Chemical Reactivity Indices as a Tool for Understanding the Support

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J. Phys. Chem. C 2009, 113, 19905–19912

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Chemical Reactivity Indices as a Tool for Understanding the Support-Effect in Supported Metal Oxide Catalysts Tim Fievez,† Bert M. Weckhuysen,‡ Paul Geerlings,† and Frank De Proft*,† Eenheid Algemene Chemie, Vrije UniVersiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium, and Department of Inorganic Chemistry and Catalysis, Debye Institute for Nanomaterials Science, Utrecht UniVersity, Sorbonnelaan 16, 3584 CA Utrecht, Netherlands ReceiVed: April 28, 2009; ReVised Manuscript ReceiVed: August 18, 2009

The oxidation of methanol to formaldehyde on supported vanadium oxides is investigated with chemical reactivity indices. Starting from a simple model for isolated vanadium oxides supported on SiO2, Al2O3, TiO2, and ZrO2, a detailed investigation of the reaction mechanism for methanol oxidation on these catalysts is presented. Our results follow current insights into the reaction mechanism and provide a new interesting way for rationalizing the support-effect on the basis of the concept of bond ionicity as probed by computed electrostatic potential based atomic charges for the vanadium and oxygen atoms. The origin of this rationalization is further investigated by visualizing the density of the determining vanadium-oxygen-support structure for the different supports. 1. Introduction 1-3

are an important group of Supported vanadium oxides heterogeneous catalysts. Consisting of a vanadium oxide phase dispersed on the surface of another oxide (e.g., SiO2) which acts as support, they catalyze a variety of important reactions like the selective oxidation of alkanes and alkenes, the oxidation of o-xylene to phtalic anhydride, and others (see ref 2 and references therein). Originally, the oxide support was intended to improve the catalytic activity because of an increased surface area and higher mechanical strength, yet current insights state that the support choice has a considerable additional effect in the selectivity and activity of the oxides.4 This effect, often named the support-effect, is still not completely understood, and its understanding through chemical concepts that can be computed from first principle is the principal aim of this investigation. Depending on the composition of the support, different activity patterns were reported. More specifically, the turnover frequency (TOF) in the selective oxidation of methanol to formaldehyde varies dramatically when changing the support leading to the following reactivity trend:4 ZrO2 ∼ TiO2 > Al2O3 > SiO2. This reactivity sequence will be highlighted by (*). Further spectroscopic research has provided additional insight into these systems and serves as foundation for the study of the support-effect. It has been reported that the TOF is independent of the vanadia loading suggesting that only isolated vanadium sites are active in this reaction.4 As the Raman frequency of the V)O bond in these isolated sites is almost identical for various supports and as labeling experiments show that O18exchange rates in this bond are much slower than the reaction rate, the catalytic activity seems primarily controlled through the vanadium-oxygen-support (V-O-S) structure.5 Electronegativity differences between the different supports have therefore been used as an initial explanation for this metal oxide support-effect.6 Furthermore, detailed atomic extended X-ray * To whom correspondence should be addressed. † Vrije Universiteit Brussel. ‡ Utrecht University.

Absorption Fine Structure (XAFS) experiments have probed directly the changes in the electronic nature of V and have reported relations between the electron charge on support oxygen atoms and the catalytic activity.7 In an attempt to rationalize the origin of the support-effect, different computational studies have been carried out.8-10,12,13 The first computational study focusing on the support-effect was published in 2001 by Khaliullin and Bell.9 In this paper, an elementary model of vanadium oxides supported on SiO2, TiO2, and ZrO2 was proposed for the study of the selective oxidation of methanol to formaldehyde: a distorted tetrahedral VO4 unit attached with Si, Ti, and Zr atoms. All dangling bonds were terminated with the corresponding number OH-groups. To model the surface of the support, distances between the different support atoms were fixed to experimental data. Density functional theory (DFT) was used to examine the energetics and kinetics of formaldehyde formation on the basis of an experimentally backed reaction mechanism. Obtained methanol adsorption energies were in good agreement with experimental observations. Apparent activation energies were slightly overestimated with 6-7 kcal/mol while apparent first-order rate constants were significantly underestimated compared to experimental results (Table 1). Because of the resemblance of apparent activation energies for the different studied clusters, they suggested that support-effects are influenced by factors different from support-composition. The 2005 paper of Do¨bler et al.10 proposed a more elaborate structure on the basis of polyhedral oligomeric silsesquioxanes (POSS) to model vanadium oxides supported on SiO2. Their in-depth DFT study of the reaction mechanism of methanol oxidation led to the proposal of a biradicaloid transition state for the actual oxidation mechanism. The produced apparent activation energies with this new model matched the results obtained by Khaliullin and Bell,9 but apparent first-order rate constants were 4 orders of magnitude smaller than experimentally observed. Additionally, this study provided a thorough comparison with other structural models to validate their use in the study of this oxidation reaction. From this comparison, the O)V(OCH3)3 model came out as a reliable model for the

