5402
J. Phys. Chem. C 2007, 111, 5402-5408
Theoretical Study of Palladium Cluster Structures on Carbonaceous Supports Dario Duca,†,* Francesco Ferrante,‡ and Gianfranco La Manna‡ Dipartimento di Chimica Inorganica e Analitica “S. Cannizzaro”, UniVersita` degli Studi di Palermo, Viale delle Scienze, Parco d’Orleans II - 90128 Palermo, Italia, and Dipartimento di Chimica Fisica “F. Accascina”, UniVersita` degli Studi di Palermo, Viale delle Scienze, Parco d’Orleans II - 90128 Palermo, Italia ReceiVed: October 31, 2006; In Final Form: February 3, 2007
DFT calculations have been performed on a palladium cluster adsorbed on two different carbonaceous supports, namely, two stacked polycircumcoronene units mimicking a double layer of graphite and a portion of an armchair (6,6) carbon nanotube. All of the systems have been subjected to geometry optimization and electronic structure investigation. This work, which is part of an extensive computational study on heterogeneous catalytic systems, is devoted to identify electronic and geometrical changes in which metal clusters and supports are involved upon interaction. Such analysis is helpful in designing new heterogeneous metallic catalysts, namely, new metal-supported carbonaceous catalysts. Calculations reveal a major geometrical distortion occurring in the palladium cluster supported on both graphite and nanotubes, which is caused by strong Pd-C interactions. The curvature of the nanotube surface seems to provide the basis for a stronger interaction with respect to the flat surface of graphite. This evidence is also pointed out by the atomic orbital overlap occurring between the cluster and the nanotube, as revealed by the density of states analysis.
1. Introduction An important class of heterogeneous catalysts is composed of transition-metal particles, with diameters less than 5 nm, anchored on a surface. Owing to the extremely small sizes of the metal particles, the experimental identification of the cluster geometry, size and shape distribution, and its interaction with the support still represents a difficult task involving complex integrated approaches,1,2 also considering quantum mechanical methods.3 Computational chemistry, in particular within the frame of density functional theory, finds in this field a major source of new challenges in testing its methods and algorithms4 as well as in helping the interpretation of the experimental studies or even filling the gaps where they are lacking.5 In various common approaches to the computational study of catalytic systems formed by supported metal particles, the geometry of the support is kept frozen while structural optimizations are devoted to locally describe small reactive portions of the supported metal particle surface, eventually including the adsorbed reagents involved. Alternatively, it is well known that the nature of the support can affect in different ways the physical structure and the chemical properties of the supported metal particles, namely, in determining the strong metal support interaction (SMSI) phenomena6 and in governing metal particles’ shape and size distributions.7 The number of active sites that are present on the catalyst surface are intimately connected to its size; in fact, a size variation changes the superficial/bulk atom ratio in the particle and, accordingly, its electronic structure and catalytic properties.8 Activated carbon9,10 as well as carbon single-walled nanotubes,9 nanotubes,11,12 and graphite10,13 are often used as a * Corresponding author. Dr. Dario Duca, Professor of General and Inorganic Chemistry - Dipartimento di Chimica Inorganica e Analitica “Stanislao Cannizzaro” dell’Universita`, viale delle Scienze Ed. 17, I-90128 Palermo, Sicily, Italy. E-mail:
[email protected]. † Dipartimento di Chimica Inorganica e Analitica “S. Cannizzaro”. ‡ Dipartimento di Chimica Fisica “F. Accascina”.
