Adsorption of Small Palladium Clusters on the Relaxed Î±-Al2O3 (0001

J. Phys. Chem. B 2003, 107, 6411-6424

6411

Adsorption of Small Palladium Clusters on the Relaxed r-Al2O3(0001) Surface J. R. B. Gomes,†,§ Z. Lodziana,‡ and F. Illas*,† Departament de Quı´mica Fı´sica i Centre de Recerca en Quı´mica Teo` rica, UniVersitat de Barcelona i Parc Cientı´fic de Barcelona, C/ Martı´ i Franque` s 1, E-08028 Barcelona, Spain, and Center for Atomic Scale Materials Physics, DTU, Building 307, DK-2800 Lyngby, Denmark ReceiVed: December 3, 2002; In Final Form: March 11, 2003

The interaction of small Pdn clusters (n ) 3, 4) with the relaxed Al-terminated R-Al2O3(0001) surface has been investigated using embedded cluster and periodic slab models within a first principles density functional approach. From the present study, it is concluded that the structure of supported Pd3 is largely distorted from the gas-phase equilibrium geometry whereas the structure of supported Pd4 is less distorted and reminiscent of the most stable gas-phase isomer. Consequently, the adhesion energy of Pd3 on the relaxed R-Al2O3(0001) surface is smaller than that of Pd4. The presence of Pd atoms induces a rather large reorganization of the atomic structure of the surface. The results obtained for the different structures of supported Pd4 suggest that there is a competition between 2D and 3D growth of the supported crystallites. Also, in contrast to the results obtained for Pd adsorption on other oxide surfaces, there are no preferred adsorption sites for Pd deposited on the corundum surface.

I. Introduction Heterogeneous catalysis is widely and routinely used in a large majority of chemical industries to produce thousands of different products in massive amounts. The technological and economical importance of catalysis is one of the main reasons for intense research in this field. Palladium chemistry has recently attracted attention because under certain conditions this metal is able to replace effectively the three-way catalysts.1 This has prompted several experimental and theoretical studies concerning palladium catalytic properties.2-11 Single-crystal metal-surface studies indicate that these model systems are not capable of reproducing the behavior of real supported catalysts.2 However, real catalysts used in industry are generally too complex to permit a clear identification of the relevant chemical mechanisms involved in the catalytic process. Supported model catalysts seem to provide a convenient solution,2 and this has generated a rather large number of studies on the metal-support interaction (cf. ref 12 and references therein). Several factors may be responsible for the different chemical activity of a given supported metal catalyst, namely, the support composition, surface structure, presence of promoters or poisons, and the size and structure of the metal particles placed above the support.2,13-15 Initially, experimental studies aimed at disclosing the role of each particular effect involved relatively large metal particles with sizes ranging from 10 to 100 nm. New experimental settings have permitted to focus on smaller metal particles and to study the growth of these nanoparticles on active or inactive supports16 and their reactivity toward some well-defined chemical reaction.17,18 The aim of these approaches is to provide simple experimental model systems for the understanding of the metal/support interface and to predict properties of possible new materials. Also of interest is the fact * Corresponding author. E-mail: [email protected]. Fax: +34 934021231. † Universitat de Barcelona i Parc Cientı´fic de Barcelona. ‡ Center for Atomic Scale Materials Physics. § Current address: CIQ-UP, Centro de Investigao em Quimica da Universidade do Porto, R. Campo Alegre, 687, 4169-007 Porto, Portugal.

that some properties of catalysts, such as efficiency and resistance, are governed precisely by the metal-support interaction.5 This is the case for CO dissociation on alumina-supported Rh particles, which is particle size-dependent.19,20 Clearly, the geometry and size of the metal particles are closely related to the strength of the metal-support and metalmetal interactions. In previous work concerning the adsorption of Pd atoms on the R-Al2O3(0001) surface, it was found that the preferential sites for adsorption may change with Pd coverage.21 This means that both metal-support and metal-metal interactions play a crucial role in the final geometry of the adsorbed particle. One may argue that strong metal-metal interactions favor 3D metal growth whereas strong metal-support interactions favor 2D growth. Nevertheless, the situation is more complicated because possible support-surface reconstruction induced by metal deposition cannot be neglected. From an atomistic point of view, the understanding and prediction of metal particle growth on supports is far from being unequivocally established. The use of theoretical models based on either quantum chemical or solid-state approaches is of enormous interest because it is possible to model specific sites of a specific catalyst and to obtain structural information about these sites and about the effects on the structure of the model catalyst induced by controlled modifications. In this way, logical steps in the study of the metal-support interaction involve studying the deposition of single metal atoms above the oxide support and, in a subsequent step, consider the interaction of small metal clusters with the surface. This strategy should permit to extract important information about the early steps of metal nucleation on the support surface. In the present work, we use this approach to study the structure and interaction of Pd3 and Pd4 clusters adsorbed on the relaxed Al-terminated R-Al2O3(0001) surface. The present paper is organized as follows: In section II, the two different surface models used to represent the Al-terminated R-Al2O3(0001) surface are described. The computational details are given in section III whereas

10.1021/jp022520h CCC: $25.00 © 2003 American Chemical Society Published on Web 06/06/2003

6412 J. Phys. Chem. B, Vol. 107, No. 26, 2003

Gomes et al.

Figure 1. Top view of the two cluster models used in the present work. These are the Al26O15 Al-centered (a) and the Al24O22 O-centered cluster models (b). Large spheres represent anions, and small spheres, the cations that were treated as all-electron during the computation procedure. The embedding Al3+ TIPs are represented by small spheres in the cluster edge whereas the array of point charges used to account for the long-range Madelung potential is not included. Notice that some cluster atoms are not visible in this perspective because they are located exactly below the outermost Al atoms.

section IV presents the whole set of results. Finally, the most representative conclusions of this work are summarized in section V. II. Surface Models of the Al-Terminated r-Al2O3(0001) Surface The present work focuses on the interaction of small Pd clusters on the relaxed Al-terminated R-Al2O3(0001) surface. This is a logical choice because this surface seems to be the most stable termination of R-Al2O3 even under high oxygen partial pressure.22,23 Two different and complementary approaches have been used to model this surface. These are the repeated slab and the embedded cluster model approaches. The two models represent limiting situations of the real systems. Moreover, the former is the natural choice when looking at a surface from a solid-state point of view whereas the latter naturally arises when the focus is on local interactions. In the slab model, the Born-von Karmann boundary conditions are imposed on the system. The surface of interest is represented by a slab that is infinite in two dimensions and consists of a finite thickness of oxide with additional vacuum in the direction perpendicular to the surface; only the stoichiometric surface has been considered. In the periodic calculation, a vacuum width of more than 12 Å is used to minimize the interaction between subsequent slabs. Each slab contains 12 layers obtained by repeating the (Al-O-Al) sequence 4 times. In the first step, the nine outermost layers are relaxed. With the computational methods described in the next section, the relative changes of the interplanar distances in percent with respect to the original bulk spacing are -87.5, 3.2, -46.6, 20.4, and 5.2%. This is in very good agreement with previous accurate results.24-27 Because the main objective of the present study is to extract details of metal/oxide interactions, some attention must be paid to the exclusion of mutual interactions between adsorbed metal units. This requires quite a large lateral surface, and in the present study, the 2 × 2 supercell is considered. In this system, the smallest distance between metal atoms and their periodic image is larger than 6 Å, but to accomplish this requirement, the slab must contain at least 80 atoms. Additionally, the dipole layer was applied in the vacuum region of the supercell to exclude any electrostatic effect induced along the z direction. In the cluster model approach, the surface is represented by a finite number of suitably embedded atoms. The crystal

