DFT Study of Bimetallic PalladiumâGold Clusters PdnAum of Low

J. Phys. Chem. A 2010, 114, 10345–10356

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DFT Study of Bimetallic Palladium-Gold Clusters PdnAum of Low Nuclearities (n + m e 14) Giuseppe Zanti and Daniel Peeters* Institute of Condensed Matter and Nanosciences, Quantum Chemistry Group, UniVersite´ catholique de LouVain, Baˆtiment LaVoisier, Place Louis Pasteur 1, B-1348 LouVain-la-NeuVe, Belgium ReceiVed: May 6, 2010; ReVised Manuscript ReceiVed: August 19, 2010

Bimetallic palladium-gold PdnAum clusters of low nuclearity (n + m e 14) are studied using the density functional theory at B3LYP level with a Lanl2DZ pseudopotential to understand the evolution of various structural, electronic, and energetic properties as a function of size (n + m) and composition (n/m) of the system. The potential energy surfaces have been explored for many different structures, and the minima obtained were then collected and used as a starting point for comparing the selected properties. Theoretical results show a logical evolution of the properties depending on the size and the composition of the system. Pdn clusters clearly prefer 3D structures while Aum clusters favor planar configurations. The geometry of the bimetallic PdnAum clusters mainly depends on their composition, i.e., clusters enriched in palladium atoms prefer 3D structures while increasing gold contents promotes planar configurations with deviation from planarity near Pd centers. Regarding the electronic properties, NBO analysis reveals that the unique closed-shell electronic structure of Pd atoms (4d10) requires a (4d f 5s) promotion to form stable bonds. In contrast, the halfoccupied Au 6s AO implies effective Au-Au interaction and the electronic structure of Au atoms remains almost unchanged upon formation of bimetallic bonds. Consequently, clusters enriched in palladium atoms have spin multiplicities that increase with the cluster size while clusters enriched in gold atoms maintain the lowest possible spin multiplicity. Finally, the stability of these systems shows a synergic gain in cohesion for mixed PdnAum clusters compared to their monometallic Pdn and Aum counterparts. The maximal stabilization effect corresponds to n ≈ m, compositions for which the number of mixed Pd-Au bonds is maximized. 1. Introduction Metal clusters are molecular-like entities, formed by assembling a small number of atoms ranging from a few to several hundred. The number of studies concerning their properties has strongly increased in recent years because nowadays metal clusters are widely used in nanotechnologies, as well as in catalysis. In the latter, they may be deposited on a surface (heterogeneous catalysis) or synthesized in solution as small particles surrounded by ligands (homogeneous catalysis).1 Clusters are distinguished from “bulk” by their particular properties, which depend on the size and composition of the system. These differences are mainly linked to quantum size effects and to a surface/volume ratio larger than that observed in the solid state.2 Before studying the catalytic processes, one has to understand the structure and stability of these small clusters. The main goal of this paper is therefore to bring a first insight to this problem considering palladium and gold, as these metals present an interest to the experimental group of our institute. Currently, monometallic palladium3-7 and gold8-13 clusters have been studied by various theoretical methods among which DFT. A growing interest in theoretical modeling of bimetallic clusters has raised specific questions, such as: (1) How do optimal structures change with cluster composition? (2) What are the optimal positions of the atoms in the cluster? Do different metal types mix or segregate within the clusters? (3) How does the cluster depend on the electronic structure of individual atoms? (4) Is there a change in the stability with respect to the * To whom correspondence should be addressed, daniel.peeters@ uclouvain.be.

composition? Answering such questions and predicting properties require a good understanding of the relation between properties and composition of the system. In this work, bimetallic palladium-gold PdnAum clusters with low nuclearity (n + m e 14) have been studied using the density functional theory with the aim to understand the behavior and the evolution of structural, electronic, and energetic properties as a function of size (n + m) and composition (n/m). Mixed clusters have been theoretically studied in earlier contributions, but these studies are generally incomplete and do not take in consideration all possible compositions. A series of papers concerning mixed clusters obtained by a combination of noble metals (Cu, Ag, Au) and platinum group atoms (Ni, Pd, Pt) can be found in the literature. Pd-Au,14-17 Pd-Cu,18 Ni-Au,19 and Pt-Au20 are some typical examples. In the field of catalysis, adsorption of CO on these clusters has also been considered,21-24 not forgetting to mention the interesting work on Pt-Pd25 and Cu-Au26 nanoalloys. These contributions introduce discussions on “homotops” and “mixing energy” which we also include in the present work. While large clusters are simulated by an empirical atomic potential, the small clusters considered here may be studied using ab initio methods. Unlike some of the other contributions mentioned, we will not go through the different clusters by detailing geometric parameters, or other features, one by one, but prefer to consider the results as a whole in order to present a coherent and original study of such materials, integrating the geometric, electronic, and energetic point of view. For the interested reader, the Supporting Information contains the Cartesian coordinates of the lowest energy minima.

10.1021/jp1041298  2010 American Chemical Society Published on Web 09/02/2010

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2. Methodology and Pitfalls The bimetallic palladium-gold clusters were computed using the density functional theory (DFT27). This method was chosen because transition metal clusters present a great number of electrons. DFT allows introducing some of the electronic correlation required to study such systems while maintaining a good quality/computing time ratio. We opted for the B3LYP28 exchange-correlation hybrid functional, which appears to give consistent results for the considered systems. Treating metal clusters requires an appropriate basis set, providing sufficient flexibility to describe as faithfully as possible electronic relocation while limiting the number of electrons and thus allowing computations to be completed in an affordable time. For these reasons the Lanl2DZ29-31 basis set was chosen, which deals explicitly with valence electrons through a split valence polarized basis set, retaining 18 electrons per Pd atom (4s2 4p6 4d10) and 19 electrons per Au atom (5s2 5p6 5d10 6s1). The remaining core electrons are modeled through an effective core potential taking into account some relativistic corrections (RECP). All computations and geometry optimizations were carried out using the Gaussian 03 package.32 The choice of the most adequate functional and ECP remains an open question, with no clear-cut answer. In this study, a series of calculations have been performed combining another functional (BPW91) and pseudopotential (MWB) in order to justify the choice made. A test set has been selected considering the nuclearity m + n ) 4. The energy results are given with comments in the Appendix. Most of the time, the geometry of the most stable structures does not alter significantly, with respect to the functional or pseudopotential used. The B3LYP observed sequences are usually maintained. Only those isomers presenting very close relative energies may be affected by energy sequence inversions. Nevertheless, these do not affect the general discussion nor the evolution of the properties discussed in this publication. A. Structures. All compositions (n/m) were taken into account for each considered nuclearity (n + m). As the number of possible structural isomers grows exponentially with the size of the cluster, it is essential to establish a strategy for exploring the different local potential energy surfaces (PES) that will be considered. The potential energy surfaces of clusters have been explored over a wide variety of geometries build on the various symmetry point groups. This allows locating the main stationary points of low energy, and this for several spin-multiplicities. Furthermore, the presence of two different metals in the system introduces additional complexity due to all the possible permutations of the different atom types in the structure. So, the regular structural isomers are completed by the formation of new isomers obtained by permutation of unlike atoms. For this reason, we have decided to use the term “homotops”,33-36 introduced by Jellinek and co-workers. It describes AaBb cluster isomers, with a fixed number of atoms (N ) a + b) and defined composition (a/b ratio), having further the same geometrical arrangement of atoms but which differ solely by the way Aand B-type atoms are arranged. Considering the number of homotops grows in a combinatorial way with the size of the system, one can imagine the difficulty to find the global minimum during the optimizations. Ignoring point group symmetry, a single geometrical isomer of an N-atom AB cluster will give rise to NPA,B homotops:26 N

PA,B )

N! N! ) NA!NB! NA!(N - NA)!