support for catalysts because they are usually stable under different conditions and allow an economical and ecological recovery of the catalytic metal by simply burning off the carbon. Usually, carbon surfaces are modified by chemical reactions with oxygen. The role of the carbon surface sites has been investigated in a number of experiments,14 and the development of carbon-supported catalysts is bound to the research on fuel cells.15,16 Among metal catalysts, palladium is one of the most used. Its peculiar interaction with hydrogen made it a fundamental catalyst for (i) hydrocarbon hydrogenation,17 (ii) selective reduction of functional groups,18 (iii) synthesis of vinyl acetate from ethylene, oxygen, and acetic acid,19 and (iv) synthesis of methanol.20 In these applications, palladium is supported as small particles on alumina, silica, and on their mixtures or it is very often used as coordination center of organometallic complexes in homogeneous catalysis.21 More recently, a number of computational studies have been afforded on the catalytic properties of palladium clusters, mainly on their ability to adsorb hydrogen, CHx fragments, and ethylene.22,23 The calculations above were performed considering the clusters as isolated molecules, whereas, in our opinion, the mutual effects of the support and the model cluster have to be taken into consideration to obtain a reliable model of the metallic cluster properties. Alternatively, palladium clusters interacting with small portions of supporting materials can be considered effective models for heterogeneous palladium-based catalysts because the metal is usually adsorbed as a microaggregate on the support, in a form that is an intermediate state between the single atom and the bulk solid.24 To investigate the geometrical and electronic changes of supports and metal clusters caused by their mutual interaction and eventually by their interaction with catalytic substrates, we are now studying, by computational methods in the frame of the NanoCat Project, adsorption25 and catalytic reactions on different materials including zeolites,26 hyper-cross-linked poly-
10.1021/jp067167k CCC: $37.00 © 2007 American Chemical Society Published on Web 03/20/2007
Palladium Cluster on Carbonaceous Supports
J. Phys. Chem. C, Vol. 111, No. 14, 2007 5403
Figure 1. Optimized geometry of the Pd9/ccc2 system. The insets show the carbon atoms, labeled a-c, of the central coronene nucleus, to which two palladium atoms are bound (medium position m, vertex position V) and the corrispondent Pd-C distances.
styrene, block copolymers, and carbonaceous derivatives. Here we report on the energetics and structural properties of two systems containing one palladium cluster interacting with two different carbonaceous supports, namely, graphite and singlewalled carbon nanotube models, studied by means of DFT calculations. The ability of the Pd/C systems above to adsorb small molecules and eventually react will be discussed later in following papers. In the next section, the models adopted for the supports and the Pd9/support systems are presented, along with the details of the computational methods. Afterward, in the results and discussion section, the optimized structures will be discussed and, finally, the molecular orbitals will be analyzed with the help of the density of states. 2. Models and Computational Methods The first system is composed by a Pd9 cluster adsorbed on the central position of the sheet of a two-stacked polycircumcoronene molecule, mimicking a graphite bilayer (the optimized structure is showed in Figure 1). The polycircumcoronene is formed by 37 fused benzene rings (C96H24), and the size of the Pd9 cluster is such to cover just its central nucleus (C24H12). Hereafter, we will use the abbreviation ccc2 for the bilayer polycircumcoronene system (C96H24)2, and later we will extend this notation to smaller and greater homologues by using the abbreviation ...cn, where the dots will be replaced by as many c as the number of circles surrounding the coronene nucleus and n is the number of layers. The starting geometry of ccc2 was that of graphite: two molecules of polycircumcoronene were stacked according to an AB structure, and the distance between any two facing carbon atoms was exactly 3.35 Å, that is, half of the length of the c unit cell vector in the graphite lattice.27 The second system is composed by the same Pd9 cluster adsorbed on a portion of a single-walled open-ended armchair (6,6) carbon nanotube, whose surface is formed alternatively by five and four benzene units (the optimized structure is showed in Figure 2); hydrogen atoms were used to saturate the dangling bonds. The palladium cluster was posed atop a central coronenelike portion of the nanotube surface. The Pd9 was obtained by a truncation of the fcc lattice; its starting geometry was a triangular face-centered square pyramid having C4V symmetry: there were four Pd atoms with coordination 5, four atoms with coordination 3 and one with coordination 8. This geometry was
Figure 2. Optimized geometry of the Pd9/nanotube system. The insets show the carbon atoms, labeled a-e, of the central coronene-like portion, to which three palladium atoms are bound (medium position m, vertex position V) and the corrispondent Pd-C distances.
