DFT Study of CO Oxidation Catalyzed by Au/TiO 2 : Activity of Small Clusters (cid:3)

CO oxidation over a rutile TiO 2 (110) surface supporting a tetrahedral Au 10 cluster has been examined by plane-wave DFT calculations. O 2 adsorbs sideon to the pentacoordinate Ti site of the oxide support with a large energy gain ( ∼ 2 eV), activated to a peroxide state. O 2 adsorption on the cluster is much weaker. The stability and activation state of sideon O 2 depends weakly on distance to the cluster. On a Ti site next to the cluster, a sideon O 2 reacts with CO adsorbed on the cluster to yield CO 2 with a very small energy barrier of 0.13 eV. On a more remote Ti site, a sideon O 2 reacts with a gaseous CO to yield CO 2 with a barrier of 0.55 eV. Thus, O 2 + CO reaction is much faster at the perimeter even for a small cluster such as Au 10 . Similar results are obtained for a truncated pyramidal Au 9 , except that a carbonate is formed at the perimeter. The carbonate formation is inhibited if H 2 O is adsorbed next to O 2 . [DOI: 10.1380/ejssnt.2015.129]


INTRODUCTION
Gold nanoparticles (∼ 3 nm in diameter) supported on metal oxides such as TiO 2 exhibit excellent catalytic activities toward low-T CO oxidation [1,2] and other important reactions [3]. Because gold generally lacks the ability to adsorb and activate O 2 , it is viewed that reactions occur at the perimeter of a Au nanoparticle where it adjoins the oxide surface [4]. For a well-studied example of Au/TiO 2 at least, this has been supported by experiments showing the proportionality between the rate of CO oxidation and the length of the perimeter [5,6]. Yet, it is unclear whether this picture applies to supported clusters of smaller sizes (∼ 1 nm in diameter). This question is becoming more important with growing interest in the sizeand shape-specific activity of small Au clusters [3].
In the field of heterogeneous catalysis, computational methods such as density-functional theory (DFT) [7,8] are indispensable for identifying reaction sites, active species, and reaction paths. There are now a number of DFT studies (and joint ones) on CO oxidation over Au/rutile TiO 2 [9][10][11][12][13][14][15][16]. Earlier DFT calculations for supported Au nanorods [9,10] have shown that O 2 adsorbs and activates on the pentacoordinate Ti site (Ti 5c ) of the oxide surface. This is because the strong positive field of the Ti cation lowers O 2 π * states and induces electron transfer from the Au to O 2 , resulting in Ti-O 2 ionic bonding and O-O bond weakening; naturally, the TiO 2 surface itself is * This paper was presented at the 7th International Symposium  [9,14], but adsorption on more remote sites ('off-perimeter') is possible. Indeed, a DFT study for TiO 2 -supported Au N clusters (N ≤ 7) [17] noted that O 2 adsorbs on a Ti 5c site that is not directly next to a cluster. However, reactions by such O 2 have been neglected in most DFT studies. In our previous work [18], we have examined CO oxidation over a TiO 2 -supported Au nanorod by DFT and found that an off-perimeter O 2 reacts with CO(g) with an energy barrier of 0.57 eV; (g) denotes a gaseous molecule. The perimeter hypothesis still holds because an on-perimeter O 2 reacts with a Au-adsorbed CO (Au-CO) with a smaller barrier of 0.22 eV. The aim of the present DFT study is to examine how the balance between these on-and off-perimeter reactions changes when the supported Au particle is downsized to ∼ 1 nm. Since it is impractical to study all the possible sizes and shapes of Au clusters, we use a tetrahedral Au 10 as a model of small FCC clusters. This is a minimal FCC cluster and a building block for magic clusters such as 20-atom tetrahedron and 55-atom icosahedron. For comparison, we also briefly examine a truncated pyramidal Au 9 cluster.
The rest of this paper is organized as follows. Section II describes the details of calculation. Section III.A examines O 2 adsorption on Au 10 /TiO 2 and finds that offperimeter O 2 are nearly as stable as on-perimeter O 2 . Section III.B examines CO oxidation on Au 10 /TiO 2 and finds that an on-perimeter O 2 reacts with Au-CO with a very small barrier while an off-perimeter O 2 reacts with CO(g) with a barrier similar to that obtained for the supported rod. Section IV examines CO oxidation on Au 9 /TiO 2 and finds that a carbonate is formed at the perimeter. Sec-tion V summarizes and concludes that O 2 + CO reaction is much faster at the perimeter also for small clusters such as Au 9 and Au 10 .

