The Mechanism of Propane Oxidation over Iron Antimony Oxide - The

J. Phys. Chem. C 2008, 112, 9783–9797

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The Mechanism of Propane Oxidation over Iron Antimony Oxide Changjun Zhang and C. Richard A. Catlow* The Royal Institution of Great Britain, 21 Albemarle Street, London, W1S 4BS, Department of Chemistry, UniVersity College London, 20 Gordon Street, London, WC1H 0AJ, U.K. ReceiVed: December 10, 2007; ReVised Manuscript ReceiVed: February 22, 2008

Density functional theory has been used to investigate propane oxidation over iron antimony oxide, an important process in the petrochemical industry. Detailed microscopic mechanisms have been revealed for the following three key reactions: (i) the initial hydrogen abstraction from propane, the rate-determining step in propane oxidation to acrolein (CH2dCH-CHO), (ii) the formation of propene, a possible intermediate in the process, and (iii) the production of acrolein via the economically valuable one-stage mechanism. We have found that in the initial C-H splitting, the most feasible cleavage takes place via a homolytic dissociation, involving two oxygen atoms along the [010] direction of the surface and occurring in the methylene group. The heterolytic dissociation paths are generally less favorable than the homolytic processes; and in the former, there is almost no preference in abstracting H from methylene or methyl group. Subsequent reactions, after the first H abstraction via homolytic splitting, cannot lead to propene formation due to the large energy barriers encountered. In contrast, when the first H abstraction takes place on the CH2 species via a heterolytic splitting path, propene can subsequently be readily formed. Moreover, following a heterolytic splitting path for the first H abstraction from a CH3 species, we have identified a facile one-stage mechanism for the direct conversion of propane to acrolein, without having to proceed via the propene intermediate. The mechanistic details presented in this work are consistent with experiment, and lay the foundations for an understanding of activity and selectivity of this catalyst toward propane oxidation. 1. Introduction The oxidation of propene to acrolein (CH2dCH-CHO) and the ammoxidation of propene to acrylonitrile (CH2dCH-CtN) represent major uses of selective oxidation catalysis in the petrochemical industry.1,2 Since these processes were commercialized in the 1960s, intense efforts have been made to utilize propane instead of propene as a feedstock, primarily due to the greater availability and the lower cost of the former.3–6 However, catalysts for the propane-based route in industrial manufacture are yet to emerge. Among many challenges in realizing such reactions, the activation of propane is a limiting step.7 The reaction conditions for activating the C-H bond are usually highly demanding in energy, which would also have negative effects on selectivity of catalysts. In addition to the activation of propane, there are two important technological options, which need to be considered in the conversion of propane to acrolein/acrylonitrile:8 (i) a two-stage process based on an initial dehydrogenation step of propane to propene integrated with a second conventional unit for propene to acrolein/acrylonitrile; or (ii) a direct one-stage propane conversion. Although the first option could benefit from existing technologies, the extra expense of adding a dehydrogenation unit to a propene (amm)oxidation plant may be economically unfeasible. Thus, the one-stage process may be the more promising route. These issues highlight the importance of understanding mechanisms of propane activation and conversion. Many catalysts, mainly multicomponent mixed oxides, have been investigated for propane (amm)oxidation. Those emerging so far as promising include the antimonates, for example, V-Sb-W-Te-Sn-Ox and the molybdates, for example, * Author to whom correspondence should be addressed. E-mail: [email protected].

Mo-V-Nb-Te-Ox.9–12 However, the complex structures of these multicomponent oxides make their study difficult. The present study has therefore chosen a binary-component oxide, iron antimony oxide (FeSbO4), as a prototype. FeSbO4 is wellknown for its high selectivity in propene (amm)oxidation to acrolein and acrylonitrile, and has been used as an industrial catalyst.13–19 It has also been successfully applied to the (amm)oxidation of propane, although high operating temperatures are needed and yields of acrolein and acrylonitrile are low.20–22 In a detailed study of Bowker et al.,21 it was suggested that the rate-determining step in the propane (amm)oxidation on FeSbO4 is the initial hydrogen abstraction to activate propane. The dehydrogenation proceeds via the Mars-van Krevelen mechanism,1 as the surface lattice oxygen is the active species. These findings appear to be general for such reactions over many oxides such as Mo3O9 and V2O5.23,24 In their temperatureprogrammed data (TPD) for propane on FeSbO4, Bowker et al. observed two partially oxidized species, propene and acrolein, at the same temperature (∼340 K). They speculated that both species are formed directly from a common alkyl intermediate, implying the one-stage reaction mechanism, i.e. direct propane conversion to acrolein. However, the nature of the alkyl intermediate and the details of the mechanism are unclear. They further postulated that while the one-stage mechanism is dominant under fully oxidizing conditions, the reaction is mainly a two-stage mechanism via a propene intermediate when the catalyst surface becomes more oxygen depleted. The latter mechanism is kinetically more difficult, as shown from the TPD spectrum of propane on partially reduced FeSbO4, where a higher temperature (∼530 K) peak was observed for the acrolein formation. In addition, they and others19,25 also found that excess Sb on FeSbO4 enhances the formation of (amm)oxidation products, although the location and nature of the excess Sb are

10.1021/jp711611d CCC: $40.75  2008 American Chemical Society Published on Web 06/10/2008

