Computational and Theoretical Chemistry 966 (2011) 375–382

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Computational and Theoretical Chemistry

journal homepage: www.elsevier .com/locate /comptc

A DFT investigation of the effects of doped Pb atoms on Pdn clusters (13 6 n 6 116)

Lu Wei a,b, Xiaoqian Yao b, Xiao Tian b, Meijuan Cao a, Wenkai Chen c, Yuanbin She a,⇑, Suojiang Zhang b,⇑a Institute of Green Chemistry and Fine Chemicals, Beijing University of Technology, 100124 Beijing, Chinab State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, 100190 Beijing, Chinac Department of Chemistry, Fuzhou University, 350108 Fuzhou, China

a r t i c l e i n f o

Article history:Received 24 January 2011Received in revised form 26 March 2011Accepted 26 March 2011Available online 1 April 2011

Keywords:Pd–Pb clusterPd clusterDFTGeometryElectronic properties

2210-271X/$ - see front matter � 2011 Elsevier B.V.doi:10.1016/j.comptc.2011.03.041

⇑ Corresponding author.E-mail addresses: sheyb@bjut.edu.cn (Y. She),

Zhang).

a b s t r a c t

Basic properties of cuboctahedral Pd–Pb clusters ranging from 13 to 116 atoms were studied by compu-tational analysis, and the effects of doped Pb atoms on Pd clusters were investigated. The average bondlength of Pd–Pb clusters was found to be �0.1 Å longer than pure ones, but doped Pb atoms did not con-stantly expand the Pd–Pd bond lengths in Pd–Pb clusters owing to size effect. In addition, doped Pb atomchanged the thickness of surface phase and surface morphology of Pd cluster. The chemical activity of Pdclusters could be enhanced by the doped Pd atoms, although an enough size was required. Lead atomsessentially changed the surface charge population of Pd clusters. The Pd atoms in Pd–Pb clusters wereseen to become more electrophilic than in pure Pd clusters, and the probability of being attacked bynucleophilic reagent could be comparable with that of being attacked by electrophilic reagent. Total elec-tron density and deformation electron density revealed that the nature of interaction between metalatoms was metal bond. Weak covalent bond might exist when clusters were in small size.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

Palladium clusters often exhibit unusual physical and chemicalproperties due to the sizes intermediate between molecules andbulk phases, having various existing and potential applications,e.g., in heterogeneous catalysis processes [1–3]. Recent reportsreveal that the palladium cluster may have better performancesor novel properties when other element is introduced into pureone, for these reasons bimetallic clusters containing Pd are beingwidely used [4–12] and investigated [13–23].

Many researchers have paid attention to the clusters in a theo-retical way. For example, Giuseppe Zanti and Daniel Peeters [24]studied PdnAum clusters of low nuclearity (n + m 614) at B3LYP/Lanl2DZ level to explore the evolution of various structural, elec-tronic, and energetic properties with the change of size and com-position of the system. The results showed that the compositionplayed a major role in determining the geometry of PdnAum clus-ters, that is, clusters with more Pd atoms preferred 3D structureswhile ones with more Au atoms were inclined to be planar config-urations in spite of deviation from planarity near Pd centers. ByNBO analysis, they revealed that the spin multiplicities of Pd-en-riched clusters increased with the cluster size whereas Au-en-riched ones maintained the lowest possible spin multiplicity. Asynergic effect was found in terms of the stability of PdnAum

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sjzhang@home.ipe.ac.cn (S.

clusters. When n approximated to m, the stabilization effect andthe number of mixed Pd–Au bonds were both maximized. Gobalet al. [25] performed a comparative investigation of atomic andmolecular oxygen adsorption on neutral and negatively chargedPdxCu3-x (x = 0–3) clusters with density functional theory (DFT)at B3PW91 level. It was found that for neutral clusters, higher cop-per content reduced the adsorption energy of molecular and atom-ic oxygen, whereas the reverse trend was suitable for negativelycharged ones. Besides, higher copper contents of neutral andnegatively charged clusters weakened O–O bond, increasing theactivity of clusters for dissociation of molecular oxygen. Thermo-dynamically, Pd–Cu cluster was more favorable for dissociationof molecular oxygen than pure Pd cluster. Neyman et al. [26] em-ployed an all-electron scalar relativistic density functional methodto study cuboctahedral clusters Pd140-nZnn (n = 0, 8, 24, 32) as localmodels of the active component of novel Pd/ZnO catalysts, tryingto explain the influences of Zn on Pd nanoclusters at varying andrelatively low concentrations. They believed that ‘‘this is the firsthigh-level electronic structure study of bimetallic clusters contain-ing over 100 heavy element atoms and approaching the size of2 nm’’ [26].

