Density functional study of structural and electronic ...physics.mff.cuni.cz/kchfo/burda/Clanky/37_02jcp_vbk.pdf · Electronic mail: [email protected] b!Present address: Department

JOURNAL OF CHEMICAL PHYSICS VOLUME 117, NUMBER 7 15 AUGUST 2002

Density functional study of structural and electronic propertiesof bimetallic silver–gold clusters: Comparison with pure goldand silver clusters

Vlasta Bonacic-Koutecky,a) Jaroslav Burda,b) Roland Mitric, and Maofa Gec)

Institut fur Chemie, Humboldt-Universita¨t zu Berlin, Brook-Taylor-Straße 2, D-12489 Berlin, Germany

Giuseppe Zampella and Piercarlo FantucciDipartimento di Biotecnologie e Bioscienze Universita´ degli Studi di Milano Bicocca, Piazza della Scienza2, I-20126 Milano, Italy

~Received 28 March 2002; accepted 20 May 2002!

Bimetallic silver–gold clusters offer an excellent opportunity to study changes in metallic versus‘‘ionic’’ properties involving charge transfer as a function of the size and the composition,particularly when compared to pure silver and gold clusters. We have determined structures,ionization potentials, and vertical detachment energies for neutral and charged bimetallicAgmAun @3<(m1n)<5# clusters. Calculated VDE values compare well with availableexperimental data. In the stable structures of these clusters Au atoms assume positions which favorthe charge transfer from Ag atoms. Heteronuclear bonding is usually preferred to homonuclearbonding in clusters with equal numbers of hetero atoms. In fact, stable structures of neutral Ag2Au2 ,Ag3Au3 , and Ag4Au4 clusters are characterized by the maximum number of hetero bonds andperipheral positions of Au atoms. Bimetallic tetramer as well as hexamer are planar and havecommon structural properties with corresponding one-component systems, while Ag4Au4 and Ag8

have 3D forms in contrast to Au8 which assumes planar structure. At the density functional level oftheory we have shown that this is due to participation ofd electrons in bonding of pure Aun clusterswhile s electrons dominate bonding in pure Agm as well as in bimetallic clusters. In fact, Aun

clusters remain planar for larger sizes than Agm and AgnAun clusters. Segregation between twocomponents in bimetallic systems is not favorable, as shown in the example of Ag5Au5 cluster. Wehave found that the structures of bimetallic clusters with 20 atoms Ag10Au10 and Ag12Au8 arecharacterized by negatively charged Au subunits embedded in Ag environment. In the latter case, theshape of Au8 is related to a pentagonal bipyramid capped by one atom and contains three exposednegatively charged Au atoms. They might be suitable for activating reactions relevant to catalysis.According to our findings the charge transfer in bimetallic clusters is responsible for formation ofnegatively charged gold subunits which are expected to be reactive, a situation similar to that of goldclusters supported on metal oxides. ©2002 American Institute of Physics.@DOI: 10.1063/1.1492800#

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I. INTRODUCTION

Increasing interest in structural and electronic properof small gold clusters as function of their size has beentiated by the discovery of unusual catalytic activity of smsupported gold clusters1 in contrast to the inert bulk materiaAlso, in the reaction study of combustion of CO on sizselected small monodispersed gold clusters supportedmagnesia, it has been found that Au8 is the smallest catalyti-cally active cluster size.2 It has been shown that the aniongold clusters with even number of atoms react with molelar oxygen having low values of electron affinities in contrato those with odd number of atoms, thus exhibiting teven–odd oscillatory behavior as a function of the clus

a!Electronic mail: [email protected]!Present address: Department of Chemical Physics and Optics Charles

versity, CZ-12116 Praha, KeKarlovu 3, Czech Republic.c!Present address: Institute of Chemistry, the Chinese Academy of SciZhongguancun, Beijing 100080, Peoples Republic of China.

3120021-9606/2002/117(7)/3120/12/$19.00

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size.3 The connection between electron affinity and activtion of molecular oxygen by gold clusters at low temperatuhas been also established.4

The experimental values of electron affinities, verticdetachment energies, and ionization potentials of pure gclusters as function of their size are known from eainvestigations.5–7 Structural properties of small anionic anneutral Aun (n53 – 8) clusters have been theoreticainvestigated.8–11 In the case of cationic Aun

1 (n,14) clus-ters, the structures have been determined in the framewothe density functional method and used for structural assment in ion mobility measurements.12 There are similaritiesfor small clusters (n53,4), but also significant differencebetween the structures of cationic gold and silver clustlarger than tetramers. The latter are known from our earwork.13,14This has been also confirmed by recent ion mobity measurements and calculations on cationic silclusters.15 Since the calculated values of vertical detachmenergies, electron affinities, and collision cross sections

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3121J. Chem. Phys., Vol. 117, No. 7, 15 August 2002 Silver–gold clusters

strongly structure dependent, the energy sequence of themers remains still an important issue and can stronglypend on the theoretical method applied. The experimeconditions, in particular the temperature, may also signcantly influence the measured properties. Therefore, an arate determination of structural properties of pure gold clters is important in order to address aspects of threactivity. In fact, the theoretical treatment of the gold cluters is much more demanding than of silver clusters, sincthe former cased electrons are expected to participate in tbonding and in the latter case they are localized in the corthe Ag atoms and do not play a key role for structuproperties.16