10.1021/jp903913m CCC: $40.75  2009 American Chemical Society Published on Web 10/26/2009

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SCHEME 1: Selective Oxidation of Methanol to Formaldehyde on Supported Vanadium Oxide Catalysts

TABLE 1: Comparison of Principal Energetic and Kinetic Parameters from Computational Studies on Supported Vanadium Oxides Khaliulin and Bella Eabs, kcal/mol Eact, kcal/mol Eapp, kcal/mol kapp, s-1 P a-1 Eapp (exp) kJ/mol kapp0 (exp) s-1 Pa-1 a

Do¨bler et al.b

Goodrow and Bellc

SiO2

TiO2

ZrO2

SiO2

SiO2

TiO2

TiO2*

-20.8 47.6 26.8 1.22 × 100 18.9d 1.26d

-21.7 51.1 29.4 1.3 × 100 21.0d 3.32 × 105 d

-22.9 50.4 27.5 7.4 × 10-1 21.5d 6.57 × 105 d

-9.5 36.8 27.3 1.34 × 106

-15.5 39.8 24.3 4.00 × 107 23 ( 1 e 1.9 × 107 e

-15.7 38.5 22.8 1.11 × 107 15.93f 2.38 × 106 f

-15.9 31.8 15.9 4.00 × 106 15.93f 2.38 × 106 f

Reference 9. b Reference 10. c References 12 and 13. d Reference 4. e Reference 34. f Reference 11.

actual oxidation step, although it did not contain any reference to supportive oxide material. In other words, support-specific contributions to the reactivity were not taken into account, and it was therefore suggested that reactivity differences between different supports might originate from fundamental differences occurring in other reactions steps perhaps noticeable through, for example, heats of adsorption. More recently, Goodrow and Bell12,13 performed further investigations of the reaction mechanism with this new POSS model. In these contributions, both Si and Ti supports were examined, and also the effect of the reoxidation mechanism was included for the first time. Consistent with experimental conclusions, the reoxidation step was found to be very fast in both cases (Ti, Si) and thus was irrelevant for reaction kinetics. The oxidation pathway studied here was slightly different from the one suggested by Do¨bler et al.10 by having an alternative mechanism for formaldehyde desorption. Incorporation of this new finding into the global reaction gave a reasonable analogy with experiment. For the Ti support case, however, energetic results were almost identical to the ones for Si thus minimizing the occurrence of the support-effect. The apparent first-order apparent rate constant for Ti supported VOX was 1 order of magnitude smaller than for Si, which was again in contradiction with experimental trends. This remarkable discrepancy could be solved with the incorporations of O-vacancies. Such defects are known to occur in titania, and computational evidence points out that they are preferentially located near vanadate species. Incorporation of this defect in the models and appropriate scaling of their influence (not all vanadate species have adjacent O-vacancies) yields surprisingly good agreement with experimental observations suggesting that support-effects work through the rate-determining step as adsorption energies remain almost identical for the nondefect and defect Ti cases. It should be clear, however, from this overview of different computational studies that no general consensus about the origin of the support-effect has yet been obtained with the presentday computational explorations. Nevertheless, theoretical studies combined with experimental kinetic studies have given rise to several slightly different mechanisms for the selective oxidation of methanol on supported vanadium oxide catalysts.9,10,12-14 Basically, the same reaction steps exist for each mechanism (Scheme 1):