Zanti and Peeters where N is the total number of atoms, NA is the number of A-type atoms, and NB is the number of B-type atoms. The total number of homotops of any composition for a given structural isomer is 2N. A full relaxation of symmetry constraints during the optimization processes allows for structural distortions, which may introduce further stabilizing effects, such as for example a Jahn-Teller effect, and affect the system. Analytical frequencies were calculated for all stationary points in order to select the true minima. The latter were then collected and used as a starting point for comparing the selected properties. Different spin multiplicities should also be considered, as the palladium atom presents a closed-shell electronic configuration (4d10), and part of its 4d electronic density thus necessarily must be promoted into the nearest orbital, in this case 5s, to enable the formation of stable metal-metal bonds. As a consequence, all palladium clusters and mixed palladium-gold clusters have to be optimized for the various accessible spin multiplicities. This is not the case for pure gold clusters as the single (6s1) electron available in the gold atom valence shell allows stable metal-metal bond formation. Gold clusters thus present only singlet or doublet spin multiplicities depending on the even or odd number of electrons. Finally, to ensure that each identified extremum belongs to its electronic ground state, a stability test of the electronic density was achieved for each spin multiplicity. The many crossings between potential energy surfaces corresponding to different accessible electronic states explain why some published structures and energies may differ from one paper to another even when identical methods and basis set are used. Due to the presence of many “low-lying electronic states” for metal clusters, one must be aware that the result of an optimization will depend on the initial chosen geometry, which selects the potential energy surface on which the system evolves. Due to the number of possible geometries and permutations of different atom types, it is almost impossible to fully explore the potential energy surfaces of the highest nuclearities. However, the large number of structures screened should ensure that the true minima were obtained, which allows analyzing the evolution of structural, electronic, and energetic properties with the size and the composition of bimetallic PdnAum clusters. Looking at higher nuclearities requires other methods such as combination between empirical potentials and DFT (DF-EP approaches) coupled with structural algorithms.37 B. Properties. The evolution of several interesting properties will be discussed in the following section. We briefly recall some useful concepts related to the size and the composition of the clusters. a. AWerage Pair Distances. Pair distances correspond to the distances between all distinct pairs of atoms in the cluster, including nonbonded atoms. For a cluster of nuclearity N, the number of different pair distances is given by

P ) [N(N - 1)/2] The average pair distances (APDs) are thus obtained after summing up all pair distances within the clusters. For bimetallic systems, three types of atom pairs can be found, two homonuclear pairs (Pd-Pd and Au-Au) and one mixed pair (Pd-Au).

PPd-Pd ) [NPd(NPd - 1)/2]

Study of Bimetallic Palladium-Gold Clusters

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PAu-Au ) [NAu(NAu - 1)/2] PPd-Au ) NPdNAu ) P - (PPd-Pd + PAu-Au) where NPd and NAu are the number of Pd and Au atoms, respectively, in the cluster. So for Pd8Au5, we have 78 distinct pairs of atoms, constituted by 28 Pd-Pd pairs, 10 Au-Au, pairs and 40 Pd-Au pairs. These APD values for mixed clusters allow a quantitative evaluation of structural changes with respect to the composition but also of the distribution of different metals within the clusters. A good degree of mixing of the two atom types leads to similar APD for all types of pairs while a perfect segregation of the two metals presents smaller average distances for homogeneous pairs than for mixed pairs. Moreover, high values for (APD)Au-Au when compared to (APD)Pd-Pd are consistent with a PdcoreAushell structure whereas the opposite promotes a AucorePdshell structure. b. Stability. Cluster stability can be evaluated by several means, the most common consisting of computing the energy released during the formation of metal clusters starting from isolated atoms. This leads to the binding energy ∆EB. The latter divided by the nuclearity of the cluster gives the cohesive energy ∆EC of the system. Relations 1 and 2 define these two quantities for PdnAum clusters.

∆EB(PdnAum) ) [EPdnAum - (nEPd + mEAu)]

(1)

∆EC(PdnAum) ) ∆EB(PdnAum)/(n + m)

(2)

where EPd and EAu are palladium and gold atomic ground states energies, respectively. A more direct way to calculate the increased stability of bimetallic PdnAum clusters is given by the mixing energy ∆EMIX (eq 3) where pure Pdn and Aum clusters are considered as a reference.

∆EMIX(PdnAum) ) ∆EC(PdnAum) - [XPd∆EC(Pdn+m) + XAu∆EC(Aun+m)] (3) where XPd and XAu are the Pd[n/(n + m)] and Au[m/(n + m)] fraction in the cluster. Numerical results reported in the next sections refer to 0 K fixed nuclei structures. Corresponding free energies at 298.15K (1 atm.) are given in the Supporting Information file. It must be mentioned here that discussing the free energies does not change the conclusions obtained despite entropic effects. 3. Results and Discussion Structures of the low-lying minima are reviewed, starting by the bare Pdn and Aum clusters, ending with the mixed PdnAum clusters. The lowest minima found are shown on the figures while their main physicochemical characteristics are listed in tables. By low-lying minima we mean only those structures presenting an energy at most 6 kcal · mol-1 (0.01 hartree) above the global minimum. Not much importance is paid to the ordering of those minima as, even though the sequence may slightly change from one functional to the other, the properties discussed here after will not be affected nor will the main conclusions change. A. Pdn and Aum Bare Clusters. Some palladium and gold bare clusters have already been explored using DFT.3-13 We

Figure 1. Most stable structures for Pdn clusters (2 e n e 14).

present and discuss our results hereafter and compare them to those that can be found in the literature. a. Pdn Clusters. Figure 1 shows the lowest minima found for Pdn clusters while Table 1 reports their main physicochemical characteristics. It appears that the most favored structures adopt preferentially deltahedral compact structures, as planar configurations are significantly higher in energy and, usually, do not correspond to minima on PES. The fundamental spin multiplicities are higher than the singlet 4d10 Pd atom. This can be explained by the fact that part of the 4d density is promoted in the 5s orbital to provide stable metal-metal bonds. An analysis of natural atomic populations shows an average 4d(10-x) 5sx electronic configuration of Pd atoms in those clusters with x close to 0.5. Clusters with n ranging from 2 to 7 present a triplet ground state, while a n value between 8 and 10 gives a quintet ground state. A septet ground state is obtained when n ranges between 11 and 14. These results are in good agreement with previous work.3-7 The Pd2 dimer (2.A) presents a triplet ground state while the nearest singlet state lies some 8 kcal · mol-1 above. The atomic population analysis explains this result showing a higher 5s atomic population in the triplet state, resulting in a larger bonding character. Indeed, the natural population analysis gives an occupation of 0.58e- for the 5s orbital compared to 0.09efor the singlet. As the bonding character is mainly defined from the 5s population, its increase will reduce the bond length, as can be seen by comparing the singlet (2.76 Å) and triplet (2.53 Å) states. Linear and triangular geometries were explored for Pd3. The latter are found to be the most stable, while the linear structure corresponds to a transition state. As for dimers, triplet states are located below the singlet states (about 6 kcal · mol-1). The ground state corresponds to the 3B2 state while the 3B1 and

