Oxidative Dehydrogenation of Methanol to Formaldehyde by Isolated

J. Phys. Chem. C 2009, 113, 16083–16093

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Oxidative Dehydrogenation of Methanol to Formaldehyde by Isolated Vanadium, Molybdenum, and Chromium Oxide Clusters Supported on Rutile TiO2(110) Hyun You Kim,† Hyuck Mo Lee,† Raj Ganesh S. Pala,‡,§ and Horia Metiu*,‡ Department of Materials Science and Engineering, KAIST, 335 Gwahangno, Yuseong-gu, Daejeon 305-701, Korea, and Department of Chemistry and Biochemistry, UniVersity of California, Santa Barbara, Santa Barbara, California 93106, USA ReceiVed: April 9, 2009; ReVised Manuscript ReceiVed: June 11, 2009

We use density functional theory to examine some of the important aspects of methanol oxidation to formaldehyde catalyzed by isolated MO3 (M ) V, Mo, and Cr) clusters supported on rutile, TiO2(110). Thermodynamic analysis led us to conclude that in the presence of oxygen, the M (M ) V, Mo, and Cr) atom takes three oxygen atoms from the gas phase and this MO3 species is the oxidant in the catalyst. We calculate the structure of these clusters, their Bader charge, the structure of the methoxide formed by methanol adsorption, and the activation energy for the dehydrogenation of the methyl group in the methoxide. We find that VO3 is a substantially better catalyst than MoO3 or CrO3. 1. Introduction The chemical industry uses many catalysts consisting of oxide clusters on an oxide support (OCOS),1-5 and a large number of academic studies have been devoted to this class of catalysts. In many cases it is fairly well documented that these catalysts consist of either isolated oxide clusters bound to the surface of the support or of “polymers” in which the cations of the clusters are connected by bridging oxygen atoms. It is believed that the coverage of the oxide on the support does not exceed a monolayer. In this article we use density functional theory to examine the conversion of methanol to formaldehyde (CH3OH + 1/2O2 f CH2O +H2O), catalyzed by isolated clusters of vanadia, chromia, or molybdena, supported on rutile TiO2(110). Given the complexity of these systems it is difficult to determine experimentally, beyond reasonable doubt, the stoichiometry and the structure of the supported clusters. Because of this we use DFT to answer this question. To do this we imagine the following experiment: the TiO2(110) surface is covered by a submonolayer of isolated M (M ) V, Cr, or Mo) atoms and is exposed afterward to gaseous oxygen, at a given temperature and pressure, until thermodynamic equilibrium is established. We want to know the equilibrium composition of the surface layer. The presence of oxygen can oxidize M to any one of the clusters MO, MO2, MO3, and MO4 (M ) V, Cr, and Mo). This notation includes only those oxygen atoms that the metal gains by reacting with gaseous oxygen; it excludes the oxygen atoms of the support, even though some of them may be bonded to M. Our computations find that all clusters MOn, n ) 1-4 (M ) V, Cr, or Mo) are stable, in the sense that they all correspond to minima on the potential energy surface. In principle, they can all be present on the surface, in different proportions, when the system is in equilibrium with gas-phase oxygen. However, our equilibrium calculations show that, under * Corresponding author. E-mail: [email protected]. Fax: 805-8934120. Tel: 805-893-2256. † KAIST. ‡ University of California, Santa Barbara. § Present address: Department of Chemical Engineering, India Institute of Technology, Kanpur, India.

the conditions of preparation, the MO3 clusters are the dominant species on the surface. This conclusion should be valid not only for the clusters prepared as described above but also for those obtained by a variety of “wet chemistry” methods if they are calcined for a sufficiently long time in the presence of gaseous oxygen; the equilibrium state of the system does not depend on the method of preparation. It is known from experiments that methanol adsorbs on these surfaces dissociatively and molecularly. Methanol dissociates to form a methoxy (-OCH3) radical and a hydrogen atom which will bind somewhere on the surface (in principle it could make either a hydroxyl or a hydride). The rate-limiting step, for CH2O production, is the dehydrogenation of -Me-O-CH3: a H atom leaves the methyl group and binds somewhere on the cluster or the support. It is not clear whether the molecularly adsorbed methanol is a spectator or it participates in formaldehyde formation. It is difficult to learn from experiments any details about the reactions taking place after the rate-limiting step, because they are much faster. It is known that some of the hydrogen atoms recombine with the methoxide to form methanol;6 others must form water, which desorbs. Water desorption may (or may not) create oxygen vacancies on the surface and these must be subsequently annihilated by reacting with oxygen from the gasphase and/or with the water formed by the reaction. Due to the complexity of the system we concentrate on the rate-limiting step (the dehydrogenation of the methoxide) and study how this changes when we change the oxide cluster from VOx, to MoOx and to CrOx. Such studies are useful if one wants to screen a large number of systems to find which OCOS combinations have the best chance of being good dehydrogenation catalysts. Given the possibility that the density functional theory may have difficulties in describing accurately narrow band oxides (see section 2), we think that it is safer to study trends in the rate-limiting step, rather than focus on determining all of the details of the reaction mechanism. We find that the activation energy for the dehydrogenation of VO3/TiO2(110) is substantially smaller than that of CrO3/ TiO2(110) or MoO3/TiO2(110). In fact, the activation energy for the last two is so large that it leads us to suggest that the

10.1021/jp903298w CCC: $40.75  2009 American Chemical Society Published on Web 08/14/2009

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Figure 1. [4 × 1] supercell used in the DFT calculations: (a) side view and (b) view from above. We used 12 atomic layers for the slab, but the figure shows only a few layers near the surface. The oxygen atoms are red, and the Ti atoms are gray.