• Adsorption of methanol on supported vanadium oxide • Oxidation of the adsorbed methanol • Desorption of the formaldehyde molecule In this work, we will tackle the support-effect problem from a different perspective. With the use of chemical reactivity indices, we will put forward a framework of thinking allowing us to rationalize the metal oxide supporteffect on the basis of the chemical reactivity indices for the key atoms involved in the reaction. The main added values of this approach are (1) the relatively easy quantification of the reactivity of atoms involved in the reaction with indices making comparisons between supports more straightforward and (2) its limited dependence on the extensiveness of models. The present study will focus on the reactivity trend described above (see previous *) by studying the oxidation of methanol to formaldehyde on supported vanadium oxides for the SiO2, Al2O3, TiO2, and ZrO2 supports. 2. Reactivity Descriptors Two different categories of reactivity indices will be used throughout this article. For frontier orbital controlled15 reaction steps, the atom condensed Fukui function derived within the context of density functional theory (DFT) will be used to characterize the reactivity16-18 while charge-controlled steps will be investigated with the molecular electrostatic potential (MEP);19 this MEP approach is in line with many applications that have been presented in the area of conceptual DFT or chemical DFT. Apart from being a quantumchemical method with one of the most interesting accuracy/CPU time ratios, DFT almost naturally provides a series of tools for the discussion of chemical reactions. As such, old vaguely defined chemical concepts and principles, such as electronegativity,20 softness,21 or Pearsons principle of hard and soft acids and bases,22 received an unambiguous definition or proof. Deeper insight into these descriptors showed that their definitions could be rewritten as derivatives of the energy to the external potential or the number of electrons. Following this reasoning, the introduction of higher derivates gave new descriptors, which could be identified with other or new reactivity descriptors. One of these descriptors is the Fukui function,23 which is intimately related to Fukui’s frontier molecular orbital concept.24

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TABLE 2: Comparison of a Selected Number of Structural Properties of the Supported Vanadium Oxide Models from Different Experimental and Computational Studiesa experimental characteristic d (Å), freq (cm-1)

system VOX/SiO2

VOX/Al2O3

VOX/TiO2

VOX/ZrO2

a

theory Khaliullin and Bell9

Goodrow and Bell12,13

Keller et al.35

Keller et al.7

Bronkema et al.36

d(V)O) d(V-O) d(S--S)

1.58 1.76

1.58 1.80

1.58 ( 0.03 1.79 ( 0.02

1.59 1.77 5.00

1.58 1.76

freq(V)O)

1041

1035

1052

1033

d(V)O) d(V-O) d(S--S)

1.58 1.72

freq(V)O)

1022

1.58 1.73

1.58 1.79

1.60 1.76 3.50

1.57 1.77

freq(V)O)

1026

1046

1033

1.58 1.77

freq(V)O)

1020

1.57 1.76 4.65 1080 (1071) 1.58 1.76 3.23 1055 (1054)

d(V)O) d(V-O) d(S--S)

d(V)O) d(V-O) d(S--S)

this paper

1.58 1.68

1.60 1.77 3.90

1.57 1.77 3.78 1058 (1057) 1.58 4.00 3.97 1052 (1052)

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The vibrational frequencies between () are computed with a fixed support.

f+(rj) )

f-(rj) )

(

∂2E[F] ∂Nδν(rj)

(

∂2E[F] ∂Nδν(rj)

) ( )

) FN+1(rj) - FN(rj)

) ( )

) FN(rj) - FN-1(rj)

+

)

-

)

∂F(rj) ∂N

∂F(rj) ∂N

+ ν(rj)

ν(rj)

(1)

(2)

where FN+1(rj), FN-1(rj), and FN(rj) are the densities of the anionic, cationic, and neutral systems at the geometry of the neutral system. To go deeper into the meaning of these formulas, f+ gives the regions of the molecule which are suited for adding an extra electron, which is typical for a nucleophilic attack. In an analogous way, f- depicts regions in a molecule that are suited for electrophilic attacks. In addition to these Fukui functions, a third Fukui function was proposed for radicalar attacks, which is the average of the Fukui functions for a nucleophilic and an electrophilic attack:

f+(rj) + f-(rj) f (rj) ) 2 0

(3)

A fA+ ) pN+1 - pNA

(4)

A fA- ) pNA - pN-1

(5)

fA+ + fA) 2

s(rj) ) f(rj) · S

(6)

where f A+, f A-, and f A0 are the atom condensed Fukui functions for nucleophilic, electrophilic, and radicalar attack, while pAN+1, pAN, and

(7)

Charge-controlled reaction steps will be analyzed with the molecular electrostatic potential (MEP, see eq 8) and its derived charges from electrostatic potentials using a grid based method (CHELPG) charges as proposed by Brenneman and Wiberg.28 cores

To simplify the interpretation of the different Fukui functions, we will use atom condensed Fukui functions as defined in eqs 4-6.

fA0

pAN-1 correspond to the electron population on atom A for an anionic (N + 1 electrons, charge ) -1), neutral (N electrons, charge ) 0), and cationic (N - 1 electrons, charge ) +1) system. When comparing the reactivity in different molecules, the local softness, s,25 turns out to be a more appropriate descriptor than the Fukui function.26,27 It is obtained by multiplying the desired Fukui function with the global softness, S, giving rise to the local softness for nucleophilic, electrophilic, or radicalar attack where S principally serves as scale factor for the size of the system.