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TABLE 1: Physicochemical Properties of Low Energy Pdn Clustersa cluster

SM

PGS

∆EC

∆EF

APD

cluster

SM

PGS

∆EC

∆EF

APD

2.A 3.A 4.A 5.A 5.B 6.A 7.A 7.B 7.C 8.A 8.B 8.C 8.D 9.A 9.B 9.C 9.D

3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5

D∞h C2V C3V D3h C4V D4h C2 Cs C2 Cs C2 Cs Cs C3 C2 Cs C2

-11.07 -19.66 -28.80 -30.51 -30.00 -32.53 -33.19 -32.86 -32.61 -33.84 -33.80 -33.70 -33.50 -35.26 -34.72 -34.71 -34.61

0 0 0 0 2.58 0 0 2.32 4.05 0 0.31 1.08 2.72 0 4.84 4.94 5.82

2.53 2.62 2.66 2.87 2.87 2.94 3.16 3.18 3.25 3.36 3.52 3.34 3.45 3.52 3.47 3.54 3.55

10.A 10.B 10.C 10.D 11.A 11.B 11.C 11.D 11.E 12.A 12.B 12.C 12.D 13.A 13.B 14.A 14.B

5 5 5 5 7 7 7 7 7 7 7 7 7 7 7 7 9

Ci C1 C1 Cs C2 C1 C1 C2 C1 C2 C2 Cs C1 C3 C1 C2 Cs

-35.88 -35.71 -35.61 -35.56 -36.59 -36.40 -36.34 -36.34 -36.27 -37.37 -37.15 -37.02 -37.01 -38.16 -37.83 -38.46 -38.27

0 1.61 2.64 3.15 0 2.11 2.76 2.78 4.26 0 2.70 4.16 4.31 0 4.28 0 2.55

3.66 3.64 3.64 3.69 3.72 3.71 3.75 3.72 3.73 3.80 3.81 3.83 3.85 3.93 3.91 4.04 3.89

a SM, spin multiplicity; PGS, point group symmetry; ∆EC, cohesive energy in kcal · mol-1 · atom-1; ∆EF, energy difference between the ground state and local minima in kcal · mol-1; APD, average pair distances in Å.

A2 are slightly higher in energy by 0.4 and 1.0 kcal · mol-1, respectively. In contrast to the singlet state, the triplet D3h state shifts to a distorted C2V geometry (65.5° for the apex angle) due to a Jahn-Teller effect (3.A). The 3B2 electronic ground state is also found by Morokuma’s group.38 The most stable structure for Pd4 is a distorted tetrahedron of C3V symmetry (4.A). Results predict that for both triplet and singlet multiplicities the linear, square, and rhomboid planar structures are significantly higher in energy compared to the tetrahedral arrangement. Extensive calculations at the multireference configuration interaction with single and double excitations (MRSDCI) level confirm this finding.39 The most stable structure for Pd5 is a trigonal bipyramid of D3h symmetry (5.A). The squarepyramidal structure (5.B) is about 2.6 kcal · mol-1 higher than the ground state. These structures were confirmed in the work of Morokuma and co-workers at the DFT level.40 Pd6 shows a distorted octahedron ground state with D4h symmetry (6.A). The determination of the ground state for Pd6 is unquestionable as other geometries are significantly higher in energy. This is confirmed by other DFT studies.3-7 For Pd7, the most stable structure seems to be the distorted pentagonal bipyramid of C2 symmetry (7.A). The other structures like capped octahedron (7.B) and the bicapped trigonal bipyramid (7.C) remain however close in energy, 2.3 and 4.1 kcal.mol,-1 respectively. A molecular dynamic study confirms this energetic sequence for Pd7.41 In this approach, any deltahedral structure leads to a minimum but it is difficult to link these minima on a reaction pathway as they often refer to different electronic states. The low energy structures for nuclearities (Pd8-14) are shown in Figure 1 and Table 1 lists the energy difference between these various structures. Let us mention here that the use of another functional or basis set could slightly change the ordering of the listed structures. This justifies why more than one structure is given in Table 1. b. Aum Clusters. Low minima found for Aum clusters are shown in Figure 2 while their main physicochemical characteristics are listed in Table 2. Low nuclearities present planar configurations. These are observed for m values up to 9. A threedimensional transition occurs when pseudoplanar configurations become the favored structures. In our approach, this transition takes place at m ) 10 but the precise size for which gold clusters change from 2D planar structures to 3D structures remains an open question as this transition depends strongly on the method used. Ha¨kkinen et al.42 suggest that planar structures are favored 3

Figure 2. Most stable structures for Aum clusters (2 e n e 14).

until Au13 while Xiao and Wang9 suggest that the 2D-3D structural transition occurs at Au15. However, the recent work of Assadollahzadeh and Schwerdtfeger with the B3PW91 functional43 shows structures similar to ours. Concerning the spin multiplicity, Au atoms, unlike the Pd atom, have a sharable 6s electron able to induce a stable metal-metal bond. This results in low spin multiplicities for the most stable structures, thus showing singlet or doublet spin state according to the even or odd number of atoms in the cluster. In agreement with other DFT studies8-13 no high spin/low energy structures are found. For Au2, a computed bond length of 2.57 Å is obtained, a value in accordance with other DFT studies and slightly longer than the experimental value (2.47 Å).44 For Au3, the lowest-



TABLE 2: Physicochemical Properties of Low Energy Aum Clustersa cluster

SM

PGS

∆EC

∆EF

APD

cluster

SM

PGS

∆EC

∆EF

APD

2.A 3.A 4.A 4.B 5.A 6.A 7.A 7.B 8.A 9.A 9.B 9.C 9.D 9.E 10.A 10.B 10.C 10.D

1 2 1 1 2 1 2 2 1 2 2 2 2 2 1 1 1 1

D∞h C2V C2V D2h C2V D3h Cs C2 D4h C2V C2V C2V C2V Cs D2 Cs D2h C2V

-21.60 -21.15 -27.30 -26.88 -29.54 -34.68 -33.23 -32.44 -36.07 -34.83 -34.61 -34.47 -34.35 -34.27 -36.39 -36.38 -36.32 -36.10

0 0 0 1.69 0 0 0 5.56 0 0 2.02 3.22 4.96 5.05 0 0.50 0.73 2.85

2.57 3.42 3.55 3.10 3.41 3.70 4.01 3.78 4.28 4.39 4.16 4.46 4.47 4.00 4.70 4.21 4.54 4.15

11.A 11.B 11.C 11.D 12.A 12.B 12.C 12.D 13.A 13.B 13.C 13.D 14.A 14.B 14.C 14.D 14.E

2 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 1

Cs Cs D2h Cs Cs C3h Cs Cs Cs Cs Cs C2V Cs C2V Cs Cs Cs

-36.50 -36.12 -35.99 -35.97 -37.38 -37.33 -37.28 -36.92 -37.18 -37.08 -37.00 -36.96 -37.92 -37.83 -37.80 -37.69 -37.68

0 4.23 5.60 5.82 0 0.57 1.20 5.56 0 1.31 2.33 2.91 0 1.24 1.71 3.18 3.38

4.33 4.76 4.95 4.89 4.61 4.88 4.68 4.45 4.76 5.12 4.64 4.79 4.87 4.33 4.79 5.03 4.82

a SM, spin-multiplicity; PGS, point group symmetry; ∆EC, cohesive energy in kcal · mol-1 · atom-1; ∆EF, energy difference between the ground state and local minima in kcal · mol-1; APD, average pair distances in Å.