obtained previously at the same level of calculation used here and a number of studies were performed on the CO/Pd9 system.28 The carbonaceous supports, the Pd9 cluster, and the Pd9/ support systems were subjected to geometry optimization and molecular orbitals analysis. All of the systems were treated as supermolecules, and preliminary studies revealed that the singlet state of the Pd9/support is the most stable one. Conversely, calculations performed at the same level on isolated Pd9 clusters showed that the latter are preferably in higher multiplicity states (see section 3.5), according to the literature findings.29,30 Geometry optimizations were performed by using a QM/MM approach within the ONIOM strategy31 as implemented in the package Gaussian 03.32 Regarding the ccc2 molecule, the ONIOM model system was formed by the two facing coronene central nuclei (c2) and was treated at the DFT level by using the B3LYP hybrid functional33 joined to the Dunning D95 basis set. The universal force field34 was used for the low-level MM calculations on the real system. This choice was necessary because preliminary studies have shown that a simpler model formed by two stacked coronene or circumcoronene units were unable to keep a suitable stacked geometry, thus being inadequate for mimicking a bilayer graphite system. The use of the ONIOM procedure on the extended ccc2 model can, however, be seen as a strategy, which helps (i) to maintain a suitable bilayer structure as well as (ii) to keep the computational time lower. The Pd9 cluster was added to the ONIOM model system when the Pd9/ccc2 was considered; the LANL2DZ effective core potential was used for palladium. The starting geometry of Pd9/ccc2 has been constructed by positioning the cluster symmetrically with respect to the coronene portion, blackened in Figure 3, with its square base parallel to the ccc2 layer. Two opposite Pd atoms were at the medium point of C-C bonds, while the other two were close to the center of benzene rings (see inset in Figure 3). An analogous procedure was used for the carbon nanotube and the Pd9/nanotube system: the ONIOM model systems were formed by the central coronenelike structure in the first case and by this portion plus the cluster in the second case. The cluster in the starting geometry was
5404 J. Phys. Chem. C, Vol. 111, No. 14, 2007
Figure 3. Schematic picture of the graphite and nanotube models: the blackened portions in the 3D representations were treated at high level in the ONIOM approach. The 2D inset shows the contact points of the palladium cluster with both of the mimicked supports employed in starting the model optimizations.
localized symmetrically with respect to a central coronene-like portion in the nanotube surface as in the case of Pd9/ccc2 (see Figure 3). Once we obtained the optimal geometries, Kohn-Sham orbitals and interaction energies were obtained by single-point calculations for the whole systems using the generalized gradient functional BP8635 in conjunction with the resolution of identity approximation36 in its multipole accelerated variant.37 In the RIDFT approximation, the electron density was expanded in a set of auxiliary basis functions centered on the nuclei. This procedure allowed a more efficient calculation of Coulombian integrals, thus reducing the computational time remarkably. These calculations were accomplished by using the TURBOMOLE v5.8 package.38 In all of the cases, a double-ζ plus polarization basis set,39 with contraction scheme (7s4p1d/4s2p)/ [3s2p1d/2s1p], was employed for light atoms and an all electron basis set,40 with contraction scheme (17s12p8d)/[6s4p3d], was used for palladium. The auxiliary basis sets for light atoms were those contained in the TURBOMOLE basis library, whereas the auxiliary basis set for palladium was automatically generated by means of the fitting procedure available in Gaussian 03, comprising functions with l ) 4. 3. Results and Discussion 3.1. ccc2 System. The geometry optimization of the stacked polycircumcoronenes model revealed a tendency of the bilayer to bend slightly in the central portion: the deviations from the graphite distance (3.35 Å) between the facing carbons in the central portion of ccc2 do not exceed 0.35 Å, and this value is consistent with the deviation obtained using van der WaalsDFT procedures.41 This gave us enough confidence in using ccc2 as a model for a graphitic bilayer and B3LYP in ONIOM mixture with UFF as reliable method of calculation. Finite portions of graphite have a finite HOMO-LUMO gap, and in the ccc2 system this value is 1.04 eV. To investigate the dependence of the HOMO-LUMO eigenvalue difference on the dimension of the model, a parallel study on ideal graphitemimicking molecules (not optimized), ranging from coronene (c1) to a trilayer ABA polycircumcoronene (cccc3; C450H90), was afforded at the B3LYP/3-21 G(d) level of calculation. As shown in Figure 4, the decrease of the gap value on the sheet size as well as on the number of layers was found. It is
Duca et al.
Figure 4. HOMO-LUMO gap in ideal graphite-mimicking mono-, bi-, and tri-layered polycircumcoronene families, ranging from C24H12 to (C150H30)3.
