å vacuum slab within which the formation of the peroxide takes place. The models including gold atoms in the surface are derived by the Pd supercell, in which two Pd atoms are substituted by Au atoms. One of the Au atoms is in the surface, taking place in the reaction mechanism, while the other is in the second layer assuring the singlet ground-state of the surface. In some cases both Au atoms are in the surface layer. In addition, we have calculated model systems consisting of pure Au(111) surface and Au(111) surface with Pd impurities. The Pd impurities consist of two Pd atoms, one situated in the surface layer and taking part in the reaction and second, situated in the deeper layer. A larger supercell will certainly lead to more accurate result on the cost of computational time because it will minimize the influence of the reagents in neighboring supercells. However, a supercell with 32 metal atoms do not change significantly the obtained results while it increases drastically the calculation time. 3. Results and Discussion We assume that the hydrogen peroxide formation is a two step mechanism, as schematically shown in Chart 1. The oxygen is in its superoxo state,21 activated by the surface, and the hydrogen molecule is dissociated prior to the reaction. In the first step a hydrogen atom interacts with the superoxo oxygen. An intermediate hydrogen peroxo state is formed which, in the

second step, enters in a reaction with a second hydrogen atom leading to the formation of hydrogen peroxide. The O-O bond dissociation would compete with the main reaction on the surface, and the produced atomic oxygen leads to the undesired formation of water. It was reported by several experimental studies that while the presence of Au atoms in the surface does not influence significantly the peroxide formation rate, it increases significantly the selectivity of the reaction.5,12,18 This can be achieved by the partial or complete suppress of the formation of the byproductswater. We expect that the Au significantly reduces the dissociation rate of the oxygen molecule. As a result, no atomic oxygen is available on the surface and the formation of water is minimized. We have investigated the O2 dissociation on both Pd and Pd/ Au surfaces as a key reaction determining the selectivity of the catalyst. Calculations for the main reaction mechanism, the H2O2 formation, on the both surfaces were performed. Additionally, H2 dissociation was studied. 3.1. The Superoxo Precursor State on Different Metal Surfaces. The geometry of the superoxo precursor state is important for both reactionssH2O2 formation and O2 dissociation. The length of the oxygen-oxygen bond in the free O2 molecule is 1.21 Å. The superoxo precursor state is a stable chemisorption state characterized with transfer of electron density between the molecule and the surface.21 As a result the oxygen-oxygen bond is weakened and the bond length is increased. This bond length stretch is a measure for the activation of the oxygen molecule. We failed to optimize the precursor state on the pure Au(111) surface. This result is in agreement with the experimental inactivity of O2 toward gold, making it a valuable noble metal.27 Small Pd impurities within the Au(111) surface can activate the oxygen molecule and the precursor state is characterized with 1.30 Å bond length. The pure Pd(111) surface can activate and dissociate the oxygen molecule. The precursor state bond length on the Pd(111) surface is calculated to be 1.34 Å. The longest oxygen-oxygen bond, 1.38 Å, is calculated for Pd(111) surface with Au impurities, making it very suitable for both H2O2 formation and O2 dissociation. 3.2. Formation of H2O2 on Pd(111) Surface. We assume that the starting geometry for the hydrogen addition to the oxygen molecule is the superoxo precursor state. The superoxo state is symmetrical and favors reactions with same reagents on each oxygen atom. Our second assumption is a two step reaction mechanism with the formation of OOH hydrogen peroxo intermediate. That assumption is based on the fact that in the superoxo state the oxygen molecule accepts an electron from the surface21 and changes its spin from triplet to doublet and reacts as a monoradical with the atomic hydrogen. The hydrogen molecule is easily dissociated on the Pd surface as we show in section 3.5. The optimized geometry shows a preferred 3-fold position, hcp or fcp site, of the hydrogen atom.20 The migration barrier of the hydrogen atom between two 3-fold positions is calculated to be 5 kcal/mol20 with a transition state over the bridge site. In the first step of the H2O2 formation, the superoxo molecule interacts with a hydrogen atom situated over the nearest 3-fold

Direct Synthesis of H2O2

J. Phys. Chem. C, Vol. 112, No. 49, 2008 19503

Figure 2. Catalytic formation of H2O2 over Pd(111) surface. The energies are given in kcal/mol and the distances in Å.