reactivity of the isolated clusters is very low and that the reactions observed in experiments are likely to take place on polymerized CrOx or MoOx. The paper is organized as follows. In section 2 we describe the method of computation and also explain possible difficulties density functional theory has in describing oxides that have narrow d or f bands. As suggested in previous work7,8 we assume that the reactions in which the spin-polarization changes from reactant to product are very slow and are to be ignored in catalysis. Consequently, we study only reactions in which the system maintains the spin polarization of the reactants at all points along the reaction coordinate, until the products are reached. Section 3 summarizes the existing experimental information about these systems. Our results are presented in section 4. A summary is given in section 5. The idealized slab models used here are different from the high-surface-area catalysts used in experiments and there are uncertainties regarding the accuracy of DFT when applied to oxides. Therefore, we are more confident in the trends obtained while comparing similar systems than we are in the absolute values of the numerical results. 2. Computational Methods We perform spin-polarized Kohn-Sham DFT calculations with the plane-wave VASP code9-12 and the Perdew-Wang functional.13 The ionic cores are described by the PAW method implemented in VASP.9-12 To describe the surface we used a rutile TiO2(110) slab having 12 atomic layers and a surface supercell of [4 × 1] (see Figure 1). The surface energy of rutile TiO2(110) slab and the binding energy of molecules to the surface depend on slab thickness.14-18 However it appears that these quantities are converged if we use 12 atomic layers and fix the atoms in the bottom six layer in the bulk positions.15,19 The atomic positions in the top 6 layers are allowed to relax during geometry optimization. A 5 × 3 × 1 k-points mesh was applied to all calculations. The plane wave energy cutoff was 300 eV. The convergence criteria for the electronic wave function and the geometry were 10-5 and 10-4 eV, respectively. We used the Gaussian smearing method with initial window size of 0.02 eV, which was gradually decreased down to 0 during geometry optimization, to prevent partial

Kim et al. occupancy. Monopole, dipole, and quadrupole moment corrections to energy were applied in the direction perpendicular to the slab. The nudged elastic band method with at least 6 images was applied to find the transition state of different dehydrogenation paths of methoxide. In previous work7,8 we have suggested that reactions in which the spin-polarization (the number of electrons with spin up minus the number of electrons with spin down) of the reactants differ from that of the products are slow because the internal magnetic fields in molecules are too small to be able to “flip” the spin effectively as the nuclei move from the reactant structure to that of the product. Because of this, we look only at reactions which preserve spin-polarization. When we determine the activation energy we force spinpolarization conservation on all points along the reaction coordinate. The initial states examined here (the cluster on the rutile and methanol in the gas phase) have the lowest energy when the spin state is a doublet. Threfore we maintain the spin polarization to be a doublet when we calculate the reaction path, the transition state and the final state in the reaction steps that we examine. 3. Background Information: Previous Work In this section we summarize the extensive and sometimes conflicting information on the structure of VOx, CrOx, and MoOx submonolayers supported on titanium oxide and on the mechanism of methanol oxidation by these catalysts. 3.1. VOx Supported on TiO2. Several reviews20-27 pointed out that supported vanadium oxide is the most versatile and useful OCOS. The VOx supported on titania has been studied by Raman,28-32 IR,29,31,33-37 NMR,38,39 XPS,25,26,39-45 X-ray absorption,46 and UV-vis31 spectroscopy. These experiments have found that at low vanadium loading the catalyst consists of isolated VOx clusters, and at high loading, VOx forms “polymers” in which the vanadium atoms are connected through -V-O-V- bonds. The catalytic activity decays markedly when the amount of VOx exceeds that required for forming a monolayer on the surface of the support. The structure of the VOx clusters is still debated.46-48 The most frequently held view is that the oxygen atoms around the vanadium form a distorted tetrahedron and oxygen atoms bridge the vanadium atom to the Ti atoms in the support. Each cluster contains a vanadyl group (VdO). The XPS spectrum before methanol oxidation is close to that of pentavalent vanadium compounds; after methanol oxidation took place, the spectrum resembles that of trivalent vanadium compounds. The structure and the stoichiometry of VOx on rutile TiO2(110) and CeO2(111) were examined by using density functional theory.49 The calculations assumed that the VOx clusters were prepared by placing isolated V atoms on the support, exposing them to gas-phase O2, at a given pressure and surface temperature, and allowing them to reach thermodynamic equilibrium. All methods of preparation must lead to the same equilibrium state, as long as the supports are identical. The calculations found that under the conditions of pressure and temperature used by some of the experiments almost all V atoms are oxidized to VO3. This formula includes only the oxygen atoms that came from gas-phase; the surface oxygen atoms to which V is bonded are not represented in it. We are using this convention throughout this article. The experiments6,31,33-35,50-55 give the following information about the steps in the reaction mechanism. (1) Methanol adsorbs dissociatively and forms a methoxide (CH3O-) and a hydroxyl. The IR measurements have detected

Oxidative Dehydrogenation of Methanol

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TABLE 1: Energies of Various Oxidation Reactions MOn + 1/2 O2(g) f MOn+1 where M Can Be V, Cr, or Moa VO2 f VO3

VO3 f VO4

CrO2 f CrO3

CrO3 f CrO4

MoO2 f MoO3

MoO3 f MoO4

-1.40

-0.17

-1.71

-0.08

-4.02

+0.86

The reaction energies are calculated from E(MOn+1) - 1/2 E(O2(g)) - E(MOn) where E(MOn) is the energy of the cluster MOn supported on the rutile TiO2(110) surface and E(O2(g)) is the energy of a gaseous O2 molecule. These energies are calculated by using DFT. a

