First-Principles Studies of Vanadia−Titania Catalysts: Beyond the

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First-Principles Studies of Vanadia-Titania Catalysts: Beyond the Monolayer Andrea Vittadini* CNR-ISTM and INSTM, Via Marzolo 1, I-35131 PadoVa, Italy

Maurizio Casarin and Mauro Sambi Dipartimento di Scienze Chimiche, UniVersita` di PadoVa, Via Marzolo 1, I-35131 PadoVa, Italy

Annabella Selloni Chemistry Department, Princeton UniVersity, Princeton, New Jersey 08540 ReceiVed: July 6, 2005; In Final Form: September 19, 2005

Periodic density functional calculations have been used to investigate the structure and stability of epitaxial vanadium oxide films grown on the TiO2(001) anatase surface. The formation energy of films of V2O5 stoichiometry, initially low, is found to rapidly increase with the film thickness, at variance to what is obtained for reduced pseudomorphic VO2 films. This is in tune with results of oxygen-assisted molecular beam epitaxy. The oxidation of thick, viz. >2 monolayers (ML), VO2 films yields a c(2 × 2) reconstructed surface, in agreement with low energy electron diffraction. These films are composed by partially reduced inner V atoms in a distorted-octahedral environment, and by isolated surface dioxovanadium centers exhibiting a distorted trigonal-bipyramidal coordination. Single scattering simulations of X-ray photoelectron diffraction patterns have also been performed, taking both 2- and 3-ML surface surface-oxidized films as models. Results are in fair agreement with experiments referring to films grown in oxidizing conditions, which suggests that coherent vanadia ultrathin films could be formed in vanadia-titania catalysts. The electronic structure of the films has been finally studied, finding that the terminal oxygens carried by the surface dioxovanadium species have a strong nucleophilic character, which makes them potential active centers for selective oxidation catalysis.

1. Introduction Catalysis by vanadia supported on anatase (A-TiO2) has been extensively studied for many years,1 but several of its fundamental aspects are still poorly understood. These include the structure and composition of the active part of the catalyst, that is believed to be a thin layer (possibly a monolayer) strongly interacting with the support. It is generally accepted that, after an initial presence of tetrahedral monomeric and dimeric species, 5-fold- and 6-fold-coordinated V species become prevalent at higher coverage, which is explained with the formation of the so-called “polymeric” phase. In this regard, while recent 51V magic angle spinning (MAS) NMR spectra of Nielsen et al.3 showed that vanadium atoms in a distorted octahedral coordination are formed, Izumi et al.4 found that a satisfactory fitting of X-ray absorption near-edge structure (XANES) is obtained by admitting the presence of 5-fold coordinated dioxovanadium (OdVdO) species. A further issue concerns the concentration of vanadium (4+) species, whose formation readily occurs even in the absence of reducing agents. Whereas some authors claimed a preponderance of V(4+) ions,5 other ones6 found that these represent only a 20% of the total V atoms. A related and much debated hypothesis, originally put forward in the 1970s by Vejux and Courtine,7 is whether vanadia can grow epitaxially on the anatase support. Some years ago, model potential simulations for a variety of vanadia/titania interfaces have been reported,8 but more recent density functional calcula* Corresponding author. [email protected].

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tions show that epitaxial vanadia films thicker than 1 ML are energetically unfavored.9 On the experimental side, initial attempts to grow epitaxial vanadia layers on anatase single crystals10 by using reactive magnetron sputtering on the (001) surface of anatase mineral samples, yielded poorly ordered films, giving X-ray photoelectron diffraction (XPD), but no energy electron diffraction (LEED) patterns. More recently, Silversmit et al.11 investigated similar films by synchrotron UV photoelectron spectroscopy, finding that the vanadium oxide layer undergoes a slight photoreduction under irradiation with the synchrotron beam. On the other hand, Guo et al.12 showed that vanadium oxide films can be successfully obtained by oxygenplasma assisted molecular beam epitaxy (OPA-MBE) on (001)oriented anatase films grown on LaAlO3(001) at high temperature (T > 750 K). Characterization carried out by X-ray photoelectron spectroscopy (XPS), LEED, reflection high energy electron diffraction (RHEED), and X-ray diffraction indicates the formation of a pseudomorphic VO2 multilayer film terminated by an oxidized surface layer, whose structural details are unknown. The initial (1 × 4)/(4 × 1) LEED pattern of the clean anatase (001) surface appears to change to (1 × 1) after deposition of 1 ML of vanadia, and, subsequently, to c(2 × 2). Consistent with theoretical calculations,9 vanadium oxide films are not observed to grow beyond 1 ML in oxidizing (T ) 525 K) conditions. These films display a (1 × 1) reconstruction, but it is not clear whether this is due to the overlayer or to the support. In this work we want to study the structure and the stability of multilayer vanadia films on A-TiO2(001) with a twofold aim. On one hand, we intend to find a microscopic model able to