position. The reaction is exothermic and the activation energy is 12.2 kcal/mol. In the transition state the hydrogen atom is situated over a bridge site. The oxygen atom of the OH group is situated 0.2 Å higher from the surface than the second oxygen. The intermediate is negatively charged with singlet spin as a result of the electron transfer between the surface and the molecule. The O-O bond is 1.52 Å. The optimized structures of the reactant complex, the transition state and the intermediate, as well as the reaction enthalpies, are shown in Figure 2. In the second step, the intermediate reacts with the second hydrogen situated over the nearest 3-fold position. The reaction is exothermic. A transition state with energy of 15.9 kcal/mol, corresponding to a hydrogen over a bridge site, was found. The final product, H2O2, is situated at 2.5 Å over the surface. The optimized structures of the second reactant complex, the second transition state and the final product as well as the reaction enthalpies of the second step are given in Figure 2. 3.3. Formation of H2O2 on Pd/Au Surface. In several papers the improved selectivity for Pd/Au surfaces compared to pure Pd surface was reported.5,12,18 This selectivity varies depending on the Pd/Au ratio and the experimental conditions for the preparation of the catalyst.12 The experimental studies do not necessarily report an increase of the reaction rate. The structure of the Pd/Au surface was not investigated theoretically and the effect of the Au atoms on the geometry and the electronic properties of the crystal were not reported. In order to study the influence of the Au atom on the mechanism proposed in Chart 1 and to explain the higher selectivity, we have performed CASTEP calculations for supercells containing Au atoms. Three possible positions of the gold on the surface were investigated for the first step of the H2O2 formation. Two of the positions were chosen below the oxygen atoms, i.e., under the oxygen reacting with the hydrogen (A) and under the second oxygen (B), and one on a neighboring center as a part of the bridge site under the transition state (C). The optimized reactant complexes, the estimated transition states, and the optimized intermediates, as well as the reactions energetics, are shown in Figure 3. The larger radius of the Au determines the longer distance between the oxygen molecule and the surface. We have calculated higher activation barriers for all structures compared to those for the pure Pd surface. These results correlate well with the experiment as no experimental paper shows significant increase of the reaction rate for the Pd/Au catalysts. A reason for this higher activation energy is the larger radius of the gold atom. In case A the Au-O distance is 2.65 Å. As a result the distance between the oxygen and the hydrogen is significantly longer and the transition state is localized higher over the surface. Such position of the transition state requires higher activation energy. In case B, the conclusions are similar but the activation energy is lower because the influence of the Au

Figure 3. Catalytic formation of H2O2 (Step 1) over Pd/Au surface. Three different positions of the Au-atom on the surface are considered: (A) under the reacting oxygen, (B) under the second oxygen, and (C) as a part of the bridge site under the transition state. The energies are given in kcal/mol and the distances in Å.

CHART 2

is limited. In case C, the oxygen molecule is not risen over the surface but the hydrogen in the transition state is higher which determines the higher energy barrier. 3.4. Adsorption and Dissociation of O2 on Pd and Pd/Au Surfaces. A theoretical study of the adsorption and the dissociation of molecular oxygen on small Pd clusters was performed by Roques et al.20 They have investigated only one pathway, corresponding to the hcp-fcc initial adsorption positions of the oxygen and have determined an activation energy of 7 kcal/mol. However, as they have pointed out, the adsorption energy on small clusters is different form that on infinite Pd surface. They failed to determine any precursor states for this path although experimentally three precursor states are identifiedsa supreoxo species and two peroxo species.23,24 Honkala et al.21 investigated the adsorption and the dissociation of molecular oxygen on Pd(111) infinite surface. They have studied different pathways and have determined two of the three precursor states. The superoxo state is situated on 2.0 Å from the surface in a top-bridge-top symmetric position. The peroxo state is situated on 1.8 Å from the surface in a top-3-fold (hcp or fcc)-bridge asymmetric position. The activation energy for the dissociation determined there differs for the different starting geometries. The lowest estimated is 13 kcal/mol for a starting geometry close, but not matching, to the superoxo precursor state. The dissociation is performed toward a third Pd atom after a slipping from the top-bridge-top state, as shown in Chart 2. No transition state search was performed and the energy barrier is determined as a function of the distance between the oxygen molecule and the surface.21 The adsorption and the dissociation of molecular oxygen on Pd and Pd/Au surfaces are important issues for understanding the mechanism of direct synthesis of H2O2. We found that the superoxo precursor state is a local minima and we failed to determine any other minima with close geometry. We determined the activation energy for the O-O bond cleavage to be 20.3 kcal/mol. The reaction energetics is schematically shown

19504 J. Phys. Chem. C, Vol. 112, No. 49, 2008

Staykov et al. CHART 3

Figure 4. Dissociation of O2 over Pd(111) surface. The energies are given in kcal/mol and the distances in Å.