Figure 5. Deviations from the coordinates of ideal graphite for any facing carbon atoms in the optimized structures of ccc2 (a) and Pd9/ ccc2 (b) systems.
interesting to note that, when passing from a member of a series to the member with the same number of layers in the successive series (e.g., cc2 and ccc2), there is an almost uniform decrease of the HOMO-LUMO gap, and the difference becomes smaller as the size of the model increases. Also, within a series, the difference in the gap value between the third and the second member is always smaller than the difference between the second and the first member, and this trend seems to reach a plateau already after the third member. This suggests that the number of layers has a minor influence on the frontier Kohn-Sham orbitals eigenvalues. More importantly, the analysis shows that in the HOMO and LUMO regions there are molecular orbitals that are more localized on the edge of the graphitic layers, as happens in a stepped graphite surface.42 This is in agreement with the HOMO stabilization that is observed on passing from the third member of a series to the first member of the successive one. In fact, in the latter the HOMO is always delocalized between more edge carbon atoms.
Palladium Cluster on Carbonaceous Supports
Figure 6. C4V isolated geometry (upper structure) of the Pd9 cluster and D3h geometry as optimized in the carbonaceous supports (lower structure).
3.2. Pd9/ccc2 System. The optimization of the system composed by Pd9 supported on ccc2 reveals two important features. The first is the enhanced curvature of the bilayer in the region where the cluster is adsorbed, being the maximum deviation of the distance between facing carbons by about 0.5 Å from the starting value of 3.35 Å. We can try to quantify the curvature by considering the angles formed between some opposite edge atoms and the C atoms of the central benzene ring in the ccc structure. We selected those angles that would have been 180° in the graphite lattice. Of course, the curvature of the ccc layer modifies this value. Fourteen of such angles have been measured in the two layers of both the ccc2 and Pd9/ccc2 systems and then averaged. As one can expect, in ccc2 the curvatures of the two layers have the same magnitude (176.7°) and opposite signs (Figure
J. Phys. Chem. C, Vol. 111, No. 14, 2007 5405 5a). In Pd9/ccc2 one can identify an upper ccc layer, where the Pd9 is supported, and a lower layer. By averaging the same set of angles as in ccc2, the curvature of the upper layer is 168.6° and that of the lower layer is 174.8°. More interestingly, the two curvatures in Pd9/ccc2 have the same signs, clearly showing that the upper layer dragged the lower one (Figure 5b). This behavior has a physical correspondence in the adsorbate-induced surface reconstruction.43 As will be shown later, a comparison of these results with those regarding the Pd9/nanotube system reinforces this inference. The second issue is about the distortion of the original C4V geometry of the palladium cluster. The optimized structure of the metal cluster upon ccc2 is a square face-centered triangular prism with symmetry D3h (slightly distorted due to the asymmetry of the interactions), where six Pd atoms have coordination 4 and three Pd have coordination 6. This distortion is due to the interaction of the basis of the palladium cluster with some carbon atoms of the ccc2 touching layer. The D3h structure is obtained easily from the C4V one simply by downing the positions of Pd atoms labeled A and A′ in Figure 6 with respect to the plane of the C4V square base and, accordingly, approaching one toward the other couples of atoms B, B′ and C, C′ in the center of the triangular faces. Because the two Pd atoms that are downed are those showing the highest proximity with the support (one Pd is placed over a C vertex atom, V position, at 2.42 Å, the other among two C side atoms, m position, at 2.33 and 2.84 Å; see Figure 1), the distortions are attributable to strong metal-support interactions. 3.3. Carbon Nanotube System. After optimization, the structure of the nanotube does not show sensible variations with respect to the accepted geometry of a single-walled open-ended armchair (6,6) carbon nanotube; minor deviations can be found at the structure edges, obviously due to boundary effects. The trend of the HOMO-LUMO gap as a function of the nanotube length has been investigated in ref 44 by using a generalized gradient functional and a minimal basis set. The carbon nanotube
TABLE 1: Significant Pd-Pd and Pd-C Bond Lengths in the D3h Pd9 Cluster, Occurring in the Pd9/ccc2 and Pd9/Nanotube Systems
5406 J. Phys. Chem. C, Vol. 111, No. 14, 2007
Figure 7. Calculated density of states from the ccc2 (a) and from the Pd9/ccc2 molecular orbitals (b). The dashed line in b is the partial DOS referring to the atomic functions centered on the nuclei of the palladium cluster.