9784 J. Phys. Chem. C, Vol. 112, No. 26, 2008 not clear. They suggested that Sb plays the major role in activating propane. To improve the activity of the catalyst, studies have also been made on some VSbO4 related oxides.26,27 With the aim of understanding the mechanisms of propane activation and conversion, we have undertaken a detailed theoretical investigation of the reactions on an FeSbO4 surface. Our calculations have three main components. First, in order to understand the (amm)oxidation mechanism, it is essential to know where and how the initial H atom abstraction occurs on the surface. Therefore, we examine various possible dehydrogenation paths, including C-H bond splitting via both homolytic and heterolytic paths and H abstraction from both the methyl and the methylene groups. Whereas the homolytic splitting, taking place only on oxygen, seems to be the natural path for the oxidative dehydrogenation, the heterolytic process, involving metal-C bond formation, can also be important in understanding the activity of the catalyst. On the other hand, although the methylene C-H bond is weaker than the methyl C-H bond by approximately 15 kJ mol-1 (0.16 eV),28 the end-on alkyl intermediate may be preferred sterically. Thus, both groups are considered. Given the suggestion from experiment that the initial H abstraction from propane is the rate-determining step in the propane (amm)oxidation, a thorough investigation of this fundamental issue is undoubtedly of great importance. However, as we will show later, examination of this process alone does not necessarily provide clear insight into the whole oxidation mechanism. In fact, understanding subsequent reactions after the initial propane activation can be equally important. In our second step, we have examined the formation of propene, which could be strongly involved in both one- and two-stage mechanisms. Following the reaction paths identified for the first H abstraction, we considered various reaction scenarios of the second H abstraction leading to propene formation. In the third component of our study, we have probed the mechanism of formation of acrolein, the final product in the oxidation, which involves many elementary steps, such as consecutive C-H bond-breaking and CdO bond-making. A complete picture of propane oxidation on FeSbO4 generated in this study allows us to understand and clarify the fundamental mechanism, as well as to link with and interpret experiment. Our study builds upon substantial previous work on understanding the complex crystal structure and surface chemistry of FeSbO4,29–33 in which Sb and Fe cations distribute in the octahedral sites within the oxygen lattice, and where the cation distribution has been investigated in recent years. Grau-Crespo et al.30–32 carried out extensive first-principles calculations to show that Sb and Fe cations have a clear preference to alternate along the c axis of the crystal, while these chains of alternating cations connect laterally with significant disorder in the a-b plane, which prevents three-dimensional long-range ordering. These findings interpret well the corresponding experiments.34 Therefore, in this study we built the FeSbO4 surface from the bulk structure established in their work. We chose the FeSbO4(100) surface that is the most prominent surface in experiments,35 as shown schematically in Figure 1b, which has also been studied by Grau-Crespo et al. very recently.33 2. Calculations All calculations were performed using the Vienna Ab initio Simulation Program (VASP), a widely used plane-wave pseudopotential DFT package.36–39 We used the DFT+U methodology,40–43 instead of the commonly used local density (LDA) or the generalized-gradient approximation (GGA), to describe the exchange and correlation terms, as these latter methods are

Zhang and Catlow known to fail in the description of the electronic properties of some metal oxides. The DFT+U technique combines DFT and a Hubbard Hamiltonian to account for the intra-atomic Coulomb repulsion, which is not well described in standard DFT. In FeSbO4, the DFT+U approach has been proved to be essential in obtaining correct electronic and magnetic properties, as shown by Grau-Crespo et al.34 We therefore used the GGA+U approximation with a GGA functional built from the Perdew and Zunger local functional, with the spin interpolation formula of Vosko et al. and the gradient corrections of Perdew et al.44–46 The Ueff, i.e. the difference between the spherically averaged Hubbard parameter U and the screened exchange energy I in the formulation of Dudarev et al.,43 was chosen to be 4 eV, and determines an orbital-dependent correction to the DFT energy. For the choice of the optimum Ueff, we refer to the work of Grau-Crespo et al.32 The details of the implementation of the DFT+U technique in the VASP code can be found in the work of Rohrbach et al.47 In addition, the interaction between the valence electrons and the core was described with the projected augmented wave (PAW) method in the implementation of Kresse and Joubert.48 The number of plane waves is controlled by a cutoff energy, which was chosen as 500 eV, sufficient to obtain well-converged energies. In our surface model, we used a 2 × 2 unit cell (9.37 × 12.46 Å2 surface area), in order to accommodate the propane molecule. The model also contains nine atomic layers or three layers of FeSbO4 units and ∼12 Å vacuum region. Tests showed that these are adequate to obtain satisfactorily converged adsorption energy for propane: calculations with a larger 4 × 2 unit cell and a slab of five layers of FeSbO4 units gave a variation of ∼0.05 eV and ∼0.08 eV, respectively. The k-point spacing used to sample the Brillouin zone was chosen as 0.03 Å-1, which corresponds to a 4 × 3 × 1 k-point mesh for the 2 × 2 unit cell. Another important aspect is the ordering of the Fe3+ magnetic moments in the systems. As found by GrauCrespo et al.,33 the antiferromagnetic ordering of the Fe3+ in the FeSbO4(100) surface, with electrons of the diagonal Fe-Fe pair orientating in antiparallel directions, is the same as that in the bulk. In the propane adsorption systems, we have also found that this ordering is the most stable spin configuration. In the adsorption energy calculations, we report all the energies with respect to the isolated propane molecule (unless otherwise stated). To investigate the reaction pathway and mechanism, we employed the climbing image nudged elastic band (CI-NEB) algorithm.49 In the regular NEB algorithm, the minimum energy reaction pathway (MEP) is found by constructing a set of images between a given initial and a final state. A spring interaction between adjacent images is added to ensure continuity of the path; the energies of this string of images are then minimized, and the MEP is consequently obtained. In addition to calculating the MEP, the CI-NEB algorithm drives the image with the highest energy up to the saddle point and thus is also able to locate the transition state configuration. In practice, eight images are generally used in between initial reactants and final products via a linear interpolation, and are then optimized with the CINBE algorithm to locate the saddle points. Reaction barriers are determined as the energy differences between the saddle points and the starting points of the MEP. 3. Molecular Adsorption on FeSbO4 We first consider molecular propane on the surface. Due to different surface sites and orientations of the molecule, many adsorption configurations are possible. The molecule can locate

Propane Oxidation over Iron Antimony Oxide

J. Phys. Chem. C, Vol. 112, No. 26, 2008 9785

Figure 1. Top view (a) and side view (b) of the FeSbO4(100) surface. O atoms are in red, Sb in violet, and Fe in light blue. The [100] direction is perpendicular to the surface plane; the [001] and the [010] directions are along and perpendicular to the bridging O rows, respectively.