Our attention is focused on bimetallic Pd–Pb clusters for thespecial role that Pb plays in Pd clusters. Generally, Pb is perceivedas a significant poison of catalysts, especially for those containingtransition metals (TM), e.g., three-way automotive exhaust gasones. However, the evidences from different researchers provedthat the performance of palladium could be dramatically improvedby doping into lead [27–31]. Comparing to the numerous reports

376 L. Wei et al. / Computational and Theoretical Chemistry 966 (2011) 375–382

on the Pd catalysts combined with Pb [32–43], there has been fewtheoretical studies on this area, especially for larger size clustermodel of Pd–Pb catalysts. So the cuboctahedral Pd–Pb clusters,ranging from 13 to 116 atoms, were constructed to calculate theirgeometric and electronic properties as a function of cluster size.Meanwhile, the corresponding Pd clusters were also studied forcomparison. It is hoped that the basic properties about Pd–Pb clus-ter can be revealed and the results are helpful for deeply under-standing the behavior of bimetallic cluster in larger size, as wellas applications in material science and heterogeneous catalysis.

Fig. 1. Fcc Pd3Pb crystal, where Pd atom is marked by , and Pb .

2. Computational details

All calculations were carried out using DFT with the programpackage DMol3 [44,45] in Materials Studio from Accelrys Inc. Theexchange–correlation energies were calculated under the localdensity approximation (LDA) [46] with Vosko–Wilk–Nusair’s ex-change–correlation functional (VWN) [47]. It is generally acceptedthat LDA is more suitable for yielding excellent geometric param-eters of metallic systems. To describe the valence electrons, a dou-ble-numerical basis with polarization functions (DNP) wasemployed for the Pd and Pb atoms, both core electrons of whichwere described with an effective core potential (ECP) that tookthe relativistic effect into account since the effect was expectedto be significant for heavy elements. For geometry optimization,the converged thresholds were set as 0.004 Ha/Å for the forces,0.005 Å for the displacement, and 2.0 � 10�5 Ha for the energychange. The density mixing criterion for charge and spin was setas 0.2 and 0.5, respectively. In order to minimize the computa-tional time, Direct Inversion in an Iterative Subspace (DIIS)approach and Harris approximation were used. A 0.005 Ha of ther-mal smearing was applied to the orbital occupation. No atom wasfixed in the calculation, so the clusters were allowed to deviatefrom the initial structure, but the optimized results showed thatthe framework was still maintained after optimization. The vibra-tional frequency analysis confirmed that all the structures weretruly local minima in the potential energy surfaces.

Many researches have shown that spin polarization effectscould be negligible for larger particles, for example, Pd140 [48,49].Vines et al. [50] took Pd79 as an example, showing the total ener-gies calculated in a spin polarized solution were only slightly lowerthan the ones corresponding to the closed-shell solution and spinpolarization did not lead to any change in the geometric structure.As a result, the calculations of Pd clusters in this paper were carriedout without the spin polarization. Meanwhile, only spin-restrictedresults of Pd–Pb clusters were discussed for comparison.

Despite the developments of the hardware and quantum chem-istry, accurate density functional calculations for metal clusters of�100 atoms remain hardly possible without the symmetry con-straints [50,51]. Thus all calculations in our work were under Oh

symmetry constraint.

3. Results and discussion

The spatial arrangement of different elements in bimetallicclusters is crucial for both theoretical and experimental studies,since many macro and microscopic properties depend on it. Inprinciple, all possible isomers should be discussed in order to ob-tain the ‘‘best’’ arrangement. It is reasonable and practical for smallbimetallic clusters, just as many researchers do [52–61]. But in lar-ger size, the strategy is unpractical and exhausting since the num-ber of possible isomers grows exponentially with the size of thecluster [62]. Thus we have to select the ‘‘useful’’ geometric arrange-ment and structure by means of experiments and applications.