10.1021/jp0536910 CCC: $30.25 © 2005 American Chemical Society Published on Web 10/19/2005

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explain the experimental results on epitaxial growth of VO2 films in ref 12. On the other hand, we want to investigate possible connections between such films and the vanadia phases present in vanadia-titania catalysts. It seems indeed natural to connect the facile epitaxial growth of VO2 onto A-TiO2(001)12 with the recurring observations of V(4+) species in vanadiatitania catalysts.5 This idea is also supported by recent experimental studies,13 showing that the X-ray absorption fine structure (EXAFS) spectra of 6 wt % V2O5/TiO2 samples calcined at 723 K are very similar to those of pure VO2. 2. Computational Approach 2.1. Computational Details. As in our previous work on vanadia-titania,9,14 we performed plane-wave density functional calculations, using the PBE15 functional and Vanderbilt ultrasoft pseudopotentials.16 To increase the accuracy of the results we made use of small cores, including the 1s state for O, and the 1s, 2s, and 2p states for Ti and V. The wave functions were expanded in plane waves with a kinetic energy cutoff of 25 Ry, while the cutoff for the electron density was 200 Ry. Because of the metallic character of the slabs containing reduced vanadia, we adopted here a (6 × 6 × 1) Monkhorst-Pack mesh to sample the Brillouin zone of the (1 × 1) surface cell, and equivalent17 meshes for the other cells, viz. (1 × 2), (2 × 1), (x2 × x2)R45, and (2 × 2). All calculations have been run with the PWSCF 2.1 code, part of the ν-ESPRESSO package.18 Model slabs representing anatase-supported epitaxial vanadium oxide films of thickness up to 3 ML have been employed. The theoretical19 lattice constants have been used for the anatase support. Structural relaxations were performed by using a quasiNewton algorithm, setting the convergence parameters to 0.02 eV/Å for the forces and to 0.001 eV for the energy. All of the slab atoms were allowed to relax, except for the lowest three atomic layers of the TiO2 support. To reduce the computational effort, final calculations were performed by exploiting the symmetry of the slabs. The effect of removing symmetry constraints was checked in preliminar calculations. Structures of vanadium oxide bulk structures (R-VO2 and R-V2O5) were also optimized, and the resulting lattice parameters were in good agreement with the experimental ones20,21 as well as with those obtained from previous calculations.22 Single scattering cluster spherical wave (SSC-SW) simulations23 of X-ray photoelectron diffraction spectra were performed on a cluster containing 939 atoms. A 28° polar angle was assumed. Inelastic mean free paths for the attenuation of electron amplitudes have been estimated by means of the Tanuma-Powell-Penn formula known as TPP2.24 Scattering phase shifts have been obtained in the framework of the partial wave method within a muffin-tin model using the MUFPOT program.25 Effects due to inner potential refraction at the surface and to instrumental angular averaging have been also allowed. 2.2. Formation Energies. With a procedure similar to that used in ref 9, we compute the stability of VO2 films making reference to an ideal process where they are grown starting from the (1 × 4) reconstructed TiO2(001) surface26 and from a bulk VO2 reservoir. The energy involved in this process is

1 bulk ∆Efred ) [EVnO2n/TiO2 - EA-TiO2(001) - nER-VO ] 2 A

(1)

≈ ∆Gfred where A is the area of the surface exposed by the model slab, EVnO2n/TiO2 is the total energy of the interacting vanadia-titania system;28 EA-TiO2(001) is the total energy of the (1 × 4)

Figure 1. Schematic representation of a generic n-ML thick model film. bulk is the total reconstructed (001) anatase surface, and ER-VO 2 energy per stoichiometric unit of bulk VO2 in the rutile modification. Note that if we neglect entropic contributions, which are usually small for solid phases, we can take ∆Efred as an approximation to the free energy of formation ∆Gfred. In an oxidizing environment, a more convenient bulk reference phase is V2O5. Moreover, the chemical potential of gasphase oxygen must be introduced. Thus, the free energy of formation can be written as