above bridging O atom, Sb and/or Fe atoms, orientate along different directions, and rotate in such a way that the two H of the CH2 group point either toward or away from the surface. Taking all these into account, we have examined nearly 30 possible configurations. In configurations where the molecule adsorbs along the [010] direction (i.e., the C-C-C axis is parallel to the [010]), we also carried out calculations on a 4 × 2 surface to minimize possible interaction of images between cells. Our results show that the adsorption geometries on the 4 × 2 and the 2 × 2 surfaces are very similar, and that the energy difference between the two systems is also small, of the order of ∼0.05 eV. We find that propane adsorption along [100], in which the C-C-C axis of the molecule can be viewed as being perpendicular to the surface plane, is less favorable (by ∼0.3 eV) than that along the [001] and [010] directions. In the latter cases, many stable configurations with similar energies were found when the molecule adsorbed in the different ways described above. The small variations in the energies of these configurations suggest that the adsorption is almost independent of the orientation of the molecule and the substrate beneath the molecule. Moreover, the adsorption is weak: the adsorption energies were calculated in the range of +0.05 to +0.07 eV, i.e. slightly exothermic or endothermic (although the terms of exo- or endoenergetic may be more appropriate as the calculations are performed at zero temperature and pressure). Propane

only binds to the surface via weak H · · · O interactions, as shown by the long distance (typically larger than 2.4 Å) between H atoms and bridging O atoms. Of course, the dispersive interactions are poorly represented by DFT, and the adsorption energies could be significantly underestimated. Given the large number of molecular adsorption states, many propane activation paths can be envisaged. Because there has been no clear indication as to how the dehydrogenation occurs and which path is favorable, it appears to be necessary to examine all possibilities. In general, these paths can be categorized into two kinds: homolytic and heterolytic splitting of a C-H bond. In each kind, several scenarios are also possible. The reaction may take place along different directions, and in either a CH3 or a CH2 species. In addition, in the heterolytic cleavage, the dehydrogenated propane may form a bond with either Sb or Fe on the surface; in the homolytic cleavage, the reaction may involve either one lattice bridging O or two adjacent bridging O atoms. We note that we did not consider the 3-coordinated lattice O, which is clearly less active as well as less sterically accessible than the 2-coordinated bridging O, and also that because of the vast number of possible reaction paths, one can never exhaust all the possibilities with limited computing resources. However, we consider that the paths presented here are the most representative and the most favorable.

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Figure 2. Various states in typical heterolytic splitting paths.

4. The Initial H Abstraction In this section, we explore in detail the reaction paths for both heterolytic and homolytic splitting. We consider the structures and energetics of each of the proposed mechanisms. 4.1. Heterolytic Splitting. 4.1.1. Reaction Paths. First we consider heterolytic splitting of a C-H bond in the CH3 species, where we let the propane molecule initially adsorb along the [001] direction (i.e., where the C-C-C axis is along this direction), followed by dehydrogenation with a C-Sb bond formation. An example of this reaction path is shown in Figure 2, denoted as path 1-i. We see that one H is abstracted by one bridging O and the remainder of propane forms a bond with an Sb atom. In the transition state (TS) along the path, the C-H bond of the dissociating H elongates to 1.40 Å from the initial 1.10 Å in molecular propane; meanwhile the O-H and the Sb-C distances shorten to 1.30 Å and 2.51 Å, respectively. These observations indicate an activated H and a multicentered bonding feature in the TS. The energy barrier was calculated as 1.16 eV with respect to the initial adsorbed configuration. In the final dissociated state, the C-H breaks and the C-Sb bond length is 2.21 Å; meanwhile, the distance between the other H atom of the original CH3 species and a nearby O atom is quite short, at 2.10 Å. This reaction process is exothermic (-0.40 eV). The main structural parameters in the TS are shown in the figure. Because there are two inequivalent (albeit electronically similar) bridging O atoms on the surface, there could be a

slightly different path, which would lead to bond formation between a dissociated H atom and a different O atom from that in path 1-i. We have found that this path (not shown) is slightly less favorable than path 1-i, as the reaction is less exothermic. In addition to the above processes, where the molecule initially locates along the [001] direction, we also considered the possibility of reactions in which the molecule adsorbs along the [010] and [100] directions. Along the [010] direction, we found that the heterolytic splitting in the CH3 group is sterically hindered, owing to the large repulsion between bridging O atoms and the other CH3 group. In fact, the reaction transformed to a homolytic splitting process. Along the [100] direction, a reaction path (denoted as path 1-ii), leading to the formation of a C-Sb bond, has been identified. As shown in Figure 2, the molecule is initially upright on the surface plane; as it moves toward the surface, one H atom of the CH3 group bonds with a bridging O atom and the C atom bonds with an Sb atom beneath. The energy barrier is 1.13 eV, which is very close to that in path 1-i. We note that the initial adsorption state and the final state in path 1-ii are about 0.3 eV less stable than the corresponding states in path 1-i, respectively. In other words, the reaction energies of the two paths are very similar; hence, it is not surprising that the two barriers are also similar. However, given the large barrier to activate H in propane, we speculate that the molecule would be more likely to rotate from being along the [100] direction (the initial state in path 1-ii) to the [001] direction (e.g., the more stable initial state in path 1-i), rather than losing

Propane Oxidation over Iron Antimony Oxide a H atom straightway upon contact with the surface. Thus, path 1-i should be more feasible. Nevertheless, we note that path 1-ii may become favorable on the partially hydroxylated surface, where path 1-i could be sterically hindered. Other dehydrogenation scenarios may include (i) formation of a Fe-C bond as opposed to a Sb-C bond; (ii) formation of a H-Sb bond (with the remainder of the molecule binding to the bridging O via a C). However, we found that those paths are much less favorable than those described above, and are significantly endothermic by 0.94 and 0.31 eV, respectively. The result that Sb rather than Fe is responsible for activating propane is consistent with the experiment.21 In addition, to check the feasibility on kinetic grounds, we have calculated the path leading to the H-Sb bond formation (the less endothermic one in the two cases), and found a barrier of 2.24 eV for the process. The barrier is so large that we can essentially rule out these paths. In the case of H abstraction from the CH2 species, we show a path (denoted as path 1-iii) in Figure 2, where the molecule is initially along the [001] direction; one H atom is gradually stretched toward a lattice O atom while the activated C moves toward the Sb beneath it; in the TS the O-H and C-Sb distances are 1.42 Å and 2.58 Å, respectively; in the final dissociated state, the Sb-C distance is 2.28 Å. The barrier was calculated to be 1.23 eV, which is close to that in the heterolytic cleavage in the CH3 species (i.e., path 1-i). This result is interesting, because the C-H bond in the CH2 is weaker than that in the CH3 and one might have expected the barrier in path 1-iii to be lower than that in path 1-i. We ascribe this result to the more significant steric repulsion between the molecule and the surface occurring in path 1-iii than in path 1-i. In the former, the repulsion with the surface involves the two CH3 species, because the bond formation between the CH2 and the Sb forces the two CH3 to move toward the surface, which is not the case in the latter. We have also considered other possible paths for H abstraction from CH2. As we found in the cases of H abstraction from CH3, the reaction leading to the Fe-C formation is much less favorable (by ∼1.2 eV in terms of reaction energy) than with the Sb-C formation; reactions which start with the molecule adsorbing along the [010] and the [001] directions are sterically prohibited. 4.1.2. Electronic Analysis. Dissociative adsorption via heterolytic cleavage is often described as an acid-base adsorption mechanism, i.e. the resulting anion adsorbs on the surface metal cation, and the cation on the surface O.50 It is therefore interesting to examine the charge distribution upon propane dissociative adsorption, which could also provide insight as to why Sb is more active toward propane activation than Fe. To this end, we calculated the atomic charges by using the widely used Bader charge analysis.51 We examine two systems: heterolytic cleavage of a CH2 species associated with an Sb and an Fe (denoted as hetero-Sb and hetero-Fe, respectively). To illustrate the different activity of Sb and Fe, we summarize in Table 1 the charge difference of relevant atoms by subtracting their charges in the initial adsorption state from the final dissociated state. Thus, a positive sign means an increase in electron density, and vice versa. To provide a more intuitive view, we also plot in Figure 3 the total charge density difference for the two systems, by subtracting the total electron density of the unadsorbed surface (with exactly the same structure as that in the final state but without the molecule) and that of the