structure of the corundum surface makes it difficult to design stoichiometric clusters as in simpler oxide surfaces,12 and one must be alert to prevent possible artifacts. The cluster models used in this work have been constructed using the strategy outlined in a previous study.21 One of the models is centered on an aluminum atom whereas two different clusters have been used to represent an oxygen atom-centered model. These clusters contain three different regions containing the real atoms, the embedding potentials, and an array of point charges. For the Al-centered model, the first region consists of 23 atomss8 Al and 15 Osthat are explicitly treated quantum mechanically. This inner region is embedded in 18 total ion potentials (TIPs)28 that define the second region and are included to prevent any artificial polarization of the anions’ electron density toward the point charges29 included in the third region; the inner region plus the TIPs are depicted in Figure 1a. This third region contains 2354 point charges (PCs) with values of +3|e| and -2|e| for cations and anions, respectively. Two different O-centered cluster models containing either 29 or 37 atomss7 Al and 22 O or 15 Al and 22 Os have been used. These clusters are embedded in 17 or 9 TIPs and 2794 PCs; the Al7O22 cluster plus the 17 TIPs is shown in Figure 1b. The Al15O22 cluster is almost the same, but 8 of the 17 TIPs are now treated as real atoms. This embedding efficiently accounts for short- and longrange interactions present on the infinite oxide surface.30-37 The total number of electrons explicitly introduced into the model is chosen according to an initially fully ionic description, although the use of a variational method enables any redistributions of the electronic density that lower the energy. It is worth pointing out that because the resulting cluster model contains a different number of cations and anions the quantum region is necessarily charged, although in all cases the total embedded cluster is, of course, electrically neutral. The charge excess may cause artifacts in the resulting description of surface processes, and one must be very careful in interpreting the results arising from this model. A comparison to periodic models permits a further check of the validity of the embedding scheme used in the present work. This is of importance for future work involving the interaction of metal atoms and/or metal clusters with different point defects of the R-Al2O3(0001) surface. The Alcentered cluster has six extra electrons whereas the two oxygencentered clusters have total charges of -23 and +1 in the local region, respectively. These are, of course, two extremes, and

Adsorption of Pd Clusters on R-Al2O3(0001)

J. Phys. Chem. B, Vol. 107, No. 26, 2003 6413

again the use of different models permits an internal check of the consistency of the results. Once the model clusters were constructed, surface relaxation was explicitly introduced by setting the interlayer separation to the values previously obtained by accurate slab calculations.24-26 The adequacy of the present cluster model approach was established in previous study of atomic Pd adsorption on the relaxed Al-terminated R-Al2O3(0001).38 In particular, negligible energetic and geometric differences were found for the adsorption of a single Pd atom on different surface sites that are geometrically equivalent on the infinite surface but different in the two cluster models. Further validation of these cluster models comes from the fact that they were able to reproduce the results from periodic 2D and 3D approaches.21,38 The interactions of Pd3 and Pd4 with the surface were considered in both the periodic and cluster calculations. In the periodic calculations, the initial shapes of Pd3 and Pd4 clusters are chosen to mimic their 2D and 3D geometries from the gas phase. These clusters are placed on the surface, and no constraints are imposed on the metal or the substrate during the optimization stage. This full, unconstrained geometryoptimization strategy cannot be used within the cluster model representation of the surface. Therefore, three different starting geometries were considered for the adsorption of a Pd3 cluster depending on the position of the palladium atoms above the surface. First, the Pd3 atoms were placed directly above surface aluminum atoms (Al). Next, the starting geometry involves the interaction of the Pd3 atoms adsorbed directly on top of surface oxygen (O), and finally, one consider the possibility of the Pd atoms interacting directly with the hollow sites (H). These three starting geometries are schematically shown in Figure 2. The O-centered cluster model has been used to study Pd3 adsorption above Al sites whereas the Al-centered cluster model has been employed to investigate the interaction of Pd3 above the O and H sites. The adsorption of a Pd4 aggregate on the cluster models of the R-Al2O3(0001) surface was studied by placing an extra atom in the center of the Pd3 cluster and totally optimizing the metal cluster geometry and some specific substrate atoms. This is consistent with the result of the periodic calculations and also with experimental information recently reported by Gillet et al.39 These authors have used secondary ion mass spectrometry in static mode (SSIMS) and thermal programmed desorption (TPD) to study the growth of Pd on R-Al2O3(0001), and they concluded that the Pd particles grow by following either the VolmerWeber or the Stranski-Krastanov mechanism (i.e., 3D growth or completion of a monolayer plus 3D crystallite, respectively). III. Computational Details The present calculations have been carried out in the framework of density functional theory (DFT). However, different basis sets and exchange-correlation functionals, E[F], were used in the periodic and cluster calculations. The choice of different functionals appears to be necessary because of the rather large variation of the adhesion energy on the particular form E[F] found for transition metals on MgO32,33 and more recently for Pd atoms on R-Al2O3.38 Indeed, recent work by Mattsson and Jennison40 and by Pacchioni41 strongly suggests that the final word about the proper computation of adhesion energies of metals on oxides has not yet been written. In the periodic calculations, the plane-wave expansion and the pseudopotential method was used as implemented in the DACAPO code.42 The present periodic DFT calculations employ the GGA-PW91 exchange-correlation functional.43,44 The ionic cores are represented by ultrasoft pseudopotentials,45 and the

Figure 2. Starting geometries for Pd3 adsorbed on the relaxed Alterminated R-Al2O3(0001) surface. Pd atoms appear as large spheres. Those are on top of the outermost oxygen atoms, O, sites (a), above hollow, H, sites (b), and above aluminum atoms of the outermost first, third, and fourth layers, Al sites (c).

Pd 4d, 5s, and 5p electrons are treated as valence states. The Monkhorst-Pack k-point sampling mesh of the density, 0.10.05 Å-1, together with a kinetic energy cutoff of 340-400 eV was used. The electronic density is determined by iterative diagonalization of the Kohn-Sham Hamiltonian, and the resulting Kohn-Sham eigenstates were populated according to the Fermi statistics. The finite temperature smearing of the electronic density, corresponding to kT ) 0.1 K (where k is the Boltzman constant), is applied. The Pulay mixing was applied to the resulting densities, and the procedure was repeated until self-consistency of the electron density was achieved. Once the