In contrast to the pure gold and silver clusters, considably less information is available about structural and eltronic properties of bimetallic silver–gold clusters. Excetion is an experimental work on photodetachmentAgmAun (m1n<4) clusters17 and earlier18 as well asrecent19 theoretical work on the mixed trimers. Several opquestions have not been addressed yet. The role ofhetero-polar bonding versus homonuclear metallic bondin small bimetallic clusters should be clarified, since tformer can promote charge transfer from the Ag to theatoms. Charged gold species embedded in thesurrounding might be interesting systems for studying retivity. It is known that metal oxide support which is resposible for the charge transfer plays a key role for generathe catalytic activity of supported Au catalysts. In this cotext, it is of particular interest to find the structural patterpromoting charge transfer in bimetallic clusters. For this ppose it is necessary to search for the given size and the cposition of clusters which can give rise to negatively charggold species embedded in the environment of silver atoIn other words, the investigation of ‘‘ionic’’ versus metalliproperties with charge transfer in bimetallic clusters is iportant for gaining an understanding about their possibleas reactive centers. In this regard it is also useful to compthe structural and electronic properties of bimetallic golsilver clusters with those of gold and silver one-componsystems.

In this article after a brief outline of computational aproach in Sec. II, which is based on the density functiomethod with two different effective core potentials and cresponding AO basis sets, we present structures and binenergies of the neutral gold clusters Aun (n52 – 10) in Sec.III. Results on anionic, neutral, and cationic bimetallic trimers, tetramers, and pentamers are given in Sec. IV. Propeof neutral larger bimetallic clusters such as Ag3Au3 ,Ag4Au4 , Ag5Au5 , Ag10Au10, and Ag8Au12 are presented inSec. V. The occurrence of charge transfer and formationnegatively charged gold subunits which can serve as reaccenters are addressed. Comparison of bimetallic with pgold and silver one-component systems allows us to shdifferent roles ofs andd electrons for bonding in these sytems. Conclusions and outlook are given in Sec. VI.

II. COMPUTATION

The gradient corrected density functional method wrelativistic effective core potentials~RECP! is used through-


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out the article. The aim is to investigate structural propertof bimetallic AgmAun clusters as a function of the size anthe composition for 3<(m1n)<20 and compare them withthe properties of pure Agm and Aun clusters. Therefore, weproceeded in two directions taking into account either ovalence electron per atom~1e-RECP! or 19 valence electronsper Au and Ag atom~19e-RECP!.

Recently we developed 1e-RECP for the Au atom arevised the corresponding 1e-RECP for the Ag atom togewith small AO basis sets19 based on DFT calculations withBecke and Lee, Young and Parr~BLYP! exchange,20 andcorrelation21 functionals. As described in Ref. 19, the 1RECPs were derived by starting from our 11e-RECP forAg atom16 with original uncontracted 6s5p5d AO basis setand from 19e-RECP of Hay and Wadt22 for the Au atom withtheir 8s6p4d uncontracted basis set. Our 1e-RECPssemiempirical because atomic and diatomic data have bused in the fitting procedure. Comparison of the ground sproperties of homo- and hetero-nuclear neutral and chardimers obtained employing 1e-RECP BLYP method wavailable experimental data shows that the calculated bdistances are in very satisfactory agreement with experimtal values~cf. Table I and Ref. 19!. Ionization potentials~IP!,electron affinities~EA!, vertical detachment energies~VDE!,and dissociation energies deviate mostly by;0.2 eV fromthe measured ones except for the IP of Au2 for which thisdeviation is slightly larger~cf. Table I and Ref. 19!.

In order to determine influence ofd-electrons on bond-ing properties in Au clusters and in bimetallic clusters wemploy 19e-RECP from the Stuttgart group23 with the@9s7p5d1 f #/@7s5p3d1 f # for Au atom and with@8s7p5d1 f #/@6s5p3d1 f # for Ag atom in the framework ofDFT with the S-VWN and Becke–Perdew24 parametrization~BP-86! as in Refs. 12 and 15. We have shown previousl16

that 1e-RECP configuration interaction method allowsadequate description of the ground state properties of pAg clusters13,14and compares well with results obtained wi11e-RECP coupled cluster method.16 The d electrons are lo-calized in the atomic cores and do not participate directlybonding. This has been confirmed recently for the catioAg clusters experimentally and theoretically,15 as well as forthe neutral clusters.25 The bond distances, frequencies adissociation energies for homonuclear and heteronucneutral and charged dimers obtained with 1e-RECP BLand 19e-RECP BP86 approaches are given in Table Icompared with available experimental data.26–31 Bond dis-tance obtained from 1e-RECP BLYP are in better agreemwith experimental data than those of 19e-RECP BP86 produre. The latter give rise to distances slightly larger thanexperimental ones which might influence computed strtural properties, particularly of very small systems. Dissoction energies (De) for silver and mixed dimers obtained fromboth treatments are in satisfactory agreement will the avable experimental data.De for Au2 calculated with 19e-RECP BP86 is in better agreement with the experimenvalue. Concerning the accuracy of IP values, considera


3122 J. Chem. Phys., Vol. 117, No. 7, 15 August 2002 Bonacic-Koutecky et al.

TABLE I. Ground state properties of the atoms and dimers obtained with the 1e-RECP BLYP and the 19e-RECP BP96~in square brackets! methods.

re

~Å!re(expt.)

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cm21De

~eV!De(expt.)

~eV!IP

~eV!IP~expt.!

~eV!VDE~eV!

VDE~expt.!~eV!