energy isomer found is an obtuse triangular structure (3.A) with a C2V symmetry presenting a 140.1° angle. This is the structure generally found by DFT studies whatever functional or basis set used, the linear configuration being a second-order saddle point. For Au4, B3LYP-Lanl2DZ calculations predict two nearly degenerate low-energy structures, a rhomboid planar configuration (4.B) and a triangular capped form (4.A), the latter being about 1.69 kcal · mol-1 below the rhomboid form. However, as is often the case for metallic clusters, the use of another functional can invert this order, for example using the PW91 at the GGA level.8,11 Au5 and Au6 adopt W (5.A) and triangular (6.A) planar configurations, respectively. These structures are more stable than other configurations, as agreed upon by various DFT calculations.8-13 Au7 can be formed by adsorption of a Au atom on Au6 either on an edge to give the most stable planar (7.A) configuration with a Cs symmetry or on one side to give a (7.B) pseudoplanar structure with a C2 symmetry lying some 5.56 kcal · mol-1 higher in energy. Au8 presents a very stable planar-capped rhombus configuration with a D4h symmetry (8.A). Capped hexagon and other 3D structures have been considered but all of these structures are higher in energy. Ha¨kkinen et al.13 consider that the lowest structure for Au8 is a capped bioctahedron, but this result is not in agreement with our study or with other DFT studies.8,10,11,43 Starting from Au9, the energy difference between 3D structures and planar configurations becomes very small. The global minimum corresponds to the (9.A) planar isomer but the tetracapped square pyramid (9.B) lies only 2 kcal · mol-1 above. For the higher nuclearities, a family of pseudoplanar structures based on a multicapped square pyramid or trigonal prism can be found. Such structures seem to be very good candidates for ground states, and they were not introduced in earlier works8-13 except in the recent work of Assadollahzadeh43 et al., which is in good agreement with our results. All of these peculiar structures are reported in Figure 2. B. Monosubstituted Clusters. a. PdnAu1 Clusters. In general, the substitution of one Au atom for Pd in pure clusters leading to Pdn-1Au1 leads to most stable structures close to those obtained for the pure species. These clusters are shown in Figure 3, and their main physicochemical properties are listed in Table 3. In all cases, gold is located in a capped position, the position with the lowest coordination either on a face or on an edge of

Figure 3. Most stable structures for monosubstituted PdnAu1 clusters (1 e n e 13).

the palladium cluster. As Au is more electronegative than the Pd atom, it receives a negative charge. The dimer Pd1Au1 presents a bond length (2.56 Å) and a spinmultiplicity (2) intermediate to those of pure Pd2 and Au2. Considering the mixing energy, the formation of the heteronuclear species from pure diatomics is slightly stabilizing (-1.68 kcal · mol-1), so as suggested by a slight electronegativity difference between these two elements, the heterodiatomic bond is favored. The most stable structure found for Pd2Au1 maintains the C2V triangular symmetry. For this nuclearity, the stability gain compared to pure clusters is more important than for the dimer (∆EMIX ) -5.58 kcal · mol-1). Looking at the subsequent

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TABLE 3: Physicochemical Properties of Low Energy Pd(n-1)Au1 Clustersa APD

APD

cluster

SM

PGS

∆EC

∆EF

∆EMIX

Pd-Pd

Pd-Au

cluster

SM

PGS

∆EC

∆EF

∆EMIX

Pd-Pd

Pd-Au

2.A 3.A 4.A 5.A 5.B 5.C 6.A 6.B 6.C 6.D 7.A 7.B 7.C 8.A 8.B 8.C 8.D

2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4

C∞V C2V C3V C2V C4V C3V C4V Cs Cs Cs Cs Cs C1 Cs C2V C1 Cs

-18.02 -25.74 -30.03 -31.14 -30.93 -30.75 -32.38 -31.93 -31.91 -31.78 -34.06 -33.87 -33.61 -34.91 -34.85 -34.82 -34.76

0 0 0 0 1.06 1.95 0 2.67 2.81 3.61 0 1.18 3.10 0 0.54 0.77 1.27

-1.68 -5.58 -1.61 -0.82 -0.61 -0.43 0.51 0.95 0.97 1.11 -0.86 -0.69 -0.42 -0.79 -0.73 -0.70 -0.64

2.57 2.66 2.99 3.01 2.76 2.99 2.90 2.93 3.20 2.95 2.97 3.07 3.20 3.16 3.29 3.23

2.56 2.67 2.76 2.80 2.79 3.12 2.98 3.92 3.38 2.83 4.04 3.91 3.87 4.28 4.50 4.31 4.02

9.A 9.B 9.C 9.D 10.A 10.B 10.C 10.D 11.A 11.B 11.C 12.A 12.B 13.A 13.B 14.A 14.B

4 4 4 4 4 4 4 4 6 6 6 6 6 6 6 6 8

Cs Cs C1 C1 Cs C1 Cs C1 C1 C1 C1 C1 C1 Cs Cs C2 C2V

-35.90 -35.74 -35.50 -35.39 -36.45 -36.31 -36.24 -36.04 -37.34 -37.18 -37.14 -37.94 -37.74 -38.47 -38.36 -38.92 -38.87

0 1.47 3.64 4.64 0 1.41 2.06 4.08 0 1.78 2.21 0 2.31 0 1.33 0 0.67

-0.70 -0.53 -0.29 -0.18 -0.52 -0.38 -0.32 -0.11 -0.75 -0.59 -0.55 -0.56 -0.37 -0.38 -0.27 -0.50 -0.45

3.45 3.31 3.35 3.35 3.53 3.46 3.48 3.46 3.64 3.62 3.60 3.77 3.80 3.84 3.90 3.96 4.09

3.89 4.45 3.94 4.13 4.20 4.43 4.67 4.63 4.23 4.46 4.51 4.37 4.10 4.54 4.34 4.72 4.44

a SM, spin-multiplicity; PGS, point group symmetry; ∆EC: cohesive energy in kcal · mol-1 · atom-1; ∆EF, energy difference between the ground state and local minima in kcal · mol-1; ∆EMIX, mixing energy in kcal · mol-1 · atom-1; APD (Pd-Pd), average Pd-Pd pair distances in Å; APD (Pd-Au), average Pd-Au pair distances in Å.