φMEP(rj) )

Z

∑ |rj -ARj A

A|

-

j′) drj′ ∫ |rjF(r - jr′|

(8)

These CHELPG charges are designed to reproduce the MEP in the most optimum way while being restricted to sum the total molecular charge. Practically, this is done by sampling the MEP with a grid of points while staying outside the so-called exclusion radii for each atom. The atomic charges are then determined as those parameters, which reproduce the MEP as closely as possible at the different sampling points. When comparing results from indices and energies, one should keep in mind that both quantities do not need to coincide as they probe different states in a reaction: Indices are emerging from a perturbational perspective of chemical reactivity (chemical reactivity is treated as information emerging from the perturbation of the properties of a molecule by an attacking reagent). They, thus, only give information about the very initial phases of the reaction and should essentially be used for studying

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TABLE 3: CHELPG Charges for Key Atoms in OdV(OSi(OH)3)3, OdV(OAl(OH)2)3, OdV(OTi(OH)3)3, and OdV(OZr(OH)3)3 Models and Bond Ionicity for V-O Bond in Models Compared with TOF at Low Vanadia Loadings CHELPG

VOx/SiO2

VOx/Al2O3

VOx/TiO2

VOx/ZrO2

vanadium oxygenV-O-S oxygenVdO support bond ionicity TOF (s-1)

1.68 -0.78 -0.53 1.51 1.28 3.90 × 10-03

1.68 -0.87 -0.58 1.34 1.46 3.60 × 10-02

1.80 -0.93 -0.55 1.91 1.68 2.00 × 1000

1.77 -0.99 -0.56 2.45 1.76 3.30 × 1000

the kinetic aspects of the reaction. Such an approach will consequently only probe the initial state of the reaction while energies probe the difference between the final and initial states of the reaction. 3. Computational Details Our model systems are inspired by the model proposed by Khaliullin and Bell.9 On the basis of the idea of an isolated VO4 unit as an active site for methanol oxidation, a distorted tetrahedral unit with one V)O bond and three V-O bonds was used as a starting point. Each of these V-O bonds is then used for anchorage on the support oxide, which is mimicked by one support atom for each anchor point. All the dangling bonds on the support are then terminated by the corresponding number of hydroxyl groups. Distances between atoms are allowed to relax in order to diminish the dependence of empirical parameters. Because of the high structural similarity of this model with Khaliullin and Bell’s model, energetic and kinetic parameters are expected to be similar and thus transferable. The small size of the cluster (around 25 atoms) also ensures an acceptable computational burden. As previously mentioned by Do¨bler et al.,10 this model is not without problems when calculating adsorption energies. During the adsorption, a S(OH)4 group is created where the hydroxyl groups can freely rotate around the fixed support atom changing the hydrogen-bonding pattern which influences the adsorption energies. This problem is circumvented when using indices as they are computed for the initial state of the reaction and not as the difference between begin and end states (cf. energies), making them almost insensible to such changes. All structures were optimized with Gausssian0329 at B3LYP/ 6-311+g(d, p)30 level with Stuttgart pseudopotentials and with associated basis sets on transition metals vanadium,31 titanium,31 and zirconium.32 For further optimizations (adsorbed and desorbed species), the distances between supports were kept fixed. Natural population analysis (NPA)33 was used for population analysis (to compute the condensed Fukui functions), and the CHELPG exclusion radii correspond to the van der Waals radii. 4. Results In the first part, we assess the validity of the model compounds used in our study to compute the different reactivity indices described above. Table 2 lists some geometric characteristics and the V)O vibrational frequency (scaling factor 0.96) for our models used and compares them with experimental observed values. As can be seen, all bond distances are in reasonable agreement with experimental observations; especially, the d(V)O) has been improved compared to the Khaliullin and Bell9 study which uses almost identical models but a smaller basis set. The vibrational frequencies of the V)O bonds are systematically overestimated by 30-35 cm-1 but retain the trends found. In the case of SiO2, the overestimation is significantly higher (45 cm-1) which can be improved to 36