model used here corresponds to the 11-section nanotube as defined in ref 44 and the HOMO-LUMO gap, 0.4 eV, is only 0.1 eV larger than that reported there. The 11-section nanotube gap is a minimum in the almost regular oscillation that the HOMO-LUMO difference shows as the nanotube length increases. 3.4. Pd9/Nanotube System. The geometry optimization of this system leads to the same distortions of the palladium cluster discussed in the previous paragraph: the transition from C4V to D3h structure. However, on the basis of the Pd-C bond distances, it seems that the cluster interacts more strongly with the carbon nanotube than with the ccc2 graphitic bilayer. In fact, the two interacting downed Pd atoms (A, A′) are at bond distance from four C atoms (respectively at 2.44, 2.21 Å and 2.39, 2.21 Å from two couples of C side atoms) and a third Pd is bonded to a C vertex atom (2.45 Å). The BSSE-uncorrected interaction energy between Pd9 and the carbon nanotube is 363 kJ/mol at the BP86 level; it is 99 kJ/mol higher than the interaction energy between Pd9 and the ccc2 support. The BSSE correction by using the counterpoise method45 lowers the Pd9nanotube interaction to 227 kJ/mol, which is 124 kJ/mol higher than the BSSE-corrected interaction energy for Pd9/ccc2, supporting the BSSE-uncorrected results. The enhanced interaction of the Pd9-nanotube with respect to the Pd9-graphite system seems to be due to the characteristic curvature of the nanotube surface, the geometry of the nanotube being only slightly distorted with respect to the one without clusters. The evidence of a stronger interaction is also supported by Kohn-Sham orbital analysis. This feature, in our opinion, played a role in determining the curvature of the support in the
Duca et al.
Figure 8. Calculated density of states from the carbon nanotube (a) and from the Pd9/nanotube molecular orbitals (b). The dashed line in b is the partial DOS referring to the atomic functions centered on the nuclei of the palladium cluster.
Pd9/ccc2 system. In fact, if the interaction of Pd9 with a curved surface is preferred because of a more appropriate placement of the surface atoms, then the bending of the ccc2 layer can be interpreted as the result of adjustments caused by the cluster in order to give rise to a stronger metal-surface interaction. 3.5. D3h Structure of the Pd9 Cluster. The square facecentered triangular prism structure that Pd9 adopts once supported on ccc2 and carbon nanotube can be seen as the overlap of three triangles: two of them, forming the basis, have the same orientation, while the central triangle is rotated 120° around the C3 axis. To analyze the D3h structure in terms of geometrical parameters it is useful to refer to these triangles. Table 1 reports the Pd-Pd bond lengths when Pd9 is adsorbed on the carbonaceous supports. We can note that there are not noticeable differences considering the Pd9/ccc2 and Pd9/nanotube systems. In both cases the Pd-Pd bond lengths within each triangle are almost the same, 0.06 Å being the maximum difference, and only very small deviations can be seen between the lengths, which interconnect the three triangles. The substantial overlapping between the D3h cluster geometries in the Pd9/ccc2 and Pd9/nanotube is more evidence of the fact that the curvature of the ccc2 layers is due to the presence of the metal cluster. However, in Pd9/ccc2 only three Pd-C bonds can be identified, confirming that the Pd-surface interaction is stronger in the Pd9/nanotube system. The different positions characterizing the cluster in the two systems that can be pointed out from the insets in Figures 1 and 2 are due to the different nature of the curvature of the surfaces: a local “centrosymmetric” curved surface in the ccc2 case, a natural “cylindrical” curved surface in the carbon nanotube.