nuclearities, the geometries remain close to those of pure Pdn clusters. The cohesive energy evolves as shown on the first graph of Figure 5 for pure Pdn and monosubstituted PdnAu1 clusters. As expected, the cohesive energy gets more exothermic with increasing nuclearity. Optimizations carried out for sizes up to 40 atoms47 by molecular dynamics using a Lennard-Jones type potential show that the limit of the cohesive energy is far from being achieved with a nuclearity of 14. An extrapolation obtained from the data of Table 3 leads to a -41.9 kcal · mol-1 limit. It appears that for any given nuclearity, the cohesive energy is always more exothermic for monosubstituted PdnAu1 clusters (gray curve) than for pure Pdn clusters (black curve). On the other hand, excluding the three first stoichiometries, the mixing energy is small and slightly stabilizing, with one exception, Pd5Au1 where ∆EMIX ) +0.51 kcal · mol-1. b. Pd1Aum Clusters. The introduction of a single Pd atom in gold clusters is sufficient to shift the 2D-3D transition to lower nuclearities. The transition occurs now for an 8-atom cluster (Pd1Au7) instead of 10 (Au10). Moreover, the palladium atom moves close to the center of the structure with, for the highest nuclearities, deviation from planarity near this Pd center. These trends are shown in Figure 4 where low-energy Pd1Aum clusters are presented with their main physicochemical properties listed in Table 4. For nuclearities up to 6, the most stable structure remains planar and adopts the geometry of pure Aum, with one exception for Pd1Au6 where a D6h symmetry hexagon centered on Pd becomes the lowest energy configuration. Starting from Pd1Au7, most stable structures adopt a three-dimensional, but not compact, configuration in order to meet a compromise: maximizing interactions with Pd while retaining local planarity between Au atoms. The cohesive energy is illustrated on the second graph of Figure 5. As mentioned previously for monosubstituted PdnAu1 clusters, Pd1Aum clusters retain a geometry relatively close to pure Aum clusters. The observed oscillations are due to the alternation between less stable openshell and more stable closed-shell configurations. This oscillation is such that the cohesive energy favors Au8 over Pd1Au7, the same effect being seen in Pd1Au5 and Pd1Au9. A study at GGAplane wave level with a scalar relativistic pseudopotential14 reveals similar structures for Pd1Aum clusters (m ) 1, 4). A density-functional study of small gold clusters doped by one atom of the platinum group elements (M1Aum; M ) Ni, Pd,

Figure 4. Most stable structures for monosubstituted Pd1Aum clusters (1 e m e 13).

Pt; m ) 1-7) undertaken at the GGA-PW91 level with a triple-ζ basis set including polarization functions19 shows comparable geometries for the three doping metals. Some differences appear with respect to our results as the 3D-Pd1Au7 structure found in this work is more stable than the planar capped-hexagon structure centered on the Pd atom. The difference between these two states is however very small (0.13 kcal.mol-1) presuming a high flexibility of such structures and an important mixing of various configurations at room temperature. C. Mixed Clusters PdnAum (n, m g 2). a. Structural Aspects. All global minima found for mixed PdnAum clusters are presented in Figure 6 while Table 5 lists the main



TABLE 4: Physicochemical Properties of Low Energy Pd1Aum Clustersa APD cluster

SM

PGS

∆EC

∆EF

∆EMIX

Pd-Au

2.A 3.A 4.A 4.B 5.A 6.A 7.A 7.B 7.C 8.A 8.B 8.C 9.A 9.B

2 1 2 2 1 2 1 1 1 2 2 2 1 1

C∞V C2V C2V Cs C2V C2V D6h Cs Cs Cs C2V C2V C2V D2h

-18.02 -26.05 -28.38 -27.60 -31.15 -34.20 -35.42 -35.00 -34.91 -35.27 -35.25 -35.24 -37.19 -36.39

0 0 0 3.09 0 0 0 2.91 3.57 0 0.13 0.26 0 7.15

-1.68 -5.40 -0.70 0.07 -1.42 0.12 -2.19 -1.78 -1.68 0.53 0.54 0.56 -2.31 -1.51

2.56 2.68 2.76 3.25 2.76 3.18 2.77 3.88 3.14 3.13 3.06 3.64 3.35 3.25

Au-Au 2.73 3.36 3.56 3.85 3.94 4.13 3.73 3.72 3.92 4.44 4.40 4.13 4.74

APD cluster

SM

PGS

∆EC

∆EF

∆EMIX

Pd-Au

Au-Au

10.A 10.B 10.C 10.D 11.A 11.B 11.C 12.A 12.B 12.C 13.A 13.B 14.A 14.B

2 2 2 2 1 1 1 2 2 2 1 1 2 2

Cs C1 Cs C2V Cs C2V C1 C1 Cs Cs Cs Cs Cs C1

-36.50 -36.38 -36.33 -36.13 -37.76 -37.61 -37.59 -37.78 -37.42 -37.11 -38.60 -38.50 -38.76 -38.13

0 1.17 1.71 3.75 0 1.56 1.78 0 4.23 7.95 0 1.29 0 8.89

-0.16 -0.05 0.01 0.21 -1.24 -1.10 -1.08 -0.39 -0.04 0.27 -1.34 -1.24 -0.80 -0.17

3.31 3.43 4.13 4.74 3.94 3.23 3.56 3.39 3.22 3.23 3.34 3.81 3.44 3.44

4.37 4.25 4.11 4.66 4.38 4.49 4.28 4.76 4.37 4.52 4.62 4.85 4.81 4.74

a SM, spin-multiplicity; PGS, point group symmetry; ∆EC, cohesive energy in kcal · mol-1 · atom-1; ∆EF, energy difference between the ground state and local minima in kcal · mol-1; ∆EMIX, mixing energy in kcal · mol-1 · atom-1; APD (Pd-Au), average Pd-Au pair distances in Å; APD (Au-Au), average Au-Au pair distances in Å.

Figure 5. Evolution of cohesive energy for pure (Pdn and Aum) and monosubstituted (PdnAu1 and Pd1Aum).

physicochemical properties. Most of these have never been studied in the literature. As can be seen, the sharp geometrical difference between Pdn and Aum clusters leads to a strong dependence of bimetallic PdnAum clusters on composition (n/ m). As could be expected the structure of the most stable bimetallic clusters is intermediate between the bare clusters. In fact, DFT calculations show that those rich in palladium prefer 3D structures where the gold atoms are separated from each other and in capped positions around a compact palladium core.

Such positions present the lowest coordination. On the other hand, an increasing gold content promotes planar configurations with deviation from planarity near Pd centers. It is worthwhile mentioning that when two Pd atoms are present in the cluster, all global minima are three-dimensional. Finally, for almost balanced compositions (n ≈ m), the situation gets more complicated but the most stable structures tend to meet a compromise, maximizing the number of mixed Pd-Au bonds while minimizing the average coordination number of gold atoms. To summarize, a certain degree of mixing between Pd and Au stabilizes the clusters. Full segregation minimizing Pd-Au links is clearly not favorable, neither is random mixing. Some local structuration appears where the most stable configuration is obtained by a core-shell system, Pd atoms forming the core surrounded by a shell of Au atoms. A global vision of all minima allows appreciating the structural transition that takes place when moving from compact Pdn three-dimensional structures to planar Aum configurations. For the trimers, all stable structures adopt triangular C2V geometries but the apex 140.1° angle for Au3 is much larger than that for palladium containing clusters (61.3°, 57.5°, 65.5° for Pd1Au2, Pd2Au1, and Pd3, respectively). Rhombic and “triangular plus one atom” planar configurations as well as tetrahedral geometries were tested for the tetramers. The first two are higher in energy for clusters rich in palladium (Pd4, Pd3Au1 and Pd2Au2) but Pd1Au3 and Au4 prefer planar configurations. For Au4, both planar structures are very close in energy (∆E ) 1.69 kcal · mol-1). Thus, the replacement of one Au atom in Au4 to form Pd1Au3 favors the C2V rhombic geometry where the palladium atom occupies the most coordinated position. Further substitution brings the rhombic form close to a tetrahedron with C2V symmetry for Pd2Au2. Nevertheless, Pd2Au2 presents also a pseudoplanar form lying 3.08 kcal · mol-1 above the tetrahedral geometry (not presented here). Finally, Pd3Au1 and Pd4 are exclusively tetrahedral with C3V symmetry. No stable planar conformations are found for these compositions. The same reasoning applies to higher nuclearities. The fiveatom clusters present a structural transition from the planar trapezoid like C2V configuration of Au5 to the compact TBP of Pd5. The two atoms located at the apexes of the trapezium geometry move out of plane through a simple normal mode of vibration, going to the original bipyramid found when the composition is enriched in Pd atoms. It is therefore not surprising to see that the most stable structure obtained for Pd2Au3 adopts