Au 9.25 @9.73# 9.23a 2.27 @2.44# 2.31a

Ag 7.58 @8.22# 7.58a 1.23 @1.54# 1.30a

Au2 [email protected]# 2.4719b [email protected]# 190.9b 2.52 @2.28# 2.29b 9.85 @9.50#f 9.20e

Au21 [email protected]# [email protected]# 1.92 @2.43#

Au22 [email protected]# 2.582b [email protected]# 149.0b 1.92 @2.01# 1.92b 2.12 @2.08# 2.01b

Ag2 [email protected]# 2.5303c [email protected]# 192.4b 1.83 @1.74# 1.65c 7.83 @8.18#f 7.6557b

Ag21 [email protected]# [email protected]# 1.57 @1.78#

Ag22 [email protected]# 2.600c [email protected]# 145.0b 1.40 @1.46# 1.37c 0.92 @1.31# 1.06b

AgAu [email protected]# 2.496d [email protected]# 2.00 @2.10# 2.10d 8.85 @8.92#f

AgAu1 [email protected]# [email protected]# 1.10 @1.40#AgAu2 [email protected]# [email protected]# 1.30 @1.30# 1.27 @1.72# 1.43g

aReference 26. eReference 31.bReferences 6, 27, and 28. fAdiabatic ionization potentials.cReference 29. gReference 17.dReference 30.

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deviations from the experimental results are found for Au2 at1e-RECP BLYP level and for Au and Ag atom as well asAg2 at the 19e-RECP BP86 level of calculations. The VDvalues from 1e-RECP BLYP are in good agreement withperimental data, while 19e-RECP BP86 values are in genlarger than experimental ones. Since thes–d excitation forAu and Ag atom is 1.74 and 3.97 eV, respectively, it is nsurprising that inclusion ofd electrons is important for thepure Au clusters while the 1e-RECP BLYP provides reliaresults for Ag clusters. Therefore, for the neutral gold clters we carried out 19e-RECP BP86 calculations whichpresented in Sec. III. Comparison of the results obtained w1e-RECP BLYP procedure shows that the most stable sttures obtained from both treatments differ for cluster si6<n<10.

The accuracy of electron correlation treatment atDFT level of theory for Au clusters in the framework o19e-RECP is difficult to judge. It seems that DFT procedgives rise to relatively smalls–d energy gap which mighlead to overestimated hybridization effects. The only comtationally convenient alternative to the DFT treatment ofelectrons per atom is offered by Møller–Plesset meth~MP2! which is known to be less adequate for delocalizthan for directional bonding. Both methods have been uwith 19e-RECP for determination of structures of the cionic Agm

1 clusters.15 The MP2-method gave rise to the 3structure of Ag7

1 ~pentagonal bipyramid! and DFT to the 2Dplanar structure although the energy difference betweenstructures is very small. The 3D structure is in better agrment with ion mobility measurements.15 In general MP2 andDFT yield similar results for cationic Ag clusters for whicthe correlation ofd electrons is not very important. In contrast, cationic gold clusters are predicted by DFT to be plafor larger sizes~e.g., Au7

1! in agreement with ion mobilitymeasurements,12 while MP2 predicts a 3D structure for Au7

1

similar to that of Ag71 . This indicates that MP2 might un

derestimate contribution ofd electrons to bonding in Au71

cluster. In fact, based on combined experimental and theo


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ical work12,15 conclusion has been drawn that the numberbonds in stable structures of cationic silver clusters is larthan in those of cationic gold clusters for sizes 5<n<11.Therefore, the DFT description might be more realisticAu clusters than that offered by MP2 approach. We acarried out several comparisons between DFT and MP2sults for neutral Au and for Ag clusters and they showed tthe two methods disagree mainly for gold systems. This dcrepancy is particularly large, for example in the case of A8

for which the DFT energy difference between the most staplanar structure and the 3D-Td form is ;0.5 eV, while MP2yields Td structure by;0.81 eV lower than the planar oneSince MP2 has tendency to produce similar structuresgold and silver clusters, it seems that the correlation effefor d electrons in the case of Au clusters are not sufficientaken into account. Based on these findings the DFT metis used throughout the article. However, there is no prabout its accuracy, particularly concerning the determinatof the cluster size at which the transition from 2D to 3structure occurs in the case of pure Au clusters.

In order to check the accuracy of the 1e-RECP BLYprocedure for determination of structural properties of bimtallic clusters we have carried out comparison with the 1RECP BP86 approach for the smaller clusters 3<(m1n)<8. As it will be shown in Secs. IV and V, the structurproperties of bimetallic clusters are well described by1e-RECP BLYP procedure, particularly neutral species, sithe s–d hybridization is considerably smaller than in thpure Au clusters. All geometries have been fully optimizand vibrational analysis has been carried out for the majoof structures in order to determine the local minima onenergy surfaces. We refer throughout the article to 19e-REwith BP86 parametrization as 19e-RECP and to 1e-REwith BLYP functional as 1e-RECP. Calculations have becarried out usingGAMESS-UK32 and GAUSSIAN 9833 programpackages.


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III. NEUTRAL GOLD CLUSTERS Au n „nÄ2 – 10…

The binding energies per atom obtained from the 1RECP as a function of the cluster size calculated for the mstable structures are presented in Fig. 1. The lowest enstructures as well as those corresponding to almost degeate isomers are also shown in Fig. 1. The geometriesenergies of all optimized structures corresponding to diffent isomers for each cluster size are available in the etronic form as supplement to this article~Ref. 34!. The low-est energy structures of Aun up to n510 are planar at theDFT level of theory and they are not directly related to stions of the bulk phase. Since large numbers of structuhave been investigated for each cluster size, we are confithat the global minima have been identified for the majorof clusters investigated. The binding energies per atomcrease with the cluster size, exhibiting pronounced even–alternation which indicates larger stability of clusters wthe even number of electrons than of those with odd numof electrons. This is a common feature for all clusters ofand Ib elements.