the methoxide on the surface and showed that it participates33,34 in the reaction. Raman experiments show that during this reaction a -V-O-Ti- bond is broken. It is therefore reasonable to assume that dissociative adsorption of methanol is described schematically by CH3OH + -V-O-Ti- f V-OCH3 + Ti-OH. The vibrational frequency of the vanadyl and the amount of light absorbed by it do not change during the reaction. (2) In the next step, the methoxide is dehydrogenated to form formaldehyde (CH2O), which desorbs. The consensus is that the dehydrogenation of the methyl group in the methoxide is the rate limiting step for methanol oxidation.6,20,25,33,35 As Madix pointed out,6,25 the conversion to formaldehyde takes place at very low methoxide concentration, which means that it is very likely to be unimolecular. This suggestion is further supported by the observation that the turnover frequency for the overall reaction is independent of the VOx concentration at the surface.25,26 Moreover, the oxidation of CD3OH produces exclusively CD2O indicating that the dehydrogenation of CD3O- is a simple one-step process and that no exchange between the D3CO- and the H present on the surface takes place.6 (3) The processes examined so far place two hydrogen atoms in the system, in an unknown position. Ultimately they form water, which desorbs from the surface leaving behind an oxygen vacancy. (4) To have a catalytic process, gas phase oxygen must “heal” the oxygen vacancies. Nothing is known about steps 3 and 4 except that they are very fast compared to the dehydrogenation rate. (5) In parallel with the previous steps, the methoxy radical recombines with the hydrogen atoms present on the surface to make methanol, which desorbs.6 Madix’s experiments6 with CD3OH imply that under reaction condition H has a reasonable mobility. Selectivity for formaldehyde formation, on VOx supported on titania is 90-99%. Because of this, in studying the mechanism of methanol oxidation, we need not worry about side reactions. The turnover frequency is independent of VOx loading, which suggest that the activity, per vanadium atom, of the isolated clusters is close to that of the VOx polymers.25,26 3.2. CrOx Supported on TiO2. The structure of the CrOx depends on the support and loading and probably on the method of preparation. In the case of CrOx/TiO2 a combination of Raman,56-59 XPS,56,59 and IR spectroscopies58 as well as studies of the exchange of gas-phase 18O2 with the 16O from the surface57 have established that at very low loading the surface consists of isolated Cr(VI) clusters. At higher loading, Cr(III) is present and “polymers” of CrOx are formed. In both cases there is only one CrdO group per chromium atom (monooxo as opposed to dioxo chromium).57 Methanol oxidation by supported CrOx was studied by Wachs and his collaborators.60-62 The mechanism of methanol oxidation to formaldehyde by supported CrOx is very similar to that on supported VOx.

3.3. MoOx Supported on TiO2. MoOx supported on TiO2 was studied by Raman63-65 and X-ray adsorption spectroscopy.64,66-68 Several works63,65,67 concluded that the vanadium atom is tetrahedrally coordinated but others64,66 proposed an octahedral coordination. The structure depends on coverage and on the method of preparation and this might explain why different groups reached different conclusions. In principle the MoOx may have one (monooxo) or two (dioxo) molybdyl (ModO) groups. Kim, Wachs, and Segawa69 found that the clusters are monooxo, at all coverages studied by them. The mechanism of oxidation of methanol to formaldehyde catalyzed by MoOx/TiO2 is very similar65,68-70 to that catalyzed by VOx/TiO2. 4. Results 4.1. Stoichiometry of the Clusters. To determine the structure and the stoichiometry of the oxide clusters we imagine that we have deposited isolated metal atoms (V, Cr, or Mo) on the TiO2 surface and then exposed them to gaseous oxygen, at a given pressure and temperature. We assume that the system undergoes the reactions

M + 1/2 O2 h MO

(1)

MO2 + 1/2 O2 h MO

(2)

MO2 + 1/2 O2 h MO3

(3)

MO3 + 1/2 O2 h MO4

(4)

(M ) V, Cr, or Mo) and reaches thermodynamic equilibrium. The energy change in reactions 1-3 is very large (see Table 1) and therefore M, MO and MO2 will not be present on the surface at equilibrium. Because of this, we need to consider only reaction 4, to determine the coverage of MO3 and MO4 on the surface. The equilibrium condition is71

µ(MO4) - µ(MO3) - 1/2µ(O2) ) 0

(5)

where µ(x) is the chemical potential of species x. The equilibrium composition is characterized by the coverages θ(VO3) and θ(VO4) (since θ(V), θ(VO), and θ(VO2) are practically zero), where θ(x) is the number of molecules x divided by the initial number of V atoms in the system. These coverages must satisfy eq 5 and the conservation condition

θ(VO3) + θ(VO4) ) 1

(6)

Since we deal with a low initial V coverage and assume the V atom to be isolated, we can calculate the chemical potential of the adsorbed species by using an ideal lattice-gas model.72

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TABLE 2: Lengths of Several Bonds in the Supported VO3 Cluster Shown in Figure 2a (Where the Symbols Used in This Table Are Defined) bond length (Å) VO3 methoxy formaldehyde

V-b1

V-b2

V-O1

V-O2

V-O(VdO)

V-O(C)

O2-Ti1

2.08 1.91 1.93

2.06 1.99 2.00

1.85 1.85 1.95

1.85

1.61 1.62 1.63

1.98 2.04

1.98 2.19

This gives a chemical potential having three terms: the electronic energy of the species, a contribution from the configurational entropy arising from the fact that n particles can occupy m lattice sites in many equivalent ways, plus a contribution from the vibrations.72 The expression for the chemical potential of gas phase O2 is well-known.73 Using these formulas in eq 5 allows us to calculate the value of θ(VO3) and θ(VO4) at equilibrium, as a function of oxygen pressure and temperature, by solving eqs 5 and 6. The result is

θ(MO4) ¯ /kT] ) exp[-∆ θ(MO3)

(7)

with

( )

( )

¯ ) ∆(E) + ∆Zp - kT ln kT - kT ln T ∆ 2 2 2Tr p0Λ3 1 p kT ln 2 p0

()

(8)

Here ∆(E) is the change in the electronic energy due to the oxidation reaction (i.e., E(MO4) - E(MO3) - 1/2 E(O2(g))), where E(x) is the electronic energy of the species x), ∆Zp is the change in the zero point energies caused by the reaction eq 4, p0 is 1 atm, Tr is the rotational temperature of O2, p is the pressure,