An fcc Pd3Pb crystal (Fig. 1) was used to determine the relativepositions of Pd and Pb atoms in bimetallic clusters. The crystal is atypical phase in Pd–Pb catalysts [29–31,38,63], making our clustermodels more practical. The cuboctahedral Pd–Pb clusters, includ-ing 13, 38, 55, 79 and 116 atoms (Fig. 2), were constructed onthe basis of fcc Pd3Pb lattice. The cuboctahedral clusters are partic-ularly stable at intermediate size [64] and widely employed in thecluster science [26,49,50,65–68]. In addition, the structure is veryconvenient for studying the effects of corners, edges and differentfacets on the reactivity of metal nanoparticles, providing a founda-tion for our further work. To built them, corresponding octahedralclusters should be cut from an ideal fcc Pd3Pb bulk crystal, thenthey were truncated at the vertex to yield (0 0 1) and (1 1 1) facets.For comparison, the counterparts of Pd cluster were also built (alsoshown in Fig. 2).

3.1. Geometry properties

3.1.1. Average bond lengthInitially, average bond lengths of Pd and Pd–Pb clusters were

calculated, which can be defined as follows,

R ¼ RRij=nb ð1Þ

where Rij is the bond length between i and j atoms, lying within adistance not exceeding 15% [48] of the minimum distance of bulkPd metal (2.75 Å), and nb the total bond number.

Fig. 3 showed that the average bond lengths of both Pd and Pd–Pb clusters changed as a function of size. For Pd clusters, the valueincreased rapidly in the range from 13- to 38-atom, and thenthrough a slight descent at Pd55 it converged very slowly to thenearest-neighbor distance in bulk Pd (2.75 Å), in accord with ear-lier researches [50,64,66]. For Pd–Pb clusters, there was no obviousvariation in small and medium size from 13- to 38-atom. But theaverage bond length kept rapidly increasing from 38- to 79-atom.After the peak at 79-atom, the average bond distance decreasedgently as the size increasing.

On the whole, the bond lengths of both clusters increased withthe clusters growing and almost all the average bond lengths ofPd–Pb clusters were �0.1 Å longer than those of correspondingPd clusters. Thus Pd–Pb clusters were relatively incompact, whichwas a reasonable result since the van der Waals radius of Pb atom,2.02 Å, is longer than that of Pd atom, 1.63 Å [69].

In order to investigate the influence of doped Pb atoms on theinternal structure of Pd–Pb cluster, the average Pd–Pd bond lengthin Pd–Pb clusters was designedly calculated, also plotted in Fig. 3.Compared with pure palladium clusters, the average Pd–Pd bonddistance in Pd–Pb clusters varied more complex. The curve dis-played a severe contraction appeared at 38-atom where the Pd–Pd bond length was only 2.67 Å, even shorter than that of Pd38,2.70 Å.

The unexpected contraction evoked our great interest. Directly,it could explain the constant average bond length during the

Pd12Pb1 Pd13

Pd30Pb8 Pd38

Pd36Pb19 Pd55

Pd60Pb19 Pd79

Pd84Pb32 Pd116

Fig. 2. Pd and Pd–Pb clusters, ranging from 13 to 116 atoms, where Pd atom is marked by , and Pb .

L. Wei et al. / Computational and Theoretical Chemistry 966 (2011) 375–382 377

growth process of Pd–Pb cluster from 13- to 38-atom. Theoreti-cally, the average bond length of Pd–Pb cluster is contributed fromthree parts, namely, the bond distances of Pd–Pd, Pd–Pb and Pb–Pb. But according to the definition of Rij, the distance of Pb–Pbactually have no contribution to the average value since it ex-ceeded 15% of the shortest bond distance in bulk Pd metal; hence

in fact, the average bond length of Pd–Pb cluster only contains twocomponents, the bond lengths of Pd–Pd and Pd–Pb. It could bereadily accepted that the Pd–Pb bonds are usually longer thanPd–Pd ones, apt to make the clusters expand. As far as the Pd30Pb8

cluster was concerned, more Pb atoms and higher Pb/Pd ratioshould lead to a longer average bond length than that of Pd12Pb1

Fig. 3. Average bond lengths of Pd and Pd–Pb clusters as a function of cluster size.