The stable structures are well separated in energy fother isomers in all cases with the exception of Au3 , Au4 ,and Au7 ~cf. Fig. 1!. For trimer the linear and isosceles trangular geometries are almost degenerate, for tetramerhombic and T-form are very close in energy, and for theptamer two planar geometries with different patternscompeting in stability. The energy ordering of close lyinisomers can depend on the details of the theoretical trment. This has been illustrated by the study carried outstructures of Au3 employing different methods.35 The isosce-les triangular geometry is the most stable structure atlevel of the coupled cluster theory including single, douband triple excitations CCSD~T! with the two states, the2A1

and2B2 close in energy, arising from the Jahn Teller effeThe linear form is slightly higher in energy. In the preseDFT study the 1e-RECP gives rise to very similar results,the energy of the linear form is slightly lower when the 19RECP is used~cf. Ref. 34!. This confirms that accurate determination of the bond lengths such as at 1e-RECP Dlevel might be very important for structural properties

FIG. 1. Binding energies per atom for neutral gold clustersEb /n5@E(Aun)2nE(atom)#/n as a function of the cluster sizen calculated forthe most stable structures on Fig. 1~cf. also Table I S and Fig. shown on ofsupplement Ref. 34!. For isomers with energy difference smaller than 0.1both structures are shown~cf. n53, 4, and 7!.


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small systems such as Au3 , as pointed out in Sec. II.At this point it is useful to address the role ofd electrons

for bonding in Au clusters. The rhombic and T-form of thtetramer are closer in energy if thed electrons are accountefor with 19e-RECP, but the former remains the most stastructure as in the 1e-RECP treatment. In contrast, 19e-Rpredicts planar structures of the heptamer to be considerlower in energy~by 0.9 eV! than the 3D structures~cf. Ref.34!, while the 1e-RECP gives rise to the pentagonal bipymid as the most stable form. Discrepancies between theapproaches in predicting the transition from 2D to 3D strutures indicate that the inclusion ofd electrons in the treat-ment is important for the ground state properties of the pAu clusters with nuclearity larger than 6. This finding is alsupported by the investigations carried out on the cationicclusters using the same 19e-RECP BP86 treatment as inarticle. Therefore a comparison of our results obtainedthe neutral Au clusters can be made with those of Ref. 12cationic species.

The stable structures of the neutral Au clusters presenin Fig. 1 differ from those found for the cationic clusterwith the exception of the tetramer and the hexamer whassume rhombic and the planar triangular forms in bcases. According to Ref. 12 cationic Au clusters larger thheptamer have 3D forms related to the sections of the bphase, which indicates a substantial influence of the posicharge on the structures of gold clusters. This is also edenced by the form of the stable planar structures ofneutral Au clusters~cf. Fig. 1! which favor maximum num-ber of exposed atoms accommodating negative charge.lowest energy structures of Aun (n54 – 7) can be derived byadding a single atom to the lowest energy structure of Aun21

cluster, thus forming an additional triangular subunit. Thpattern changes for the most stable structure of Au8 in whichthe square subunit is capped by four atoms on each side.structural motive changes again for Au9 and Au10. In theformer case the single atom assumes central positiontherefore is highly coordinated, and in the latter case tcentered highly coordinated atoms are present~cf. Fig. 1!.

What is the reason for the 2D forms of Aun clusters? Thes–d energy separation in Au atom is relatively small anda consequence thed electrons might participate in bondingHowever, the degree of their participation seems to bependent upon structural properties. We have carried outanalysis of DFT density of states~DOS! in terms ofs-, p-,andd-contributions which allowed us to identify them in thenergy interval important for the bonding. Two differecharacteristic features have been identified for the 2D andstructures, for example in the case of Au8 . The DOS corre-sponding to the HOMO of the planar structure is dominaby the d-contributions and the energy gap with respectother DOS with mixeds- and d-character is very small. Incontrast, DOS obtained for the Td structure corresponding tothe HOMO has largers- thand-contributions and is stronglyseparated from lower energy DOS which are dominatedd-contributions. The above analysis indicates that the hig


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stability of the planar structure of Au8 is due to larger con-tributions ofd electrons to the bonding than in the case ofTd-3D structure. This explains qualitatively also why thneutral silver clusters which are characterized bys-typebonding assume 3D structures already for larger sizeshexamer.

As pointed out in Sec. II, structural properties of Aclusters are very dependent on the particular method adofor description of electron correlation effects. Accordingion mobility measurements12 on cationic Au clusters it is tobe expected that also larger neutral Au clusters than hexers assume planar structures as obtained from thetheory. Whether the neutral gold clusters are still planar un510 or not remains to be verified. Notice that the enedifference between 2D and 3D structures is smaller for A9

and Au10 clusters (DE'0.2 eV) than for Au7 and Au8

(DE'0.5 eV) at the DFT level of calculations. Since DFtends to favor planar structures of Au clusters, the error;0.2 eV can not be presently excluded.

The above findings are particularly important for tstudy of the structural and electronic properties of bimetaclusters. The key role of the polar hetero bonds and a chtransfer to the gold atoms is of crucial importance for strtural properties of these systems as it will be shown infollowing sections.

IV. BIMETALLIC CHARGED AND NEUTRALGOLD–SILVER TRIMERS, TETRAMERS, ANDPENTAMERS

Systematic investigation of the structural and groustate properties of small bimetallic clusters have been carout with the aim to establish the role of the heteronuclversus homonuclear bonding in these systems. Due to laelectronegativity of the Au than of the Ag atom the chartransfer ofs electrons occurs to the gold atoms in bimetalsystems. Consequently, Au atoms prefer positions whichlow the largest charge transfer from Ag atoms.