II. DETAILS OF CALCULATION
As in our previous work [18], total energies and optimized geometries were calculated by STATE [19], a plane-wave DFT code. This code has been applied to a wide range of systems including Au/TiO 2 [20,21]. Ultrasoft pseudopotentials [22] and the exchange-correlation functional by Perdew, Burke, and Ernzerhof [23] were used. Kohn-Sham orbitals and the charge density were expanded into plane waves up to the cutoff energies of 25 and 225 Ry, respectively. The number of valence electrons was 1, 4, 6, 10, and 11 for H, C, O, Ti, and Au, respectively. Unless otherwise noted, the spin unpolarized (polarized) state was calculated for a system with an even (odd) number of electrons. The transition state (TS) of a reaction was searched by constrained optimization and then refined by force inversion [24]. The initial and final states (IS and FS) of the reaction were found by relaxation from TS. If this resulted in the detachment of a molecule from the surface, then the desorption limit was identified as IS/TS, and its total energy was obtained as the sum of total energies of the gaseous molecule and the rest, calculated separately. The Bader method [25,26] was used to determine the charge (and spin charge) carried by each atom. Negative charge on O 2 and the O-O bond length were used as indicators of O 2 activation state. Note that the Bader charge may differ from the formal oxidation number, e.g., the Bader charge on O of TiO 2 is calculated to be -1.1e. The charge density was visualized using VESTA [27]. The total energy of a gaseous molecule was calculated using a 24-Bohr cubic cell; O 2 was calculated as a triplet. Figure 1(a) shows the Au 10 /TiO 2 model used in the present study. The rutile TiO 2 (110) surface was represented as a four-trilayer slab placed in a 2 × 4 cell (sampled at 1 × 2 k-point mesh). The thickness of a vacuum layer was 1.39 nm. The atoms of the bottom trilayer were constrained to their bulk positions. A tetrahedral Au 10 cluster was placed on this surface with the orientation of Au(111)[110] ∥ TiO 2 (110)[001]. This choice reduces the lattice mismatch along the Au-Au bond to less than 2%. The average distance between the bottom facet of Au 10 and the uppermost Ti layer is calculated to be 0.31 nm, similar to 0.33 nm measured for Au nanoparticles deposited on TiO 2 [28]. Naturally, it is difficult to prove that this is the most stable geometry for the supported Au 10 , but at least this is 0.24 eV more stable than a planar geometry shown in Fig. 1(b). The Au 9 /TiO 2 model was obtained from Au 10 /TiO 2 by removing the Au atom at the apex ( Fig. 1(c)).
The adsorption energy is referenced to the desorption limit of O 2 , CO, and/or H 2 O. In our convention, a more stable state has more negative adsorption energy. Charge density difference due to O 2 adsorption was obtained as where ρ is the charge density of the whole system, and ρ(Au N /TiO 2 ) and ρ(O 2 ) are those of Au N /TiO 2 and a spin-polarized O 2 , respectively, calculated using the same cell and atomic coordinates as in the whole system.
The accuracy of the present calculation has been estimated as follows. The uncertainty associated with the cell size would be ∼ 0.06 eV because difference in O 2 adsorption energies between Ti (2,3) and Ti (2,1) is 0.12, 0.16, and 0.06 eV for 2 × 4, 2 × 5, and 3 × 4 cells, respectively (all sampled at 1 × 2 k-point mesh). Dependence on the slab thickness and k-point mesh would be similar to that (∼ 0.03 eV) found for the supported rod [18].

