双金属表面相互作用机理

J.Phys.Chem.B2001,105,1817-18221817

TheoreticalStudyoftheInteractionofMolecularHydrogenwithPdCu(111)BimetallicSurfaces

CarmenSousa,VirineyaBertin,andFrancescIllas*

DepartamentdeQu?´micaF?´sicaiCentreEspecialdeRecercaenQu?´micaTeo`rica,UniVersitatdeBarcelonaC/Mart?´iFranque`s1,08028Barcelona,SpainReceiVed:September18,2000;InFinalForm:NoVember27,2000

AdensityfunctionalclustermodelapproachhasbeenappliedtothestudyoftheinteractionofmolecularhydrogenwithtwodifferentclustermodelsofthePdCu(111)surfacecorrespondingtoadifferentformalalloycompositionbothhavingasinglePdatominthesurface.Despitethesimilarsurfacemorphologyofthetwobimetallicclusters,theyexhibitaratherdifferentreactivitytowardmolecularhydrogen.ThecoordinationofthesurfacePdatomtootherPdatomsinthesecondlayerappearstobenecessaryforthisatombeabletotrapanddissociatemolecularhydrogenwithaverylowenergycost,thusbeingapotentialactivesiteforcatalysis.Thisimportantresultpointsoutthatelectronic,orligand,effectsdoalsoplayanimportantroleintheactivityofthePdCu(111)surfacesitestowardmolecularhydrogen.

I.Introduction

Bimetallicsystemsconstituteabroadclassofselectivecatalyststhatattempttoexploitandcombinethedifferentchemicalpropertiesofvariousmetalstowardagivenchemicalreaction.1-3Inparticular,bimetallicsystemshavebeenlongusedforhydrocarbonreforminginthepetrochemicalindustry.4-6Therequirementforefficientchemicalprocessesderivedfromthehugedemandinthehydrocarbonmarkettriggeredaratherlargenumberoffundamentalstudiesaimedtobetterunderstandtheparticularitiesofthesecatalyticsystems.Thedifferentactivityofbimetallicsystemswithrespecttothepuremetalshasbeenoftenrationalizedintermsoftwomaineffects;6-10thoseareusuallytermedasstructuralandelectronicorligandeffects,respectively.Thestructuraleffectreferstothepossiblechangesinthetypeanddistributionofactivesitesinanalloywithrespecttoasinglecomponent,whereastheelectroniceffectsareduetoprofoundchangesintheelectronicstructureofametalcausedbythepresenceofthesecondcomponent.Theconceptsofstructuralandelectroniceffectshavebeenveryusefultojustifythesuperiorcatalyticactivityofbimetallicsystems.However,fromamicroscopicpointofviewonemaywonderwhetherthedistinctionbetweenthetwoeffectsisstraightforwardorifitrequiresadetailedanalysisoftheelectronicstructureofeachparticularalloyandofitsreactivitytowardprobemolecules.LetusconsiderasingleAatominasimpleABbinarysystem.Fromapurelystructuralpointofview,theactivityofthissurfaceatomwillbethesame,independentofitscoordinationtootheratomsinthesecondlayer.However,itispossiblethatthisAsiteexhibitsadifferentreactivitydependingonitscoordinationinthesecondlayertoonlyAatomsoralsotoBatoms.

Amidtheseveralbinarysystemsthatareoftenusedinbasicandpracticalresearch,PdCuprovidesanexampleofaratherversatilecatalyticsystem.IthasbeenshownthatPdCucatalystsareabletosimultaneouslyoxidizeCOandtoreduceNO,11thusbeingofpracticalinterestintheautomotiveindustry.Likewise,PdCuisefficientinalkeneoxidation,12ethanoldecomposition,13