∆Gf(T, p) ≈

1 E - EA-TiO2(001) A VnOm/TiO2 n bulk 5 E - m - n µO(T, p) (2) 2 R-V2O5 2

[

(

)

]

bulk where ER-V is the total energy per stoichiometric unit of 2O5 bulk V2O5 in the R modification; µO(T, p) is the O chemical potential, which determines the oxidizing/reducing conditions. As in previous work (see, e.g., ref 29), the zero for the chemical potential scale is fixed at -(1/2)EO2, which represents the most oxidizing environment at T ) 0.30 This means replacing µO in eq 2 by (1/2)EO2 + ∆µO(T, p). ∆µO(T, p) can be in turn computed from tabulated experimental values32 using the following relation:

1 ∆µO(T, p) ) [H(T, p0) - H(0 K, p0) 2 TS(T, p0) + KT ln(p/p0)] (3) At each ∆µO(T, p) value, the most stable film is the one with the lowest ∆Gf. While the formation energies in eqs 1 and 2 are referred to the separated anatase (001)-(1 × 4) surface and bulk vanadium oxide, it may be more realistic to use as a reference an unsupported vanadium oxide film rather than the bulk material. To model the film, we consider a slab exposing the most stable surface of the each bulk phase, i.e., the (110) surface for R-VO2, and the (001) one for R-V2O5. The expressions in eqs 1 and 2 for the formation free energies are modified as follows:

∆γred ) ∆Gfred - 2γR-VO2(110)

(4)

∆γ ) ∆Gf - 2γR-V2O5(001)

(5)

Here γR -VO2(110) and γR-V2O5(001) denote the surface free energies of R-VO2 and R-V2O5, respectively. It should be noticed that, due to the different nature of the vanadia phases, the effect of the 2γ correction is much stronger in the reducing environments. In fact, whereas for R-V2O5, a layer compound, γR-V2O5(001) ) 0.048 J/m2,33 we compute a substantially higher surface energy for R-VO2 (γR-VO2(110) ) 0.284 J/m). This difference is likely to play a role in the growth of vanadia films (vide infra). 2.3. Modeling of VOx Layers. On the basis of the experimental results in ref 12, model slabs have been built as sketched in Figure 1: a terminating layer of VOx stoichiometry has been placed on top of n - 1 layers of pseudomorphic VO2. After

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Figure 2. Favored arrangements for VOx phases of increasingly oxidized stoichiometry, shown in the case of 1-ML thick films. To make it easier to understand their details, structures are shown from two orthogonal viewpoints. The overlayer atoms are represented in a ball-and-stick style, the support atoms in a licorice style.

considering a number of possibilities, we have found the following VOx terminations (whose structures are shown in Figure 2 for the case of 1-ML films) to be the most stable in the chemical potential range of interest: (i) The first is the pseudomorphic VO2 reduced phase, from which all the other phases can be formed, either by adding O atoms or by removing V atoms. (ii) Second is VO2.5, obtained by adding a O atom on half of the V atoms of the VO2 phase. This causes a remarkably large structural relaxation, which makes all the V atoms carry a oxo ligand, so that they are ultimately equivalent. Though this result can be obtained by arranging the overlayer both in a c(2 × 2) and in a (2 × 1) fashion, we found the latter to be energetically favored. This (2 × 1) phase consists of OdV-O-VdO units arranged in rows (see Figure 2). (iii) Third is a VO3 phase, obtained by placing an O atom onto each cation of the VO2 phase. In this case, no major restructuring occurs for the surface, which can be described as a (1 × 1) array of vertically oriented vanadyls. (iv) Fourth is a VO4 phase: this could be in principle obtained by placing two O atoms onto each V cation of the VO2 phase. However, this gives rise to unlikely 7-fold coordinated V species. Actually, a more sensible choice to obtain a VO4 stoichiometry is that of removing one-half of the V atoms from the reduced phase, thus forming a c(2 × 2) array of OdVdO dioxovanadium species. Because the obtained phase is characterized by a 0.5-ML coverage, we will refer to it by the formula V0.5O2.

Vittadini et al.

Figure 3. Stability diagram for 1-ML (bottom), 2-ML (middle), and 3-ML (top) VOx films supported on anatase (001) as obtained by eq 2. Films are made of an outermost layer of the indicated stoichiometry and of n - 1 inner layers of pseudomorphic VO2, as sketched in Figure 1. Structural models are shown in Figure 2 for the 1-ML case. The vertical gray line indicates the theoretical boundary between the stability of the R-V2O5 and rutile-type R-VO2 bulk phases.