A. O2 adsorption
Earlier DFT studies [9,10,17,18] on TiO 2 -supported Au clusters and nanorods have found that O 2 adsorbs strongly to the Ti 5c site in a sideon configuration (Ti-O 2 ). This is also the case for Au 10 : O 2 adsorbs sideon to the Ti (2,1) site with a very strong adsorption energy of -2.35 eV (Fig. 2(a) (Fig. 3(a)). An overlap between O p z and Ti d xz states around -1.4 eV indicates a π-type interaction between the out-of-plane O 2 π * and Ti 3d orbitals. An overlap between O p y and Ti d xy states around -0.2 eV indicates a δ-type interaction between the in-plane O 2 π * and Ti 3d orbitals; the diagonal orien- tation of O-O is key to this interaction. With both π * orbitals lowered below the Fermi level, O 2 is activated to a peroxide state. This can also be seen in the charge density difference due to O 2 adsorption ( Fig. 3(b)): As a result of electron transfer to both π * orbitals, a ringshaped region of electron accumulation appears on each O of O 2 . A spin-polarized calculation also confirms that O 2 is in a singlet state. We add that, in spite of the O-O bond weakening, O 2 dissociation between two Ti sites is unlikely because the resulting configuration is much less stable (Fig. 2(d)).
O 2 adsorbs at a dual perimeter site consisting of Ti (2,1) and Au sites (Ti-OO-Au) with a strong adsorption energy of -1.91 eV (Fig. 2(b)). O 2 activation is not so strong as in Ti-O 2 . The striking feature of this configuration is that O 2 extrudes a Au atom out of the cluster, causing the cluster to shrink by 10% along the TiO 2 [001] direction. Extrusion by O 2 is barely noticeable on the Au rod [18] because a continuous structure would be unable to accommodate the resulting strain. difference between Ti-O 2 and Ti-OO-Au decreases from 0.71 eV [18] to 0.44 eV, although Ti-O 2 is still the more stable configuration.
Compared to these Ti-adsorbed ones, O 2 on the apex of Au 10 is much less stable, with an adsorption energy of -0.51 eV (Fig. 2(c)). This O 2 is barely activated, as can be seen in the O-O bond length and the charge and spin it carries. In addition, the positive charge induced on the top Au atom is small (+0.13e), indicating the weakness of the Au-O 2 ionic bonding.
Having confirmed the greater stability of the sideon configuration, we now examine the relative stability between various Ti 5c sites (Fig. 4). Ti (1,2) -O 2 is practically degenerate with Ti (2,1) -O 2 in spite of a contact with the Au cluster. Ti (1,3) -O 2 is not directly next to the cluster, but is only marginally less stable than the on-perimeter ones. Ti (2,3) -O 2 is slightly less stable than Ti  ilar for all the Ti-O 2 . The stability and activation state of Ti-O 2 thus depends weakly on distance to the Au cluster.

B. CO oxidation
As a typical example of CO oxidation on the perimeter of a Au cluster, we have examined a process whereby Ti (2,1) -O 2 reacts with CO adsorbed on the adjacent Au site (Figs. 5(a), (b), and (c)). As the figures show, CO approaches the left O of O 2 on its C end, extract the O to form CO 2 , which desorbs spontaneously. The O adatom left on the Ti site is expected to react readily with CO [13]. Compared to the rod model [18], the calculated energy barrier for the Ti-O 2 + Au-CO step is smaller (0.13 vs. 0.22 eV). It is difficult to explain such a small difference, although a possible cause seems to be the extrusion of a Au atom by CO (Fig. 5(a)); extrusion by CO is noted in earlier work on free Au clusters [29]. In the Au 10 model, the Au atom is already extruded at IS, so it needs not be extruded further in going to TS. In the rod model, the corresponding Au atom must be extruded by 11 pm in going from IS to TS.
As an example of CO oxidation over an off-perimeter site, we have examined a direct reaction between Ti (2,3) -O 2 and CO(g) (Figs. 5(d), (e), and (f)). The calculated energy barrier of this reaction, 0.55 eV, is very close to 0.56 and 0.57 eV we obtained for Ti-O 2 + CO(g) reaction at the first and second nearest Ti site of the supported rod model, respectively [18]. Without CO activation by the Au [18], the reaction depends heavily on O 2 activation, as can be seen in O-O stretching and negative charge on O 2 at TS (Fig. 5(e)). Because the state of O 2 activation differs little between various Ti 5c sites (Fig. 4) and Au models, a similar barrier can be expected for Ti-O 2 + CO(g) reactions.

