ISSN 0036�0244, Russian Journal of Physical Chemistry A, 2014, Vol. 88, No. 3, pp. 457–465. © Pleiades Publishing, Ltd., 2014.

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1 INTRODUCTION

With the single�component clusters gradually in�depth study, mixed doped clusters gradually becomethe cluster physics topics at the forefront in recentyears. Super alloy materials, the magneto�opticalrecording material, and the most important catalystsin the chemical industry are the transition metal alloy,so the transition metal alloy has aroused great con�cern. In a variety of metal materials, due to the largework function, very stable chemical properties, goodelectrical properties, therefore, platinum in the metalalloy has a wide application prospect. A lot ofresearches have been carried out on platinum dopedalloy material of the other metal elements and clusters[1–13], Chen et al. [1] use of Monte Carlo methods tostudy on the structures of the atomic number 147 inthe range of 139 of Pd–Pt alloy clusters; Corina et al.study the kinetic and optical properties of Pt–Au alloy[2], Yuan et al. study AunM (n = 1–7, M = Ni, Pd, Pt)small clusters of structures and electronic properties[3]; Gou et al. [4] use the first principle method tostudy the growth characteristics of the neutral AunPt2

(n = 1–4) clusters; Jian jun Guo et al. [5] study the anionAunPt small clusters geometries and electronic statesusing density functional method; Xiu�rong Zhang et al.[6, 7] use density functional studies of the structures andproperties of small clusters, and PtnMn (n = 1–5) clustersstructure and magnetic PtnNim (n + m = 6).

1 The article is published in the original.

Jun�Qing Wen and Zhen�Yi Jiang [14] using den�sity functional study of the structures and magneticproperties of Ptn (n = 1–9), PdnAl (n ≤ 5), PtnAl (n =1–8), NinAl (n = 1–8), PtnAl+ (n = 1–8), Pt–Al alloyhas a high melting point, hardness and other specialfeatures, so they are good in many aspects of the mod�ern industrial catalytic technology, fuel cell applica�tions prospects. Further study, it is also found that thePt doped the Al metal can be better than pure Pt cata�lytic effect on the Pt surface, Pt–Al alloy the mixedcoating than a single Al coating in the resistance tooxidation and corrosion have better results, prepara�tion of Pt–Al alloy coating to improve, the small Pt–Al alloy clusters structure research has been conducteda lot of researches [15–17], but less theoretical studyof the structure of the original Al clusters doped Pt ele�ments.

We have carried out a detail systematic study of theequilibrium structure and various electronic�structurerelated properties of these clusters, employing thehybrid generalized gradient approximation (GGA) forthe exchange�correlation potential. We investigate therelative ordering of these structures with the Pt impu�rity occupying the internal and other position. Herewe study the evolution of binding energy, the adsorp�tion energy, dissociation energy, the second�orderenergy differences, HOMO–LUMO gap, ionizationpotential, electron affinity for AlnPt (n = 1–15) clusters.

Density Functional Theory Study of the Structures, Electronic States and Stabilities of AlnPt (n = 1–15) Clusters1

Xiao Zhanga, Ling Guoa, Jian Guob, and Ning�Ning Rena

aSchool of Chemistry and Material Science, Shanxi Normal University, Linfen 041004, ChinabSchool of Management Science and Engineering, Central University of Finance and Economics, China

e�mail: 304400311@qq.comReceived March 4, 2013

Abstract—The binding energy, dissociation energy, ionization potentials, electron affinities, gap and stabilityof small AlnPt (n = 1–15) clusters, in comparison with pure aluminum clusters have been systematicallyinvestigated by means of density functional calculations at the B3LYP level. The growth patten for AlnPt clus�ters is that the Pt atom substituted the surface atom of the Aln + 1 clusters for n < 13. Starting from n = 13, thePt atom completely falls into the center of the Al�frame. The Pt atom substituted the center atom of the Aln + 1clusters to form the Pt�encapsulated Aln geometries for n > 13. We also find that the impurity Pt atom causeslocal structural distortion due to different atomic radii and different bonding characteristics. The clusters withtotal atom numbers of 2, 7, and 11 exhibit high stability.