6414 J. Phys. Chem. B, Vol. 107, No. 26, 2003 self-consistency was achieved, the total energy was extrapolated to T ) 0 K. The atomic structure was optimized according to the calculated Hellmann-Feynman forces. To find the ultimate surface geometry, the following optimization procedure was used. For the first few steps, the modified Verlet optimization with atomic velocities V set to zero was applied at each step to approach the equilibrium configuration. Then, the atoms were relaxed according to the conjugate gradient (CG) method until the forces exerted on the atoms were smaller than 0.05 eV/Å. Finally, the structure was reoptimized with modified Verlet method again. This procedure was found to be superior to the application of CG optimization only because the latter procedure may result in large false atomic displacements when the system is far from equilibrium, thus slowing down the optimization process. To test the convergence with respect to various computational parameters, calculations were performed by either increasing the k-point sampling density or the kinetic energy cutoff in the plane-wave expansion. Value of 0.1 Å and 340 eV for k-point sampling and the energy cutoff are found to be sufficient for the present calculations. In the cluster calculations, the energy is computed using the hybrid B3LYP method46 as included in the Gaussian 98 package.47 This hybrid functional includes a mixture of HartreeFock gradient-corrected exchange48 terms plus the gradientcorrected correlation functional of Lee, Yang, and Parr,49 which is based on the original work of Colle and Salvetti on the correlation factor.50,51 The three parameters of the exchange functional are fit in order to reproduce experimental thermochemical data, with the optimum mixing being found for ∼20% of the Fock exchange in the exchange term. It is worth pointing out that quite surprisingly the B3LYP hybrid functional is able to reproduce the thermochemistry of molecules containing transition-metal elements although no transition metal-compounds were included in the data set used in the fit.52-55 In the cluster calculations, all of the electrons of the Al and O atoms of the inner region were explicitly included in the calculations. The standard split-valence 6-31G Gaussian basis proposed by Pople et al.56,57 was used for both aluminum and oxygen atoms; however, for the oxygen atoms, this basis was augmented with one diffuse s and p orbital and with one polarization function of d symmetry, the final basis being of 6-31+G* quality.58,59 The palladium atoms have been described within the LANL2 relativistic effective core potential, RECP, of Hay and Wadt and the LANL2DZ basis set.60 In this way, the outer 4s24p64d10 electrons of the palladium atoms are treated explicitly by a double-ζ basis set, and the effect of the inner core electrons on the valence electrons is taken into account through the RECP.60 The geometry-optimization procedure consists of a series of well-controlled steps. The geometry-optimization procedure starts from the structures shown in Figure 2. Hence, we consider starting geometries with the Pd atoms on top of the outermost oxygen atom, O, sites, on top of the oxygen atoms in the hollow, H, sites, and above aluminum atoms from the outermost, third, and fourth layer, Al, sites . In the first step, the positions of the oxide substrate atoms were kept fixed, and only the z coordinate of palladium atoms was allowed to vary but with the constraint that the three palladium atoms of the Pd3 cluster, both in the study of Pd3 and Pd4 adsorption, are at the same distance from the surface. In the second step, the substrate was still kept fixed, but the z coordinate of each palladium atom was allowed to relax independently. In subsequent steps, the z coordinate of the substrate aluminum and oxygen atoms close to the adsorption sites was also relaxed. In the final step, the three Cartesian coordinates of the transition-

Gomes et al. metal atoms were included in the optimization procedure. It must be emphasized that this optimization scheme has been shown to be adequate in previous work dealing with the adsorption of a single palladium atom on the relaxed Al-terminated R-Al2O3(0001) surface.38 In that work, it was concluded that the cluster approach is able to reproduce the results obtained by 2D or 3D periodic models provided that the same exchange-correlation functional is used and that a minimum number of atomic layers are included in the optimization procedure.38 In the present case, the systems under study are more complex. Nevertheless, this step-by-step geometry optimization is aimed at ensuring that the structure found by the energy-minimization procedure is as close as possible to the starting geometry and at preventing the metal cluster from migrating to the clusters’ edge. Because during the last step all constraints are removed and the geometry optimization is carried out with no symmetry, it is likely that the procedure converges to a local minimum. Finally, it is well known that basis set superposition errors (BSSE) are especially severe in the calculation of adsorption energies on oxide surfaces31,61 and, in particular, in the metalsupport interaction.32,62 Thus, it is essential to remove the BSSE unphysical contribution to the interaction energy. This has been accomplished using a variant of the standard counterpoise method of Boys and Bernardi.63 The need to use a slightly different procedure arises from the fact that the final geometries of the R-alumina(0001) surface model and of the adsorbed particle are largely distorted from the one corresponding to the isolated particles. Therefore, it is necessary to obtain the counterpoise-corrected adsorption energies in a two-step procedure. First, the standard BSSE correction is obtained by computing the energy of each subunit at the geometry of the fragments in the supersystem and the total basis set and, in the second step, the energy deformation of the fragment is computed from the energy difference corresponding to the fragment-inthe-supersystem and isolated geometries and the fragment basis set. Here it is worth pointing out that after the BSSE correction the final energy is no longer variational. Unless otherwise specified, we will refer to the BSSE-corrected values. IV. Results and Discussion First, we briefly discuss the structure of the separated systems, R-alumina and gas-phase palladium clusters, to be able to discuss the metal-support effect on the structure of these metal particles adsorbed on R-alumina. This will facilitate the discussion of the influence of the substrate on the geometry and on the properties of supported palladium clusters. Likewise, it is also important to compare the structure of the metallic gas-phase clusters arising from the two different approaches described in the previous section. This is because the electronic structure within the plane-wave slab and Gaussian basis set cluster calculations is treated differently . In the plane-wave calculations of gas phase Pd clusters, a 10 × 11 × 12 Å3 orthorhombic supercell is used. The choice of the symmetry of the supercell ensures that there are no artificial constraints imposed on the Pd clusters. Additionally, the k-point sampling was increased to the density of 0.02 Å-1. The optimized lattice parameters for the corundum unit cell obtained from the periodic approach are a ) 5.151 Å and R ) 55.285°. The internal coordinate of the Al is x ) 0.3525, and for the oxygen, z ) 0.3063, in very good agreement with experiment.64 The calculated band gap is 7.2 eV at the GGAPW91 level, which is also in reasonably good agreement with the experimental value of 8.75 eV.65 Here, it is worth pointing out that GGA approaches tend to underestimate the band gap



TABLE 1: Theoretical Results for Gas-Phase Pd Clusters as Obtained from B3LYP and PW91 Methods within GTO and Plane-Wave Basis Sets, Respectivelya symmetry method Pd3

Pd4

Pd (bulk)

spin state

d(Pd-Pd)/Å BE/n/eVb BE/n/eVc

C2V D3h

B3LYP triplet 2.77, 2.55 singlet 2.52

C2V D3h

PW91

Cs Cs

B3LYP triplet 2.71, 2.61 singlet 2.84, 2.58

Cs

PW91

FCC

0.85 0.77

triplet 2.59, 2.52 singlet 2.58

1.27 1.28 1.25 1.07

triplet 2.63, 2.66 singlet 2.66, 2.59 2.75

0.74 0.65

1.11 0.93 1.70 1.62

3.92

a

Nearest-neighbor distance d(Pd-Pd) and binding energy per atom BE/n calculated with respect to the isolated atoms in the singlet state. For the GTO calculations, two values of BE/n are given; these correspond to the uncorrected and BSSE corrected values, respectively. b Not corrected for the BSSE. c Corrected for BSSE.