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Figure 6. Most stable structures for mixed PdnAum clusters (2 e n e 12; 2 e m e 12; 4 e n + m e 14).

a pseudoplanar trapezoid configuration intermediate to those of Pd5 and Au5 pure clusters. Other isomers like square pyramid configurations can be found. For six- and seven-atom clusters, the transition occurs from the D3h planar configuration (Au6) to the octahedron (Pd6) and from the Cs planar configuration (Au7) to the pentagonal bipyramid (Pd7), respectively. At higher nuclearities, the analysis becomes more complex as the number of accessible geometries at low energies gets larger; nevertheless the structural transition can still be seen in Figure 6. The evolution of the structure with the composition for higher nuclearities (10 e n + m e 14) is different. For these nuclearities the most stable structures are obtained from the assembly of capped octahedrons, structures very rich in Pd or Au atoms being exceptions. Looking at the literature, small PdnAum (n ) 1-4; m ) 1-4) clusters were studied with the same methodology (B3LYPLanl2DZ).15-17 The low energy structures found are similar to ours except for Pd2Au3 and Pd3Au2 where the TBP geometry is presented as the most stable. This is probably due to the fact that structures intermediate to Au5 and Pd5 were not tested. This illustrates once again the difficulties encountered when studying systems whose geometry depends greatly on the composition, as is the case for PdnAum clusters. Finally, contributions on mixed PtnAum20 and PdnCum18 clusters taking into account all the compositions show an analogous structural transition between planar configurations for noble metal clusters and 3D compact structures for platinum group elements. In order to conclude this structural section, the average pair distances are shown in Figure 7 for (n + m) ) 13, and the discussion presented hereafter can easily be extended to other nuclearities. Globally, it appears that average Au-Au pair

distances are much larger than average Pd-Pd pair distances. This result is consistent with a structure centered on a compact palladium core surrounded by a shell of gold atoms in capped positions. These distances decrease when the composition of the cluster is enriched in Au atoms. For Pd-Pd distances, this is due to a decrease in the size of the Pd core as Au atoms replace the Pd atoms. On the other hand, the Au-Au distances decrease because Au atoms, which are separated from each other in Pd enriched clusters, get closer to each other with the enrichment in Au atoms. Values for mixed Pd-Au pairs are intermediate. The evolution of the global average pair distances (i.e., no distinction between the two metal types) with the composition for the higher nuclearities (10 e n + m e 14) is reported in Figure 8. An increase of the average pair distance with the gold contents indicates an evolution to less compact structures when Au atoms substitute Pd atoms. b. Spin-Multiplicities and Charges. The formation of stable metal bonds requires the presence of nonpaired electrons. For this reason, part of the 4d electron density of the palladium atom, which presents a closed-shell 4d10 ground state, should be promoted to its empty 5s orbital. This is not the case for the gold atom, which has an unpaired electron available in its 6s orbital and allows for the formation of metal-metal bonds. Considering dimers as an example shows that, according to the natural population analysis (NAO),45,46 the electronic structure of the Pd atom in PdAu (5s0.40 4d9.33) is highly excited with respect to its atomic ground state and is close to Pd2 in its triplet state (5s0.58 4d9.41) while the Au atom maintains almost the same orbital populations as those observed in Au2. A small electron transfer (0.24e-) from Pd is found. Globally, atomic populations remain almost constant whatever the composition, with a well-



TABLE 5: Physicochemical Properties of Low Energy PdnAum Clustersa APD

APD

cluster

SM

PGS

∆EC

∆EMIX

Pd-Pd

Pd-Au

Au-Au

cluster

SM

PGS

∆EC

∆EMIX

Pd-Pd

Pd-Au

Au-Au

Pd2Au2 Pd3Au2 Pd2Au3 Pd4Au2 Pd3Au3 Pd2Au4 Pd5Au2 Pd4Au3 Pd3Au4 Pd2Au5 Pd6Au2 Pd5Au3 Pd4Au4 Pd3Au5 Pd2Au6 Pd7Au2 Pd6Au3 Pd5Au4 Pd4Au5 Pd3Au6 Pd2Au7 Pd8Au2 Pd7Au3 Pd6Au4 Pd5Au5 Pd4Au6 Pd3Au7 Pd2Au8 Pd9Au2 Pd8Au3 Pd7Au4 Pd6Au5 Pd5Au6

1 3 2 3 2 3 3 4 3 2 3 4 3 2 1 3 4 3 2 3 2 5 6 5 4 3 2 1 5 6 5 4 3

C2V C2 C2 C2V Cs C2V Cs C2V Cs C2V C1 C2 C2V C2V Cs C1 Cs Cs C2V C2 C1 C2V C3V C2V C2V C2V C2 D2d C1 Cs Cs Cs Cs

-28.90 -31.69 -31.15 -33.30 -33.38 -33.30 -34.72 -35.10 -35.49 -35.78 -35.53 -36.43 -36.48 -36.54 -36.33 -36.33 -37.22 -37.33 -37.48 -37.30 -37.35 -37.25 -38.39 -38.87 -39.07 -39.22 -38.74 -38.47 -7.81 -38.50 -39.21 -39.39 -39.25

-0.86 -1.56 -1.21 -0.06 0.22 0.65 -1.52 -1.89 -2.28 -2.56 -1.13 -1.75 -1.52 -1.31 -0.82 -1.17 -2.10 -2.26 -2.46 -2.32 -2.43 -1.27 -2.36 -2.79 -2.94 -3.04 -2.51 -2.18 -1.23 -1.93 -2.65 -2.84 -2.71

2.84 2.68 2.63 2.77 2.69 2.90 2.95 2.79 2.73 2.55 3.23 2.97 3.03 2.68 2.70 3.40 3.06 3.27 3.07 2.85 2.67 3.41 3.26 3.10 3.07 3.16 3.17 4.00 3.54 3.44 3.28 3.23 3.50

2.72 2.82 3.21 3.23 3.18 3.25 3.35 3.37 3.29 3.26 3.50 3.44 3.35 3.53 2.98 3.62 3.76 3.63 3.53 3.24 3.49 4.20 4.01 3.78 3.67 3.50 3.47 3.35 4.11 3.99 3.88 3.81 3.65

2.89 4.73 3.57 4.99 4.29 4.35 5.09 5.24 4.32 3.90 5.10 5.19 4.21 3.93 4.00 5.49 5.43 4.26 4.00 4.26 4.29 5.41 5.43 5.48 4.83 4.57 4.27 4.11 5.12 5.43 5.49 4.84 4.51

Pd4Au7 Pd3Au8 Pd2Au9 Pd10Au2 Pd9Au3 Pd8Au4 Pd7Au5 Pd6Au6 Pd5Au7 Pd4Au8 Pd3Au9 Pd2Au10 Pd11Au2 Pd10Au3 Pd9Au4 Pd8Au5 Pd7Au6 Pd6Au7 Pd5Au8 Pd4Au9 Pd3Au10 Pd2Au11 Pd12Au2 Pd11Au3 Pd10Au4 Pd9Au5 Pd8Au6 Pd7Au7 Pd6Au8 Pd5Au9 Pd4Au10 Pd3Au11 Pd2Au12