Keywords: AlnPt bimetallic cluster, DFT calculations, geometric configuration, stability.

DOI: 10.1134/S0036024414030273

STRUCTURE OF MATTERAND QUANTUM CHEMISTRY

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METHODOLOGYAND COMPUTATIONAL DETAILS

The selection of distinct initial geometries isimportant to the reliability of the ground state struc�ture obtained. As the cluster size increases, the num�ber of the possible geometries increases dramatically.In this paper, the conformations of the pure Aln clus�ters are obtained firstly by reference to the configura�tions in [18]. The geometries with different symme�tries are also optimized for each size. During thecourse of choosing initial structure of the AlnPt clus�ters, we have considered possible isomeric structuresby placing the Pt atom on each possible site of the Aln

cluster as well as by substituting one Al atom by the Ptatom from the Aln + 1Pt cluster. The TinAl [19] andGanAl [20] stable isomers are also considered as can�didates. For all isomers of each cluster, the local min�ima of the potential energy surface are guaranteed bythe harmonic vibrational frequencies without imagi�nary mode. Further, different spin multiplicities of thelowest�energy isomers are considered. In case the totalenergy improves with increasing spin multiplicity, we

consider an creasing higher spin state until the energyminimum with respect to spin multiplicity is reached.

All calculated were performed using the densityfunctional theory (DFT) provided by the Gaussian 03suite of programs [21]. Full optimized structures andnormal�mode frequencies are found using the hybridB3LYP functional [22, 23]. An all�electron basis set 6�31G* is used for Al atom. The LANL2DZ pseudopo�tential is adopted for the valence electrons of Pt atom,and its core electrons are represented by theLANL2DZ effective core potential (ECP). Thisscheme is a good compromise between accuracy andcomputational effort.

RESULTS AND DISCUSSION

Atomic Structures

The ground state geometries of AlnPt clusters, andsome low�lying metastable isomers are showed inFig. 1. For proper comparison we have also showed theground state geometries of pure Aln (n = 2–16) cluster.The symmetries, the spin multiplicities, and the elec�tronic states of the most stable and low�lying AlnPt

Table 1. Multiplicity (M), symmetries (Sym), HOMO–LUMO gap (Gap), averaged binding energy (Eb), the dissociationenergy (ΔE), the second�order energy differences (Δ2E), the adsorption energy (Ead), vertical ionization potential (VIP),and vertical electron affinities (VEA) (all in eV) for the most stable AlnPt (n = 1–15) clusters

Cluster M Sym Gap Eb ΔE Δ2E Ead VIP VEA NBO

AlPt(1a) 2 C∞v 3.622

1.3501.723 3.444 7.600 1.976 –0.510

Al2Pt(2a) 1 C2v 2.960 2.392 3.732 1.769 6.587 7.325 0.844 –0.861

Al3Pt(3a) 2 C3v 1.4893.326

2.285 1.960 0.544 5.972 5.850 1.162 –0.711

Al4Pt(4a) 3 C4v 1.8392.631

2.111 1.418 –0.264 5.845 5.987 1.630 –0.675

Al5Pt(5a) 2 Cs 1.3751.583

2.044 1.683 –0.789 5.107 6.202 1.766 –0.404

Al6Pt(6a) 1 C2v 1.761 2.103 2.487 –0.014 5.343 6.302 1.820 –0.530

Al7Pt(7a) 2 C1 1.5202.044

2.153 2.501 0.593 4.998 6.063 1.799 –0.633

Al8Pt(8a) 1 Cs 1.714 2.128 1.922 –0.147 5.004 6.188 1.818 –0.495

Al9Pt(9a) 2 C1 1.4611.415

2.122 2.072 –0.082 5.246 6.150 2.435 –0.439

Al10Pt(10a) 1 C1 1.260 2.125 2.152 –0.351 4.861 6.123 2.378 –0.495

Al11Pt(11a) 2 C1 1.4961.579

2.156 2.505 0.220 5.091 5.864 2.316 –0.634

Al12Pt(12a) 1 C1 1.410 2.166 2.283 –0.034 4.771 6.123 2.343 –0.343

Al13Pt(13a) 2 Cs 2.0441.099

2.241 3.208 0.031 5.458 5.925 2.878 –1.145

Al14Pt(14a) 1 Cs 2.064 2.249 2.366 0.025 5.409 6.011 1.602 –0.798

Al15Pt(15a) 2 Cs 1.2671.608

2.214 1.688 5.329 5.626 2.235 –1.030

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DENSITY FUNCTIONAL THEORY STUDY OF THE STRUCTURES 459

(n = 1–15) clusters are summarized in Table 1. Thelowest�energy structure of Al2 is an linear structurewith C