value;66 a better but still too low value of 8.06 eV is obtained by means of the Perdew-Burke-Ernzerhorf (PBE) functional.67 The presence of the surface diminishes the value of the band gap, which for the (0001) surface becomes 4.0-4.5 eV at the GGA-PW91 level. This quantity can also be used to check the consistency of the different cluster models. In the cluster model approach, it is not possible to compute the band gap, but a rough estimate can be obtained from the energy difference of the highest occupied molecular orbital, HOMO, and the lowest unoccupied molecular orbital, LUMO. For the Al-centered model, the HOMO-LUMO energy difference is 5.8 eV, indicating that this is a reliable cluster model. For the Al7O22 O-centered cluster model, this energy difference drops to 2.5 eV, and this is reduced to 1 eV for the Al15O22 O-centered cluster model even if the charge in the inner region changes from -23 to +1! To some extent, this large decrease is due to the use of diffuse functions in the oxygen basis set. Removing these diffuse functions results in HOMO-LUMO splittings of 2.8 and 1.8 eV for Al7O22 and Al15O22, respectively. Nevertheless, this analysis shows that the results obtained from the cluster approach have to be handled with extreme care. Most of the calculations have been carried out using the smaller Al7O22 O-centered cluster model. The adsorption energies of selected optimized geometries have been recomputed using the larger Al15O22 model. In all cases, the energy difference was smaller than the energy difference between different isomers. For the small metal particles, the orbital overlapping and localized bonding defines their electronic ground state properties. Thus, it is important to define accurately the ground states of Pd3 and Pd4 in the gas phase. There is extensive literature dealing with the electronic and geometrical structures of Pd3 and Pd4 clusters. However, there is quite a large disagreement between different authors concerning the most stable structure, the PdPd distance, and even the order of low-lying electronic states.68-71 In principle, one should rely on the accurate relativistic multireference configuration interaction calculations of Balasubramanian72 and Dai and Balasubramanian,73 which indicate that Pd3 has a closed-shell ground state whereas for Pd4 the lowest singlet and triplet states are nearly degenerate. The present B3LYP calculated geometric and energetic parameters for fully optimized Pd3 and Pd4 gas-phase clusters are summarized in Table 1, where results for the gas-phase clusters obtained using the PW91 plane-wave method have been added for comparison. At the B3LYP level, the closed-shell state for Pd3 has D3h symmetry with optimized Pd-Pd distances of 2.52 Å, which

as expected are shorter than the experimental bulk value of 2.75 Å. Another isomer with an open-shell triplet electronic structure and with longer Pd-Pd distances (two of 2.55 and one of 2.77 Å) is found at a lower energysthe energy stabilization is about 0.09 eV/atom. We must point out that for Pd3 B3LYP predicts another isomer with a closed-shell electronic structure and a longer Pd-Pd distance (2.82 Å) lying at a higher energy. For Pd4, the most stable structure has a triplet ground state and symmetry that is close to Cs with three distances of ∼ 2.61 Å and three distances of ∼ 2.71 Å. The closed-shell structure lies 0.54 eV higher in energy, and the geometrical structure is also Cs but with two short and four long Pd-Pd distances of ∼ 2.58 and ∼ 2.84 Å, respectively. Hence, the resulting geometry is almost the same as that reported recently by German et al.69 using the same method and basis sets. However, the present total energies are slightly lower than those reported by these authors because of the fact that the geometry optimization has been carried out with no symmetry constraints. For the metal clusters in their electronic ground state, the existence of metalmetal distances shorter than that corresponding to the bulk metal has been customarily interpreted as a consequence of the lack of coordination of the cluster metal atoms. In addition, one must point out that these metal clusters exhibit a small binding energy per atom, suggesting that, in principle, they can be deformed without significant energetic requirements. Indeed, this can be a very important effect because in the initial steps of the metal adhesion as it permits the metallic particles to grow in many different ways. The analysis above is consistent with the results obtained for both Pd3 and Pd4 clusters with the GGA-PW91 functional and either the Gaussian or the plane-wave basis sets although the singlet-triplet energy difference is much smaller within the PW91 functional. In the periodic calculations, the nonequivalent Pd-Pd distances in Pd3 are 2.52 and 2.59 Å for the triplet state and 2.58 Å for singlet (Table 1). The tetrahedral Pd4 spacings are 2.59 and 2.66 Å for the singlet and 2.63 and 2.66 Å for the triplet state. All bonds are noticeably shorter than the bulk value. The different shape of the singlet-triplet states is also reflected in the difference in the formation energies. For Pd3, it equals ∆E ) -0.006 eV/atom, and for Pd4, ∆E ) 0.08 eV/atom. These energy differences shall be compared with the energy related to the deformation of each of the clusters. For example, the deformation of Pd3 by extending one of the bonds by 3% results in an energy increase on the order of 0.04 eV, which is comparable with the magnetic one. Moreover, no significant differences between the deformations of the singlet- and tripletstate clusters have been found in the PW91 calculations. The large dependence of the singlet-triplet splitting with respect to the particular DFT method used is in line with previous findings.74,75 Therefore, it has been decided to carry out all subsequent calculations for the supported Pd3 and Pd4 clusters by assuming a closed-shell electronic structure. We must point out that very recent results for Pdn (n ) 2-7 and 13) supported on MgO suggest that clusters with n > 3 with the magnetic character of the gas-phase counterpart remain.76 These authors also found that clusters that adopt a flat shape tend to quench the spin more efficiently. Below, we will show that these are indeed the preferred structures of Pd3 and Pd4 adsorbed on the relaxed Al-terminated R-Al2O3(0001) surface, thus giving support to the choice of a closed-shell electronic structure for these systems. Nevertheless, the precise determination of the energy difference between the different spin isomers probably


Gomes et al.

TABLE 2: Optimized Parameters for the Pd3 Cluster above the Al-Center Surface Modela parameter

fully optimized Pd3 (Figure 3)

z(Al1-Al10)/Å z(O2-O20)/Å z(Pd)/Å q(Pd)/e Eads/eV

A 1.63 -0.01

0.40 -0.15 B 1.75 -0.01 1.61

TABLE 3: Optimized Parameters for the Two Different Forms of a Pd3 Cluster Adsorbed above the O-Centered Surface Modela parameter

C 1.60 -0.02

Compare with Figure 3. Symbols are the following: z(Al1-Al10) and z(O2-O20) are the vertical displacements of the Al1 and O2 atoms from their initial positions in the clean substrate, respectively, and positive or negative signs mean outward or inward relaxation, respectively; z(Pd) is the vertical distance between the Pd and Al1 atoms; q(Pd) is the Mulliken charge on the Pd atoms; Eads is the total adsorption energy; A, B, and C are used to distinguish the three Pd atoms. a

goes beyond the accuracy of the present exchange-correlation functionals and requires the use of explicitly correlated wave functions. IV.I. Cluster Model Results for Pd3 Supported on R-Al2O3. As outlined in a previous section, three different starting orientations were considered for the interaction of a Pd3 cluster with the relaxed Al-terminated R-Al2O3(0001) surface. To facilitate the discussion and subsequent analysis of the computed values, each starting orientation will be discussed separately. Table 2 reports a summary of the energetic and geometric parameters corresponding to the most stable adsorbed structure with the Pd atoms sitting near the O sites, Figure 2a depicts the initial structure whereas the optimized geometry is sketched in Figure 3. The final optimized structure obtained by a full optimization of the Pd3 cluster and of the nearest-neighbor oxygen and aluminum atoms is very close to a perfect equilateral triangle with the Pd atoms sitting near but not completely on top of the cluster oxygen atoms. This final structure is the result of the optimization steps described in the previous sections and is aimed at identifying the most important physical effects. First, the Pd atoms were placed exactly on top of second-layer oxygen atoms, and only the vertical distance of the Pd3 plane with respect to the surface was optimized. The resulting vertical distance between the outermost aluminum layer and the cluster plane is 2.23 Å with an adhesion energy of -0.13 eV. Allowing the relaxation of the neighboring first-layer aluminum atom and optimizing the Pd3 plane distance to the substrate leads to a significant increase in the adsorption energy, which becomes 1.19 eV. Indeed, this adsorbate-induced relaxation of the outermost aluminum atom outward from the surface appears to be the most important contribution to the energetics of adsorbed

z(Al1-Al1 z(O2-O20)/Å z(Al3-Al30)/Å z(Al4-Al40)/Å 0)/Å

z(Pd)/Å q(Pd)/e Eads/eV

Pd3 with Pd atoms fixed above Al sitesb 0.26 -0.29 -0.31 -0.19 A B 2.39 1.32 -0.12 0.21 2.61