*Correspondingauthor.E-mail:f.illas@qf.ub.esandinseveralhydrogenationprocesses,e.g.,inCO,benzene,andtoluenehydrogenation.13-16Becauseofthesepeculiarities,PdCualloyshavealsobeeninvestigatedtheoretically.ThenatureoftheheterometallicbondinthesebinarysystemshasbeenstudiedbyFerna´ndez-Garc?´aetal.17usingaclustermodelapproachandfirstprinciplesdensityfunctionalcalculationsincludinganenergypartitioninganalysisbasedonthecon-strainedspaceorbitalvariation,CSOV,method.18-20ThepictureoftheelectronicstructurearisingfromthesestudiesisrathercomplexandinvolveschargetransferfromCu(4sp)orbitalstothePd(5sp)ones,Pd(4d)fPd(5sp)rehybridization,andalmostnegligiblechangesintheCu(3d)population.Indeed,itwasfoundthatsurfacePdatomscarryonasmallbutnoticeablenegativecharge.ThisfactisnotincontradictionwithapositiveshiftofthePdcore-levelsthatarisespreciselyfromthelargePd(4d)fPd(5sp)rehybridizationthatmoveselectrondensityawayfromthecoreregion.

Thechangesintheelectronicstructuredescribedabovehaveamarkedinfluenceinthechemicalreactivityofthesebinaryalloys.Foralargenumberofalloys,RodriguezandGoodman21werethefirsttoshowastrongcorrelationbetweenthecore-levelshiftsonthealloyinducedbyCOchemisorptionandtheCOdesorptiontemperature.Thiscorrelationwaslaterinterpretedasoriginatedbytheextentofπ-back-donationand,hence,attributedtothepositionofthemetaldband.22SubsequentclustermodelcalculationshavealsofoundanalmostlinearcorrelationbetweenthecalculatedinteractionenergiesandthePdcore-levelshifts.23However,theCSOVanalysisshowsthatthiscorrelationcannotbeexplainedintermsofback-donationonly.ThecomplexbehaviorofthebimetallicsystemsisfurtherillustratedbytheveryrecentstudyofLo´pezandNorskøv24concerningtheinteractionofCOonseveralPdCualloys.TheseauthorsshowthateventheinteractionofCOwiththeinactivecomponentofthealloyisenhancedwithrespecttothepuresystem.

AdditionalinformationaboutthereactivityofPdCubimetallicsurfacesrequirestheuseofaprobemoleculethatcouldexperiencesomechemicalreactionwithbreakingandforming

10.1021/jp003349hCCC:$20.00©2001AmericanChemicalSociety

PublishedonWeb02/08/2001

1818J.Phys.Chem.B,Vol.105,No.9,2001

bonds.MolecularhydrogenisnodoubtagoodcandidatebecauseH2dissociationisoneoftheimportantelementaryreactionsrelevanttovariouscatalyzedprocesses.1-4InthecaseofPdCutheH2dissociationisespeciallyimportantbecausethisbinarysystemiscurrentlyusedinhydrogenationprocesses.Furthermore,H2dissociatesonPdsurfaceswithalmostnoactivationenergy,25,26whereasitisratherunreactivetowardCusurfaces.Infact,ithasbeenshownthatH2doesnotdissociateonCu(111)atlowtemperatures.27Ontheotherhand,H2dissociatesonPd0.7Cu0.3surfaces,andtheexperimentalresultssuggestthatevensingleisolatedPdatomsonthesurfacesurroundedbyCuatomsareabletotrapandpossiblydissociateH2.28FromtheseexperimentsitissuggestedthatthestructuralfactorisimportantfortheinteractionofCOonPd0.7Cu0.3surfacesbutnotforH2dissociation.ThisconclusionfollowsfromthefactthatH2dissociationonPdCudoesnotrequirehavingthree-fold-likesitesinthePdCusurfacethataresimilartothoseofPd(111).ThisisbecausesinglePdatomsonPdCuarealsoreactiveforH2dissociation.28However,itisclearthattherearedifferentpossibilitiesforthecoordinationofPdatomsatthePdCu(111)surface,i.e.,withorwithoutPdatomsonthesecondlayer,andonemaywonderwhetherthisdifferencecanaffectthereactivityofthisactivesite.ThedifferentreactivityofsinglePdatomsonPdCusurfacestowardH2dissociationcanbeinvestigatedwiththehelpofcomputationalmodels.FollowingthestudyoftheinteractionofCOandNOonPdCu(111)byIllasetal.,23inthisworkwepresentatheoreticalmodelstudyoftheinteractionofmolecularhydrogenwithPdCusurfacesofdifferentcomposition.FromthisstudyitclearlyappearsthatevenifPdsingleatomsonthePdCusurfaceareabletotrapanddissociatemolecularhydrogen,ingoodagreementwithexperimentalobservations,theenvironmentofsuchactivesiteplaysafundamentalrole.