Λ)

h2 2πmkT

are VO3 or CrO3, even though the oxidation of VO3 or CrO3 to VO4 or CrO4 is slightly exothermic (see Table 1). For MoOx, the oxidation of MoO3 to MoO4 is so exothermic that eq 7 or eq 10 lead to the same conclusion: at equilibrium, the surface is covered mainly with MoO3. 4.2. Structure of the MO3 Clusters. In Figures 2a, 3a, and 4a, we show the calculated structures of the MO3 clusters (M is V in Figure 2a, Cr in Figure 3a, and Mo in Figure 4a), and in Tables 2-4, we give the lengths of the important bonds. For example, the first line in Table 3 tells us that V binds to two bridging oxygen atoms on the TiO2(110) surface (denoted b1 and b2 in Figure 2a), with bonds of equal length (∼2.07 Å). V also binds to two oxygen atoms which were taken from the gas phase (denoted O1 and O2 and colored blue in Figure 2a); both of these bonds are 1.85 Å long. The O1 and O2 oxygen atoms bind the cation in the cluster to the 5c-Ti atoms in the surface and are often called the bridging oxygen atoms. They should not be confused with the bridging oxygen atoms on the clean rutile (110) surface, which are colored red. Finally, V also binds to an oxygen atom (colored orange) to form a vanadyl, which is identified by the shorter bond length (1.61 Å). The orange oxygen atom is captured from the gas phase when the V atom is oxidized. The structures of the CrO3 cluster (Figure 3a and Table 4) and that of the MoO3 cluster (Figure 4a and Table 5) are similar to those of VO3. This similarity is puzzling considering the difference in the valences of these elements and their positions in the periodic table. However, after the dissociative adsorption of methanol, the cluster structures are different (for different cations M), and this explains, to some extent, the difference in reactivity for dehydrogenation.

(9)

is the de Broglie thermal wavelength, h is the (old) Planck constant, k is the Boltzmann constant, and m is the mass of the molecule. In writing this formula we used the fact that highfrequency vibrations do not contribute to the chemical potential and assumed that the low-frequency lattice vibrations terms in the equilibrium condition cancel each other. These assumptions simplify the equations without altering the qualitative conclusions derived from eq 7. If we considered, as is customary, only the change in the electronic energy during the reaction then

θ(VO4) ) exp[-(∆(E) + ∆Zp)/kT] θ(VO3)

(10)

The difference between the oversimplified eq 10 and the more accurate eq 7 comes from the inclusion in eq 8 of the translational and rotational energy and entropy of the gaseous oxygen and the configurational entropy of the lattice-gas model. With the reaction energies given in Table 2 the oversimplified eq 10 tells us that VO4 and CrO4 are present on the surface. However, if the improved eq 7 is used, most surface clusters

Figure 2. (a) VO3 cluster supported on rutile TiO2(110). (b) The VO3 cluster after the dissociative adsorption of methanol. A methoxy radical is bound to the V atom and a hydroxyl was made with the oxygen atom bonded to a 5c-Ti atom. (c) The product formed by the dehydrogenation of the methyl in the methoxide. A dihydroxyl (or a water molecule) bound to the 5c-Ti atom is formed by dehydrogenation. The blue and orange oxygen atoms are acquired when V is oxidized. The red ones belonged to the rutile before the cluster was adsorbed.


Figure 3. (a) CrO3 cluster supported on rutile TiO2(110). (b) The CrO3 cluster after the dissociative adsorption of methanol. A methoxy radical is bound to the Cr atom and a hydroxyl was made with the oxygen atom bonded to a 5c-Ti atom. (c) The product formed by the dehydrogenation of the methyl in the methoxide. The hydrogen atom produced by the dehydrogenation binds to the oxygen in the chromyl and the organic molecule resembles formic acid. The blue and orange oxygen atoms are acquired when Cr is oxidized. The red ones belonged to the rutile before the cluster was adsorbed.

Figure 4. (a) MoO3 cluster supported on rutile TiO2(110). (b) The MoO3 cluster after the dissociative adsorption of methanol. A methoxy radical is bound to the Mo atom and a hydroxyl was made with the oxygen atom bonded to a 5c-Ti atom. (c) The product formed by the dehydrogenation of the methyl in the methoxide. The hydrogen atom produced by the dehydrogenation binds to the oxygen in the molybdyl and the organic molecule resembles formic acid. The blue and orange oxygen atoms are acquired when Mo is oxidized. The red ones belonged to the rutile before the cluster was adsorbed.

It is not possible to compare unambiguously these bond lengths to those obtained by EXAFS. There is evidence that the structure of a cluster and even its stoichiometry depend on the crystal face of the support. For example, calculations that deposited a MoO3 cluster on anatase74 found that on the (101) surface the cluster is stable, but on the (001) surface the cluster removes an oxygen atom from the surface to make a dioxo, MoO4 group. Different structures were also found, by DFT