Palladium Cluster on Carbonaceous Supports
J. Phys. Chem. C, Vol. 111, No. 14, 2007 5407
Although C4V Pd9 is a truncation of the bulk palladium fcc lattice, we found that it cannot maintain its symmetry when interacting with the carbonaceous supports. Indeed, the D3h Pd9 cluster is the geometry of a minimum also in the potential energy surface of the isolated cluster and is more stable than the C4V structure (66 kJ/mol at the B3LYP/lanl2dz level of calculation with the zero-point vibrational energy correction), the D3h and the C4V clusters being in the quintet and triplet states, respectively. It is surely an important issue, and subject of future investigations, to explore the C4V f D3h conversion in the gas phase by means of kinetic approaches. 3.6. Calculation and Analysis of DOS. The total density of states (DOS) at the energy value E is defined by the expression
DOS(E) )
∑i δ(E - i)
where the sum runs on all of the molecular orbital eigenvalues i. In this work, the delta function was substituted by a pseudoVoigt function
DOS(E) )
∑i
[
(1 - η)e-(E-i) /2σ + 2
η
2
]
∆/2π (E - i)2 + (∆/2)2
≡
∑i F(E - i)
where the values ∆ ) 0.5 and η ) 0.2 were chosen, with σ ) ∆/(2 ln 2). In all of the DOS graphs reported here, the range [-10,0] eV has been divided in 5000 small intervals and DOS(E) has been calculated in the middle point of each of them. The partial density of states (PDOS) is defined by the expression
PDOS(E) )
∑i CA,i F(E - i)
where the character CA,i of the fragment A (an atomic orbital, all of the AOs of an atom or of a group of atoms, etc.) has been obtained from a Mulliken population analysis:
CA,i )
∑ cai ∑b cbi Sab
a∈A
Here cai and cbi are the LCAO coefficients of the atomic functions φa and φb in the ith MO and Sab is their overlap integral. To calculate DOS and PDOS, the Kohn-Sham molecular orbitals as obtained at the level of theory described in Section 2 have been used. In Figure 7, the DOS for the Pd9/ccc2 system is reported along with the PDOS calculated from the atomic orbitals centered on all of the palladium atoms. The molecular orbitals that fill the HOMO-LUMO gap of the isolated support are all formed by Pd atomic functions, as can be inferred by the essentially perfect overlap between the DOS and the PDOS curves in this region. The presence of the cluster seems to have only a small influence on the frontier molecular orbitals of the support, these being more localized at the edges. Alternatively, Figure 8 shows the analogous graph for the Pd9/nanotube system: in the HOMO-LUMO region a substantial combination of atomic orbital from the cluster and the nanotube can be inferred, showing the existence of a good overlap between their atomic functions. The gap decreases to 0.005 eV, one tenth of the gap in the isolated nanotube. DOS analysis therefore reveals the presence of a relevant effect of the adsorbed Pd9 on the molecular orbitals of the support, which