J. Phys. Chem. C, Vol. 112, No. 26, 2008 9787 TABLE 1: Charge Differences between the Initial Molecular Adsorption State and the Dissociated State for the Two systems, Hetero-Sb and Hetero-Fea H O C Sb Fe

hetero-Sb

hetero-Fe

-0.55 +0.18 +0.42 -0.01

-0.57 +0.17 +0.20 +0.31

a

The positive sign indicates charge increase. The H, O, C and Sb (or Fe) symbols refer to those atoms that are directly involved in the dissociation process in hetero-Sb (or hetero-Fe).

isolated molecule (with exactly the same structure as that in the final state but without the surface) from that of the final state. Table 1 shows that, for both hetero-Sb and hetero-Fe, the dissociated H lose ∼0.5e and the O (attached to the H) gain ∼0.2e. However, much more charge has been transferred to the C in the former than in the latter; Sb loses more electrons than does Fe. In fact, upon propane dissociative adsorption, the Fe gains electron density along a d orbital direction (see Figure 3), and the overall result is that Fe is more negative than that in the initial state. Therefore, the more positively charged metal atom and the more negatively charged C in the hetero-Sb indicates a stronger ionic character than that in the hetero-Fe, which explains the activity of the Sb toward the propane dissociative adsorption. 4.2. Homolytic Splitting. 4.2.1. The Homolytic CleaWage InWolWing One Lattice Oxygen. Because the active bridging O atoms are present on the top layer of the surface, homolytic splitting, without directly involving any substrate metal atoms, appears to be a more natural reaction path. Also the steric repulsion between the molecule and the surface during this reaction would have insignificant effects, leading us to expect that the C-H bond in CH2 would be more easily activated than that in CH3. We first therefore consider the homolytic splitting of the C-H bond in CH2, an example of which (denoted as 1-iV) is shown in Figure 4. We see that a H atom in the CH2 is abstracted by an O atom, and a TS forms when the H-O and H-C distances are 1.19 Å and 1.39 Å respectively. The barrier is calculated to be 1.00 eV. After the TS, a propyl-like species appears on the surface, which bonds weakly (via C) to the dissociated H (the H-C distance being 2.04 Å), and is ∼0.5 eV higher in energy than the initial state. Owing to the loss of an H atom, the radical-like structure (denoted as intermediate) can develop bonding with the O atom beneath, and form a final structure as shown in Figure 4 (path 1-iV). Such a process is substantially exothermic (1.60 eV) because of the strong C-O bond formed. However, the search for a TS of this process is problematic. As can be seen from the energy profile plotted in Figure 5b (the red curve in the bottom panel), the potential energy surface in the vicinity of the intermediate is very flat, making identification of a TS very difficult. We have found that the structure at the highest-energy point in the red curve has more than one imaginary vibrational frequency (albeit small), indicating that it is not a true TS, although the optimization was converged within the set tolerances. Moreover, it would also appear that the intermediate might not even be a true minimum but, owing to the extreme flatness of the potential energy surface in its vicinity, appeared to be so within the set force tolerances. The origin of the flatness of the PES can be attributed to the weak H · · · O bond in the intermediate, implying that the molecule can orientate easily.


Zhang and Catlow

Figure 3. Propane dissociative adsorption: electron density difference in the case of a heterolytic cleavage of a CH2 species associated with (a) an Sb and (b) an Fe, denoted as hetero-Sb and hetero-Fe, respectively. Blue areas indicate electron density accumulation, and yellow areas indicate density depletion. For clarity, the surfaces are rotated and the charges are plotted half-transparent.

There is an alternative path, which leads to the same dissociated state as that of path 1-iV. By carefully choosing the initial molecular state (i.e., the molecule is directly above the target O and the C · · O axis is parallel to [100]), we identified a one-step dissociation path which involves a C-O-H threecentered TS, shown in Figure 5(a). In the TS structure, the C-H, O-H, and C-O distances are 2.00, 1.04, 2.49 Å, respectively. The barrier is 0.94 eV, very close to that in path 1-iV. We note that, in path 1-iV, propane initially locates along the [001] direction, and in the final state, the dissociated H and the radical bond to the O in directions to which the lone pairs of the O point, indicating that the dehydrogenation would be more difficult if the molecule initially locates along the [010] direction (i.e., the reaction proceeds along [001]). Indeed, we found that if the reaction were to happen in the latter case, the lattice O has to break the bonding with all the substrate atoms; in the final state a CH3CH(OH)CH3 forms above the surface; the reaction is ∼0.5 eV less exothermic than path 1-iV. For H abstraction from the CH3 via the homolytic splitting, we have identified the first barrier for a path (denoted as 1-V in Figure 4) to be 1.28 eV. This value is higher than that for the H abstraction from the CH2, which is consistent with the fact that the C-H bond is stronger in the CH3 than that in the CH2. Because this barrier is higher than that in path 1-iV, we do not consider this possibility further. 4.2.2. The Homolytic CleaWage InWolWing Two Lattice Oxygen. Homolytic splitting may also involve two bridging O atoms. As shown in Figure 4 (denoted as path 1-Vi), lying along the [001] direction, the molecule initially locates above the trough in between the two bridging O rows, and the two H atoms of the CH2 point toward two adjacent O atoms. As the reaction proceeds, one H in the CH2 species is abstracted by an O and the radical shifts toward the other O, and the TS is formed when the C-H and the O-H distances are 1.35 and 1.27 Å respectively. The barrier of this step is 0.81 eV, which is relatively small. Our calculations also showed that the dissociated entity (which may be viewed as an intermediate) moves further away from the H, so that the C atom gradually bonds with the O beneath. The structure formed (i.e., the final state in path 1-Vi) is very stable, being 1.36 eV lower in energy than the initial molecular adsorption. Analogous to the situation in path 1-iV, we should be cautions about the calculated intermediate structure and the reaction path, because the potential energy surface in the vicinity of the intermediate is again very flat, and the calculated barrier from the NEB method is merely 0.05 eV.