∞v symmetry, Bond length is 2.564 Å, harmonic

frequency (ω1e) is 300.59 cm–1, which is consistentwith experimental [24–26]. For the AlPt dimer withC∞v symmetry, the optimized results indicate that the

doublet spin state is lower in total energy than thequartet and the sextet isomers by 2.04 and 5.51 eV,respectively. Therefore, the double AlPt dimmer witha band length of 2.391 Å is the most stable structure.

The lowest�energy structure of Al3 is an equilateraltriangle structure with D3h symmetry, harmonic fre�quency (ω1e) is 340.56 cm–1, which is consistent withexperimental (357 ± 10 cm–1) [26]. For Al2Pt, the low�est�energy structure is an isosceles triangle (C2v), inwhich the Al atom is at the apex. The Al–Al distance(3.065 Å) is longer than that of Al2 dimer, and the bondlength of Al–Pt is 2.325 Å. It is a spin singlet and lowerby 1.68 and 3.61 eV in energy than the triplet and thequintet state.

(1a0) (1a) (2a0) (2a) (3a0)

(4a0) (4a) (4b) (5a0) (5a) (5b)

(6a0) (6a) (6b) (7a0) (7a) (7b)

(8a0) (8a) (8b) (9a0) (9a) (9b)

(10a0)

(3a)

(10a) (10b) (11a0) (11a) (11b)

(12a0) (12a) (12b) (13a0) (13a) (13b)

(14a0) (14a) (14b) (15a0) (15a) (15b)

Fig. 1. Lowest�energy and low�lying structure of AlnPt (n = 1–15) clusters and lowest�energy structures of Aln (n = 2–16) clusters.The black and gray balls represent Pt and Al atoms, respectively.

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Al4 is a parallelogram with C2h symmetry [26]. Butthe Al3Pt is a triangular pyramidal structure with C3v

symmetry [27], which can be generated by occupyingthe Al atom in the center of the Al3 equilateral triangle.Moreover the doublet isomers with electronic state 2A1

is lower in total energy than the quartet and the sextetisomers. Therefore, the spin doublet configuration isthe most stable structure.

As for Al5, the most stable structure is a pentagonstructure with Cs symmetry [26], in agreement with theGa5 geometry [20], which is different from the resultobtained by Song et al. [28]. For Al4Pt we notice thatin the optimization process, by the means of addingone Al atom to the different isomers of Al3Pt clustersor substituting one Al atom in the stable structure ofAl5 cluster, a variety of structure such as square pyra�mid structure deformed, rectangular pyramid, ingotstructure and planar trapeziform structure can beobtained. But the most ground state structure is 4awith C4v symmetry [27] and the corresponding elec�tronic state is 3B1. The spin multiplicity of 3 is morestable structure than other spin states. The low�lyingisomer with a higher energy (0.33 eV) is a pentagonconfiguration where the impurity Al atom is at its ver�tex position.

For Al6, the distorted tetragonal bipyramid struc�ture with D3d symmetry [26, 29] is the most stable iso�mer for pure Al6 cluster. The first three�dimensionalstructure occurs at n = 6. The D3d structure is regardedas a distorted anti�trigonal prism. But Fournier [30]found that the ground state structure for the Al6 clusterwas a distorted trigonal prism by the BPW91/lanl2dzmethod. For Al5Pt cluster with one Pt atom have sim�ilar ground state structure to corresponding pure Al6

clusters. But the impurity Pt atom results in seriousstructural distortions, making their symmetriesdecrease Cs [27]. This doublet isomer with electronicstate 1A1 is lower by 0.22 and 1.92 eV in energy thanquartet and sextet isomers. The low�lying configura�tion with Cs [27] symmetry above 0.05 eV in energy isregarded as a capped Al atom on the base of the lowest�energy structure of the Al4Pt cluster.