J. Phys. Chem. C, Vol. 113, No. 36, 2009 16087 calculations, for MoOx bound to the (110) and the (100) faces of γ-alumina.75 In addition, on a given face, clusters located at kinks, steps, or point defects are likely to have different bond lengths or even structures, than the clusters bound to a terrace. If the support is not well faceted or is amorphous, the surface of the support is disordered and the structure of the cluster depends on the local surface environment. EXAFS measurements will give an ill-defined average over various structures. For this reason we do not compare our results with those derived from EXAFS. In general, DFT calculations give fairly good bond lengths. 4.3. Charges on the Atoms. The charges on various atoms were calculated by using Bader’s method,76-79 and the results are presented in Figures 5-7. The two oxygen atoms that bridge the metal atom of the cluster to the 5c-Ti atom of the surface have the same charge (∼-1.1 electron) for all clusters (i.e., VO3, CrO3, or MoO3). The charge on V is 2.20, on Cr is 2.01, and on Mo is 2.62. The positive charge shows how much electron charge is removed from the neutral atom when the cluster is formed. The amount of missing electron charge does not correlate with either the electronegativity of the metal in the cluster, or with its electron affinity. Note that the charges in these figures do not add up to zero because other Ti and O atoms lose or gain charge upon cluster adsorption (those changes are not indicated in the figure). We have found no correlation between the charges on the atoms and their chemical activity. 4.4. Methoxide Formation. It is well documented, for all three clusters, that methanol adsorbs dissociatively to form a methoxide (CH3O-) and a hydroxyl. The methoxide is a precursor for formaldehyde formation. Since this dissociative adsorption is not the rate limiting step, we did not study the activation energies of this process but limited ourselves to searching for the most stable structures of the methoxide and the hydroxyl. These are shown in Figures 2b, 3b, and 4b. In all cases the methoxy radical is formed by breaking the bond between the metal atom in the cluster and the oxygen that bridges it to the Ti atom, in agreement with the experimental determinations based on vibrational spectroscopy. The metal atom in the cluster binds the methoxide; the hydrogen atom, originating from CH3OH, binds to the bridging oxygen atom (M-O-Ti) to form a hydroxyl bound to a 5c-Ti atom; the oxygen atom in this hydroxyl is no longer bonded to the metal atom of the cluster. The central atom in the cluster maintains its valence during this reaction: the M-OTi bond is broken but M makes a bond with the methoxide. One expects that dissociative adsorption of methanol will disrupt the bond lengths in the cluster. In the case of VO3 the disruption is relatively small. In Table 2 we see a slight tightening of the bonds of V with the b1 and b2 oxygen atoms (these are bridging oxygen atoms in the TiO2(110) rutile support) from ∼2.07 Å to 1.91 and 1.99 Å. Shortening of bonds indicates, usually, that they have become stronger. The lengths of the V-O1 and the VdO bonds are not modified when methanol adsorbs dissociatively. It is interesting to note that the length of the V-OCH3 bond is practically the same as that of V-Ob1 and V-Ob2. There have been suggestions in the literature that the dissociative adsorption of methanol may take place through an addition to the vanadyl double bond. We found that this would require too much energy to be competitive with the mechanism discussed above. The same is true for a dissociation process in which the hydrogen formed by the dissociation of the hydroxyl in methanol binds to the oxygen in the vanadyl group.

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TABLE 3: Lengths of Several Bonds in the Supported CrO3 Cluster Shown in Figure 3 bond length (Å) CrO3 methoxy formaldehyde

Cr-b1

Cr-b2

Cr-O1

Cr-O2

Cr-(CrdO)

Cr-O(C)

O2-Ti1

C-O2

2.01 2.10 1.97

1.98 1.71 1.89

1.80 1.76 1.86

1.79

1.59 1.62 1.78

1.82 1.85

1.76 2.23

1.45

TABLE 4: Lengths of Several Bonds in the Supported MoO3 Cluster Shown in Figure 4 bond length (Å) MoO3 methoxy formaldehyde

Mo-b1

Mo-b2

Mo-O1

Mo-O2

Mo-O (ModO)

Mo-O(C)

O2-Ti1

C-O2

2.07 2.08 2.06

2.06 1.85 1.97

1.88 1.92 1.90

1.87

1.71 1.72 1.91

1.94 1.95

1.76 2.14

1.47

TABLE 5: Reaction Energies and the Activation Energies of the Three Pathways for the Dehydrogenation of the Methyl Group in the Methoxy Radical dehydrogenation energy (eV)

activation energy (eV)

rutile TiO2(110) supported catalyst

H2O like dihydroxyl

M)O

two hydroxyls

H2O like dihydroxyl

M)O

two hydroxyls

VO3 CrO3 MoO3

-1.22 -0.05 +0.81

-0.45 -0.67 +0.57

-0.73 +0.70 +1.29

0.88 1.64 1.98

1.96 1.34 1.40

1.92 1.75 1.67

The dissociative adsorption of methanol on CrO3 causes a more substantial disruption of the bond length in the cluster (Table 3). The bonds Cr makes with various oxygen atoms are no longer having similar lengths. One can see in Figure 3b that the b2 oxygen atom is pulled out from its position in the bridging oxygen row of the TiO2 surface. However, the cromyl group is undisturbed by all these changes. The situation for Mo is similar to that on Cr (see Figure 4b or Table 4). 4.5. Change in Atomic Charges upon Dissociative Adsorption of Methanol. The Bader charges in Figure 5 show that the dissociative adsorption of methanol on VO3 causes

Figure 5. Bader charges on various atoms. (a) The VO3 cluster, (b) the cluster with methoxide and a hydroxyl, (c) the cluster with formaldehyde and a dihydroxyl, and (d) the cluster with formaldehyde and a hydroxyl on the vanadyl.

practically no change in the charge of the atoms involved, except for the oxygen receiving the H atom to make the hydroxyl. The charge disturbance that might be caused by cutting the V-O bond in the -V-O-Ti- group is compensated by the formation the -V-OCH3 bond; the charge on the oxygen atom in the -V-OCH3 group is the same as the charge on the oxygen atom in the V-O-Ti group prior to methanol dissociative adsorption. As far as the electrostatics is concerned the V atom sees the same environment after methanol dissociative adsorption as before. As a result, its charge is not changed. This does not mean that the vanadium XPS spectrum will not change; the peak position depends on the difference between the total energy of the ionized system and the total energy of the neutral one, not on the change in the total charge of the atom (as is often assumed). CrO3 is different (see Figure 6) from VO3. The b2 oxygen atom, which is pulled out of its place when the methoxy is bonded, loses a substantial electron charge (from -1.1 to -0.87). The oxygen atom in Cr-OCH3 has a much higher charge than the same atom in V-OCH3. It is also interesting that the atoms in the CH3 group also have more charge than in the case of vanadium cluster. In spite of this, the Cr and the oxygen atom in the chromyl group are hardly affected: their charge is very close to that prior to methoxy adsorption. Similar comments pertain to the Mo case (see Figure 7) except for the large negative charge induced on carbon. This analysis of the bond length and atomic charges shows that VO3 differs from MoO3 and CrO3 in the manner in which it forms the methoxide, even though the structures of the clusters prior to the dissociative adsorption of methanol were rather similar. 4.6. Dehydrogenation Reaction. For all clusters examined here, the rate limiting step in formaldehyde formation is the dehydrogenation of the methyl group in the methoxide. Figure 8 shows three possible binding sites for the H atom removed from the methyl group (8a for VO3, 8b for MoO3, and 8c for CrO3). In each of these figures the upper-left corner shows the cluster before the dehydrogenation of the methyl. In the upper right corner of each figure, we show the structure formed when a H atom from -OCH3 is moved onto the hydroxyl group to from a dihydroxyl; one can equally view the dihydroxyl as


Figure 6. Bader charges on various atoms. (a) The CrO3 cluster, (b) the cluster with methoxide and a hydroxyl, and (c) the cluster with formaldehyde and a hydroxyl on the chromyl.