C 1.44 0.18

fully optimized Pd3c

A 1.82 0.15

0.13 -0.33 -0.36 -0.19 B 1.32 0.19 2.61

C 1.57 0.16

a See Figure 4a and b. Symbols are the following: z(Al1-Al10), z(O2-O20), z(Al3-Al30), and z(Al4-Al40) are the vertical displacements of the Al1, O2, Al3, and Al4 atoms, respectively, from their initial positions in the clean relaxed substrate, and positive or negative signs means outward or inward relaxation, respectively; z(Pd) is the vertical distance between the Pd and Al1 atoms; q(Pd) is the Mulliken charge on the Pd atoms; Eads is the total adsorption energy; A, B, and C are used to distinguish the Pd atoms. b See Figure 4a. c See Figure 4b.

Pd3. This is in full agreement with previous results for the adsorption of a single palladium atom on the Al-terminated R-Al2O3(0001) surface.21,38 This effect can be understood rather easily; it permits the material surface to recover, at least partially, the bulk coordination, hence the response of the surface is opposite to the surface relaxation occurring when corundum is cleaved and the resulting (0001) surface is exposed to the vacuum.24-26 Notice that the inward relaxation of the free surface with respect to the bulk structure is -0.72 Å and the outward relaxation of the aluminum layer induced by the presence of the Pd3 cluster is +0.48 Å. Another important consequence of allowing only the z coordinates of the Al atom and of the Pd3 plane to vary is to shorten the palladium-toaluminum distance to 1.46 Å. Allowing the nearest oxygen atoms to relax, its vertical coordinate leads to a further noticeable increase of 0.27 eV in the adsorption energy to 1.46 eV. The oxygen atoms move inward by 0.14 Å whereas in this case the aluminum atom reduces its outward relaxation to 0.36 Å. As a consequence, the final calculated Al-O interplanar distance remains almost unchanged with respect to the previous optimization step, and the vertical distance between the Pd and Al planes is also preserved. The inward motion of the oxygen atoms allow the Pd atoms to penetrate the surface slightly, and this is accompanied by a decrease in the Al degree of relaxation. The full optimization of the Pd positions causes a clockwise rotation of the Pd3 cluster that is accompanied by a 10% increase in the Pd-Pd distance, a noticeable decrease in the distance to the

Figure 3. Top and side views of the final optimized geometry for Pd3 resulting from geometry optimization starting from Pd atoms adsorbed above either O or H sites of the relaxed Al-terminated R-Al2O3(0001) surface. Further details are given in Table 2.

Adsorption of Pd Clusters on R-Al2O3(0001) oxide surface, and another significant increment in the adsorption energy, which becomes 1.61 eV. In the final structure, sketched in Figure 3, the Pd atoms point midway between the aluminum and oxygen sites of the second and fifth layers. Interestingly enough, the amount of relaxation of the first-layer aluminum atoms and of the second-layer oxygen atoms is identical to that calculated in the preceding optimization step. Notice that the Pd-Pd distance is much larger than that corresponding to the gas-phase cluster. Finally, it is worth mentioning that the Mulliken charge on the Pd atoms is close to zero, indicating that the interaction is driven essentially by electrostatics and metal polarization without the perceptible contribution of a covalent chemical bond. This is reminiscent of the result obtained for a 1/3 ML palladium coverage on the relaxed Al-terminated R-Al2O3(0001) surface, where the Pd atoms are also located close to the oxygen atoms of the second layer. Now we turn our attention to the case where the Pd3 cluster is initially placed above the surface with the Pd atoms pointing toward H sites (Figure 2b). Allowing only the Pd atoms’ z coordinate to relax results in a calculated adsorption energy of -0.32 eV. This is the first indication that this situation is less favorable than the one described above. The final optimized geometry, full relaxation of the Pd3 aggregate and of the z coordinate of neighboring first-layer Al and second-layer O atoms, is almost undistinguishable from the optimized structure obtained when the Pd3 cluster is initially placed with the metal atoms pointing toward the O sites. However, in this case, the Pd3 cluster rotates anticlockwise until the Pd atoms sit above the positions depicted in Figure 3. Therefore, it is quite clear that the structure shown in Figure 3 is a true minimum in energy; both initial structures converge to it after optimization. Finally, we consider the situation where palladium atoms are initially placed above Al sites (Figure 2c). This leads to the most favorable case for the adsorption of Pd3. In fact, by optimizing only the perpendicular distance of the Pd cluster plane to the surface, the calculated adsorption energy is ∼3 times larger than the computed value for adsorption on O sites (0.26 eV vs -0.13 eV). However, the vertical distance of the Pd3 cluster to the outermost substrate aluminum layer is almost the same (2.27 Å). At first sight, this result may be surprising because at low coverage the adsorption of Pd atoms on top of the oxygen atoms of the relaxed Al-terminated R-Al2O3(0001) is preferred.21,38 However, the structure of supported Pd3 is reminiscent of that encountered for the adsorption of Pd atoms on this surface but for a larger coverage. Recent density functional calculations have predicted an increasing stability for adsorption on the Al sites when going from the 1/3 ML to 1 ML coverage; in the later situation, the Pd-Pd distance is indeed close to the one predicted here.21 Hence, it is possible to argue that the adsorption site is determined by the presence or absence of the metal-metal bond. If the metal-metal bond is broken, then the oxygen sites are preferred; if it is maintained, then there is a clear preference for aluminum sites. Likewise, the present prediction of the H site as the less stable one for the adsorption of the Pd3 cluster is also in agreement with the fact that for a 1 ML coverage this is the less favored atomic arrangement.21 The above discussion has concentrated on a planar Pd3 above Al sites that is constrained to be parallel to the oxide surface. Now, let us return to the description of the step-by-step optimization procedure. Because in this case the Pd atoms sit above Al sites, they are not equivalent because they correspond to the first, third, and fourth atomic layers, hence two of them can be viewed as open sites. The independent variation of the perpendicular distances