The homolytic splitting may also occur with the aid of two bridging O atoms that are along the [010] direction, in which case the reaction takes place along the [001] direction. However, this is likely to be less favorable than path 1-Vi, because the reaction path along [001] does not accord with the O lone pair directions. To support this speculation, we carried out NEB calculations for the reaction occurring along the [001] direction (path 1-Vii, as shown in Figure 4). We found the barrier to be 1.12 eV, which is significantly higher than that in path 1-Vi. Finally, we show in Figure 4 an example of H abstraction from the CH3 species, i.e. path 1-Viii. This process is similar to path 1-Vi. As expected, it has a higher barrier (1.24 eV). 5. The Second H Abstraction Leading to the Formation of Propene 5.1. Reactions That Follow the First H Abstraction via the Homolytic Splitting Paths. To examine propene formation, we started from the most favorable path identified for the first H abstraction, i.e. path 1-Vi. One likely scenario is that an H atom in a CH3 group is abstracted by an adjacent O atom, leading to the formation of the structure shown in Figure 6(a) or 6(b), where, to gain a clearer view, these and subsequent structures are shown schematically as top views. However, we found these processes to be very unfavorable, with reaction energies of +1.67 eV and +1.39 eV, respectively, which suggests that the barriers for these processes could be prohibitive. We have also considered the other possible scenario for the abstraction of the second H atom: an H atom is abstracted toward a nearby Sb atom, leading to the formation of the structure shown in Figure 6(c), which was, however, also found to be an endothermic process with a reaction energy of +0.69 eV. We have calculated the minimum energy path for the H-Sb formation, and we found the barrier to be very large (2.28 eV). We therefore examined the possibility of the second H atom abstraction following paths 1-iV, 1-Vii and 1-Viii for the first H atom abstraction, and some examples of the resultant structures are shown in Figure 6(d-f), respectively. In the former two cases, the second H abstraction takes places from the CH3 species, whereas in the latter case, it occurs at the CH2 species, and consequently leads to water formation. In all cases, we found that the second H abstraction is significantly endothermic (0.90, 1.25 and 1.38 eV, respectively). All these calculations clearly suggest therefore that abstraction of the second H atom would be very difficult.



Figure 4. Various states in typical homolytic splitting paths.

5.2. Reactions That Follow the First H Abstraction via the Heterolytic Splitting Paths. We turn now to examine the abstraction of the second H atom following the abstraction of the initial H atom by heterolytic splitting. Based on path 1-i, the only way to form propene is to abstract an H atom from the CH2 toward a neighboring bridging O. However, the molecule initially adsorbs in such a way that the H in the CH2 points away from the surface. In order to form an H-O bond, the H-C bond must twist to a large extent toward the O, which is unfavorable as it is against the tetrahedral bonding directions

owing to the C sp3 hybridization. Indeed, the NEB calculation could not find any transition state leading to H-O bond formation. Following path 1-iii, the reaction to form propene must take place on the end-on CH3 species. As shown in Figure 7 (denoted as path 2), an H atom in a CH3 species is abstracted toward a nearby bridging O, and the C-Sb distance gradually elongates; a TS is formed when the H-C and the C-Sb distances are 1.25 and 2.89 Å respectively; and in the final state, C-Sb distance becomes 3.49 Å, and the resultant propene molecule


Zhang and Catlow

Figure 5. (a) The one-step homolytic splitting path, which leads to the same final state as that of path 1-iV in Figure 4. (b) The energy profiles of the one-step (in the top panel) and two-step (i.e., path 1-iV in the bottom panel) homolytic dissociations.

only interacts with the surface via weak H · · · O bonding. The barrier for this reaction was calculated to be 0.67 eV, which is significantly smaller than that for the first H abstraction, and the process is exothermic by -0.60 eV. Another possible reaction, following path 1-iii, is to abstract the H atom from the CH species, leading to the formation of a (CH3)2Cd type product, which might compete with propene formation. However, we have found that this process is much less favorable than the reaction leading to propene, as it is endothermic by 0.82 eV. 5.3. Electronic analysis. From above results, the second H abstraction would be prohibited if the first follows a homolytic splitting path, whereas it would be more feasible if the first abstraction occurs via a heterolytic splitting path. To understand this interesting phenomenon, we carried out charge analyses for the two final structures (Figure 6a and 7c) after the second H abstraction, which are denoted as homo-2nd and hetero-2nd, respectively. As with the definitions in section 4.1.2, we summarize in Table 2 the charge difference of relevant atoms by subtracting their charges in the initial molecular adsorption state from those in homo-2nd or hetero-2nd; we also plot in Figure 8 the total charge density difference, defined as previously. From Table 2 and Figure 8, a striking feature can be seen in both homo-2nd and hetero-2nd: there are significant electron

density accumulations near an Sb and a C (i.e., the C which is nearest to the Sb), with these features being slightly more evident in homo-2nd. We consider that the electron accumulations around the Sb and the C are largely induced by the π bonding in propene, which is perpendicular to the Sb-O bond axis beneath. Indeed, on a pure FeSbO4 surface, we found that propene bonds with the Sb-O beneath through its CdC π bonding. The feature is slightly more evident in homo-2nd due to the shorter C-Sb distance (by ∼0.2 Å) than that in hetero2nd. However, in the former, because the C (i.e., the C which is bonded to O) is still sp3-alike, the CH-CH2 bond axis points away from the Sb, leading to an unfavorable geometry for the C-Sb bonding. In other words, there would be a significant competition between the C-O and the C-Sb bonding. As a result, the CH-CH2 distance is large (1.48 Å) compared to that in the gas phase propene molecule (1.33 Å). In addition, the H neighboring to the CH2 species may also sterically hinder the C-Sb bonding. All these features illustrate the lesser stability of homo-2nd. We note that there are similarities in the structure in Figure 5b, in which electron density accumulates around an Fe and a C. On the other hand, unlike with homo-2nd, there is no such constraint as a C-O bond in the case of hetero-2nd. The propene molecule is formed well above the surface: the C-Sb distance is large (3.49 Å), and the CH-CH2 distance



Figure 6. Various possible final structures in the processes of forming propene, in which the first H atom abstraction takes places via homolytic splitting paths. For clarity, both top and side views are shown.