A. Ag mAun0,¿,À

„n¿mÄ3…

The results on trimers with one- and two-gold atomobtained using 1e-RECP and 19e-RECP are summarizeFig. 2. Both anionic trimers Ag2Au2 and AgAu2

2 are linearwith peripheral positions of Au atom~s! minimizing the re-pulsion of the excess electron localized at the ends ofchains. Both RECPs give rise to the same energy orderinthe isomers. The bond lengths are shorter in the former c~cf. Fig. 2! as pointed out in Sec. II. For neutral Ag2Au thelinear form with two hetero bonds is close in energy with tisosceles triangular structure in both RECPs although tenergy ordering changes; linear structure is more stabl1e-RECP and the triangular form in 19e-RECP. In contrthe neutral AgAu2 prefers obtuse triangular form in bottreatments. The cationic trimers Ag2Au1 and AgAu2

1 haveobtuse and isosceles triangular geometries with posicharge localized at silver atoms~atom!, respectively. The energies of all isomeric forms are given in Table II S of thsupplement.34 The vertical ionization potentials (IPv) andvertical detachment energies~VDE! obtained from both 1e-RECP and 19e-RECP differ by 0.2–0.5 eV~cf. Table II!. The


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VDEs for Ag2Au2 are in acceptable agreement with thavailable experimental data17 while for AgAu2

2 the 19e-RECP yields VDE value which is closer to experiment17 thanthat obtained with 1e-RECP~cf. Table II!.

B. Ag mAun0,¿,À

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We present the structural and ground state propertiebimetallic tetramers starting with doping the silver trimerone Au atom and then increasing the Au-content. In tmanner the transition from ‘‘metallic’’ system doped by thone Au atom to the ‘‘ionic’’ AgAu–AgAu versus segregateAg2– Au2 system back to the ‘‘metallic’’ species doped bthe one Ag atom can be followed.

Since the 1e-RECP is applicable to considerably larsystems than the 19e-RECP, bimetallic tetramers offegood opportunity to check the reliability of the 1e-RECapproach against the results obtained with 19e-RECP~cf.

FIG. 2. Structures of charged and neutral bimetallic trimers AgmAun0,6 (n

1m53) optimized at the 1e-RECP BLYP and 19e-RECP BP86 leveltheory. The energy differences~in eV! with respect to the most stable structure obtained from the former and the latter approach are given in the roand square brackets, respectively. I–III denote energy sequence of themers according to 1e-RECP BLYP results. Labels of the symmetry grand of the ground electronic states are also given. Dark circles indicateatom~s! and light ones Ag atom~s!. For energies cf. Table II S of Ref. 34.


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Fig. 3!. Therefore the structures and their energy orderobtained from both treatments are given in Fig. 3 and engies are listed in Table III S of the supplement.34

Bimetallic neutral and charged tetramers tend to assurhombic structures with a number of hetero bonds demined by the composition. The gold atoms prefer expopositions while the silver atoms form a higher numberbonds. Such topologies are convenient for charge tranfrom Ag to Au atoms and seem to be independent fromdetails of theoretical treatment.

In the stable structures of the anionic Ag3Au2 and theneutral Ag3Au clusters the Au atom is located at the londiagonal of the rhombus being doubly coordinated toatoms in both RECP treatments. The energy ordering ofhigher lying isomers of Ag3Au2 ~the linear and T-form! ismore influenced by the details of the method. In contrast,the neutral Ag3Au the most stable structure is considerablower in energy than all other isomeric forms, independfrom the treatment~cf. Fig. 3!. In the case of the cationicAg3Au1 tetramer, the 19e-RECP gives rise to two structuwith almost equal energies in which the Au atom is locatedthe long and the short diagonal of the rhombus, respectivThey contain the Ag3

1 subunits with different geometries iwhich the positive charge is mainly located. The 1e-REinverses the energy sequence of these two isomers~cf. Fig.3!.

The stable structures of the anionic Ag2Au22 and the

neutral Ag2Au2 tetramers assume rhombic forms with twAu atoms located at the long diagonal, thus favoring shdistance Ag–Au and Ag–Ag bonds. This situation is convnient for charge transfer from Ag to Au atoms and simulneously allows us to minimize repulsion of charges locaat Au atoms. The global minimum of Ag2Au2 is well sepa-

TABLE II. Vertical ionization potentials (IPv) and vertical detachment energies ~VDE! for AgnAum (n1m52,3,4,5), AgnAun (n53,4,5,10), andAg12Au8 clusters obtained with 1e-RECP BLYP and 19e-RECP BP86~insquare brackets! methods.

AgnAum

IPv~eV!

VDE~eV!

VDE~expt.!a

~eV!

AgAu [email protected]# 1.27 @1.72# 1.43Ag2Au [email protected]# 2.78 @3.09# 2.97AgAu2 [email protected]# 3.47 @3.68# 3.86Ag3Au [email protected]# 1.56 @1.97# 1.66Ag2Au2 [email protected]# 1.62 @2.01# 1.62AgAu3

b ~I! @II # [email protected]# 2.00 @2.17#AgAu3

b ~II ! @I# 2.79 @3.02# 3.00AgAu3

b ~III ! @III # 3.13 @3.49#AgAu3

b ~IV ! @IV # 2.72 @3.17#Ag4Au [email protected]# 2.18 @2.47#Ag3Au2 [email protected]# 2.44 @2.70#Ag2Au3 [email protected]# 2.76 @3.02#Ag1Au4 [email protected]# 2.98 @3.17#Ag3Au3 [email protected]# 1.76 @2.13#Ag4Au4 8.44Ag5Au5 6.70Ag10Au10 6.37Ag12Au8 6.31

aExperimental results from Ref. 17.b~I–IV !, @I–IV # label isomers according to the energy sequence obtawith 1e-RECP and 19e-RECP, respectively.


gr-

er-dfere

e

r

t

st

ly.