J. Phys. Chem. B, Vol. 107, No. 26, 2003 6417 of the palladium atoms to the surface leads to an increase of 0.30 eV in the interaction energy. Now, the two Pd atoms located above the Al atoms of the third and fourth layers move toward the surface, and the Pd atom on top of the outermost aluminum atom moves in the opposite direction. This is simply a response to the different repulsion of the Pd atoms above Al in the first layer (toplike site) and above Al in the third and fourth layers (openlike sites). As a consequence, the Pd3 cluster plane is no longer parallel to the oxide surface, but the Pd-Pd distances are still close to those of the initial configuration (i.e., the shape of the Pd3 cluster is still almost an equilateral triangle). The two steps considered above refer to the adsorption of the Pd3 cluster on a frozen R-alumina substrate. Additional calculations were performed for a cluster parallel to the alumina surface and for a tilted cluster. In both cases, the four outermost substrate layers are allowed to relax vertically. As expected, surface relaxation has an important effect on the interaction energy for both parallel and tilted Pd3 adsorbates. The corresponding adsorption energies become 1.15 and 2.61 eV, respectively. The optimized geometry of a tilted Pd3 adsorbate is shown in Figure 4a, and in this case, the structure resembles an isosceles triangle with Pd-Pd distances that are significantly longer that those for the gas-phase cluster. The huge difference reported for parallel and tilted Pd3, 1.46 eV, is a consequence of the difference in the induced relaxation of the first-layer aluminum atom. For a planar Pd3 adsorbate, the Al1 atom is relaxed inward toward the surface by 0.57 Å, and for nonplanar Pd3, the relaxation is outward by 0.26 Å. In the former case, the outermost aluminum atom moves below the oxygen layer, and the steric hindrance is large. In the later case, as discussed before, the oxide material recovers its bulk coordination. The preceding discussion concerns the Pd atoms adsorbed directly above Al atoms from the first, third, and fourth layers. Allowing a full relaxation of the position of the palladium atoms that are no longer constrained to be located above the Al site leads to the geometry depicted in Figure 4b. A close inspection of the geometry of the supported particle reveals that one of the PdPd distances becomes very large and that the other two Pd-Pd distances are close to each other. Therefore, as a result of the metal-support interaction, one metal-metal bond is broken. The total interaction energy of the resulting Pd3 surface-model supersystem is almost the same (2.61 eV) as that in previous situations where the Pd atoms are constrained to lie above the Al sites. Therefore, one must conclude that these are the most stable structures of supported Pd3. Geometrical parameters and Mulliken charges for these two most stable structures of Pd3 on the R-alumina surface are summarized in Table 3. Differences are not significant, except for the negative charge on the Pd atom placed above the first-layer aluminum atom of the partially optimized Pd3 cluster and the relative height of two Pd atoms to surface Al1. The strong metal-support interaction predicted by the present density functional calculations is at variance with previous findings for metal clusters adsorbed on MgO.77 The structure and chemical nature of the support appear to play a decisive role in the final geometry of the supported particle and probably in its chemical reactivity. IV.II. Cluster Model Results for Pd4 Supported on R-Al2O3. To mimic the initial steps of the growth of Pd clusters supported on R-Al2O3, different structures that add a fourth atom to the adsorbed Pd3 particles discussed in the previous subsection have been considered. The results concerning the addition of the extra Pd atom on top of the Pd3 cluster (Figures 2-4) are summarized in Tables 4 and 5 for the aluminum- and oxygencentered models, respectively. The final optimized geometries


Gomes et al.

Figure 4. Top and side views of the final optimized geometry for Pd3 adsorbed above Al sites of the relaxed Al-terminated R-Al2O3(0001) surface. (a) Independent optimization of the z coordinate of the Pd atoms and (b) fully optimized Pd3 geometry including the positions of Pd atoms above the surface model. Further details are given in Table 3.

TABLE 4: Optimized Parameters for the Pd4 Cluster Adsorbed above the Al-Centered Surface Modela tetrahedron with one face parallel to the surface

parameter z(Al1-Al10)/Å z(O2-O20)/Å d(Pd-Al1)/Å q(Pd)/e Eads/eV

0.35 -0.14 A 1.98 -0.05

B 1.98 -0.09

C 1.98 -0.11

D 4.03 -0.01

1.52

a See Figure 5. Symbols are the following: z(Al -Al 0) and z(O 1 1 2 O20) are the vertical displacements of the Al1 and O2 atoms, respectively, from their initial positions in the clean and relaxed substrate, and positive or negative signs means outward or inward relaxation, respectively; z(Pd) is the vertical distance between the Pd and Al1 atoms; q(Pd) is the Mulliken charge on the Pd atoms; Eads is the total adsorption energy; A, B, C, and D are used to distinguish the Pd atoms.

are illustrated in Figures 5 and 6. As in the study of Pd3 adsorption on R-Al2O3(0001), the geometry optimization is carried out in several well-defined steps. First, the Cartesian coordinates of the fourth Pd atom are fully optimized whereas only selected parameters of the rest of the atoms of the Pd4 cluster are allowed to relax. In some cases, a full relaxation of the Pd4 aggregate was also considered. Let us start by describing the situation resulting from the addition of an extra Pd atom on top of the Pd3 optimized structure where the Pd atoms are located near O sites and shown in Figure 3. As reported in the previous section, negligible geometric differences appear in the internal geometry of the Pd3 cluster when it is constrained to be parallel to the surface or when the positions of all of the Pd3 atoms are fully optimized.

TABLE 5: Optimized Parameters for the Most Stable Structure of a Pd4 Cluster Adsorbed above the O-Centered Corundum Surface Modela parameter

fully optimized Pd4

z(Al1-Al10)/Å z(O2-O20)/Å z(Al3-Al30)/Å z(Al4-Al40)/Å

0.31 -0.32 -0.35 -0.22

d(Pd-Al1)/Å q(Pd)/e Eads/eV

A 1.33 0.16

B 1.28 0.42

C 1.32 0.67 2.81

D 2.43 -0.24

a See Figure 6c. Labels are the following: z(Al -Al 0), z(O -O 0), 1 1 2 2 z(Al3-Al30), and z(Al4-Al40) are the vertical displacements of the Al1, O2, Al3, and Al4 atoms, respectively, from their initial positions in the clean substrate, and positive or negative signs mean outward or inward relaxation, respectively; d(Pd-Al1) is the vertical distance between the Pd and Al1 atoms; q(Pd) is the Mulliken charge on the Pd atoms; Eads is the total adsorption energy; A, B, C, and D are used to distinguish the Pd atoms.

As a result of the identical geometry of the adsorbed cluster, the adsorption energy is almost the same. Thus, the first model for supported Pd4 consists of keeping the Pd3 plane parallel to the alumina substrate with the Pd atoms pointing toward O sites and adding an extra palladium atom (cf. Table 4 and Figure 5). The addition of the fourth metal atom results in a decrease in the adsorption energy and also in the Pd-Pd bond length when the results are compared with those collected in Table 2. The interaction energy for the adsorbed Pd4 tetrahedron with one face parallel to the surface and the Pd atoms pointing toward O sites is now 1.52 eV, the Pd-Pd bond distances being much closer to the computed gas-phase distances. On going from three



Figure 5. Optimized structure for Pd4 obtained by placing the fourth Pd atom on top of the Pd3 cluster adsorbed on the Al-centered Al2O3 substrate from a previous optimization (cf. Figure 3). Further details are given in Table 4.