cm-1 by assigning high masses to the support atoms (2000 amu) to simulate a rigid support frame.34 For other supports, this rigid frame approach leads to a less significant downscaling (1-2 cm-1) of the V)O vibrational frequency. Next, we will investigate in detail the different steps of methanol oxidation of the different models for the supported vanadium oxides. The “consensus” reaction mechanism for this catalytic process is given in Scheme 1. The first reaction step in methanol oxidation consists of the adsorption of methanol on the supported vanadium oxide as illustrated in this scheme depicting the alcoholysis of the V-O bond leading to a system with a V-OCH3/S-OH pair.4 Because of the hard nature21 of the oxygen atom in methanol, this reaction can be assumed to be largely charge controlled, and are the appropriate quantities of electrostatic potential based atomic charges to investigate this step in the reaction. In Table 3, we list these charges for the key atoms in the models under study. Our results show that the charges of the vanadium atom systematically increase when changing the support to more reactive species (higher TOF) suggesting that the adsorption of the CH3O- will occur more easily. At the same time, the charge of the oxygen V-O-S becomes more negative facilitating the bonding of the remaining H+. On the basis of this result, the electron distribution within the V-O bonds seems crucial for the description of the adsorption step. One of the ways to define this distribution is with the concept of bond ionicity37 defined as CHELPG bond - ionicity ) |QVCHELPG · QOinV-O-S |

(9)

CHELPG where QVCHELPG and QOinV -O-S are the CHELPG charges on the vanadium atom and the oxygen atom of the V-O-S structure. Table 3 compares the values of the ionicity of the V-O bond when changing the support to the more reactive species with the experimental TOF for methanol oxidation at low loading (1 wt % V2O5). The evolution of the ionicity for the V-O bond on the different studied supports nicely parallels the TOF trends for methanol oxidation. Both SiO2 and Al2O3, systems with a low TOF, have relatively low ionicities, while ZrO2 and TiO2 with their comparably high TOF have resembling high ionicities. The similarity between ionicity and TOF is further confirmed in Figure 1 where a logarithmic fitting is made between both quantities with a remarkably high R2 of 0.99. From Scheme 1, one can see that in the second step of the catalytic process, the oxidation of methanol to formaldehyde starts. This occurs through the transfer of a hydrogen atom from the adsorbed methoxy species to the vanadyl group of the vanadium oxide; however, other potential acceptor sites are also available. By determining the local softness for a radicalar attack (s0) for these different suitable acceptor sites, a classification of the best acceptor sites can be obtained for each support. In Table 4, we list the values for the vanadyl oxygen, the oxygen in the V-O-S structure, the vanadium atom, and the support

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Figure 1. Bond ionicity versus turnover frequency on supported vanadium oxides for SiO2, Al2O3, TiO2, and ZrO2 supports (R2 ) 0.99).

TABLE 4: s0 Values for Best Radical Acceptor Atoms for the Methanol Adsorbed OdV(OSi(OH)3)3, OdV(OAl(OH)2)3, OdV(OTi(OH)3)3, and OdV(OZr(OH)3)3 Models s0

VOx/SiO2

VOx/Al2O3

VOx/TiO2

VOx/ZrO2

oxygenVdO oxygenV-O-S vanadium support

0.51 0.29 0.09 0.00

0.42 0.37 0.07 0.03

0.44 0.18 0.010 0.05

0.46 0.26 0.07 0.08

atom for the methanol adsorbed vanadium oxide species. For all supports, the oxygenVdO atom is unambiguously identified as the favored acceptor site for the hydrogen atom, which is in line with observations made in previous studies. However, a plot of the trend of the local softness s0 on these oxygenVdO atoms as a function of the support given in Figure 2 reveals that both VOx/SiO2 and VOx/Al2O3 appear as the most reactive systems, which clearly suggests that there is no direct contribution to the support effect. Next, we will focus on the final step in the catalytic mechanism, that is, the desorption of the adsorbed product molecule formaldehyde. During the oxidation step, the valency of V changes from a formal +5 (singlet) to a formal +3 with two unpaired electrons (triplet). Analysis of the different NBO38 orbitals in this species indicates that the Wiberg indices39 of the bond between formaldehyde and the supported oxide varies between 0.24 and 0.28 for all supports. The bonding interaction between formaldehyde and the remaining cluster is therefore expected to have predominantly electrostatic character.