(1.34 Å) is close to that in the gas phase molecule, indicating only small interactions between the molecule and the surface. The CdC bond axis in the molecule is also parallel to the O-Sb bond axis: if there were no H atoms attached to the surface O atom, the molecule would form a bond with them via the π orbital. 6. Reactions Leading to the Formation of Acrolein The formation of acrolein involves several elementary reactions, and it could proceed through many different routes and with different bond making/breaking sequences. Based on the knowledge we have so far achieved, we are able to rule out some possibilities. First, we can exclude those reactions which

follow the first H abstraction via the homolytic splitting paths, because the second H abstractionsan essential step in forming acroleinsappears to be prohibitive in those cases. Second, we can omit any possible reaction after propene formation, since, in that case, propene would be an intermediate in forming acrolein, which points to the two-stage mechanism; but, according to experiment, the two-stage mechanism is only prominent on the reduced surface. Therefore, we now examine the reaction path via a one-stage mechanism, without involving the propene intermediate. We started from the first H abstraction from a CH3 species via heterolytic splitting (i.e., path 1-i). We considered all the necessary steps in the process of forming acrolein, for which


Zhang and Catlow

Figure 7. The initial, transition and final states in the second H abstraction in the propene formation (i.e., path 2), in which the first H atom abstraction takes places via heterolytic splitting. For clarity, both top and side views are shown.

TABLE 2: Charge Differences between the Initial Molecular Adsorption State and the Final Dissociated State after the Second H Abstraction for the Two Systems, Homo-2nd and Hetero-2nda H O C Sb

homo-2nd

hetero-2nd

-0.57 +0.22 +0.14 +0.43

-0.56 +0.19 +0.02 +0.27

a The H, O, C and Sb symbols refer to those atoms that are directly involved in the second H dissociation process in the two systems.

we identified six distinct steps, shown in Figure 9, which we now discuss in turn: (i) Path 3-i (a f c): An H atom in the CH2 species attached to the Sb is abstracted by an adjacent O. The barrier is 1.19 eV, and the reaction is endothermic by 0.90 eV. We note that other possible C-H splitting paths are less favorable. For example, the H atom in the other CH2 group points away from the surface, hence prohibiting the C-H bond breaking; breaking a C-H in the CH3 group may proceed via a heterolytic splitting path, in which case the C-Fe bond formation (Fe is underneath the CH3 species) is significantly more endothermic (1.35 eV). (ii) Path 3-ii (c f e): From the product of the last step (structure c), the C (attached to the Sb) moves to bind with the nearest neighbor O, resulting in a CH3CH2CHO entity attached to the surface via the O (structure e). In structure e, the C-Sb bond is broken, and the O-Fe bond elongates to 2.17 Å. This step can readily occur, as the barrier is only 0.17 eV, and the reaction energy is highly exothermic (-2.2 eV), which can be

ascribed to the C-O bond strength being much stronger than that of the C-Sb bond. (iii) Path 3-iii (e f g): This step may be viewed essentially as desorption of the CH3CH2CHO entity. In structure g, the distances between the O and the substrate metal atoms are over 3.2 Å; the shortest H-O (bridging O) distance is 2.60 Å. These features suggest that the CH3CH2CHO interacts weakly with the surface, implying that the molecule may easily diffuse away. The barrier for this step is 0.25 eV, indicating that the change from structure e to g could readily occur. (iv) Path 3-iV (g f · · · f m): In forming acrolein from propane, a total of four C-H bonds needs to be broken. Thus, the availability of four adjacent bridging O, which could accommodate the four dissociated H atoms, would be important. In structure e or g, it would be unfeasible to break any further C-H bonds, which would involve either water formation (one O atom accommodates two H atoms) or the H-Sb formation, both of which are highly unfavorable. Therefore, in order to form acrolein, the CH3CH2CHO molecule must diffuse to surface sites where several bridging O sites are available. Meanwhile, the Sb site is also important because of its activity toward the activation of C-H. Such a surface structure is shown in Figure 9(m).52 As with structure g, the molecule in structure m also interacts weakly with the surface (the shortest H · · · O distance is 2.53 Å). The energy difference between structure m and structure g is merely 0.10 eV, suggesting that diffusion from g to m may be facile. To demonstrate this feature, we have calculated a number (more than 10) of structures in between these two by shifting the molecule gradually from structure g to m along the [001] direction. Some examples of these structures are shown in Figure 9(h-l). We found that the energy



Figure 8. Top and side views of electron density difference: (a) the second H atom abstraction leading to the formation of the structure 6a (Figure 6), in which case the first H abstraction follows a homolytic splitting path; (b) the second H abstraction leading to the formation of the structure 7c (Figure 7), in which case the first H abstraction follows a heterolytic splitting path. Blue areas indicate electron accumulation, and yellow areas indicate electron depletion. For clarity, top and side views are shown.

differences of all of these configurations lie in the range of 0.18 eV, which clearly shows that the potential energy surface for the adsorption of this molecule is flat. (v) Path 3-V (m f o): From structure m, one H atom of the CH3 group is abstracted by an adjacent O atomsa heterolytic splitting path which is very similar to path 1-i, for which a similar barrier is also obtained (1.21 eV). (vi) Path 3-Vi (o f q): From structure o, one H of the CH2 species is abstracted by an adjacent O, as a result of which, the final product (acrolein) forms above the surface. In the final structure q, the C-Sb bond is broken, as the distance increases to 3.4 Å, and the molecule interacts with the surface by H · · · O bonding (the shortest being 2.2 Å). The barrier for this step is 0.71 eV. From above results, it can be seen that the reaction to form acrolein is the most favorable among many possibilities, and thus is very selective. The energy profile along the whole reaction path, including the first H abstraction, is plotted in Figure 10. 7. Discussion In their experimental studies, Bowker et al.21 observed the formation of propene and acrolein at the same temperature (∼350 K), from which they suggested that propene and acrolein are formed directly from a common alkyl intermediate, and that the production of acrolein from propane is a direct one-stage mechanism. Having identified various propane oxidation paths, we are now in a position to interpret these experiments.