Figure 7. Bader charges on atoms. (a) MoO3 cluster, (b) MoO3 cluster with methoxide and a hydroxyl, and (c) MoO3 cluster with formaldehyde and a hydroxide on the molybdyl group.

a water molecule bonded to a 5c-Ti atom. In the lower-left corner of each figure we show the structure formed when the H atom from the methyl group is transferred to the sMdO group, to form sMdOsH. Here M can be V, Mo, or Cr, and the hydrogen is transferred to the vanadyl, the molybdyl, or the chromyl, respectively. In the lower-right corner of each figure we show the structure formed when a H atom from the methyl inserts in the M-OTi bond to break it and form a hydroxyl bound to a 5c-Ti atom; this structure has two hydroxyls on the surface, both bonded to 5c-Ti atoms. Judging by the distance between the V and the O atom, the newly formed hydroxyl is still bonded to the central atom in the cluster. The reaction energies for these three pathways are indicated in Figure 8 and are also given in Table 5. For the case of VO3, all three dehydrogenation schemes are exoergic and, therefore, thermodynamically downhill. For MoO3 they are all endoergic. For CrO3 only the formation of two hydroxyls is endoergic.

J. Phys. Chem. C, Vol. 113, No. 36, 2009 16089 The activation energies for each step and each cluster are given in Table 5. For VO3 the pathway that results in a dihydroxyl has the lowest activation energy (0.88 eV). The activation energies for the other two paths are much too large, and they do not contribute to the reaction. Brønsted, Evans, and Polanyi80,81 (BEP) have postulated that the activation energy of similar reactions are linear functions of the reaction energies. Even though there are heuristic arguments which support the rule,82 we must consider it an empirical relation. The fact that the meaning of the term “similar reactions” is not always clear makes the use of the rule difficult. Nevertheless, a number of papers83-89 have shown that the rule can be used to relate activation energies to binding energies, for catalytic reactions. Since binding energies are so much easier to calculate or measure, this capability is of great interest. These prompted us to test whether this rule applies to methoxy dehydrogenation. If we assume that the three dehydrogenation pathways are similar reactions (in the sense of BEP), then the rule tells us that the activation energy should be a linear function of the reaction energy. A plot of the data given in Table 5, for the dehydrogenation reactions on VO3, is shown in Figure 9. The three data points are represented reasonably well by a linear relationship, indicating that one could guess the ordering of the activation energies from the ordering of the reaction energies. A similar graph is obtained for CrO3. However, the “data” for MoO3 (see Table 5) deviates strongly from a linear relation; the activation energy is not even a monotonic function of the reaction energy. Table 2 shows that there is a very small change in the bond lengths in the cluster when the methyl is dehydrogenated along the pathway with the smallest activation energy: only the bonds of the vanadium with O2 and with the formaldehyde’s oxygen change significantly. Figure 5 indicates that even though the bond lengths change a little, the Bader charges are modified substantially when the dehydrogenation takes place: the charge on the oxygen atom in the methoxy goes from -0.87 to -1.97. At the same time the charge of the carbon atom changes from 0.5 (in methoxy) to 1.04 (in formaldehyde). The hydrogen atoms on the formaldehyde become more positive than they were in the methoxy, the vanadyl oxygen becomes slightly more negative, and the vanadium slightly less positive. The charge on the oxygen atom on which the dihydroxyl is formed changes from -1.34 to -1.97. It is surprising that such a large change in the atomic charges causes a small change in the bond length. The dehydrogenation reaction for CrO3 results in a transfer of a hydrogen atom from the CH3 group onto the chromyl, to form a CrdOsH group. The activation energy for this reaction is much higher than that on VO3. This is consistent with the experimental observation that isolated CrOx clusters are poorer methanol oxidation catalysts than the isolated VOx clusters. The activation energy follows an approximate Evans-Polanyi rule. In the case of CrO3 the dehydrogenation causes a larger structural change than for VO3. The carbon atom in -OCH2 binds to the oxygen atom of the hydroxyl formed earlier by the dissociative adsorption of methanol (compare panels b and c of Figure 3). The distance from the carbon to the oxygen in the hydroxyl is 1.45 Å (see Table 4) while the distance between the hydroxyl and the 5c-Ti atom increases from 1.76 Å (before dehydrogenation) to 2.23 Å (after dehydrogenation). The compound formed in this way resembles formic acid. In addition, the lengths of the bonds of Cr to the b1, b2, and O1 oxygen atoms (see Figure 3 and Table 3) change substantially and so does the CrdO bond. Only the Cr-OCH2 bond is about the same as the Cr-OCH3 one. These changes show that the

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Figure 9. Plot of the activation energies for the three dehydrogenation pathways for VO3 versus the reaction energies (data from Table 5 were used). The line is a least-squares fit to a linear relationship. The same graph for CrO3 is very similar. The one for MoO3 is highly nonlinear.