Figure 5. Dissociation of O2 over Pd/Au surface. The energies are given in kcal/mol and the distances in Å.

in Figure 4. This results are not in disagreement with the previous reported data in the paper of Honkala et al.21 The starting geometry in their work21 is closer to the transition state which we found and also they do not perform a full optimization as the distance between the surface and the molecule is kept frozen. The dissociation reaction is exothermic and the energy difference between the product and the reactant complex is -22.9 kcal/mol. The oxygen-oxygen bong length in the superoxo state is 1.34 Å. The spin is distributed between the oxygen molecule and the Pd surface. The oxygen molecule is negatively charged as a result of electron transfer to a π/ orbital of the oxygen molecule. The distance between the dissociated oxygen atoms is 2.94 Å. In order to investigate the high selectivity of Pd/Au catalysts we have studied the dissociation of oxygen molecule over Pd/ Au surface. The reaction energetics is schematically shown in Figure 5. The starting geometry is again the superoxo state over two Pd atoms but the dissociation is performed toward the gold atom, as it is shown in Chart 2. The reaction enthalpy is nearly unchanged and the energy difference between the product and the reactant complex is 1 kcal/mol. The distance between the dissociated oxygen atoms is 2.94 Å. This result shows that the presence of a gold atom on the surface significantly suppress the oxygen dissociation. The absence of atomic oxygen reduces the pathways leading to formation of water and increases the amount of the main productsH2O2. The LST/QST search failed to determine any transition state for this reaction. Due to the larger radius of the Au atom, the transition state should be situated high over the surface, but in this way the oxygen molecule will not be activated by the electron transfer on its π/ orbital. Furthermore, such rising of the oxygen molecule over the surface requires additional activation energy equal to the physiosorption energy. No other dissociation pathways of the oxygen molecule were investigated because it was indicated21 that their activation energies significantly exceed 30 kcal/mol, which is much higher than the activation energy of the rate determining step of the main reaction. The O2 dissociation is of major importance for the selectivity on the H2O2 formation. That is why we found it useful to provide information about the oxygen dissociation on Pd/Au surfaces with two Au atoms in the top layer. The reactant complexes and the activation energies for the dissociations are summarized in Chart 3. It was not possible to optimize the precursor state of the oxygen molecule parallel over two gold atoms. We have obtained similar results for the pure Au(111) surface. However,

CHART 4

the precursor state geometry was optimized in the case of oxygen molecule situated parallel over one Pd and one Au atom. The energy barriers are 31.82 and 46.12 kcal/mol when the dissociation is performed on top of a Pd atom and on top of an Au atom respectively. These energy barriers significantly exceed the rate determining step for the H2O2 formation. 3.5. Adsorption and Dissociation of H2 on Pd and Pd/Au Surfaces. The dissociation of molecular hydrogen on Pd and Pd/Au surfaces is an important precursor reaction for the H2O2 synthesis mechanism proposed in Chart 1. The dissociation over Pd clusters was investigated theoretically and low dissociation energies were reported.20 As we have seen, the addition of Au atoms on the surface can slow down significantly and eventually block tho dissociation of molecular oxygen. In this way the selectivity of the H2O2 synthesis is improved. It is essentially important that the presence of gold on the surface does not block also the H2 dissociation. CASTEP calculations were performed for both types of surfaces, pure Pd and Pd/Au. For starting point of the dissociation is chosen an on top position and the dissociation is performed toward two 3-fold positions, as shown in Chart 4. In the pure Pd surface case the H-H distance in the transition state is 1.56 Å and the activation energy is 8.7 kcal/ mol. In the case of Pd/Au surface the hydrogen molecule is dissociated on the top of a gold atom. Its larger radius determines a higher starting position and longer H-H bond in the transition state - 1.92 Å. This longer distance determines the higher activation energy, 15 kcal/mol. Our calculations show that the H2 dissociation is the process with the lowest energy barrier for the both types of surfaces. The presence of Au atoms does not block the reaction nor changes significantly the energetics of the process. These calculations prove the assumption that the hydrogen molecule is the first one to be dissociated and that the atomic hydrogen takes part in the formation of H2O2 4. Concluding Remarks We have investigated the direct synthesis of hydrogen peroxide on Pd and Pd/Au catalysts with first-principle DFT methods for periodic Pd and Pd/Au surfaces. A two-step reaction mechanism was proposed starting from a superoxo precursor state of the oxygen molecule. The activation energies for the both steps were determined to show that the synthesis of the peroxide is the preferred process on the catalytic surface. A competitive reaction of the dissociation of oxygen leading to the nonselective formation of water was found on the Pd(111) surface. The presence of gold atoms in the Pd/Au surface blocks this dissociation and increases the selectivity toward the main productsH2O2. The theoretical results are in a good agreement with the experimentally reported data concerning the selectivity and the formation rate of the direct formation of H2O2. Acknowledgment. K.Y. acknowledges Grants-in-Aid (Nos. 18350088, 18066013, and 18GS0207) for Scientific Research