Q(V · · · O) ) |Q(V)| + |Q(OCH2O)|

(10)

The charge difference between the vanadium atom and the oxygen atom of formaldehyde, the two main contributors of the electrostatic interaction, can be quantified using eq 10 to obtain a rough estimate of the strength of the interaction. This quantity is listed in Table 5. It was found that the strongest interaction ()highest sum) occurs for VOx/TiO2, while the weakest interaction occurs when SiO2 acts as support. The speed of desorption is therefore expected to increase from VOx/SiO2 to VOx/TiO2 over VOx/ZrO2 and VOx/Al2O3. This analysis was further confirmed using the nucleofugality concept for leaving groups.40 The contribution of this step to the support-effect seems therefore negligible. 5. Discussion On the basis of the correlation between TOF and ionicity, our results suggest that the only step which has a significant

TABLE 5: CHELPG Atomic Charges of the Vanadium Atom, the Oxygen Atom in Formaldehyde, and Their Absolute Sum for the Vanadium Oxide Models OdV(OSi(OH)3)3, OdV(OAl(OH)2)3, OdV(OTi(OH)3)3, and OdV(OZr(OH)3)3before Desorption CHELPG

VOx/SiO2

VOx/Al2O3

VOx/TiO2

VOx/ZrO2

vanadium oxygenV-O-S sum

1.58 -0.42 2.01

1.71 -0.46 2.17

1.80 -0.47 2.27

1.66 -0.40 2.06

contribution to the support-effect and which parallels this effect is the adsorption step. As the ionicity is only dependent on the atomic charges on the vanadium and oxygen atoms in the V-O-S structure, the principal origin of the striking similarity between TOF and ionicity should be the electronic influence of the surrounding atoms which are all similar except for the support species. The origin of the support-effect can therefore be reduced to the influence of the support atoms on the V-O bond. Therefore, we have performed an in-depth investigation of the density in this bond as shown in Figure 3. The straigthforward visualizations of the electron density are hard to interpret because of the minor influence of reactivity related effects compared to total electron densities. Therefore, usually differences between densities are used for reactivity related comparisons (cf. Fukui functions). In our cases, we subtracted the density of each of the clusters with the density of a hypothetical O)V(OCH3)3 molecule, which has exactly the same geometry as the considered cluster but with CH3 as support. In addition, this density subtraction also cancels out any electron withdrawal effect of the oxygen (or carbon) on the vanadium atom. Any occurring density shifts are therefore purely related to the additional inductive electron withdrawal effects caused by the support. The density analysis depicts that the density in the bond increases near the oxygen site, while it decreases in the neighborhood of the vanadium atom proving that electronwithdrawal effects of the support strengthen the electronwithdrawal effect of the oxygen in the VO bond. Further on, comparison of the extensiveness of the contours makes it possible to distinguish support-related effect between the different systems under consideration. To facilitate interpretation, we will focus on the 0.01 au contour line. At first glance, for this particular contour, Ti and Zr seem similar except for some minor differences mainly situated near the oxygen site. If we compare them with the Si support case, it is clear that the density is much more concentrated on the oxygen atom for Ti and Zr cases. For the Al support, the interpretation is less evident

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Figure 2. The s0 values for vanadyl oxygen versus turnover frequency on supported vanadium oxides for SiO2, Al2O3, TiO2, and ZrO2 supports.

Figure 3. Contour plots for the density of the VOV-O-S bond in supported vanadium substrated from a reference OdV(OCH3) for oxides with SiO2 (left up), Al2O3 (left down), TiO2 (right up), and ZrO2 (right down) as supports. Contour values are displayed on the contours in atomic units, and so are the axes. The vanadium atom is placed in the origin and the oxygenV-O-S atom is placed at {0, bonding distance from V}.

because of the various fluctuations in the neighborhood of the core. Yet, on the basis of the extensiveness of the 0.01 au contour line, one can see that the density concentration near the oxygen atom is smaller than for the Zr and Ti cases and larger than for the Si case. It thus seems that the reported sequence of bond ionicity can be traced back to density differences in the VO bond caused by the electron-withdrawal effect of the support on the oxygenV-O-S, which responds with additional electron withdrawal on the vanadium atom as depicted in Figure 3. Although this particular electron distribution is an intrinsic property of each considered vanadium oxide, the effect can only play when the affected VOV-O-S bond is directly involved in the reaction. We, therefore, foresee that only the adsorption step will be influenced by support-effects perhaps visible through heats of adsorption as previously proposed by Do¨bler et al.10 However, as already stated in the Introduction, other opinions about the origin of the support-effect exist. Goodrow and Bell13 published computational evidence showing that support-effects on TiO2 supported vanadium oxides are related to structural effects through so-called O-vacancies near active vanadium