Figure 8. Three different dehydrogenation pathways: (a) VO3 cluster, (b) MoO3 cluster, and (c) CrO3 cluster. For each panel of four figures we have: (1) The cluster with the methoxide and a hydroxyl (left upper corner). (2) The cluster with formaldehyde and a dihydroxyl (right upper corner). (3) The cluster with formaldehyde and a hydroxyl on the M)O bond (left lower corner). (4) The cluster with formaldehyde and two hydroxyls. The figures also give the energy of all three dehydrogenation pathways. For example, the energy of the dehydrogenation reaction of Mo-OCH3 to form a dihydroxyl is 0.8 eV.

reaction is not local: dehydrogenation affects remote regions of the cluster not just the -Cr-OCH3 group. The Bader charges on the dehydrogenated compound on CrO3 system are shown in Figure 6. The largest changes are on the oxygen in the chromyl (from -0.57 to -1.35) and on the carbon atom (from 0.26 to 1.22). Other atoms undergo smaller charge changes (see Figure 6). These modifications in the atomic charges show that the reaction changes the state of many atoms in the system, not just of those involved in the bonds broken or formed in the reaction. The activation energies given in Table 5 show that the isolated MoO3 cluster is a worse catalyst than CrO3 cluster. This is in agreement with experiments in which isolated MOx clusters were prepared. The dehydrogenation on MoO3 is very similar to that on CrO3 (compare Figures 3 and 4 and Tables 3 and 4). It is interesting to point out that iron molybdate is one of the industrial catalysts for methanol oxidation to formaldehyde. While the catalytic activity of vandates is similar90 to that of the supported VOx this is not the case for supported MoOx whose activity is substantially smaller than that of the iron molybdate, but still higher than that of bulk MoO3. 4.7. Evolution after Dehydrogenation. Our purpose in this study was to compare the ability of VO3, MoO3 and CrO3 to dehydrogenate the methoxide, which is the rate limiting step in the oxidative dehydrogenation of methanol. Therefore, a comparison of the efficiency with which different catalysts convert methanol can be confined to a comparison of the dehydrogenation activation energies. Of course, such a comparison tells us nothing about the nature of the final products (i.e., the methoxy may undergo other processes besides dehydrogenation and the formaldehyde formed by dehydrogenation may be converted to other compounds). The processes following dehydrogenation are so much faster that very little can be learned about them from experiments. Nevertheless, we did investigate some of the steps following the dehydrogenation on VO3. The results are shown in Figure 10 where ∆En gives the reaction energy for the nth step. The third step (after methanol dissociative adsorption and methyl dehydrogenation) is the desorption of the formaldehyde, which requires only 0.23 eV. When CH2O is removed, the vanadium atom breaks the bond of the oxygen in the dihydroxyl with the 5c-Ti atom and makes a -V-OH2 bond; the removal of formaldehyde does not change the valence of the V atom. The removal of the dihydroxyl (as water) from this cluster into the gas phase requires a high energy and it will not happen. We found that oxygen from the gas phase adsorbs and binds to


Figure 10. Energies along the catalytic cycle for methanol oxygenation on VO3/TiO2(110). The cycle starts at the top and follows the arrows. ∆E indicates the reaction energies. At the bottom we give the reaction energy for the gas phase methanol oxidation. The total energy in the cycle is equal to the total energy of the gas-phase reaction.

the V atom and simultaneously breaks the -V-OH2 bond; the OH2 group shifts its position and binds to a 5c-Ti atom. Now the system can release water without lowering the valence of the V atom. The desorption of water from this new location is endoergic by 0.34 eV and it is therefore likely. After water desorption a VO4 cluster is left on the surface. This is thermodynamically unstable49 and will be converted, even in the presence of O2 in the gas phase, into VO3. We have not studied the mechanism of this conversion and the fate of the O atom released in the conversion of VO4 to VO3, which is likely to be complicated. 4.8. Comparison with Previous Theoretical Work. We found two articles that have used DFT to model methanol oxidation by using small cluster models of vanadia supported on titania.91,92 We will not discuss similar work modeling methanol oxidation by vanadia on silica:91,93 the activity of this catalyst is 3 orders of magnitude smaller than that of titania supported VOx, and the structure of VOx on silica is likely to be different25,26 from that of VOx on titania. Because of this, we believe that the results for VOx/SiO2 are not relevant to VOx/ TiO2. Moreover, we limit our analysis to the paper of Goodrow and Bell (GB)92 which is more recent than that of Khaliullin and Bell.91 There are two substantial differences between our results and those of GB for the supported vanadium oxide cluster: (1) we find that the dehydrogenation takes place by forming a dihydroxyl, whereas GB find that the hydrogen leaving the CH3 group in the methoxy binds to the oxygen of the vanadyl; (2) GB propose that the active catalyst is the vanadia cluster with an oxygen vacancy next to it, while we find that the presence of a vacancy does not affect substantially the activity. Both our calculations and those of GB have limitations. The quantum mechanical methods used are approximate and it is not possible to say which is more accurate. Comparison with experiments is also questionable since we are not sure that the