Direct Synthesis of H2O2 from Japan Society for the Promotion of Science (JSPS) and the Ministry of Culture, Sports, Science and Technology of Japan (MEXT), the Nanotechno-logy Support Project of MEXT, and the Joint Project of Chemical Synthesis Core Research Institutions of MEXT for their support of this work. T.K. acknowledges a Grant-in-Aid for Young Scientists (No. 18750048) from JSPS. Supporting Information Available: Tables giving Cartesian coordinates of the atom in the unit cells of all structures. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Enders, D.; Wortmann, L.; Peters, R. Acc. Chem. Res. 2000, 33, 157. (2) Vaino, A. Org. Chem. 2000, 65, 4210. (3) Lee, S.; Fuchs, P. J. Am. Chem. Soc. 2002, 124, 13978. (4) Nomura, Y.; Ishihara, T.; Hata, Y.; Kitawaki, K.; Kaneko, K.; Matsumoto, H. ChemSusChem 2008, 1, 619. (5) Ishihara, T.; Hata, Y.; Nomura, Y.; Kaneko, K.; Matsumoto, H. Chem. Lett. 2007, 36, 878. (6) Chinta, S.; Lunsford, J. H. J. Catal. 2004, 225, 249. (7) Edwards, J. K.; Solsona, B. E.; Landon, P.; Carley, A. F.; Herzing, A.; Kiely, C. J.; Hutchings, G. J. J. Catal. 2005, 236, 69. (8) Han, Y.-F.; Lunsford, J. H. J. Catal. 2005, 230, 313. (9) Enache, D. I.; Edwards, J. K.; Landon, P.; Solsona-Espriu, B.; Carley, A. F.; Herzing, A. A.; Watanabe, M.; Kiely, C. J.; Knight, D. W.; Hutchings, G. J. Science 2006, 311, 362.

J. Phys. Chem. C, Vol. 112, No. 49, 2008 19505 (10) Huber, B.; Hakkinen, H.; Landman, U.; Moseler, M. Comput. Mater. Sci. 2006, 35, 371. (11) Choudhary, V. R.;Ingole, Y. V.;Samanta, C.;Jana, P.; Ind. Eng. Chem. Res. 2007. (12) Edwards, J. K.; Solsona, B. E.; Landon, P.; Carley, A. F.; Herzing, A.; Kiely, C. J.; Hutchings, G. J. J. Catal. 2005, 236, 69. (13) Weissermel, K.; Arpe, H. Industrial Organic Chemistry; VCH Publishers, Inc., New York, 1997. (14) Lunsford, J. J. Catal. 2003, 216, 455. (15) Dissanayake, D. P.; Lunsford, J. H. J. Catal. 2002, 206, 173. (16) Landon, P.; Collier, P. J.; Papworth, A. J.; Kiely, C. J.; Hutchings, G. J. Chem. Commun. 2002, 2058. (17) Okumura, M.; Kitagawa, Y.; Yamagcuhi, K.; Akita, T.; Tsubota, S.; Haruta, M. Chem. Lett. 2003, 32, 822. (18) Ishihara, T.; Ohura, Y.; Yoshida, S.; Hata, Y.; Nishiguchi, H.; Takita, Y. Appl. Catal., A 2005, 291, 215. (19) Landon, P.; Collier, P.; Papworth, A.; Kiely, C.; Hutchings, G.; Burrows, A. Phys. Chem. Chem. Phys. 2003, 5, 1917. (20) Roques, J.; Lacaze-Dufaure, C.; Mijoule, C. J. Chem. Theory Comput. 2007, 3, 878. (21) Honkala, K.; Laasonena, K. J. Chem. Phys. 2001, 115, 2297. (22) Olivera, P. P.; Patrito, E.; Sellers, H. Surf. Sci. 1994, 313, 25. (23) Imbihl, R.; Demuth, J. Surf. Sci. 1986, 173, 395. (24) Kolasinski, K. W.; Cemic, F.; Hasselbrink, E. Chem. Phys. Lett. 1994, 219, 113. (25) Clark, S. J.; Segall, M. D.; Pickard, C. J.; Hasnip, P. J.; Probert, M. J.; Refson, K. M. C. P. Z. Krist. 2005, 220, 567. (26) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (27) Xu, Y.; Mavrikakis, M. J. Phys. Chem. B 2003, 107, 9298.

JP803021N