P

rt--d

rated in energy from all other isomers, independently frothe treatment. In contrast, in the case of an anionic Ag2Au2

2

cluster the 19e-RECP gives rise to small energy differenbetween the stable rhombic structure and other isomforms. Similarly, for Ag2Au2

1 cluster, four isomers close inenergy have been found. The structure with homonucbonding (Ag2

1) – (Au2) is in competition with the heterobonded one due to the lack of one electron and the enesequence is influenced by the treatment.

Finally, the structures of tetramers with a single Ag atoare characterized by high coordination of Ag. For the neuAgAu3 and cationic AgAu3

1 clusters the Ag atom is locateat the short diagonal. In the case of the anion AgAu3

2 therhombic structure with the Ag atom at the short diagonal halmost the same energy as the T-form with the Ag atomthe central position at the 1e-RECP level of calculations. T19e-RECP gives preference to the T-form with respect torhombic form. However, in both structures the Ag atomthree-coordinated. It seems that the energy ordering ofisomers for the neutral species is less dependent on theoretical treatment employed than for the charged system

The calculated ionization potentials and VDEs are givin Table II. The values of the VDEs for the stable rhombstructures of Ag3Au2 and Ag2Au2

2 obtained from 1e-RECPare in excellent agreement with the experimental dat17

while the VDEs obtained from the 19e-RECP are higher ththe measured ones. In the case of AgAu3

2 the VDE value forthe T-form is considerably closer to the experimenfinding17 than the one for the rhombic structure, thus t19e-RECP gives rise to an excellent agreement with expmental data.17

In conclusion, the determination of structural propertof the neutral bimetallic tetramers is not dependent on incsion of d electrons, but for the charged tetramers the inflence ofd electrons on energy sequence of isomers might tplace. However, the general trend concerning structural perties of bimetallic tetramers remains the same in both trments. The Au atoms prefer hetero bonding than the honuclear bonding and tend to take peripheral positionsorder to withdraw charge from Ag atoms which are therefohigher coordinated.

C. AgmAun0,¿,À

„n¿mÄ5…

Stable structures of anionic and neutral bimetallic petamers assume planar trapezoidal structures with triangsubunits, in contrast to the cationic stable structures whprefer 3D forms as shown on Fig. 4. The energies ofstable structures as well as other isomeric forms obtaiwith 1e-RECP are given in Table IV S of the supplemen34

The calculations using the 19e-RECP have been carriedonly for the cases for which the energies of the stable strtures are very close to the other isomers. Both treatmegive rise to the equivalent stable structures as shownFig. 4.

In all anionic and neutral stable trapezoidal structurespentamers one Ag atom remains four-coordinated indepdently from the composition. In fact, the common structuproperties of anionic and neutral pentamers concerning p

d


ory.re bracelectronic


FIG. 3. Structures of charged and neutral bimetallic tetramers AgmAun0,6 (n1m54) optimized at the 1e-RECP BLYP and 19e-RECP BP86 level of the

The energy differences with respect to the most stable structure obtained from the former and the latter approach are given in the round and squakets,respectively. I–IV denote energy sequence of the isomers according to 1e-RECP BLYP results. Labels of the symmetry group and of the groundstates are also given. Dark circles indicate Au atom~s! and light ones Ag atom~s!. For energies cf. Table III S of Ref. 34.

Downloaded 04 Dec 2002 to 195.113.35.232. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp

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tions of hetero atoms are present with the exceptionAg3Au2

2 and Ag3Au2 as can be depicted from Fig. 4. Eventhis case Au atoms prefer hetero bonding, which meansno segregation between the silver and the gold subunitscur for the compositions~312! and ~213!.

The stable structures of cationic bimetallic pentamtend to deviate from planarity. The lowest energy structuof Ag4Au1, Ag2Au3

1 , and AgAu41 assume double triangula

forms sharing the Au atom~cf. Fig. 4!. In the case ofAg3Au2

1 the trigonal bipyramed with peripheral positionsAu atoms competes in energy with the double trianguform.

D. Ionization potentials and vertical detachmentenergies

Results obtained from both 1e-RECP and 19e-RECPbimetallic AgmAun trimers, tetramers, and pentamers asummarized in Figs. 5 and 6. They are plotted as a funcof the number of Ag atomsm for the fixed number of goldatomsn51,2,3. Both VDE and IPv values show in generaeven–odd behavior with increasingm. An exception is al-most equal VDE values for AgAu3

2 and Ag2Au32 ~cf. Fig. 6!.

The VDEs obtained from 19e-RECP are on average by;0.4eV higher than those obtained from the 1e-RECP and

FIG. 4. Stable structures of charged and neutral bimetallic pentamAgmAun

0,6 (n1m55) obtained from 1e-RECP BLYP procedure. Dacircles indicate Au atom~s! and light ones Ag atom~s!. For the energy dif-ferences of other isomers with higher energies for the given compositioatoms compare Table IV S of Ref. 34. The atoms are numbered or labeleletters in order to identify the position of Au atom~s! in different isomericforms in Table IV S of Ref. 34. For this purpose two isomers of Ag2Au3

2

and of Ag4Au1 are shown.