In the case of n = 7, the pure Al7 adopted the dis�torted capped trigonal prism with Cs symmetry [26].For Al6Pt the most stable structure 6a with C2v symme�try is the bicapped square pyramid by adding one Al tothe 5a. Moreover the singlet isomer with electronicstate 1A1 is lower in total energy than the triplet andquintet isomers by 0.10 and 0.86 eV, respectively.Therefore, the spin singlet configuration is the moststable structure. In addition capped octahedron, tri�capped tetrahedron are considered. However, theseisomers are higher in energy than the ground statestructure, of which 6b with C2v symmetry [27] is a low�lying structure with higher energy 0.02 eV, it is also the

capped trigonal prism with an impurity Al atombecoming the capped atom.

For Al8 cluster, our result is a distorted transcappedoctahedron with C1 symmetry and this is agreementwith Fournier’s report [30], the ground�state structureis a distorted transcapped octahedron; or an anti�trig�onal prism with a face�capping atom and an�edge�capping atom. The lowest energy configuration of Al8

can be obtained from capping two Al atoms on theperipheral sites of the deformed stable frame of Al6.The ground state geometry of Al7Pt (7a) and the low�lying structure 7b are similar only the capped atom Ptis in the top of the square and the triangle, their energydifference is only 0.01 eV. Furthermore, 7a with dou�blet is lower in total energy than those spin quartet andsextet isomers by 0.65 and 1.41 eV, respectively. There�fore, the spin doublet configuration with electronicstate State 2A is the most stable structure.

The lowest�energy structure of Al9 can be seen thatAl atom capped on the distorted quadrangular prism ofthe Al8. The ground state geometry of Al8Pt with Cs

symmetry is one Pt atom substituting capped Al atomin Al9 configuration. Moreover, the singlet structure islower in total energy than the triplet and quintet iso�mers by 0.26 and 0.84 eV. Indicating that the singlet ismore stable than other spin states, the correspondingelectronic state is 1A'. It is more stable than an Pt atomcapped on the distorted quadrangular prism of the Al8

cluster 8b by 0.10 eV.The most stable structure of pure Al10 cluster can be

obtained from Al9 ground state isomer by putting acapping Al atom with C1 symmetry. For Al9Pt clusterthe ground state 9a develops hexagon arrangements ofatoms. The total energy with spin doublet is lower by0.37 and 1.34 eV than the quartet and sextet isomers.The structure of isomer 9b with Cs symmetry is thetwin four corners bipyramidal structure and the Ptatom is no longer two pyramids shared.

For Al11 develops pentagonal arrangements ofatoms, which is the same as Ga11 [20], and consistentwith Song’s results [28]. In these Al clusters with n > 11,an interior atom with bulk like coordination emerges.The ground state geometry of Al10Pt (10a) and thelow�lying structure 10b all with C1 symmetries are twoAl atoms substituting different Al atoms in the Al11

configuration. Their energy difference is only 0.16 eV.Furthermore 10a with spin singlet is lower in totalenergy than those the triplet and quintet isomers by0.14 and 0.89 eV. Therefore, the spin singlet configura�tion with electronic state 1A is the most stable structure.

Al12 with Cs symmetry could be obtained by con�tinuing to develop pentagonal arrangements of atoms.When the Pt was adsorbed on the surface of the dis�torted pentagonal arrangements. It forms the groundstate geometry 11a with C1 symmetry and the low�lying structure 11b with C1 symmetry. The optimized

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DENSITY FUNCTIONAL THEORY STUDY OF THE STRUCTURES 461

results indicate that the doublet spin state is lower intotal energy than the quartet and sextet isomers by 0.29and 1.20 eV, respectively.

Capped one Al atom on the Al12 with Cs symmetryis obtained for pure Al13. For Al12Pt cluster, the groundstate geometry 12a is the Pt substitute one Al atom ofAl13 with C1 symmetry. The total energy of Al12Pt withspin singlet is lower by 0.24 and 0.93 eV than the tripletand quintet isomers. 12a structure on the basis of slightdistortions could get the low�lying structure 12b withC1 symmetry by 0.12 eV.