can be explained in terms of a stronger interaction between the cluster and the support. This result indirectly confirms our deductions performed along the comparison of the palladium cluster interacting with the nanotube and graphite models. 4. Conclusions and Future Directions The natural curvature of an armchair (6,6) carbon nanotube seems to be more suitable in order to support small palladium clusters obtained from fcc lattice truncation than the flat surface of graphite. To give rise to stronger interactions, the cluster bends the graphite surface so that the process of supporting palladium particles on graphite could result in a local “surfaceatoms” extraction process. The distorted D3h structure of the palladium adsorbed on the ccc2 and carbon nanotube shows the relevant influence of the supports on the cluster geometry and the importance of macromolecular treatments for the investigation of the interactions between the clusters and small molecules. Because the CO/Pd9(C4V) systems are investigated extensively in the present studies, we aim to calculate, as the following step in studying Pd/C models, the structure of the combinations CO/Pd9(D3h)/ccc2 and CO/Pd9(D3h)/carbon nanotube. The ONIOM procedure will allow us to use extended basis sets and high correlated methods for the CO/Pd subsystem. Acknowledgment. This work was supported by the NANOCAT Project: funded in the frame of the sixth Framework Program of the European Community, Contract no. NMP3-CT2005-506621, and by the University of Palermo. References and Notes (1) Boudart, M.; Djega-Mariadossou, G. Kinetics of Heterogeneous Catalytic Reactions; Princeton U. Press: Princeton, NJ, 1984. (2) Dumesic, J. A.; Rudd, D. F.; Aparicio, L. M.; Rekoska, J. E.; Trevin˜o, A. A. The Microkinetics of Heterogeneous Catalysis; ACS Professional Reference Book, Washington, DC, 1993. (3) van Santen, R. A.; van Leeuwen, P. W. N. M.; Moulijn, J. A.; Averill, B. A. Catalysis: An Integrated Approach, 2nd ed.; Elsevier: Amsterdam, 1999. (4) van Dam, H. J. J.; Guest, M. F.; Sherwood, P.; Thomas, J. M.; Van Lethe, J. H.; van Lingen, J. N. J:; Bailey, C. L.; Bush, I. J. J. Mol. Struct.: THEOCHEM 2006, 771, 33-41. (5) Nieminem, V.; Sierka, M.; Murzin, D. Y.; Sauer, J. J. Catal. 2005, 231, 393-404. (6) Ueckert, T.; Lamber, R.; Jaeger, N. I.; Shubert, U. Appl. Catal., A 1997, 155, 75-85. (7) (a) Fernandez-Garcia, M.; Gomez, Rebollo, E.; Guerriero, Ruiz, A.; Conesa, J. C.; Soria, J. J. Catal. 1997, 72, 146-159. (b) Escobar, J.; De Los Reyes, J. A.; Viveros, T. Appl. Catal., A 2003, 253, 151-163. (8) (a) Duca, D.; Barone, G.; Varga, Zs.; La Manna, G. J. Mol. Struct.: THEOCHEM 2001, 542, 207-214. (b) La Manna, G.; Barone, G.; Varga, Zs.; Duca, D. J. Mol. Struct.: THEOCHEM 2001, 548, 173183. (9) Corma, A.; Garcia, H.; Leyva, A. J. Mol. Catal., A 2005, 230, 97105. (10) Auer, E.; Freund, A.; Pietsch, J.; Tacke, T. Appl. Catal., A 1998, 173, 259-271. (11) Zhang, A. M.; Dong, J. L.; Xu, Q. H.; Rhee, H. K.; Li, X. L. Catal. Today 2004, 93-95, 347-352. (12) Vu, H.; Gonc¸ alves, F.; Philippe, R.; Lamouroux, E.; Corrias, M.; Kihn, Y.; Plee, D.; Kalck, P.; Serp, P. J. Catal. 2006, 240, 18-22. (13) Baker, R. T. K.; Laubernds, K.; Wootsch, A.; Paa´l, Z. J. Catal. 2000, 193, 165-167. (14) Fraga, M. A.; Jorda˜o, E.; Mendes, M. J.; Freitas, M. M. A.; Faria, J. L.; Figueiredo, J. L. J. Catal. 2002, 209, 355-364. (15) Takasu, Y.; Itaya, H.; Iwazaki, T.; Miyoshi, R.; Ohnuma, T.; Sugimoto, W.; Murakami, Y. Chem. Commun. 2001, 341. (16) Liao, S.; Holmes, K. A.; Tsaprailis, H.; Birss, V. I. J. Am. Chem. Soc. 2006, 128, 3504-3505. (17) Tysoe, W. T.; Nyberg, G. L.; Lambert, R. M. J. Phys. Chem. 1986, 90, 3188-3192. (18) (a) Tsuji, J.; Manday, T. Synthesis 1996, 1 and references therein. (b) Hayashi, J. J. Organomet. Chem. 1999, 576, 195-202. (19) Greenberg, H.; Ba¨ckvall, J.-E. Chem.sEur. J. 1998, 4, 1083-1089 and references therein.