3. Results and Discussion 3.1. Pure VO2 Films. We first consider completely reduced films. By using eq 1, we find ∆Gfred ) 0.385, 0.450, and 0.578 J/m2 for 1-, 2-, and 3-ML films, respectively. Thus, the corresponding values of ∆γred (see eq 4) are negatiVe (or zero). Adding the second layer on top of the first one, and the third on top of the second one costs very little energy (∼0.1 J/m2), in line with the experimentally observed facile epitaxial growth of pseudomorphic VO2 films.12 3.2. Surface-Oxidized VO2 Films. To address the effects of oxidizing environments on the VO2 films, we optimized a number of slab models as described in section 2.3, and evaluated their stability by applying eq 2. The results are reported in Figure 3. Below is a brief description of the results for each film thickness. 1-ML CoVerage. The VO2.5 film is stable for the 0 e ∆µO e -2.6 eV range, while the over-oxidized VO3 phase is never stable, as it can be expected on the basis of electron counting. As we previously reported,9 the VO2.5 film has a slightly negative formation energy, However, this (2 × 1) phase is possibly difficult to observe, possibly because it is competition with phases composed by isolated tetrahedral dimeric units, as described in ref 9. 2-ML CoVerage. In this case, we find stability intervals to exist for the VO2, the VO2.5, and the VO3 terminations, whereas the V0.5O2 one is never stable. The stability of the VO3terminated 2-ML film in the wide 0 e ∆µO e -1.4 eV range can be understood by noticing that the oVerall stoichiometry of

First-Principles Studies this (VO2)(VO3) film is V2O5. Though low (0.41 eV/(1 × 1) cell, or 0.456 J/m2), the free energy of formation of the (VO2)(VO3) film is 1 order of magnitude higher than the V2O5 surface energy γR-V2O5(001), and therefore the picture is not changed if we consider ∆γ values instead of ∆Gf. We want to emphasize that the layer by layer formation energy for films of V2O5 stoichiometry follows an opposite trend with respect to that found for films of VO2 stoichiometry, because it sharply increases with film thickness. This explains why ordered vanadium oxide films cannot be grown in an oxidizing environment.10,12 3-ML CoVerage. For 3-ML films, all the possible film terminations have a stability range, the V0.5O2 one being favored in the most accessible region, i.e., at high ∆µO. This imposes a c(2 × 2) surface reconstruction which agrees with the LEED pattern observed for OPA-MBE grown vanadium oxide films.12 Interestingly, the (VO2)2(V0.5O2) film has an overall VO2.4 stoichiometry, so that the most stable termination for any film thickness is the one giving a film stoichiometry which is closest to V2O5. 3.3. Simulation of XPD Patterns. As mentioned in section 1, Devriendt et al.10 found that vanadium oxide layers grown by d.c. reactive magnetron sputtering do not give well-defined LEED patterns. However, they were able to obtain azimuthal XPD curves, which implies the presence of a short-range order in the film. SSC simulations carried out on monolayer models suggested a “flattened V2O5 (001) layer” model, as the most promising one.10 Other structures, and in particular the one proposed by Kozlowski and Haber,34 which displays a local structure around the V atoms that is identical to that of our V0.5O2 terminating layers, were discarded because of the absence of the 90° periodicity in the azimuthal curve. However, the absence of long range order in the films grown by magnetron sputtering suggests that islanding and towering probably occur in the overlayer. Thus, the 90° periodicity can be readily recovered because, depending on the height of the VOx “tower”, the orientations of the VdO bonds of the termination are rotated by 90° (the same effect could be actually obtained by simply admitting the presence of steps on the support, which is very likely, because it consists of a natural anatase crystal). On the basis of these considerations, we performed SSCSW simulations of the XPD patterns for the V 2p, O 1s, and Ti 2p shells, assuming photoemission from two domains rotated by 90°. We present the results for two models:35 (i) the thickest model film, which we computed to be compatible with the experimental V2O5 stoichiometry and thus possibly representative of the structure of the films grown by Devriendt et al.,10 viz. (VO2)(VO3); and (ii) the partially reduced (VO2)2(V0.5O2) model film, which is suitable to describe the pseudomorphic films grown by Guo et al.12 The resulting curves are plotted in Figure 4 together with the experimental ones taken form ref 10. As it can be seen, the V 2p and O 1s patterns are fairly well reproduced with both models, considering the high noise of the experimental curves,36 and the well-known overestimation of forward scattering given by SSC calculations. The agreement is poorer for the photoemission from Ti 2p, but this is explained by the partial coverage of the support, which makes the curve to be dominated by the photoemission from uncovered Ti atoms (see 4, bottom). Overall, it seems interesting that both model films are predicted to give a V 2p XPD pattern which is compatible with the experiment. Ultimately, this suggests that, though thinner and disordered, V2O5 films are structurally similar to ordered, pseudomorphic films obtained under reducing conditions.