f

atc-

ss

r

r

n

e

available experimental values lay in between. The ionizatpotentials obtained from both treatments are in fairly goagreement~cf. Fig. 6!. These results indicate that the 1RECP at the DFT level is also suitable for determinationthe ground state properties of the bimetallic clusters sincthis case thes–d hybridization is not so strong as for thpure Au clusters. The absolute values of VDE for the givcluster size increase with the number of Au atoms, aspected. The values of ionization potentials can serve asindicator of the ‘‘ionic’’ character of the cluster when compared with the IP of the AgAu dimer which is;9 eV. In fact,the IPv values above 7.5 eV have been obtained for Ag2Au2

and Ag3Au3 clusters which assume planar structures wmaximum number of hetero bonds as shown in Fig. 7. Tproperties of Ag3Au3 will be addressed in the next section

rs

ofby

FIG. 5. Comparison of experimental~Ref. 17! vertical detachment energieVDE’s ~!! ~in eV! with calculated values obtained from 1e-RECP BLYP~+!and 19e-RECP BP86~,! methods for AgmAu2, AgmAu2

2 , and AgmAu32

clusters as a function ofm(1<m<4) ~cf. Table II!. The most stable struc-tures of anionic clusters are drawn. Dark circles indicate Au atom~s! andlight ones Ag atom~s!. In the case of AgAu3

2 the VDE’s obtained at 1e-RECP level of calculations are shown for all four isomers~h!. The first twoisomers have almost degenerate energies~cf. Table III S of Ref. 34! and theVDE for isomer II ~– • –! with the T-form which is drawn is in betteragreement with experiment.


erfordeed-

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1e-cturey

al

y

rgy

kets,1e-

lec-


FIG. 6. Vertical ionization potentials~in eV! obtained from 1e-RECP BLYP~+! and 19e-RECP BP86~,! methods for AgmAu, AgmAu2 , and AgmAu3

clusters as a function ofm (1<m<4). The most stable structures of neutrclusters are drawn. Dark circles indicate Au atom~s! and light ones Agatom~s!.

FIG. 7. Vertical ionization potentials~in eV! obtained from 1e-RECP BLYPmethod for (n51,2,3,4,5,10) and for Ag12Ag8 clusters. The lowest energstructures are drawn. Dark circles indicate Au atom~s! and light ones Agatom~s!.


V. NEUTRAL BIMETALLIC SILVER–GOLDAgnAun „nÄ3,4,5,10… AND Ag 12Au8 CLUSTERS

The study of the bimetallic clusters with equal numbof silver and gold clusters aims to find out the preferencecharge transfer in different structural patterns which inclumaximal number of hetero bonds and segregation or embding of two components. The other aspect of this investition is connected with the transition from 2D to 3D strutures which occurs for one-component systems at differcluster sizes. For the neutral clusters Ag7 assumes the 3Dpentagonal bipyramid form and gold clusters are planar uten atoms as shown in Sec. III. In addition to systems wequal number of silver and gold atoms the investigationthe Ag12Au8 cluster serves as a model for studying embeding of Au8 in the surrounding of silver atoms in connectiowith the possible reactivity of bimetallic species.

The results for Ag3Au3 and Ag4Au4 are presented onFig. 8. Both systems have been calculated using theRECP and 19e-RECP approaches. The most stable struof the Ag3Au3 is the planar triangular form with negativel

FIG. 8. Structures of neutral bimetallic Ag3Au3 and Ag4Au4 clusters opti-mized at 1e-RECP BLYP and 19e-RECP BP86 level of theory. The enedifferences with respect to the most stable structure~in eV! obtained fromthe former and latter approach are given in round and square bracrespectively. I–IV denote the energy sequence of isomers according toRECP BLYP results. Labels of the symmetry group and the ground etronic states are also given. Dark circles indicate Au atom~s! and light onesAg atom~s!.


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charged Au atoms located at the peripheral position indepdent from the treatment. The pentagonal pyramid and tehedral type of structures with different locations of heteatoms have been systematically investigated at the 1e-Rlevel. Several 3D structures optimized with 19e-RECPfor illustration shown in Fig. 8, but all of them also havsubstantially higher energies than the planar Ag3Au3 . Incontrast, the Ag4Au4 assumes 3D tetrahedral type of struture with negatively charged Au atoms located at the outstetrahedron capping the inner silver tetrahedron and formhetero bonds. Again systematic investigation of differentand 2D structures has been carried out with the 1e-RECPenergy ordering of several structures was checked aga19e-RECP results as shown in Fig. 8. All of them lie engetically above the bimetallic Td structure. The pure Ag8assumes also the Td structure in contrast to the planar forof Au8 . In other words, the hetero bonding influences sstantially the structural properties of gold octamer. Sinces–d separation in bimetallic systems is substantially larthan in the pure Au clusters, as evidenced by analysis baon DFT density of states~DOS!, the structural properties oAg4Au4 are closer to the ones obtained for Ag8 . Moreover,the ‘‘ionic’’ nature of Ag3Au3 and Ag4Au4 is evidenced bylarge values of ionization potentials. They are only by 0and 0.5 eV lower than the IPv value of the hetero dimeAgAu as shown in Fig. 7.

After the transition to 3D structures has been determiwe employed the 1e-RECP for larger systems whichcomputationally more demanding. Since we found thatstable structure of Ag4Au4 is closer related to the structure othe silver than of the gold octamer, the optimization of Ag10

and Ag20 has been first carried out and the correspondstructures were used as the starting point for consideratiothe bimetallic structures. Of course for the cluster of this sit cannot be guaranteed that the absolute minimum has bfound.