For Al14, the lowest�energy structure with Cs sym�metry could be obtained by capping one Al atom on adistorted decahedron. For Al13Pt cluster the groundstate geometry 13a is the Pt atom falls into the centerof Al14. The total energy of 13a with pin doublet islower by 0.92 and 1.78 eV than the quartet and sextetisomers. Another low�lying isomer 13b with C1 sym�metry is 0.38 eV higher in energy. The optimizedresults indicate that the grow behavior of Al13Pt iso�mers tends to form the Pt�encapsulated Aln geometriesand not capped on the surface of the Al�frame. Itcould be expected that the Pt�encapsulated Aln willform the most stable structure from n > 13.

For Al15, the geometry results by capping one of thesquare faces of the decahedron by two atoms. Thisresults in a slight distortion of the decahedron with C1

symmetry. For Al14Pt, adding an Pt atom on the sur�face of Al14 is obtained the ground state geometry 14awith Cs symmetry. The total energy of 14a with spinsinglet is lower by 0.92 and 2.07 eV than the triplet andquintet isomers, another low�lying isomer 14b with C1

symmetry is obtained by adsorbing one Al atom on thetop of capped decahedron, their energy difference is0.05 eV.

The lowest�energy structure of Al16 is formed bycapping one the square faces of Al15. The ground stategeometry of Al15Pt can be seen as capping two squarefaces of Al14Pt (13a) by two Al atoms, the impure Pt isin the center of 15a. The total energy of 15a with spindoublet is lower by 0.60 and 1.62 eV than the quartetand sextet isomers.

In summary, the growth pattern for AlnPt (n = 2–4,7, 8, and 12) clusters is Pt atom occupying a peripheralposition of Aln clusters. And the growth pattern forAlnPt (n = 10 and 11) clusters is Pt�substituted Aln + 1

clusters. It is found that the Pt atom substituted thesurface atom of Aln + 1 cluster and occupies a periph�eral position. Al13Pt is that the Pt atom substituted thecenter atom of Al14. The structures of Al5Pt, Al6Pt,Al9Pt, Al15Pt, and Al14Pt don’t meet the above rule.

Molecular dynamics simulations also confirmedthat the ground states structure we propose are stable.The structures of the ground state are in a simple cube20 × 20 × 20, with 0.5 fs step size in the Born–Oppen�heimer MD simulations. Structures in the NVEensemble 1500–2500 K temperature simulation step5000. The results show that our AlnPt (n = 1–15) clus�ters intact throughout the simulations. Therefore, wethink that AlnPt (n = 1–15) clusters is sufficiently sta�ble at about 300 K. Molecular dynamics simulationsare completed in the CP2K code [31].

0.8

0 4 8 12 16n

0.4

1.2

1.6

2.0

2.4Eb, eV

1

2

2'

Fig. 2. The binding energy per atom of (1) AlnPt (n = 1–15) and (2, 2') Aln (n = 2–16) clusters; (2) B3LYP, (2 ')PBE0 [26].

0

0 4 8 12 16n

−1

1

2

3

4Energy, eV

1

2

Fig. 3. The second�order energy difference Δ2E (1) and thedissociation energy ΔE (2) of the AlnPt (n = 1–15) clusters.

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The thermodynamic and dynamic results pre�sented here may give a possible explanation for theexperimental result. Further theoretical and experi�mental studies are needed to determine whether this isthe true mechanism behind experimental phenomena.

Stabilities and Electronic Properties

We now discuss the relative stability of these clus�ters by computing the energy that is indicative of thestability. We compute the atomization or bindingenergy (Eb) per atom, the dissociation energy (ΔE),and the second�order energy differences (Δ2E) as,respectively:

(1)

(2)

(3)

In general the Eb increases sharply for very smallclusters and then follows a plateau as the cluster sizegrows. Small humps or dips for the specific size ofclusters signify their relative stabilities. The Eb of theAlnPt clusters (shown in Fig. 2) is calculated using theEq. (1), where E(A1), E(Pt), and E(AlnPt) representthe energies of an Al cluster, a Pt atom, and the totalenergy of the AlnPt cluster, respectively. For compari�son, we also plot the Eb of the host Aln cluster,Eb[Aln] = (nE[Al] – E[Aln])/n, in Fig. 2. As seen inthis figure, the average binding energies of AlnPt clus�ters are higher than the Aln clusters. It indicates thatthe doped Pt atom in the Aln clusters contributes tostrengthen the stabilities of the Al framework. For