oxide units. Incorporation of these defects in the POSS-model for Ti gave results which were in very good agreement with experimental data. In spite of the fact that our model is less suited for studying structural effects because of the very limited modeling of the surface, we investigated the effect of such vacancies on the bond ionicity. Results for this investigation should, therefore, be understood as a first attempt to model the effect of O-vacancies. Defects were taken into account by the deletion of an O atom in one of the hydroxyls used to terminate the support leaving the cluster in an uncharged triplet state. According to the number of terminating hydroxyls, each support has two (for Al) or three (Si, Ti, Zr) O-atoms which can be removed. In our approach, we consistenly chose to analyze the stablest ()the lowest energy) cluster after OH removal. Table 6 gives charges of the principal atoms and the ionicity of the V-O bond. The results show that each system has its proper response to the introduction of vacancies. For VOx/SiO2, charges on the oxygenV-O-S and vanadium get more negative and positive, respectively, which is reflected in a higher bond ionicity indicating a higher reactivity. For VOx/TiO2, the introduction

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TABLE 6: CHELPG Charges for Key Atoms in OdV(OSi(OH)3)3, OdV(OAl(OH)2)3, OdV(OTi(OH)3)3, and OdV(OZr(OH)3)3 Models with and without O-Vacancies and Bond Ionicity for V-OV-O-S Bond in These Models VOx/SiO2

VOx/SiO2 defect

VOx/Al2O3

VOx/Al2O3 defect

VOx/TiO2

VOx/TiO2 defect

VOx/ZrO2

VOx/ZrO2 defect

1.68 -0.78 -0.53 1.30

1.77 -0.81 -0.56 1.44

1.68 -0.87 -0.58 1.46

1.63 -0.81 -0.60 1.32

1.80 -0.93 -0.55 1.68

1.80 -0.94 -0.58 1.69

1.77 -0.99 -0.56 1.76

1.71 -0.97 -0.62 1.65

CHELPG vanadium oxygenV-O-S oxygenVdO ionicity

of vacancies renders no significant changes as all charges remain almost identical and, consequently, also their ionicity. For the two remaining systems (Zr, Al), the introduction of an Ovacancy induces slightly changing charges both leaning toward 0 for vanadium and oxygenV-O-S. The ionicity undergoes a similar change and decreases approximately 0.1 unit in both cases. In the case of the Al support, the O-atom removal effect could be somewhat amplified because of the smaller number of surrounding stabilizing hydroxyls compared to the other cases (five against eight), which is a consequence of the different valence. Basically, comparison with defectless cases demonstrates that the reactivity decreases or remains equal for Zr and Ti cases. With the proposed models and approach, the introduction of defectuous systems does not seem to be the principal reason for the support-effect. Deeper investigations of this effect with detailed models compromising good representations of the surface remain therefore necessary to obtain more reliable results in the future. 6. Conclusions The selective oxidation of methanol to formaldehyde over supported vanadium oxide catalysts has been investigated using chemical reactivity indices. The global reaction was divided in three major parts: the adsorption, the actual oxidation, and the desorption steps, which were subsequently subjected to an extensive analysis using the appropriate chemical reactivity index. As the adsorption and desorption steps were anticipated to be a charge-controlled interaction, CHELPG charges were used for their analysis. The oxidation process, anticipated as an orbital controlled process, was studied with the local softness, a quantity emerging from the conceptual DFT. In this manner, it was possible to obtain a quantification of the reactivity of the different atoms involved in the oxidation process and, consequently, a mechanism, in line with current findings, could be deduced. In addition, the determination of the reactivity of the atoms in each step gave us the opportunity to compare reactivities for different supports in search for support-related effects. This comparison suggested that support influence mainly plays a part in the methanol adsorption step. This was further rationalized with the concept of bond ionicity, which strongly correlates with TOF. Deeper investigations on the origin of this correlation by studying the electron density in the VOV-O-S bond indicated that the support-effect originates from the slightly different inductive electron-withdrawal properties of the support metal ion on the oxygenV-O-S atom. Although also present in other reaction steps (this effect is an intrinsic property of the system), it is envisioned to only affect the adsorption as it is the only reaction step where the key bond for the reaction step is the VOV-O-S bond. On the basis of all this, it can be stated that chemical reactivity indices are valuable tools for studying the reactivity of supported metal oxide catalysts. Charges and the local softness make it possible to interpret reaction pathways and to quantify the tendencies of the different vital atoms in the proposed reaction steps. This gives additional insight into