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Figure 4. Comparison between the experimental XPD pattern observed on VOx films grown for A-TiO2(001) by magnetron sputtering (from ref 10) and the results of SSC-SW simulations. Note that the bottom panel refers to a simulation carried out on a clean A-TiO2(001) surface model.

3.4. The (VO2)2(V0.5O2) Film: Geometric Structure. We turn now to examine more closely the (VO2)2(V0.5O2) model film, which is interesting both because it is compatible with the properties of vanadium oxide films grown in reducing conditions, and because of its electronic structure (see the following section). The optimized structure of the model film is depicted in Figure 5, where the coordination polyhedra around V atoms are also shown. Bond distances, reported in Table 1, show that the V2-V5 atoms belonging to the inner layers are in a distorted octahedral environment, which is compatible both with a +5 and with a +4 oxidation state. Distances are within typical limits observed for the so-called [1 + 4 + 1] coordination in vanadium containing crystals.37 On the other hand, the topmost V atoms are in a distorted trigonal-bipyramidal [2 + 3] coordination, where the two oxo ligands lie in the equatorial plane. This arrangement is possible only for the +5 oxidation state, and it

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Figure 5. Equilibrium structure of the (VO2)2(V0.5O2) film. Distances are reported in Table 1.

TABLE 1: Interatomic Distances (Å) for the V0.5O2-Terminated 3-ML Film (See Figure 5) V1-O O1 O2 O3 O4 O5

1.614 1.614 2.029 2.029 2.172

V2-O O4 O5 O6 O7 O8 O10

1.640 1.965 1.833 2.011 2.004 2.361

V4-O O7 O9 O10 O11 O10 O13

Figure 6. Density of states (DOS) for the (VO2)2(V0.5O2) film. Top: O 2p projected DOS. Bottom: V 3d projected DOS. The vertical dashed line marks the Fermi level, which has been chosen as the origin of the energy scale. Positive/negative values refer to majority/minority spin. Atom codes are as indicated in Figure 5.

1.866 2.140 1.661 2.140 1.947 1.947

is found e.g. in the rossite structure.37 In the (VO2)2(V0.5O2) film, however, the pseudoaxial O3 and O4 atoms also belong to the vanadyl group of the V2 and V3 atoms. This makes the V1dO1/V1dO2 interactions stronger than in rossite. We now compare the computational results in Table 1 with experimental data for model vanadia-titania catalyst. Interestingly, the geometrical parameters of the distorted bipyramids almost perfectly match structural data for model catalysts recently obtained by XANES4 (V-O distances of 1.620 × 2, 1.922 × 2, 2.151 Å were used to reproduce the experimental data). Furthermore, the distorted octahedral units in our calculations are quite similar to those found in the catalysts studied by 51V MAS NMR spectroscopy.3 Thus, the (VO ) (V O ) film 2 2 0.5 2 is not only suitable to describe the properties of epitaxial vanadia films, but seems also compatible with most recent and accurate structural determinations of vanadia-titania model catalysts, suggesting that the polymeric phase of vanadia-titania catalysts could be closely related to V0.5O2-terminated pseudomorphic vanadia films. A relevant question is whether such films could be formed during a calcination treatment. Our calculations indicate that at 600 K and at p(O2) ∼ 10-10 bar the ∆Gf of (VO2)2(V0.5O2) film is positive and amounts to ∼1 eV. However, we should not forget that formation energies computed by DFT can have errors of several hundreds of millielectronvolts. Furthermore, our calculations impose a perfect matching between the support and the overlayer. This is likely to introduce artificial stresses that could be reduced by adopting larger cells. In any case, the presence of reduced V cations after calcination is an accepted experimental evidence, and, on the basis of our results, the most stable structure containing reduced V cations is the (VO2)2(V0.5O2) film. Since the reduced V atoms are in