Table 1Distances between nearest-neighbor (0 0 1) layers (in Å) of Pd clusters containing 38–116 atoms.

n 38 55 79 116

d12 1.80 1.90 1.84 1.87d23 1.95 1.90 1.89 1.91d34 – – 1.94 1.93

Table 2Distances between nearest-neighbor (0 0 1) layers (in Å) of Pd–Pb clusters containing38–116 atoms.

n 38 55 79 116

d12 1.58 2.13 1.76 2.08d23 2.21 1.94 2.08 1.95d34 � � 2.03 2.06

378 L. Wei et al. / Computational and Theoretical Chemistry 966 (2011) 375–382

cluster, so a constant bond length seemed to be counterintuitive.Fortunately, the finding of contracted Pd–Pd bonds provided anexcellent explanation for the puzzle. The shortened bond lengthof Pd–Pd balanced the expansive effect of Pd–Pb bond, inclinedto compact the cluster. The net result of these two opposite effectswas reflected as the fact that the average bond length kept con-stant with the cluster size increasing from 13- to 38-atom.

Pd30Pb8

Pd60Pb19

Fig. 4. The expansive relaxation of Pb atoms in Pd–Pb clusters w

Moreover, a further analysis revealed that the influence ofdoped Pb atoms on the internal structure of Pd–Pb cluster wasintricate. Although the Pd–Pb clusters were incompact relative tocorresponding pure clusters, doped Pb atoms did not always elon-gate the Pd–Pd bonds in the Pd–Pb cluster. In certain medium size(probably from 30 to 50 atoms), Pb atoms made Pd atoms in Pd–Pbcluster more crowded than the pure Pd cluster. It might be consid-ered as a kind of size effect because as the cluster growing bigger,the doped Pb atoms indeed stretched the Pd–Pd bond length grad-ually, as shown in Fig. 3.

Pd36Pb19

Pd84Pb32

ith 38–116 atoms, where Pd atom is marked by , and Pb .

Fig. 5. HOMO–LUMO energy gaps of Pd and Pd–Pb clusters as a function of clustersize.

Fig. 6. Three types of surface atoms: (1) the corner atom, (2) the midedge atom and(3) the midface atom.

L. Wei et al. / Computational and Theoretical Chemistry 966 (2011) 375–382 379

3.1.2. Surface relaxationSurface relaxation could be observed from the optimized struc-

tures of Pd–Pb clusters, as shown in Fig. 4. In terms of (0 0 1) layers,Pb atoms protruded out of the layers and exhibited the expansiverelaxation so that Pd–Pb clusters had more rough surfaces.

The distance between nearest-neighbor (0 0 1) layers of clus-ters, di(i+1), was calculated to quantitatively investigate the effect

Table 3The surface Mulliken charge populations of Pd and Pd–Pb clusters.

n Pd clusters

q1a q2 q3

(1 0 0) (1 1 1)

13 �0.183 – – –38 �0.244 – – �0.08755 �0.427 �0.333 �0.092 –79 �0.499 �0.301 – 0.008

116 �0.551 �0.386 �0.256 �0.145

a q1, q2 and q3 represent the charge of corner atom, midedge atom and midface atomb The charge Pb atom carries is marked with bold italic.

of surface relaxation. di(i+1) was the distance between the centroidof ith and that of (i +1)th (i = 1, 2, 3) layer, where the 1st layer re-ferred to the surface. The related data were listed in Tables 1 and 2.

The investigation on the average bond lengths of Pd and Pd–Pbcluster revealed that lead atoms were always inclined to make Pdcluster expand due to atom size effect. Comparing the data in Ta-bles 1 and 2, this conclusion can be confirmed by the elongatedd23 and d34. But with regards to d12, more caution should be usedto cope with the complicated changes. For 38- and 79-atom Pd–Pb clusters, d12 was shorter related to the corresponding Pd cluster;whereas d12 of 55- and 116-atom Pd–Pb clusters was remarkablyelongated. It could be explained with the expansive relaxation ofPb atoms and the atom size effect.

In fact, the protruding lead atoms always heightened the cen-troid of the layer. So for the cluster starting from a pure palladiumlayer, such as Pd30Pb8 and Pd60Pb19, the severe expansive relaxa-tion of Pb atoms in the 2nd layer balanced the atom size effectand shortened the distance between the centroids of two layers,leading to a contracted surface phase. On the contrary, if the Pd–Pb cluster took a Pb-containing layer as the surface, such asPd36Pb19 or Pd84Pb32, the expansive relaxation played a synergisticrole with the atom size effect and thickened the surface phase, theinterlayer spacing of which could be longer than d23 and d34 (asshown in Table 2). In one word, doped Pb atoms changed the thick-ness of surface phase and surface morphology of Pd cluster, whichwould have a profound effect on adsorption properties and chem-ical reactions on it.