2 1 2 5 6 5 4 3 2 1 2 1 7 6 5 4 5 4 3 2 1 2 7 6 7 6 5 4 3 2 1 2 1

Cs C1 C1 Cs Cs C2V C2V C1 C2V Cs C2 C2 Cs Cs Cs Cs Cs C1 Cs Cs Cs C1 C2V C2V Cs C2V Cs C2 Cs C2 C3 Cs C1

-38.91 -38.55 -37.97 -38.40 -38.95 -39.77 -39.86 -39.87 -39.87 -39.55 -39.18 -38.92 -39.11 -39.66 -40.05 -40.06 -40.15 -40.28 -40.17 -39.89 -39.70 -39.00 -39.71 -40.09 -40.53 -40.95 -40.90 -40.94 -40.81 -40.64 -40.39 -39.45 -39.29

-2.37 -2.02 -1.45 -1.03 -1.58 -2.39 -2.49 -2.49 -2.49 -2.17 -1.81 -1.54 -1.09 -1.72 -2.19 -2.28 -2.44 -2.65 -2.61 -2.41 -2.30 -1.67 -1.33 -1.75 -2.23 -2.68 -2.67 -2.75 -2.66 -2.53 -2.31 -1.42 -1.29

3.30 3.49 2.73 3.62 3.61 3.56 3.38 3.28 3.25 3.10 3.22 4.15 3.87 3.82 3.88 3.74 3.42 3.29 3.22 3.07 2.89 2.67 4.09 4.07 3.82 3.59 3.51 3.47 3.37 3.34 3.79 3.35 3.67

3.57 3.51 3.66 4.35 3.94 3.82 3.85 3.79 3.69 3.58 3.87 3.69 4.22 4.16 3.97 4.04 4.04 3.91 3.85 3.67 3.52 3.68 4.33 4.23 4.39 4.31 4.24 4.11 4.03 3.92 4.00 3.95 3.82

4.47 4.27 4.38 4.70 5.02 5.14 4.75 4.56 4.45 4.38 4.60 4.51 5.45 5.16 5.09 4.75 4.95 4.87 4.67 4.64 4.54 4.73 5.47 5.60 5.58 5.92 5.46 5.25 5.04 4.91 4.55 4.63 4.80

a SM, spin-multiplicity; PGS, point group symmetry; ∆EC, cohesive energy in kcal · mol-1 · atom-1; ∆EMIX, mixing energy in kcal · mol-1 · atom-1; APD (Pd-Pd), average Pd-Pd pair distances in Å; APD (Pd-Au), average Pd-Au pair distances in Å; APD (Au-Au), average Au-Au pair distances in Å.

Figure 7. Evolution of the average Pd-Au, Pd-Pd, and Au-Au pair distances with the number of Au atoms (m) for PdnAum with (n + m) )13.

Figure 8. Evolution of the global average pair distances with the number of Au atoms (m) for the higher nuclearities (10 e n + m e 14).

occupied 5s population for Pd atoms (∼0.4-0.5 e-). Consequently, Pdn clusters are characterized by spin-multiplicities that increase with the size of the system while Aum clusters present exclusively singlet or doublet spin-states. In the case of bimetallic PdnAum clusters, the spin-multiplicity ground state will depend on their composition. The higher the palladium contents, the higher the spin-multiplicity and vice versa. Smaller clusters studied in previous works15-17 show similar trends. As for other properties, the charge distribution in bimetallic clusters depends on the composition. For clusters rich in

palladium, the NAO population analysis confirms that the negative charges are exclusively localized on gold atoms situated in capped positions with palladium being slightly positive. When the palladium core decreases in size by gold substitution, the situation changes and the positive charges of the palladium core decrease, and finally reverse. For clusters enriched in Au, the negative charges are located on the few Pd atoms and on Au atoms with low coordination while the positive charges are found on the other Au atoms. The excess of electron density is localized mainly on low-coordinated atoms. Figure 9 illustrates

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Figure 9. Evolution of average charges of Pd and Au according to the gold composition (m) in PdnAum clusters (10 e n + m e 14). Figure 11. Evolution of mixing energy PdnAum (10 e n + m e 14) clusters as function of their composition.

Figure 10. Evolution of PdnAum (3 e n + m e 14) clusters stability as function of their composition.

this behavior by the evolution of the average charges of palladium and gold atoms in PdnAum clusters as a function of the composition of the system. As shown, the general trend remains the same for all nuclearities. The oscillations seen for the clusters with a high gold content are linked to the alternation of open-shell and closed-shell species. As the magnitude of the atomic charge does not only depend on the atoms position within the cluster but also on its structure, a simple linear dependency of atomic charges with the Pd/Au ratio cannot be expected. c. Stability. The dependence of the cohesive energy with the composition of bimetallic clusters is reported in Figure 10 for all considered nuclearities. As expected, the cohesive energy is increasingly negative with the size of the cluster. However, the gain in energy becomes less important as the cluster size increases with as limit the surface/volume ratio of the bulk. Work focusing on clusters of higher nuclearities47 shows nevertheless that this limit is not reached in our case. The most important feature is the increased stability of PdnAum clusters with respect to the Pdn and Aum monometallic clusters (except for m + n ) 6). In other words, this indicates that PdnAum clusters are favored energetically with respect to the same size pure Pdn and Aum clusters. The group of Efremenko has already shown a similar behavior for small Pd-Cu clusters.18 The evolution of the mixing energy with the composition is presented for high nuclearities (10 e n + m e 14) in Figure 11. The small change in geometry with the composition for these nuclearities, as shown in Figure 6, ensures that the gain in stability is primarly due to a variation in composition and not

Figure 12. Evolution of the number of mixed bonds with the composition for the lowest-energy PdnAum clusters (m + n ) 12, 13, and 14). (A cutoff bond length of 3.2 Å is considered for Au-Pd bonds.)

to a change in geometry. A parabolic trend is observed where the synergic stabilization is maximized for clusters with a nearly balanced composition (XAu ≈ 0.5-0.6). It is interesting to note that such behavior is not found for mixed PtnAum clusters.20 On the other hand, a study of 38-atom clusters shows that this synergetical effect is more pronounced for Ag-Au, Pd-Pt, and Ag-Pt binary clusters.48 Looking at the different nuclearities, it is easy to see that the mixing energy of PdnAum clusters is independent of the cluster size. For one given composition, similar mixing energies are observed for all nuclearities. This parabolic behavior is linked to the number of mixed Pd-Au bonds as highlighted in Figure 12. It is clear that the stability is maximized when the number of mixed bonds increases. In order to illustrate the strong dependence of the stability with the structure, a study of the cohesive energy depending on the atomic positions within the clusters was carried out for a series of Pd7Au7 homotops. A single point calculation was made for each homotop in a geometry very close to that of the ground state with a D3h symmetry. The results for the 320 homotops obtained are illustrated in Figure 13. This study reveals that the most stable structures correspond to those where the average Au-Au pair distance is maximized and Pd-Pd minimized, in other words, the PdcoreAushell structures. On the other hand, structures adopting the opposite configuration (AucorePdshell) are less stable, while full segregation and random mixing present intermediate values.



Figure 13. Evolution of the cohesive energy with average pair distances in Pd7Au7 homotops.