Our calculations of reaction pathways show that the largest barrier for propene formation is very close to that for acrolein formation: in the former it is 1.23 eV, which corresponds to the abstraction of the first H atom (path 1-iii); in the latter the largest barriers are 1.16, 1.19, 1.21 eV, which correspond to the abstraction of the first H (path 1-i) and the second H to form -CHCH2CH3 (path 3-i), and the H abstraction from another CH3 species (path 3-V), respectively. Clearly, the similar barrier heights in the two processes agree with the experimental finding that propene and acrolein form at the same temperature, although we cannot predict the reaction temperature, as our calculations consider only potential energy surfaces. Our study also allows us to clarify previous interpretations of the formation mechanism of propene and acrolein. From experiment, it was proposed that propene and acrolein are formed directly from a common alkyl intermediate. From our calculations, we have found that propene formation must originate from the initial H abstraction from the CH2 species (section 5.2), while acrolein formation is triggered by the initial H abstraction from a CH3 species. Clearly, these are two different mechanisms involving different alkyl intermediates. Interestingly, the barrier to break a C-H bond in a CH3 species is about the same height as that to break one in a CH2 species on the surface (section 4.1), although the former process is more difficult in the gas phase. Thus, the appearance of the two products at the same temperature is, we suggest, not because propene and acrolein are formed


Figure 9

Zhang and Catlow



Figure 9. The six reaction steps involved in the one-stage mechanism leading to the production of acrolein. Structures b, d, f, n and p are transition states. For clarity, both top and side views are shown, except for the structures in path 3-iV where side views do not help readability.

Figure 10. Energy profile for acrolein production from propane via the one-stage mechanism. The zero energy (eV) refers to the initial molecular propane adsorption system. The solid curves are the MEP from the NBE calculations. In the dotted curve, the energies refer to those of the structures in the diffusion process (i.e., path 3-iV), as described in the text.

from the same intermediate as proposed previously,21 but is attributable to the similar reaction barriers in the two processes. Our calculations confirm the possibility of a one-stage direct conversion from propane to acrolein, without proceed-

ing via the propene intermediate. As described in section 6, this process is highly selective toward acrolein after the first H atom abstraction. We also show that propene formation is competitive with acrolein formation via the one-stage route, due to the similar barriers in the two processes. Hence, the two-stage route via the propene intermediate could be an alternative way to form acrolein. However, we note from experiments that the two-stage route appears to be kinetically more difficult, as a higher reaction temperature is required than that for the one-stage route. We therefore do not consider this possibility further in this study. Our results allow further interpretations of the experimental data. First, it had been proposed that the initial hydrogen abstraction to activate propane was the rate-determining step in the propane (amm)oxidation on FeSbO4. However, we have found three comparable energy barriers in the process of acrolein formation, which correspond to the initial and second abstraction of H atoms and the abstraction of an H atom from another CH3 species in an elementary step at a later reaction stage (i.e., 1-i, 3-i, and 3-V, respectively). Thus, we suggest that the initial H abstraction from propane may not be the only rate-determining step; other abstractions may be as

9796 J. Phys. Chem. C, Vol. 112, No. 26, 2008 important in forming acrolein. Second, it has been suggested that excess Sb on the surface could enhance the reaction. Although we have not yet studied the Sb-rich surface, our current results provide two relevant pieces of information. As we discussed earlier, Sb plays the major role in activating propane. Thus, more Sb at the surface may facilitate the dissociative adsorption of propane. Moreover, in the process of forming acrolein via the one-stage conversion mechanism, the propane derivative has to diffuse to the available Sb and O sites, in order to break all the necessary C-H bonds. If more Sb sites are available on the surface, the molecule could reach these sites more rapidly than in the case of the stoichiometric FeSbO4 (Sb:Fe ) 1:1) surface, which would facilitate the acrolein formation. Of course, the Sb-rich surface may have quite different electronic properties from those of the stoichometric surface, so that the activity of Sb may be affected toward the initial and subsequent abstraction of H atoms. More detailed studies are needed here. Third, we can also shed some light on the oxidation on the reduced FeSbO4 surface, which occurs at a higher temperature. From a recent study of Grau-Crespo et al.,33 on a FeSbO4 surface with O vacancy, the electrons left behind by the removed O accumulate at the Sb site. From our study, we have learned that the heterolytic splitting associated with Sb is essential for the initial H atom abstraction in both the processes of propene and acrolein formation and that the reaction is an acid-base mechanism. Thus, a less positive Sb at the reduced surface would be less favorable to form bonding with the negatively charged C. Indeed, we have found in our preliminary study that a heterolytic splitting path on the reduced surface, similar to path 1-i on the perfect surface, is ∼0.5 eV more endothermic than the latter, and the resultant C-Sb bond is also weaker (0.13 Å longer) than that in the perfect surface. These results suggest that the reaction will occur less readily on the reduced surface. 8. Conclusion Our computational study has elucidated a one-stage reaction mechanism for direct propane conversion to acrolein, a desired propane (amm)oxidation process. We have shown that, in the initial propane activation, homolytic C-H splitting generally has a lower energy barrier than the heterolytic process. In the latter, Sb plays the major role in activating propane, and there is hardly any preference for the cleavage on the CH2 and CH3 species. These results enable us to map out the possible scenarios for reactions leading to the formation of propene and acrolein, and subsequently clarify the reaction mechanisms. We have found that, after the first H abstraction takes place via the homolytic splitting paths, the second H abstraction is energetically prohibited. In contrast, propene and acrolein can form following the first H abstraction via the heterolytic splitting paths. Propene formation is completed after the first H abstraction via a heterolytic splitting of the CH2 species. In forming acrolein, the reaction is first triggered by the first H abstraction via a heterolytic splitting of a CH3 species, and then followed by six more consecutive reaction steps. The pathways for propene and acrolein formation that we have identified interpret the corresponding experimental data well. Our identification of the one-stage propane conversion route is of general significance for this class of catalytic processes. Acknowledgment. The work is funded by the EPSRC Portfolio Partnership Project, Synthesis and Design of Functional