to four adsorbed palladium atoms, the positions of Al and O change slightly in the z direction, and Mulliken charges in the Pd atoms are again close to zero. The calculated adsorption energy shows that placing one extra Pd atom on top of the Pd3 structure in Figure 3 destabilizes the Pd interaction with the oxide substrate. The fact that Pd3 adsorption is much more favorable when the metal atoms are located above aluminum sites and that the Pd4 tetrahedron with one face parallel to the surface with the Pd atoms pointing toward O sites leads to a decrease in adsorption energy suggest that, as for Pd3, one must consider the Al sites as well. Thus, using the O-centered cluster to represent the R-Al2O3 (0001) surface, different starting Pd4Al2O3 geometries were tested either with a tetrahedron-like structure or with a structure resembling the Cs butterfly-like optimized gas-phase Pd4 structure. From these different initial geometrical settings, the structures compiled in Figure 6 were obtained by carrying out the step-by-step geometry optimization of selected specific variables. Using tetrahedron-like starting geometry and keeping one Pd3 plane parallel to the surface leads to the structure represented in Figure 6a. The calculated adsorption energy is 0.55 eV. This rather low value could be seen as the consequence of the huge destabilization induced on the alumina substrate. In this situation, forcing the Pd3 plane to be parallel to the surface, the Al1 atom closest to the Pd atoms relaxes inward toward the oxide substrate, and this destabilizes the substrate by 1.88 eV. Adding one extra Pd atom on top of the Pd3 structure depicted in Figure 4a and optimizing all of the coordinates of the metallic particle leads to a final structure resembling the most favorable gas-phase Pd4 geometry (Figure 6b). The calculated adsorption energy for this structure is much larger, 2.10 eV, than for the previous one. By comparing the energies of the different structures depicted in Figure 6a and b, it is easy to conclude that the difference between the two values of the adsorption energy comes from the degree of relaxation of the Al2O3 substrate. In any case, the most stable Pd4 structure adsorbed on the Al-terminated R-Al2O3(0001) surface is an almost flat structure, as illustrated in Figure 6c. The adsorption energy is 2.81 eV. Further data concerning the geometry of this fully optimized Pd4 structure is summarized in Table 5. Notice that the geometry of this adsorbed Pd4 cluster is very different from that of the structures shown in Figure 6a and b; the 3D shape is almost lost, and the resulting metallic particle is nearly flat. Three of the four palladium atoms are placed at the same perpendicular distance to the outermost Al layer whereas one of the palladium atoms is located at a larger distance from the surface. This is due to the fact that three Pd atoms are located

at hollow sitessabove the Al atoms from the third or fourth layerswhereas one of them is placed almost on top of an aluminum atom from the outermost layer. It seems that in the structure depicted in Figure 6c the palladium atoms tend to follow the irregularity of the Al2O3 surface. The degree of relaxation of the alumina surface is similar to the values reported in Tables 2-4. When compared with the results reported in the previous tables, Mulliken charges in the most stable Pd4 adsorbed geometry have larger values, possibly because the metal atoms are closer to the surface. A comparison of the adsorption energies for the most stable Pdn (n ) 3, 4) structures placed above the oxide substrate shows that the fourth Pd atom has a small stabilizing effect because the adsorption energy for Pd3 is 2.61 eV whereas for Pd4 the adhesion energy is slightly larger, 2.81 eV. The smaller interaction energy for the Pd3 particle is a consequence of a large distortion of the Pd3 internal geometry upon the adhesion on the surface. To close this section, we note that, interestingly enough, the present study shows that even for a small Pdn (n ) 3, 4) cluster the adsorption of palladium atoms on the R-Al2O3(0001) surface is much more stabilized if this occurs above Al sites. This finding is in agreement with previous calculations concerning a 1 ML geometrical coverage of Pd on R-Al2O3(0001), and this behavior contrasts with calculations concerning both the adsorption of a single palladium atom or a 1/3 ML Pd geometrical coverage on the corundum surface.21 IV.III. Slab Model Results for Pd3 and Pd4 Supported on R-Al2O3. To further check the conclusions obtained in the previous sections concerning the adsorbate-induced substrate relaxation effects, the interaction of Pd3 and Pd4 clusters with R-Al2O3(0001) has also been studied by means of a periodic model. Indeed, this allows us to gain deeper insight into the processes related to the surface relaxation and to the changes of the electronic structure of the system due to adsorption. The large size of the present unit cell (surface area ≈ 80Å2) enables a detailed study of various configurations of Pd3 and Pd4 on the surface. The choice of a (2 × 2) supercell also ensures that the direct interaction between adsorbed Pd is weak because the minimal distance between periodic images is larger than 6 Å. In principle, the entire configurational space of adsorbed metal clusters on the surface shall be investigated, but this is far beyond the available computer resources. Therefore, this study was focused on the most likely adsorption geometries, especially those described in the previous section. Some additional configurations of the most open structure of Pd have been also sampled. For every configuration, a palladium cluster was placed in the vicinity of the surface, and the full geometry optimization


Gomes et al.

Figure 6. Optimized geometries for Pd4 adsorption on O-centered Al2O3. (a) Tetrahedron-like structure with one face forced to be parallel to the surface. (b and c) Structures obtained from a full optimization of the Pd4 internal geometry and atomic position above the surface. Further details are given in Table 5.

was performed. No constraints were imposed on the system. The initial geometry of the deposited palladium clusters was either pseudomorphic with the corundum surface or representative of a gas-phase geometry. The most stable adsorption geometry of Pd3 is presented in Figure 7. It is very similar to the geometry provided by the cluster calculations (Figure 4). The structure is distorted with respect to the gas-phase ground state, and the Pd-Pd distances are equal to 2.60 and 3.00 Å. The distortion, however, keeps the area of Pd3 approximately fixed. Therefore, the main difference between the results arising from the cluster models and those found with the periodic approach applies to the extent of the relaxation of the corundum surface upon adsorption. The Al cation, which is closest to the adsorbed cluster, relaxes outward by 0.5 Å, and the relaxation of the remaining surface

Al cations pushes them below the surface anions. The vertical rearrangement of surface oxygen anions is only minor. Large distortions of the system indicate that the interaction between adsorbed Pd3 and the surface is mainly electrostatic because the cations that are far away from the adsorption site are strongly affected. This type of relaxation cannot be easily described in the cluster approach because it requires quite large models. The adsorption of linear Pd3 that fits the periodicity of the surface (Pd-Pd spacing of 2.72 Å) is very unfavorable. This is manifested by a smaller adsorption energy (as described below) and only a minor change in the surface arrangement. Among many other calculated configurations, one must mention the initial state when Pd is placed directly above surface oxygen as discussed in section IV.I. This configuration is unfavorable,



Figure 7. Final geometry of Pd3 adsorbed above the slab model of R-Al2O3 from a full optimization of all atoms in the unit cell.

Figure 8. Final geometries for the tetrahedron-like (a) and nearly planar (b) structures of Pd4 adsorbed above the slab model of R-Al2O3 arising from a full optimization of all atoms in the unit cell.

and the Pd3 triangle is twisted until each Pd atom is coordinated to more than one anion. The theoretical study of adsorption of Pd4 on R-Al2O3 is more complicated than that of Pd3 because the extra atom implies that additional configurations have to be explored. The most stable adsorption geometries correspond to a semiflat adsorbed cluster as depicted in Figure 8 and to the tetrahedron-like geometry that is similar to those for Pd4 in the gas phase; in both cases, the clusters are strained. In the quasi-tetrahedral

geometry, the Pd-Pd closest to the surface is elongated to 2.75 Å, being pseudomorphic with surface periodicity whereas the other Pd-Pd distances remain close to those of the gas phase. The 2D adsorption results in a slight contraction of the bonds up to 2.55 Å. In both cases, the volume of the cluster is semipreserved. The adsorption of Pd4 induces a similar surface rearrangement to that discussed above for Pd3. The cations in close proximity to the adsorbed Pd are pushed outward, and those further away penetrate the surface by ∼0.5 Å. Very similar