J. Phys. Chem. C, Vol. 113, No. 36, 2009 16091 models used in calculations represent the structure of the catalyst on which the measurements are made. In addition there are substantial uncertainties regarding the accuracy and sometimes the precise meaning of the quantities measured. Nevertheless, it is useful to make an inventory of the limitations of both methods. This will explain why we believe that the kind of calculations presented here are more reliable when they compare different catalysts and look for trends and make semiquantitative statements (e.g., catalyst A is more efficient than B). (1) GB used a small cluster, VOTi7O12H7, to simulate the VOx cluster on anatase. There are reasons to believe that this cluster is too small and that the results are likely to depend on the size and structure used in the calculation. Gas-phase work on the chemistry of small clusters shows that cluster size is important; sometimes adding one atom to a cluster can make a difference in the chemical activity.94 Work with mass selected Au clusters supported on oxides shows the same thing.95,96 Moreover, small clusters are very sensitive to the nature of the support: for example, Au7 on MgO does not catalyze CO oxidation while Au7 on rutile TiO2 does.96 Furthermore, work on coadsorption on TiO2(110) shows that two different adsorbates (e.g., a hydroxyl and an oxygen molecule) can influence each other97 even when separated by distances larger than the size of the clusters used by GB. Finally, the adsorption energies of molecules adsorbed on rutile TiO2(110) oscillates with the slab thickness and converge only when the slab is over 15 atomic layer thick.14-18 These observations suggest that the results of GB are likely to be affected by the cluster size. It would be useful to have calculations of similar clusters of different sizes, but we do not. On the other hand, one must recognize that using the flat TiO2(110) rutile surface as a model for the support does not provide a faithful representation of the practical catalysts (they are however relevant to work with single crystals, in ultrahigh vacuum).6,50-52,54 Vanadia clusters on other faces may be more active. In addition, the surfaces of the supports used in experiments are rough and have a variety of local geometric features. The activity of the VOx clusters bound to such features may differ from that of the same cluster bound to a flat crystal face. The upshot is that we expect the two calculations to differ from each other and from the real catalyst. (2) Employing a small cluster allowed GB to use the B3LYP functional. Experience suggests98 that this functional is more accurate than the one used in our work. Using B3LYP for the large supercells needed when using a slab model is impractical at this time. (3) We have examined four stoichiometries for the vanadia clusters (VO, VO2, VO3, and VO4) and found that under the conditions of preparation (annealing at high temperature, in the presence of oxygen) VO3 is present on the surface. We use this cluster to study the oxidation of methanol, while GB used a VO cluster (we use our nomenclature which includes in VOx only the oxygen atoms that do not belong to the surface of the support). This is another reason why the two calculations should lead to different results. (4) The dehydrogenation reaction in the GB calculation involves a conversion of a singlet to a triplet (the reaction from 2a to 3 in Figure 4 of GB paper). Such reactions are spin-forbidden99-104 and therefore are likely to be very slow. In addition, the transition state theory does not apply to them since the reaction is a transition between electronic states with different spin, not a flow of the reaction coordinate over a barrier. Our calculations have imposed the constraint that spin cannot be “flipped” as the reaction coordinate changes from

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reactants to products,7,8 and therefore, the reactions calculated here are spin allowed. (5) To bring the calculations in agreement with the experiments GB have proposed that an oxygen vacancy is present near the VO cluster. We find that, in our model, the energy required for making an oxygen vacancy on the surface is prohibitive. While it is possible that vacancies are formed when water desorbs from the surface, we have not found a fast pathway for this process. In the model proposed in Figure 10 the desorption of water does not create an oxygen vacancy in the surface. Whether the presence of vacancies is important remains, in our opinion, an open and interesting question. If a mechanism for efficient formation of oxygen vacancies does not exist, the vacancies will be filled by interaction with the oxygen in the gas and they will disappear when the reaction reaches steady state. (6) The expression obtained for the effective activation energy depends on the kinetic model used for interpreting the data. Right now several phenomenological models fit the data and the model used by GB differs from that used by other workers35,68,105 it is not clear to us which one is correct, if any. Therefore the agreement between the calculated activation energy and the one derived from experiment is not a proof that the structure and the stoichiometry of the cluster and the mechanism used in a calculation is correct. It appears likely that the conclusions reached by GB are different from ours because of differences in the models. Neither model is a faithful description of the catalysts used in practice: they represent limiting cases that will hopefully converge toward each other as larger clusters can be examined and better functionals become available (or practical) for the extended systems. Because of this, we think that such calculations are more useful for determining trends than for providing accurate values for kinetic parameters.

Kim et al. toward a complete understanding of this system. The qualitative conclusions are more reliable than the absolute values of the computed quantities. Our main conclusion is that there are substantial differences between the three clusters we studied. VO3 is by far the most active and the dehydrogenation takes place through the transfer of a hydrogen atom from the methyl group in the methoxide to an existing hydroxyl on the surface (formed by the dissociative adsorption of methanol with methoxide formation). This leads to the formation of a water molecule strongly bonded to a 5cTi atom on the surface of the support. The dehydrogenation of methoxy on MoO3 or CrO3 has much higher activation energy than on VO3 and takes place with the transfer of a hydrogen atom to the chromyl or the molybdyl group. We have explored the evolution of the system after dehydrogenation only in the case of VO3. The dehydrogenation produces a water molecule adsorbed on a 5c-Ti atom near the cluster. This molecule contains an oxygen atom that used to bridge the vanadium atom with a Ti atom in the surface of the support (i.e., an O from -V-O-Ti-), the hydrogen atom from the hydroxyl in CH3OH and a hydrogen atom from the methyl group. In principle, if one would oxidize V with 18O2 and use CD3OH then, according to this mechanism, the desorbed water would be H18OD. This suggestion could be tested, but isotope scrambling during the experiment can complicate the interpretation or render the results inconclusive. Acknowledgment. This work was supported by the Air Force Office of Scientific Research (FAA9550-06-1-0167) and the National Science Foundation (CHE 07-49489). We thank Israel Wachs and Alex Bell for useful discussions. Use of the Center for Nanoscale Materials at Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC0206CH11357.

5. Discussion By assuming that the system equilibrates with the gas phase oxygen (during annealing in oxygen atmosphere), we have concluded that the most probable stoichiometry of the cluster supported by TiO2(110) is MO3 (M ) V, Cr, and Mo); in this formula we count only those oxygen atoms acquired from the gas phase; the cation M is bonded to oxygen atoms from the surface of the support but these atoms are not included in MO3. It is quite possible that a different stoichiometry and structure will be present on other faces of the support. Moreover, the surface of a high-area support has many defects, such as kinks, steps, or oxygen vacancies, and the structure of the oxide cluster at these sites is also likely to be different from that considered here. In addition, thermodynamics gives us the structure of the catalyst before the reaction takes place. When methanol and oxygen are passed through the reactor, the catalyst reaches a steady state in which the initial MO3 cluster coexists on the surface with intermediates, with molecularly adsorbed methanol, with oxygen vacancies, with water and with hydroxyl groups, in proportions determined by the methanol and oxygen partial pressures and the temperature. Calculations have shown that coadsorption can affect strongly the binding energies of the coadsorbates. For example, the presence of hydroxyls or oxygen vacancies on the TiO2(110) surface changes affects strongly the binding energy of oxygen to the surface.96,97 The limitation we have outlined above have to do with the model used in the computation. Additional uncertainties are introduced by the approximations contained in the DFT method. For all these reasons we consider the work presented here to be a first step

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