3.2. Electronic properties

3.2.1. Chemical activityThe chemical activity of clusters can be characterized by the

HOMO–LUMO energy gap that is a significant parameter relyingon the HOMO and LUMO energy levels. Usually, a small HOMO–LUMO energy gap means a high chemical activity and a low chem-ical stability. The related data were plotted in Fig. 5 where an oscil-lating descent was displayed in both cases. The introduced leadatoms amplified the fluctuation. Two local maxima in Pd clustersappeared at 38- and 79-atom sizes, the values of which were18.7 and 16.1 kJ/mol, respectively. However, two unexpectedpeaks in Pd–Pb clusters were both above 30 kJ/mol. When the clus-ters grew bigger (more than 80 atoms), energy gaps of the clustersexhibited a decreasing process, suggesting both clusters had a re-duced chemical stability and an increased chemical activity, espe-cially Pd–Pb cluster that underwent a sharp drop from 55-atomand became more chemical active than Pd cluster from 80-atom.It was in line with the previous theoretical investigation on geo-metric and electronic properties of Pdn-1Pb (n 68) clusters by Fanget al. [70]. They reported that the HOMO–LUMO gaps of Pd–Pb bin-ary clusters were narrower than those of Pdn clusters; hence thechemical activity was systematically enhanced when Pdn clusters

Pd–Pb clusters

q1 q2 q3

(1 0 0) (1 1 1)

�0.095 – – –0.111 – – �0.307�0.913b 0.130 �0.523 –�0.184 �0.800 – 0.195�0.128 �0.787 0.121 0.157

, respectively.

380 L. Wei et al. / Computational and Theoretical Chemistry 966 (2011) 375–382

were doped with Pb. Our calculations confirmed this enhancementin larger size. But for small and medium sizes (Pd12Pb1 andPd36Pb19), the unexpected great HOMO–LUMO gaps suggested thatPd–Pb clusters might be more chemically inert than Pd cluster inthis size. Thus a relatively larger size might be required for an obvi-ous enhancement of the chemical activity caused by the doped Pdatoms.

3.2.2. Surface charge populationThe charge distribution over the surface layer of the metal clus-

ter plays an important role in heterogeneous catalysis because thecharge that metal atom carries a useful clue to electrophilicity ornucleophilicity, which is helpful to predict the active site on thesurface. In bulk phase, all atoms have nearly perfect charge neu-trality since all atoms are geometrically equivalent and protectedby a very efficient screening of electrons [64]. But for the clusters,especially those without enough size, charge transfers may be in-duced by the boundary effect and geometrically inequivalentatoms. Particularly, surface layer with asymmetry force field mayexhibit different properties compared with internal atoms. Thussurface Mulliken charge population was calculated.

Pd13 Pd12Pb1

Pd38 Pd30Pb8

Pd55 Pd36Pb19

Pd79 Pd60Pb19

Pd116 Pd84Pb32

Fig. 7. Total electron density of Pd and Pd–Pb clusters, ranging from 13 to 116atoms, where Pd atom is marked by , and Pb .

The surface atoms were classified into three types for compar-ing the charges of different locations, which are the corner atoms,the midedge atoms and the midface atoms, as shown in Fig. 6. Ta-ble 3 listed the surface Mulliken charge populations of Pd and Pd–Pb clusters to conclude the features of charge distribution andinvestigate the influences of Pb atoms. For Pd clusters, the trendswere relatively obvious. The whole surface layer of pure palladiumcluster carried negative charge which mainly concentrated at thecorner atom, then the midedge atom, at last, the midface atom.Particularly, according to the data of Pd116, it seemed that (1 0 0)planes were inclined to have more negative charge than (1 1 1)ones. The negative charge on the corner atoms was rapidly in-creased with the cluster size increasing, but the tendency wasnot apparent for the midedge and midface atoms. Compared withPd clusters, Pb atoms in Pd–Pb clusters constantly possessed muchmore negative charge than the counterparts in the pure clusters.The Pd atoms adjoined to Pb atoms carried positive charge or re-duced negative charge. Hence the surface layer of Pd–Pb clustersdisplayed a rearrangement of positive and negative charge.