Figure 7. Isosurface densities for the (VO2)2(V0.5O2) film. (a) Spin density. Displayed isovalue is 0.005 au. (b) Valence-band local DOS integrated in a 1 eV energy window close to the Fermi level. Displayed isovalue is 0.02 au.

the inner part of the film, they are protected against a further oxidizing attack. 3.5. (VO2)2(V0.5O2) Films: Electronic Structure. Useful information on the film electronic structure can be gained from the projection of the density of states (DOS) onto specific atomic species; see Figure 6. These curves show that V1 d states are only present in the valence band, largely in VdO bonding combinations, whereas V1 states are practically absent at the bottom of the conduction band. In contrast, subsurface V states predominate at the bottom of the conduction band. Hence, these atoms, and in particular those at the interface with the support, carry the spin density (see also Figure 7a), and are thus in a partially reduced state, as it was also inferred from the inspection of the coordination polyhedra. The occupied state closest to the Fermi level is strongly localized on the oxo oxygens.38 This is a lone pair combination, which is not involved in the VdO interaction (see also Figure 7b), and it could be quite important in determining the reactivity of the film.

First-Principles Studies In fact, oxidation of organic molecules on vanadia catalysts is believed to proceed through a Mars-van Krevelen mechanism.40 The rate-determining step for the oxidation of alkanes, alkynes and alkylaromatics on vanadia-titania catalysts is the organic activation by H abstraction. Experiments indicate that this occurs by nucleophilic attack from a catalyst O atom. The O atoms carried by the dioxo vanadium species are ideally suited as nucleophilic centers, since their lone pairs are highly available both spatially (they protrude vertically out of the surface; see Figure 7a) and energetically (they have an energy close to the Fermi level; see Figure 6). Because selective oxidation reactions involve as a rate-determining step H-abstraction processes by nucleophilic attack,41 the electronic properties of the (VO2)2(V0.5O2) film agree with the higher selectivity of titaniasupported catalysts. In this regard, it is worthwhile to mention that cluster calculations by Haber and Witko42 showed that the surface oxygens of the R-V2O5(001) surface interact repulsively with incoming organic molecules; i.e., they are poor nucleophilic centers. 4. Conclusion In this work, we have presented a periodic DFT study of the energetics, structure, and electronic properties of vanadium oxide films grown on (001) oriented anatase supports. Our results show that the epitaxial growth of vanadium oxide is favored in reducing condition, and yields pseudomorphic VO2 films. Exposure to oxygen tends to restore a V2O5 stoichiometry, inducing a surface reconstruction which changes from (2 × 1), to (1 × 1), and to c(2 × 2) for 1-, 2-, and 3-ML films, respectively. The c(2 × 2) phase is composed by 5-fold coordinated dioxovanadium units, acting as passivating caps of an underlying, partially reduced structure, which is made of V atoms in a distorted octahedral environment. Because most recent structural determinations of vanadia-titania model catalysts have shown the presence of similar units, we propose that surface-oxidized thin pseudomorphic films may be a good model for the polymeric phase of vanadia-titania catalysts. This hypothesis is reinforced by another finding: SSC-SW simulations based on models for oxidized 2-ML and 3-ML films are compatible with experimental XPD patterns obtained for vanadia films grown in oxidizing conditions. Finally, we have found that the oxo oxygens carried by the 5-fold coordinated dioxovanadium units have a strong nucleophilic character, which makes them interesting as active centers in oxidation catalysis. Acknowledgment. Calculations in this work have been done using the ν-ESPRESSO package,18 and they have been run at the Keck Computational Center of the Princeton Materials Institute and at CINECA (Bologna, Italy). This work has been partially supported by “Progetto FIRB - Piattaforme abilitanti per griglie computazionali ad elevate prestazioni orientate a organizzazioni virtuali scalabili” funded by MURST (Rome). We are grateful to E. Altman for interesting discussions. References and Notes (1) Busca, G.; Lietti, L.; Ramis, G.; Berti, F. Appl. Catal., B: EnViron. 1998, 18, 1. Bond, G. C. Appl. Catal., A: Gen. 1997, 157, 91. Keller, D. E.; Weckhuysen, B. M. Catal. Today 2003, 2811, 1. Grzybowska-SÄ wierkosz, B. Appl. Catal., A: Gen. 1997, 157, 263.

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