6422 J. Phys. Chem. B, Vol. 107, No. 26, 2003 relaxation patterns in both cases suggest that the mechanism of surface/metal interaction is the same in both cases.78 The adsorption energy is defined as Eads) -(Eslab - Esubs Eclus), where Eslab is the energy of the slab of alumina with adsorbed palladium, Esubs is the energy of the relaxed aluminum oxide substrate, and Eclus represents the energy of the palladium cluster in the structural ground state of the gas phase. Such a definition includes all of the effects related to the elastic deformations. The adsorption energy of the most stable Pd3 is Eads ) 2.69 eV, which agrees very well with the cluster model result even though different forms of E[F] have been used. The close similarity between cluster B3LYP and periodic PW91 results indicates that the physical nature of the interaction is well described by both methods and models. Within the periodic model, the least stable linear structure binds to the surface with an interaction energy of only 2.10 eV. Pd4 is most strongly bound when adsorbed in a quasi-2D mode with Eads ) 2.75 eV; again this compares very well with the predictions of the cluster model. Nevertheless, the 3D adsorption energy is only slightly smaller (Eads ) 2.70 eV). Such a small difference in the energy prevents the clear distinction of which adsorption mode is preferred; however, when combined with the cluster approach, it indicates that the 2D mode is slightly more stable. The two most striking effects found in the periodic approach are (a) a large modification of the corundum surface upon the adsorption of Pd and (b) the predominance of the Pd-Pd interaction. This analysis is in good agreement with the results reported in the two previous subsections where the substrate is modeled by a finite cluster. Test calculations performed for Pd4 adsorbed on a “frozen” substrate indicate that up to 50% of the adsorption energy comes from the substrate relaxation. This indicates that the interaction mechanism of Pd4 with the corundum surface involves significant polarization effects, and thus it locally modifies the substrate.79 The insight into the electronic effects related to the adsorption can be seen when examining Figure 9, which shows the local density of states (LDOS) projected on the atomic orbitals. Only the most stable configurations are considered. For Pd3, the LDOS represented in Figure 9a shows two main modifications. On one hand, the character of the palladium d band is significantly changed, and the bandwidth splits and broadens, contributing to the downshift of the band center of gravity as represented by the dashed line in the right panel of Figure 9a. The Pd atom that is most distant from the surface is only weakly affected by the presence of the oxide. The change in the electronic configuration of the Pd cluster is accompanied by a large downward shift in the p states of the oxygen anions. The effect is limited to the oxygen atoms that are in the proximity of the adsorbed metal cluster (dashed line in the left panel of Figure 9a). The bonding states of the Pd d components are populated, thus contributing to the strong adsorption. For Pd4, the situation is very similar, as evidenced in Figure 9b. The main difference comes from the stronger Pd-Pd interaction within this larger metal cluster. This limits the modification of the d band, although the formation of the bonding/antibonding states can still be observed. Finally, the integration of the electronic density within a sphere of radius 1 Å does not show any significant charge transfer between the surface and the adsorbed atoms. Therefore, the main contribution to the adhesion energy comes from the charge redistribution within the atomic orbitals. The very small change in the electronic structure of the surface anions that are far away from the adsorption site further supports the local polarization a main contribution to the bonding states.

Gomes et al.

Figure 9. Local density of states (LDOS) projected onto surface atoms for the most stable configuration of Pd3 (a) and Pd4 (b) on the relaxed R-Al2O3(0001). The left panel represents the p states of oxygen. The right panel is for the d states of palladium. Solid and dashed lines are for the atoms the most distant from and closest to the adsorption site, respectively. The dotted line in the left panel shows the p states of aluminum.

Finally, in view of the recent results reported by Moseler et al.,76 is also interesting to test the influence of the adsorption on the magnetic properties of Pd4. Hence, calculations involving the triplet state of Pd4 have also been performed. The triplet state of the gas-phase cluster (total spin 1 µB) is well preserved when the cluster is adsorbed in the 3D mode, the final magnetic moment being even slightly enhanced (1.1 µB) because of larger Pd-Pd distances. However, in the 2D adsorption mode, the magnetic structure of the cluster is practically destroyed with some remaining magnetization of the palladium atom that is furthest away from the surface. This is the line with the predictions of Moseler et al.76 for small Pd clusters adsorbed on MgO, although the strong dependence of the energy difference between states of different spin with respect to the exchange-correlation functional prevents any further consideration. V. Conclusions In this work, a density functional theory-based study of the adsorption of small palladium clusters (Pdn, n ) 3, 4) adsorbed on the relaxed aluminum-terminated R-Al2O3(0001) surface has been presented. Both cluster and periodic models of the substrate

Adsorption of Pd Clusters on R-Al2O3(0001) have been used. In the cluster model calculations, a step-bystep optimization procedure with controlled displacements has been used to find the most relevant geometrical parameters and their influence on the adsorption energy. In the periodic calculations, a full relaxation of the outermost oxide layers is carried out. It is observed that both the cluster and periodic models predict a large deformation of the structure of the alumina induced by the adsorption of the metallic particles. Also, as a result of the metal-support interaction, the metal particles are deformed with respect to the gas-phase geometry, especially for Pd3. In all cases, the adsorption of the metallic particles results in a modification of the structure of the oxide surface, which tends to recover the bulk coordination. This is clear in the case of the cluster models, but in the periodic calculations, the analysis of this effect is more complicated because large supercells are used. This analysis reveals the inhomogenity of the surface deformation with cations closest to the adsorption sites displaced in a similar way to that of the cluster approach. However, the surface cations placed far from the interaction region relax inward, thus keeping the electrostatic potential at the surface constant. In this way, the presence of Pd atoms induces the nearest-neighbor first-layer Al atoms to be displaced outward from the surface. Despite of the large deformation of the surface fragments, the final adsorption energy is only moderately strong. This is because the energy cost to deform the oxide surface is rather large (i.e., up to ∼2.0 eV). This contrasts with the small amount of energy that is required to deform the Pd clusters. In any case, it is worth pointing out that, independent of the computational methods (GGA and B3LYP) and the surface models (clusters and slabs), the Eads values of Pd3 and Pd4 per metal atom are, as expected, always smaller than that corresponding to a single Pd atom on the most stable site of the relaxed surface reported in previous work.21,38 The most stable structure of supported Pd4 suggest a competition between the 2D and 3D growth of the supported crystallites. Also, it is not possible to determine which are the preferred adsorption sites on the relaxed aluminum-terminated R-Al2O3(0001) surface, which contrasts with the behavior observed for Pd adsorption on the MgO(001) surface in which Pd atoms clearly prefer O sites. Notice that in the case of MgO the relaxation of the surface is negligible. This confirms the preference of Pd atoms to be adsorbed both on oxygen and aluminum sites, as predicted in previous theoretical work concerning the adsorption of single Pd atoms and regular Pd films on the corundum surface. Finally, it is worth pointing out that both Mulliken and LDOS analyses suggest that there is no noticeable charge transfer between the metallic particles and the oxide surface, indicating that the interaction is dominated by the polarization of the metallic particles in response to the presence of the charges of the ions of the oxide surface. This is supported by the LDOS, which shows the formation of bonding and antibonding states between the Pd 4d and the O 2p orbitals, although arising predominantly from an intra-atomic charge redistribution. Acknowledgment. This research has been supported by the Spanish DGICYT grant BQU2002-04029-CO2-01 and, in part, by Generalitat de Catalunya grant 2001SGR-00043. J.R.B.G. thanks the Fundaç aõ para a Cieˆncia e a Tecnologia for a postdoctoral grant (BPD/22098/99). Part of the computer time was provided by the Centre de Supercomputacio´ de Catalunya, CESCA, and the Centre Europeu de Parallelisme de Barcelona, CEPBA, through a grant from the Universitat de Barcelona and the Fundacio´ Catalana per a la Recerca. Z.L. is grateful to the European Community for financing his stay in Barcelona

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Adsorption of Small Palladium Clusters on the Relaxed Î±-Al2O3 (0001

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