IV. Au9/TiO2 MODEL
For comparison, we have also examined CO oxidation over the Au 9 model. Results for Ti (2,1) -O 2 + Au-CO reaction are presented in Fig. 6(a). As is the case with Au 10 , CO extracts the left O of O 2 to form CO 2 . IS and TS are similar to those found for Au 10 . In particular, O 2 is activated to a similar extent despite the odd number of electrons in the system; such a trend is also reported for Au 9 and Au 10 strips [17]. As a result, the energy barrier (0.11 eV) is very close to that for Au 10 . Furthermore, the calculated barrier for Ti (2,3) -O 2 + CO(g) reaction is again 0.55 eV. Thus, O 2 + CO reaction is faster at the perimeter also for Au 9 .
However, CO 2 formed by the Ti (2,1) -O 2 + Au-CO reaction interacts differently with the cluster, combining with the remaining O adatom to form a carbonate, which is bound to two Au sites and the Ti (2,1) site (FS of Fig. 6(a)). Bader analysis indicates that an O adatom on Ti (2,1) receives the same amount of negative charge (−0.89e) whether the cluster is Au 9 or Au 10 . On the other hand, the Au 9 cluster is in a spin-polarized state (Fig. 6(c)), with a spin charge of 0.87e, and so CO 2 does not detach from Au 9 as readily as it does from Au 10 . This leaves some room for CO 2 to react with the O adatom. The implication is that a carbonate may form on oddnumbered clusters, although more calculations are needed for confirmation.
The decomposition of the carbonate into CO 2 (g) and an O adatom is unfavorable by 0.39 eV. Thus, the carbonate may inhibit CO oxidation by rendering unavailable active Ti sites. Water may assist its decomposition [30] or prevent it from forming. Indeed, our calculations ( Fig.  6(b)) indicate that, if H 2 O is adsorbed on a Ti site next to O 2 , the barrier of the Ti (2,1) -O 2 + Au-CO reaction does not change much (0.16 eV), but CO 2 desorbs instead of forming a carbonate. Apparently, hydrogen bonding with H 2 O renders the O adatom less reactive with CO 2 .

V. CONCLUSIONS
In this plane-wave DFT study, we have examined CO oxidation on a rutile TiO 2 (110) surface supporting subnanometer Au clusters. We mainly studied tetrahedral Au 10 and also a truncated pyramidal Au 9 . We have found that O 2 adsorbs sideon to a pentacoordinate Ti site (Ti-O 2 ), activated to a peroxide state. This O 2 is more stable than O 2 at a Ti-Au dual-perimeter site or O 2 on the apex of the cluster. Moreover, the stability of sideon O 2 depends weakly on distance to the Au cluster. Thus, O 2 adsorption is dominated by the interaction with Ti sites, although the Au cluster is still essential as an electron donor to O 2 . The trend is similar to what we have found for the supported Au nanorod [18].
For Ti-O 2 + Au-CO reaction, similar barriers have been found for Au 9 and Au 10 (0.11 and 0.13 eV, respectively). These barriers are slightly lower than 0.22 eV found for the rod [18]. After the reaction, CO 2 desorbs from Au 10 while a carbonate forms on Au 9 . We have also found that more remote Ti-O 2 reacts with CO(g) with a barrier of 0.55 eV on both Au 9 and Au 10 . The barrier of this size appears to be universal for various Ti-O 2 and Au models.
In conclusion, O 2 + CO reaction is much faster at the perimeter even for small FCC clusters such as Au 9 and Au 10 . However, the interaction of product CO 2 with the surface is more dependent on the size and shape of the cluster, sometimes yielding a carbonate.