Pd13 Pd12Pb1

Pd38 Pd30Pb8

Pd55 Pd36Pb19

Pd79 Pd 60Pb19

Pd116 Pd84Pb32

Fig. 8. Isosurfaces of deformation electron density (isovalue = 0.05 e/Å3) of Pd andPd–Pb clusters, ranging from 13 to 116 atoms, where Pd atom is marked by , andPb ; the blue and the yellow color represent for electron accumulation anddepletion, respectively. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)

L. Wei et al. / Computational and Theoretical Chemistry 966 (2011) 375–382 381

Higher negative charge means more nucleophilicity and greaterprobability to be attacked by electrophilic reagent. Thus the Pdatoms in Pd–Pb clusters should have less probability of reactionwith electrophilic reagent, which might be considered as a poison-ing effect caused by lead atoms. But sometimes this property is de-sired by chemists. A case in point may be the Lindlar catalyst. It isgenerally accepted that lead acetate decreases the activity of Pdcatalyst, making it incapable of olefin hydrogenation but capableof the hydrogenation of alkynes, thus the Lindlar catalyst couldbe explored in the purification of ethylene. In addition, Pd atomsin Pd–Pb clusters are entitled to be electrophilic, essentially differ-ent from pure clusters. It might profoundly affect the type of cata-lytic reaction. It is worth noting that it is comparable for theabsolute values of charge carried by electrophilic and nucleophilicPd atoms, which implies the probabilities of being attacked bynucleophilic/electrophilic reagents should also be comparable.

3.2.3. Electron densityTotal and deformation electron densities were calculated and

displayed in Figs. 7 and 8 to elucidate the nature of interactions be-tween metal atoms. As apparent from Fig. 7, spherical distributionappeared around all metal atoms, which indicated that thereshould be little covalent bond between metal atoms. To furtherclarify the interaction, deformation electron density shown inFig. 8 was needed, which equaled to the total density subtractingthe density of the isolated atoms. The yellow isosurfaces repre-sented for electron depletion, while blue ones stood for electronaccumulation. It was clear that more external electrons could befound in the space among the metal atoms instead of near theatoms, which was an obvious evidence for metal bond.

Although metal bond was absolutely predominant in Pd andPd–Pb clusters, the slight overlap could still be observed betweencentral metal atom and peripheral Pd atoms in Pd13 and Pd12Pb1,suggesting covalent bond (even if very weak) might exist insmall-size clusters.

4. Conclusion

The Pd–Pb clusters ranging from 13 to 116 atoms cut fromPd3Pb crystal were built to investigate basic properties of Pd–Pbcluster and the effects of doped Pb atoms on Pd clusters by usingDFT-LDA. The results were summarized as follows:

Firstly, the average bond length showed that Pd–Pb clusterswere incompact compared with Pd ones. Pb atoms expanded pureclusters by �0.1 Å. Doped Pb atoms did not constantly expand thePd–Pd bond length in Pd–Pb cluster owing to size effect. Addition-ally, doped Pb atoms changed the thickness of surface phase andsurface morphology of Pd cluster.

Secondly, the chemical activity of the cluster characterized bythe HOMO–LUMO energy gap showed that the enhancement ofthe chemical activity was caused by the doped Pd atoms, althoughan enough size was required. Lead atoms essentially transformedthe surface charge populations of Pd clusters, so Pd atoms inPd–Pb clusters could be electrophilic and the probability of beingattacked by nucleophilic reagent should be comparable with thatof being attacked by electrophilic reagent. Total electron densityand deformation electron density revealed that the nature of inter-actions between metal atoms was metal bond. Weak covalent bondmight exist in small-size clusters.

Above all, pure Pd cluster is indeed altered by introducing leadatoms. It is hoped that these properties have a positive effect onexploring the laws of bimetallic clusters in larger size and providemeaningful clues for further studies on applications in material sci-ence and catalysis, for example, the adsorption properties and thechemical reactions on them.

Acknowledgements

This work was supported by the National Science Fund of Chinafor Distinguished Young Scholar (20625618), National Basic Re-search Program of China (973 Program, 2009CB219902), GeneralProgram of National Natural Science Foundation of China(50974113, 20776003) and the Funding Project for AcademicHuman Resources Development in Institutions of Higher Learningunder the Jurisdiction of Beijing Municipality (Grant Nos.PHR201107104 and PHR200907105).

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