Zhang and Catlow Materials (EP/D504872). We are grateful for an allocation of computer time on the HPCx through the Material Chemistry Consortium, also funded by the Portfolio Partnership. We also want to thank R. Grau-Crespo for helpful discussions. References and Notes (1) Grasselli, R. K.; Burrington, J. D. AdV. Catal. 1981, 30, 133. (2) Grasselli, R. K. Top. Catal. 2002, 21, 79. (3) Albonetti, S.; Cavani, F.; Trifiro`, F. Catal. ReV. Sci. Eng. 1996, 38, 413. (4) Grasselli, R. K. Catal. Today 1999, 49, 141. (5) Lin, M. M. Appl. Catal., A: General 2001, 207, 1. (6) Guerrero-Pe¨rez, M. O.; Al-Saeedi, J. N.; Giulants, V. V.; Baoàres, M. A. Appl. Catal., A: General 2004, 260, 93. (7) Grasselli, R. K. Top. Catal 2003, 23, 1. Grasselli, R. K.; Burrington, J. D.; Buttrey, D. J.; DeSanto, P.; Lugmair, C. G.; Volpe, A. F.; Weingand, T. Top. Catal. 2003, 23, 5. (8) Centi, G.; Grasselli, R. K; Trifiro`, F. Catal. Today 1992, 13, 661. (9) Guttmann, A. T.; Grasselli, R. K.; Brazdil, J. F. US Patent, 4,797,381, 1989; US Patent, 4,746,641, 1988; US Patent, 4,788,317, 1988. (10) Hatano, M.; Kayo, A. European Patent 318295, 1988. (11) Ushikubo, T.; Oshima, K.; Kayo, A.; Umezawa, T.; Kiyona, K.; Sawaki, I. European Patent, 529853, 1992. (12) Hinago, H.; Komada, S.; Kogyo, A. K. US Patent 6,063,728, 2000. (13) Burrington, J. D.; Kartisek, C. T.; Grasselli, R. K. J. Catal. 1984, 87, 363. (14) Fattore, V.; Fuhrman, Z. A.; Manara, G.; Notari, B. J. Catal. 1975, 37, 223. (15) Aso, I.; Amamoto, T.; Yamazoe, N.; Seiyama, T. Chem. Lett. 1980, 365. (16) Burriesci, N.; Garbassi, F.; Petrera, M.; Petrini, G. J. Chem. Soc., Faraday Trans. 1982, 78, 817. (17) Dziewiecki, Z.; Makowski, A. React. Kinet. Catal. Lett. 1980, 1, 51. (18) Allen, M.; Betteley, R.; Bowker, M.; Hutchings, G. J. Catal. Today 1991, 9, 97. (19) Van Steen, E.; Schnobel, M.; Walsh, R.; Riedel, T. Appl. Catal., A: General 1997, 165, 349. (20) Centi, G.; Pesheva, D.; Trifiro`, F. Appl. Catal. 1987, 33, 343. (21) Bowker, M.; Bicknell, C. R.; Kerwin, P. Appl. Catal., A: General 1996, 136, 205. (22) Roussel, H.; Mehlomakulu, B.; Belhadj, F.; van Steen, E.; Millet, J. M. M. J. Catal. 2002, 205, 97. (23) Chen, K. D.; Iglesia, E.; Bell, A. T. J. Phys. Chem. B 2001, 105, 646. (24) Creaser, D.; Andersson, B.; Hudgins, R. R.; Silveston, P. L. Appl. Catal., A 1999, 187, 147. (25) Carbucicchio, M.; Centi, G.; Trifiro`, F. J. Catal. 1985, 91, 85. (26) Allen, M. D.; Poulston, S.; Bithell, E. G.; Goringe, M. J.; Bowker, M. J. Catal. 1996, 163, 204. (27) Guerrero-Pe´rez, M. O.; Martıńez-Huerta, M. V.; Fierro, J. L. G.; Baoàres, M. A. Appl. Catal., A: General 2006, 298, 1. (28) Chaar, M. A.; Patel, D.; Kung, H. H. J. Catal. 1988, 109, 463. (29) Berlepsch, P.; Armbruster, T.; Brugger, J.; Criddle, A. E.; Graeser, S. Mineral. Mag. 2003, 67, 31. (30) Grau-Crespo, R.; de Leeuw, N. H.; Catlow, C. R. A. J. Mater. Chem. 2003, 13, 2848. (31) Grau-Crespo, R.; de Leeuw, N. H.; Catlow, C. R. A. Chem. Mater. 2004, 16, 1954. (32) Grau-Crespo, R.; Cora, F.; Sokol, A. A.; de Leeuw, N. H.; Catlow, C. R. A. Phys. ReV. B 2006, 73, 035116. (33) Grau-Crespo, R.; Catlow, C. R. A.; de Leeuw, N. H. J. Catal. 2007, 248, 77. (34) Obradors, X.; Bassas, J.; Rodriguez, J.; Pannetier, J.; Labarta, A.; Tejada, J.; Berry, F. J. J. Phys.: Condens. Matter 1990, 2, 6801. (35) Berlepsch, P.; Brugger, J. Schweizer Strahler 1999, 11, 425. (36) Kresse, G.; Furthmuller, J. Comput. Mater. Sci. 1996, 6, 15. (37) Kresse, G.; Furthmuller, J. Phys. ReV. B 1996, 54, 11169. (38) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 48, 13115. (39) Kresse, G.; Hafner, J. J. Phys.: Condens. Matter. 1994, 6, 8245. (40) Anisimov, V. I.; Zaanen, J.; Andersen, O. K. Phys. ReV. B 1991, 44, 943. (41) Rohrbach, A.; Hafner, J.; Kresse, G. J. Phys.: Condens. Matter 2003, 15, 979. (42) Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J. Phys. ReV. B 1995, 52, R5467. (43) Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Phys. ReV. B 1998, 57, 1505. (44) Perdew, J. P.; Zunger, A. Phys. ReV. B 1981, 23, 5048. (45) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200.

Propane Oxidation over Iron Antimony Oxide (46) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (47) Rohrbach, A.; Hafner, J.; Kresse, G. J. Phys.: Condens. Matter. 2003, 15, 979. (48) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758. (49) Henkelman, G.; Uberuaga, B. P.; Jońsson, H. J. Chem. Phys. 2000, 113, 9901. (50) Calatayud, M.; Markovits, A.; Minot, C. Catal. Today 2004, 89, 269.

J. Phys. Chem. C, Vol. 112, No. 26, 2008 9797 (51) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Clarendon: Oxford, 1990. (52) Note that one could also shift the molecule along the [010] to find a suitable location, where the subsequent reactions may take place. However, because the 2 × 2 cell is too small for this purpose, we neglected this possibility.

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