the support-effect, and we anticipate that its use can be extended to other metal oxide based catalytic systems. Acknowledgment. The authors would like to acknowledge Prof. A.T. Bell for providing the initial structures of the supported vanadium oxides on the basis of which we generated the different models used in the present study. T.F., P.G., and F.D.P. would like to acknowledge the Fund for Scientific Research (FWO) for a predoctoral fellowship (T.F.) and the VUB for their continuous support. Supporting Information Available: A file containing the different minimum energy structures in the XYZ format is provided. Complete ref 29. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Banares, M. A.; Wachs, I. E. J. Raman Spectrosc. 2002, 33, 359. (2) Weckhuysen, B. M.; Keller, D. E. Catal. Today 2003, 78, 25. (3) Deo, G.; Wachs, I. E.; Haber, J. Crit. ReV. Surf. Chem. 1994, 4, 141. (4) Deo, G.; Wachs, I. E. J. Catal. 1994, 146, 323. (5) Weckhuysen, B. M.; Jehng, J. M.; Wachs, I. E. J. Phys. Chem. B 2000, 104, 7382. (6) Gao, X.; Wachs, I. E. Top. Catal. 2002, 18, 243–250. (7) Keller, D. E.; Airaksinen, S. M. K.; Krause, A. O. I.; Weckhuysen, B. M.; Koningsberger, D. C. J. Am. Chem. Soc. 2007, 129, 3189. (8) Boulet, P.; Baiker, A; Chermette, H; Gilardoni, F.; Volta, J. C.; Weber, J. J. Phys. Chem. B 2002, 106, 9659. (9) Khaliullin, R. Z.; Bell, A. T. J. Phys. Chem. B 2002, 106, 7832. (10) Do¨bler, J.; Pritzsche, M.; Sauer, J. J. Am. Chem. Soc. 2005, 127, 10861. (11) Burcham, L. J.; Baldani, M.; Wachs, I. E. J. Catal. 2001, 203, 104. (12) Goodrow, A.; Bell, A. T. J. Phys. Chem. C 2007, 111, 14753. (13) Goodrow, A.; Bell, A. T. J. Phys. Chem. C 2008, 112, 13204. (14) Burcham, L. J.; Wachs, I. E. Catal. Today 1999, 49, 467. (15) Chemical ReactiVity And Reaction Paths; Klopman, G., Ed.; WileyInterscience: New York, 1974; p 59. (16) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University Press: New York, 1989. (17) Geerlings, P.; De Proft, F.; Langenaeker, W. Chem. ReV. 2003, 103, 1793. (18) Chermette, H. J. Comput. Chem. 1999, 20, 29. (19) Molecular Electrostatic Potentials: Concepts and Applications; Murray, J., Sen, K., Eds.; Elsevier: Amsterdam, 1996. (20) Parr, R. G.; Donnelly, R. A.; Levy, M.; Palke, W. E. J. Chem. Phys. 1978, 68, 3801–3807. (21) Parr, R. G.; Pearson, R. G. J. Am. Chem. Soc. 1983, 105, 7512. (22) Pearson, R. G. Hard and Soft Acids and Bases; Dowden Hutchinson & Ross: Stroudenbury, PA, 1973. (23) Parr, R. G.; Yang, W. J. Am. Chem. Soc. 1984, 106, 4049–4050. (24) Fukui, K. Science 1987, 218, 747. (25) Yang, W.; Parr, R. G. Proc. Natl. Acad. Sci. U.S.A. 1985, 82, 6723– 6726. (26) Geerlings, P.; De Proft, F.; Langenaeker, W. AdV. Quantum Chem. 1999, 33, 303. (27) Geerlings, P.; De Proft, F. Int. J. Quantum Chem. 2000, 80, 227. (28) Brenneman, C. M.; Wiberg, K. B. J. Comput. Chem. 1990, 11, 361. (29) Frisch, M. J. Gaussian 03, revision D0.01; Gaussian, Inc.: Wallingford, CT, 2004. (30) Krishnan, R.; Frisch, M. J.; Pople, J. A. J. Chem. Phys. 1980, 72, 4244. (31) Dolg, M.; Wedig, U.; Stoll, H; Preuss, H. J. Chem. Phys. 1987, 86, 866.

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