FIG. 9. Optimized structures of Ag10Au10 clusters at 1e-RECP BLYP leveof theory with relative energy differences~in eV! in brackets. Dark circlesindicate Au atom~s! and light ones Ag atom~s!.


n-a-

CPe

eg

ndst

-

-ered

5

dee

gofeen

For Ag10 two lowest energy structures can be derivedbicapping the Td and antiprism subunits, respectively. Thother higher lying isomers contain a pentagonal bipyramcapped by three atoms in different ways. A systematic invtigation of Ag5Au5 has been carried out by placing Au atomat different positions searching for the segregation betwtwo components versus other patterns, e.g., such as acing the largest charge transfer to the Au atoms. The laproved to be more successful. The lowest energy strucfound for Ag5Au5 is deformed bicapped antiprism withchain of Au atoms at the peripheral positions attractingnegative charge as shown on Fig. 8. Other structures wsegregation pattern or with larger number of hetero bohave substantially higher energies. Correspondingly,value of IPv for Ag5Au5 is considerably lower than the onobtained for the Td structure of Ag4Au4 with the maximumnumber of hetero bonds~cf. Fig. 8!.

In the case of 20-atoms we investigated first the strtural properties of Ag20 and Au20 clusters and found that thC3 form with the icosahedral subunit capped by seven atohas lower energy than different C2v and Td type of structures.For the bimetallic Ag10Au10 cluster, structures with lowesenergies contain Au atoms distributed in the icosahedral sunit of the deformed C3 structure as shown in Fig. 9. Ththree structures labeled bya, b, andc are close in energy andthey differ only in differently placed Au atom~s! within theicosahedral subunit. The structure labeled byd contains oneAu atom outside the icosahedra and has by 0.2 eV higenergy with respect to the structurea. The lowest energystructure exhibits the largest charge transfer from the sito gold atoms. All Au atoms except of the central one hanegative charge while Ag atoms are positively charged. TAu10 subunit with one central atom is embedded in the srounding of Ag atoms.

This pattern remains valid for the lowest energy struture found for Ag12Au8 as shown in Fig. 10. In this case th

FIG. 10. Optimized structures of Ag12Au8 clusters at 1e-RECP BLYP leveof theory with relative energies~in eV! in brackets. Dark circles indicate Auatom~s! and light ones Ag atom~s!. Numbers 1, 2, 3 label the Au3 negativelycharged facet which has convenient position to interact with reactants.


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Au8 assumes the pentagonal bipyramidal structure cappeone atom and is also a part of an icosahedral subunit. Allsurface atoms are negatively charged. This Au8 subunit em-bedded in Ag12 represents a good candidate for the reactcenter, since three exposed Au atoms labeled by 1,2,3 in10 have convenient positions to react with molecules. In fsuch three-atomic facets of Au8 have been found also in thmodel calculations of gold clusters supported on magnand used for the reactivity study with O2 and CO molecules.2

Notice that the structureb in Fig. 10, which does not contaiAu3-facet, has by;0.13 eV higher energy than to the struture a. In the structurec, which has even higher energy, onAu atom lies outside the icosahedral subunit. This indicathat the lowest energy structurea of Ag12Au8 represents aninteresting model for studying the reactivity of bimetallclusters.

VI. CONCLUSIONS

Our density functional study of structural propertiesbimetallic silver–gold clusters and their comparison wone-component systems allows us to draw following concsions:

~1! The charge transfer from Ag to Au atom~s! plays domi-nant role for structural properties of bimetallic clusteThe degree ofs–d hybridization lies between the lowone for Ag and the large one for Au clusters.

~2! In small bimetallic clusters 3<(n1m)<5 a general ten-dency can be observed that Ag atom~s! prefer to formmore bonds than Au atom~s! as in the case of pure Agand Au clusters, respectively. However, Au atoms favpositions at which it is convenient to withdraw thcharge from Ag atoms.

~3! Formation of hetero bonds is more favorable thanhomo bonds as shown for AgnAun (n52,3,4) speciesgiving rise to high ionization potentials and stability‘‘ionic’’ species.

~4! Segregation between two components is not energcally favorable.

~5! In both studied clusters with 20 atoms, Ag10Au10 andAg12Au8 , a negatively charged Au10 or Au8 subunit isembedded in the Ag environment.

~6! In the case of Ag12Au8 the shape of Au8 corresponds tothe pentagonal bipyramid capped by one atom in whthree exposed gold atoms form a facet capable of inacting with reactants. Small gold negatively charged sunits embedded in Ag surroundings might serve as retive centers similarly to gold clusters supported on meoxides.

~7! Structural properties of bimetallic clusters are closerlated to those of Ag than to those of Au clusters. Thedelectrons are involved in the bonding in Au clustewhile thes electrons are primarily responsible for formtion of bonds in Ag clusters. Consequently, therestructural differences between neutral Ag and Au specfor sizes larger than hexamers and for cationic cluseven for sizes larger than tetramers according to Refsand 15. Stable structures of pure Au clusters hasmaller number of bonds and tend to remain planar w


byu

eig.t,

ia

s

f

-

.

r

f

ti-

hr--

c-l

-

es

rs2

ee

the structures of Ag clusters have a larger numberbonds and tend to become three-dimensional for smasizes, similarly as bimetallic clusters.

In summary, we have shown that bimetallic silver–goclusters own interesting properties which can be importfor reactivity studies. This finding might stimulate furtheexperimental work in this area.

ACKNOWLEDGMENTS

This work was supported by the Deutsche Forschungemeinschaft SFB 450. We thank Professor M. Kappescommunicating the results prior to publication.

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truic

v

ore


34See EPAPS Document No. E-JCPSA6-117-303231 for investigated stures and energies~Table I S! of gold clusters. The energies of bimetallclusters are given in Tables II S–IV S. This document may be retrievedthe EPAPS homepage~http://www.aip.org/pubservs/epaps.html! or from


c-

ia

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Density functional study of structural and electronic ...physics.mff.cuni.cz/kchfo/burda/Clanky/37_02jcp_vbk.pdf · Electronic mail: [email protected] b!Present address: Department