Eb AlnPt[ ] = nE Al[ ] E Pt[ ] E AlnPt[ ]–+( )/ n 1+( ),

ΔE AlnPt[ ] E Aln 1– Pt[ ] E Al[ ] E AlnPt[ ],–+=

Δ2E AlnPt[ ] E Aln 1+ Pt[ ] E Aln 1– Pt[ ]+=

– 2E AlnPt[ ].

AlnPt, the Eb evolves monotonically with total numberof atoms in the cluster. The Eb increases gradually inthe range n = 6–15, in which the rate of increasebecomes weak (only from 2.103 to 2.166 eV). In addi�tion, the comparison of Al with the BE curve for AlnPtclusters shows that the small clusters of AlnPt arestrongly bound. As the clusters grows in size, the dif�ference between the BE curves of AlnPt clusters andpure Al clusters stead diminishes, indicating that thebonding in doped clusters is essentially similar to thatin pure clusters.

In cluster physics, the dissociation energy (ΔE) andthe second�order energy differences (Δ2E) are sensi�tive quantities that reflect the relative stability of theinvestigated clusters [32]. The ΔE shows the energythat one atom is separated from the host clusters. TheΔ2E is often compared directly with relative abun�dances determined in mass spectroscopy experiments.Larger positive value Δ2E represents that the previoussize of the clusters forming, the size clusters emit moreenergy, while in the formation of the next size clustersneed more energy. The larger the value, the better thecorresponding structural stability. They are defined asthe Eqs. (2) and (3). Where E(AlnPt), E(Aln + 1Pt),E(Aln – 1Pt), and E(Al) represent the total energies ofthe most stable AlnPt, Aln + 1Pt, and Aln – 1Pt clustersand a Al atom, respectively. As are showed in Fig. 3,particularly prominent maxima of Δ2E are found atn = 2, 7, 11, indicating higher stability than theirneighboring clusters. It is observed that, for the AlnPtclusters, the ΔE of Al2Pt (3.73 eV), Al7Pt (2.50 eV),Al11Pt (2.51 eV), Al13Pt (3.21 eV) and clusters are higherthan other clusters. Thus we can conclude that themagic clusters are found at n = 2, 7, 11, 13 for AlnPt.

4

0 4 8 12 16n

3

5

6

7Ead, eV

Fig. 4. The adsorption energy of Pt loading on the Aln (n =1–15) clusters surface.

1.8

0 4 8 12 16n

0.6

2.2

2.6

3.0HOMO–LUMO gap, eV

1

2

1.4

1.0

Fig. 5. The HOMO–LUMO gap of (1) the AlnPt (n = 1–15) and (2) Aln (n = 2–16) clusters.

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DENSITY FUNCTIONAL THEORY STUDY OF THE STRUCTURES 463

We have also calculated the adsorption energy ofPt, i.e., the energy released upon adsorption of Pt by apure aluminum cluster, according to

(4)

The calculated values of Ead for the clusters up toAl15Pt ranges between 3.44 and 6.59 eV (Fig. 4). Theminimum value (3.44 eV) occurs for AlPt, while ittakes the maximum value (6.59 eV) for Al2Pt.

The HOMO–LUMO gap (highest occupied�low�est unoccupied molecular orbital gap) is a useful quan�tity for examining the stability of clusters. It is foundthat systems with larger HOMO–LUMO gaps are, ingeneral, less reactive. The HOMO–LUMO gaps asthus calculated are presented in Fig. 5. For AlnPt clus�ters, local peaks are found at n = 2, 7, 11, 13 implyingthe chemical stability of these clusters is stronger thanthat of their neighboring clusters. The magic clustersmostly have a very large HOMO–LUMO gap for themetal clusters. And we observed a strong correlationbetween the HOMO–LUMO gap and the energeticstability of the AlnPt clusters except for Al4Pt.