Conclusions In this study we have shown a continuous and logical evolution of structural, electronic and energetic properties of bimetallic PdnAum clusters of small size (n + m e 14) with their composition. The main observations are as follows: I. On one hand, clusters enriched in Pd prefer 3D structures similar to those of monometallic Pdn clusters. These structures present Au atoms separated from each other and located on capped positions. On the other hand, increasing Au content favors planar shapes with deviation from planarity near Pd centers. For more balanced compositions (n ≈ m), the most stable structures seem to meet a compromise where the number of mixed Pd-Au bonds is maximized while the average coordination number of Au atoms is minimized. For the smaller clusters (n + m e 7), the structural transition with the composition seems to be continuous.

II. For a given nuclearity, the ground state spin multiplicity increases with the Pd content. This is due to the closed-shell electronic configuration of Pd atoms for which a part of the 4d electronic density must be promoted to the 5s orbital to achieve stable metal-metal bonds. For this reason, the higher nuclearities present a continuous evolution of the spin multiplicity with the composition. III. The charge distribution depends mainly on the structure and composition. The excess of electron density is preferentially confined on low-coordinated atoms. IV. PdnAum mixed clusters show an increased stability compared to the pure Pdn and Aum clusters. The evolution of stability with the composition shows a parabolic trend with a maximization of the synergic effect for balanced compositions (XPd ≈ 0.5), which seems independent on the cluster size. V. The synergic stabilization for the nearly balanced compositions is linked to the number of mixed Pd-Au bonds wich is maximized for these compositions. Therefore, a trend appears when the most stable configuration is obtained by a core-shell system: Pd atoms forming the core and Au atoms forming the shell. Acknowledgment. This work was supported by FRIA-F.NRS (Fonds pour la Formation a` la Recherche dans l’Industrie et dans l’Agriculture-Belgium, fellowship to G.Z.), and F.R.S.-FNRS by its support to access computational facilities (Project FRFC No. 2.4502.05 “Simulation nume´rique. Application en physique de l’e´tat solide, oceánographie et dynamique des fluides”). Appendix The B3LYP hybrid functional is a popular density functional used in computational chemistry. In the case of spin state

TABLE 6: Comparison between Results Obtained with Two Functionals (B3LYP/BPW91) and Two Pseudopotentials (LANL2DZ/MWB)a B3LYP LANL2DZ

MWB

cluster

SM

E

∆Ec

E

∆Ec

Au4_A Au4_B Pd1Au3_A Pd1Au3_B Pd2Au2 Pd2Au2 Pd3Au1_A Pd3Au1_A Pd4_A Pd4_A

1 1 2 2 1 3 2 4 3 1

-541.93317 -541.93047 -533.20701 -533.20209 -524.47730 -524.47238 -515.75152 -515.71060 -507.01061 -506.97767

-27.30 -26.87 -28.38 -27.60 -28.90 -28.13 -30.03 -23.62 -28.80 -23.63

-543.19234 -543.19131 -535.32777 -535.32198 -527.45898 -527.45100 -519.59721 -519.56085 -511.72263 -511.69579

-27.11 -26.94 -27.73 -26.82 -27.68 -26.43 -28.74 -23.04 -27.79 -23.58

BPW91 LANL2DZ

a

MWB

cluster

SM

E

∆Ec

E

∆Ec

Au4_A Au4_B Pd1Au3_A Pd1Au3_B Pd2Au2 Pd2Au2 Pd3Au1_A Pd3Au1_A Pd4_A Pd4_A

1 1 2 2 1 3 2 4 3 1

-542.17272 -542.17190 -533.44135 -533.43536 -524.71031 -524.70213 -515.97923 -515.94166 -507.23663 -507.21249

-30.84 -30.71 -32.95 -32.01 -35.12 -33.83 -37.27 -31.38 -37.62 -33.84

-543.51023 -543.51098 -535.62651 -535.61917 -527.74238 -527.73676 -519.86228 -519.82766 -511.97261 -511.94832

-30.56 -30.68 -32.38 -31.23 -34.13 -33.25 -36.52 -31.09 -37.41 -33.60

SM, spin-multiplicity; E(0 K, F.N.) in hartree; ∆EC, cohesive energy in kcal · mol-1 · atom-1.

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splitting it is known that problems arise with hybrid functionals overstabilizing high spin states. GGA functionals on the other hand tend to artificially overstabilize low spin states. Despite the pertinent analysis on the accuracy of density functional theory in transition metal chemistry found in Harvey’s paper,49 the absence of a general guideline as to which functional to use led us to check and compare the performances of B3LYP and BPW91, another functional commonly used in atomic clusters. The quality of pseudopotentials constitutes another open question for elements such as gold and palladium. We have opted in this paper for the often-used Los Alamos LANL2DZ. Other RECPs have been developed for heavy elements, among these the Stuttgart group offers many high-quality pseudopotentials. For comparison purposes, we have chosen their quasirelativistic MWB potential.50 Nuclearity four has been chosen to test the results obtained at B3LYP/LANL2DZ level and the corresponding energy results are presented in Table 6 after full reoptimization of the structures. Main conclusions are: Only marginal structural modifications are observed. LANL2DZ and MWB give very close results whatever functional being used. BPW91 increases slightly the reaction energies, but the ordering of the structures remains. The relative stabilization of the clusters is maintained, with one slight restriction for Au4. The latter, as mentioned in the main text, present two almost isoenergetic structures. No inversion of spin states was found. Therefore, the results further discussed in this paper, will be limited to the B3LYP/LANL2DZ method. Supporting Information Available: Reports of the required energy information for each studied cluster, i.e., at the DFT B3LYP level using the LANL2DZ pseudopotential, optimized energy; corresponding Gibbs free energy; cohesive free energy and mixing free energy; and the Cartesian coordinates for the studied clusters. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Pignolet, L. H.; Aubart, M. A.; Craighead, K. L.; Gould, R. A. T.; Krogstad, Don A.; Wiley, J. S. Coord. Chem. ReV. 1995, 143, 219–263. (2) Sattler, K.; Mu¨hlback, J.; Recknagel, E. Phys. ReV. Lett. 1980, 45, 821–824. (3) Nava, P.; Sierka, M.; Ahlrichs, R. Phys. Chem. Chem. Phys. 2003, 5, 3372–3381. (4) Luo, C.; Wu, J.; Kumar, T. J. D.; Balakrishnan, N.; Forrey, R. C.; Cheng, H. Int. J. Quantum Chem. 2007, 107, 1633–1641. (5) Zhang, W.; Ge, Q.; Wang, L. J. Chem. Phys. 2003, 118, 5793– 5801. (6) Moseler, M.; Hakkinen, H.; Barnett, R. N.; Landman, U. Phys. ReV. Lett. 2001, 86, 2545–2548. (7) Zacarias, G.; Castro, M.; Tour, M.; Seminario, M. J. Phys. Chem. A 1999, 103, 7692–7700. (8) Walker, A. V. J. Chem. Phys. 2005, 122, 094310. (9) Wang, J.; Wang, G.; Zhao, J. Phys. ReV. B 2002, 66, 035418. (10) Xiao, L.; Tollberg, B.; Hu, X.; Wang, L. J. Chem. Phys. 2006, 124, 114309. (11) Li, X. B.; Wang, H. Y.; Yang, X. D.; Zhu, Z. H.; Tang, Y. J. J. Chem. Phys. 2007, 126, 084505. (12) Bulusu, S.; Zeng, X. C. J. Chem. Phys. 2006, 125, 154303. (13) Hakkinen, H.; Landman, U. Phys. ReV. B 2000, 62, 2287–2290. (14) Sahu, B. R.; Maofa, G.; Kleinman, L. Phys. ReV. B 2003, 67, 115420.

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