5408 J. Phys. Chem. C, Vol. 111, No. 14, 2007 (20) Kirillov, V. L.; Ryndin, Y. A. React. Kinet. Catal. Lett. 1996, 59, 351-357. (21) Chaudari, R. V.; Seayad, A.; Jayasree, S. Catal. Today 2001, 66, 371-380. (22) Bertani, V.; Cavallotti, C.; Masi, M.; Carra`, S. J. Phys. Chem. A 2000, 104, 11390-11397. (23) Fahmi, A.; van Santen, R. A. J. Phys. Chem. 1996, 100, 56765680. (24) (a) Kolmakov, A. A.; Godman, D. W. Size effects in Catalysis by Supported Metal Clusters. In Quantum Phenomena in Clusters and Nanostructures; Khanna, S. N., Castleman, A. W., Jr., Eds.; Springer: Berlin Heidelberg, 2003, pp 159-197. (b) Fagherazzi, G.; Benedetti, A.; Deganello, G.; Duca, D.; Martorana, A.; Spoto, G. J. Catal. 1994, 150, 117-126. (c) Deganello, G.; Duca, D.; Martorana, A.; Fagherazzi, G.; Benedetti, A. J. Catal. 1994, 150, 127-134. (25) Duca, D.; Barone, G.; Giuffrida, S.; Varga, Zs. J. Comput. Chem., in press. (26) Barone, G; Casella G.; Giuffrida, S.; Duca D. J. Phys. Chem. B, submitted for publication. (27) Baskin, Y.; Mayer, L. Phys. ReV. 1955, 100, 544. (28) Duca, D. et al. Work in progress. (29) Moseler, M.; Ha¨kkinen, H.; Barnett, R. N.; Landman, U. Phys. ReV. Lett. 2001, 86, 2545-2548. (30) Rogan, J.; Garcia, G.; Valdivia, J. A.; Orellana, W.; Romero, A. H.; Ramirez, R.; Kiwi, M. Phys. ReV. B 2005, 72, 115421-1-115421-5. (31) (a) Svensson, M.; Humbel, S.; Froese, R. D. J.; Matsubara, T.; Sieber, S.; Morokuma, K. J. Phys. Chem. 1996, 100, 19357-19363. (b) Dapprich, S.; Koma´roni, I.; Byun, K.S.; Morokuma, K.; Frisch, M. J. J. Mol. Struct.: THEOCHEM 1999, 461-462, 1-21. (32) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.;
Duca et al. Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision D.02; Gaussian, Inc.: Wallingford, CT, 2004. (33) Becke, A. D. J. Chem. Phys. 1993, 98, 5648-5652. (34) (a) Rappe`, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A., III; Skiff, W. M. J. Am. Chem. Soc. 1992, 114, 10024-10035. (b) Rappe`, A. K.; Colwell, K. S.; Casewit, C. J. Inorg. Chem. 1993, 32, 3438-3450. (35) (a) Becke, A. D. Phys. ReV. A 1988, 38, 3098-3100. (b) Perdew, J. P. Phys. ReV. B 1986, 33, 8822-8824. (36) (a) Eichkorn, K.; Treutler, O.; O ¨ hm, H.; Ha¨ser, M.; Ahlrichs, R. Chem. Phys. Lett. 1995, 240, 283-290. (b) Eichkorn, K.; Weigend, F; Treutler, O.; Ahlrichs, R. Theor. Chem. Acc. 1998, 97, 112-124. (37) Sierka, M.; Hogekamp, A.; Ahlrichs, R. J. Chem. Phys. 2003, 118, 9136-9148. (38) (a) Ahlrichs, R.; Ba¨r, M.; Ha¨ser, M.; Horn, H.; Kolmell, C. Chem. Phys. Lett. 1989, 162, 162-169. (b) Ha¨ser, M.; Ahlrichs, R. J. Comput. Chem. 1989, 10, 104-111. (c) Von Arnim, M.; Ahlrichs, R. J. Comput. Chem. 1998, 19, 1746-1757. (39) Scha¨fer, A.; Horn, H.; Ahlrichs, R. J. Chem. Phys. 1992, 97, 25712577. (40) Pd SVPallS2, as contained in the TURBOMOLE basis set library. (41) (a) Rydberg, H.; Jacobson, N.; Hyldgaard, P.; Simak, S. I.; Lundqvist, B. I.; Langreth, D. C. Surf. Sci. 2003, 606-610, 532-535. (b) Langreth, D. C.; Dion, M.; Rydberg, H.; Schro¨der, E.; Hyldgaard, P.; Lundqvist, B. I. Int. J. Quantum Chem. 2005, 101, 599-610. (42) Kobayashi, K. Phys. ReV. B 1993, 48, 1757-1760. (43) Kolasisnky, K. W. Surface Science: Foundations of Catalysis and Nanoscience; John Wiley & Sons, LTD: Chichester, 2004; pp 7-12. (44) Rochefort, A.; Salahub, D. R.; Avouris, P. J. Phys. Chem. B 1999, 103, 641-646. (45) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553-566.