Ead E Aln[ ] E Pt[ ] E AlnPt[ ].–+=

Experimentally, the electronic structure is probedvia measurements of ionization potentials, electronaffinities, etc. Therefore, we also study these quantitiesto understand their evolution with size. These quanti�ties are determined within B3LYP for the lowest�energy structures obtained within the same scheme.

The vertical ionization potential (VIP) is calculatedas the self�consistent difference between the clusterand its positive ion with the same geometry. The VIP isplotted in Fig. 6 as a function of cluster size. The cor�responding data are given in Table 1. In general, theVIP decreases as the cluster size increase. The peaksoccurring at AlnPt (n = 1, 6, 8, 13) are prominent, withlarge drops of the following clusters. The comparisonof the two curves shows that odd�even oscillation areobserved in pure Al clusters from n = 6 in the wholerange, while in AlnPt clusters, the VIP exhibits odd�even pattern from n = 5.

We have also calculated vertical electron affinities(VEA) for these clusters (Fig. 7) by assuming thegeometry for the charged clusters to be the same as forthe neutral one. For VEA, generally lower the electron

1.8

0 4 8 12 16n

0.6

2.2

2.6

3.0Electron affinity, eV

1

21.4

1.0

Fig. 7. Electron affinity for (1) AlnPt (n = 1–15) and (2)Aln (n = 2–16) clusters.

Table 2. Bond lengths, averaged binding energies, and vertical ionization potential (experiment results [33], and this worktheoretical study)

ParameterPt2 Al2

calculated experimental calculated experimental

Bond length, Å 2.376 2.330 2.514 2.560

Ionization potential, eV 8.444 8.800 ± 0.200 6.294 6.200 ± 0.200

Eb, eV 1.288 1.570 ± 0.020 1.170 0.997 ± 0.108

6.8

0 4 8 12 16n

5.6

7.2

7.6

Ionization potential, eV

1

2

6.4

6.0

Fig. 6. Ionization potential for (1) AlnPt (n = 1–15) and(2) Aln (n = 2–16) clusters.

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affinity, and higher the stability. We found at n = 2, 3,7, 11, 14 the vertical electron affinities is lower.

CONCLUSIONS

The equilibrium geometries, relative stabilities,electronic properties of different sized AlnPt (n = 1–15)clusters are investigated systematically. Extensivestructures and different possible spin states are care�fully investigated by employing the density functionalcalculations at the B3LYP level. Their ground statestructures are obtained. It is found that the impurity Ptatom results in the local structural distortion of themixed clusters in comparison with the correspondingpure Al clusters. The distortion becomes less as thecluster size increases, the Pt impurity of the lowest�energy geometries of AlnPt (n = 1–12) is found tooccupy a peripheral position, while the Pt impuritiesof AlnPt (n = 13–15) prefer to occupy internal sites inthe Al clusters.

The ground slate of AlnPt (n = 1–15) clusters byNBO analysis results show that Al acts as an electrondonor, and the transfer of electrons from the Al atomsto the Pt atom, the Pt atom significant negative elec�trode can be see in Fig. 8. For Al2Pt, Al7Pt, Al11Pt,Al13Pt, the numbers of electrons transfer are morethan the adjacent to the numbers of transfer electrons,Al and Pt atoms effect stronger, further illustrating thatthey are stable, which is consistent with the previousΔ2E, ΔE, gap, VEA results. So the Al2Pt, Al7Pt, Al11Pt,and Al13Pt clusters exhibit high stability comparedwith their neighbors.

ACKNOWLEDGMENTS

This work was financially supported by theNational Natural Science Foundation of China (grantno. 20603021), the Natural Science Foundation ofShanxi (grant no. 2013011009�6), the High School131 Leading Talent Project of Shanxi, Undergraduate

Training Programs for Innovation and Entrepreneur�ship of Shanxi Province (grant no. 2013145) andShanxi Normal University (SD2013CXCY�65) andTeaching Reform Project of Shanxi Normal Univer�sity (SD2013JGXM�51).

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−0.6

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−1.2

−0.4

Charge

−0.8

−1.0

Fig. 8. Charge distribution on the Pt atom in the groundstate AlnPt (n = 1–15) clusters.

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