II.SurfaceClusterModelsandComputationalDetailsClustermodelshavebeenemployedtosimulatethe(111)surfaceofsubstitutionallydisorderedface-centeredcubic,fcc,alloysofformalPd40Cu60andPd8Cu92compositions.Thechoiceofthesedisorderedalloyscomesfromthefactthatpreparationmethodsofthesecatalystsfavorpreciselytheappearanceofdisorderedphases.15,29TwodifferentbutstructurallysimilaractivesitesforH2dissociationonthesePdCu(111)clustermodelshavebeenconsideredandthereactivitytowardH2comparedtothatexhibitedbythepuremetal,PdorCu,low-indexsurfaces.Bothsitesinvolveasingle-surfacePdatombutintwodifferentelectronicenvironments.Inthefirstcase,theactivesiteisrepresentedbyaPdCu12clustermodel,orPd1(1,0,0)Cu12(6,3,3)toindicatethenumberofatomsineachclusterlayer,wherethePdsurfaceatomiscompletelysur-roundedbyCuatoms.Withthismodel,onepretendstomimicaCu-richalloysuchasPd8Cu92.Inthesecondcase,thePdthreenearestneighborCuatomsinthesecondlayeraresubstitutedbyPdatoms,givingrisetothePd4Cu6clustermodel,orPd4(1,3)Cu6(6,0),whichisrepresentativeofthePd40Cu60alloys.NoticethatthisPd4Cu6clustermayalsoberegardedasatetrahedralPd4unitembeddedinCuatoms.Themetal-metaldistanceinthePdCu12andPd4Cu6clustersischosenfromthecorrespondingmeasuredvaluesforPd8Cu92andPd40Cu60alloys.22Hence,metal-metaldistancesof2.58and2.63ÅhavebeenusedforPdCu12andPd4Cu6,respectively.NoticethatthesePdCu12andPd4Cu6clustermodelshavealsobeenusedinprevioustheoreticalstudies.17,23TocomparethereactivityofthePdCualloymodelstothatofthepurecomponents,Pd10(7,3)andCu10(7,3)clustermodelshavebeenusedtorepresentthe

Sousaetal.

Figure1.SchematicrepresentationoftheBS,FS,andHSactivesitesconsideredforH2dissociativechemisorption.TheM10clustermodeldepictedinthefigurecaneitherrepresentPd10,Cu10,Pd4Cu6,orthetwofirstlayersofthePdCu12.Inthetwoformercases,allatomsareequal.InPd4Cu6,thefirstlayercentralatomandthoseonthesecondlayerarePdandthesixremainingatomsonthefirstlayerareCuand,finally,inPdCu12thefirstlayercentralatomisPdandallremainingatomsareCu.

Pd(111)andCu(111)surfaceswithmetal-metaldistancesfixedat2.75and2.56Åasinthebulk.31Theclustergeometryiseitherkeptfrozenatthegeometrydescribedaboveorfullyoptimizedfollowingtheproceduredescribedbelow.

TheinteractionofmolecularhydrogenwiththedifferentsurfaceclustermodelshasbeenstudiedbyfirstprinciplesdensityfunctionalcalculationsthatusethehybridB3LYPexchange-correlationfunctional32,33asimplementedintheGaussian98suiteofprograms.34Weusetherelativisticsmall-coreeffectivecorepotentials,ECP,derivedbyHayandWadt.35TheseECPsleaveexplicitlythe3s,3p,3d,and4selectronsofCuandthe4s,4p,4delectronsofPd.ItiscustomarytorefertotheseECPsasLANL2.Thestandarddouble-??basissetalsoreportedbyHayandWadt,35anddenotedasusualasLANL2DZ,wasusedtodescribetheelectrondensityofthevalenceelectronsofCuandPd,whereastheelectrondensityofthehydrogenatomswasdescribedwithastandard6-31G**basisset.36

BecauseitislikelythatH2willdissociateonsomeofthesurfaceclustermodelsusedinthepresentwork,astep-by-stepoptimizationgeometrystrategyhasbeenusedtobetterunder-standtheenergeticsofthedissociativechemisorptionofH2withthesebinaryalloys.Inafirststep,ageometryoptimizationfortheperpendiculardistanceoftheH2centerofmasstothesurfaceiscarriedoutmaintainingH2atitsequilibriumgeometry,0.742Å,andparalleltothesurfacewiththeclustergeometryfixedatthebulkvalues.TheH2moleculeisplacedabovethesurfacewiththeHatomspointingeachtowardonebridgesite,BS,onefccsite,FS,oronehcpsite,HS,surfacesite.(cf.Figure1).AperpendicularapproachoftheH2moleculedirectlyaboveasurfaceatom,a-topsite,isalsopossible,althoughthisisgenerallyunfavored.Ultimately,themoleculetiltsandtakesanuclearconfigurationwiththemolecularaxisparalleltothesurface.37Therefore,thisinitialperpendicularapproachhasnotbeenconsidered.ThegeometrysearchstartingfromtheBS,FS,andHSwithafixedinternucleardistanceforH2attemptstofindpossiblephysisorbedstates.

Hereitisworthpointingoutthatphysisorptionenergiesareintherangeofweakinteractionswherethecurrent

exchange-

H2InteractionwithPdCu(111)BimetallicSurfaces

correlationfunctionalshavedifficulties.38-40Nevertheless,themaingoalofthepresentapproachisnotadetaileddescriptionofphysisorption.ThestrategyfollowedinthisworkpermitsustoobtainaroughestimateoftheenergygainorcosttoadsorbundistortedH2onthevarioussurfaces.Inasecondstep,startingfromeachoneoftheconformationsabove-describedthepositionofeachHatomisallowedtovarywithoutanyfurtherconstraint.ThissecondgeometryoptimizationprovidesinformationaboutthedissociativechemisorptionofH2onthevarioussurfaces.Again,themaininterestisintheenergyprofileandfinalstructure.InsomecasesthefinalgeometrywillcorrespondtowellseparatedHatomsplacedabovethesurfacemodelandquitefarfromtheclusteredge.ThiswillbeinterpretedasthefingerprintofH2dissociation.However,inothercasesthefinalgeometrywillalsocorrespondtoseparateHatomsbutinteract-ingwiththeclusteredge.ThisfinalstructurerevealslimitationsoftheclustermodelbutdoesalsoindicatethatH2willnotdissociateintheregularsitesofthatsurface.Finally,inathirdstep,thegeometryofthewholesystemisallowedtovarywithoutanyspecificconstraint.ThisfinalsteppermitstocheckthestabilityoftheclustermodelswithrespecttodistortionandalsotoinvestigatetheeffectofH2dissociativechemisorptionontheoptimizedstructureofthenakedcluster.Thecomparisonoftheenergyprofileobtainedwiththerigidandoptimizedclusterwillalsoprovideusefulinformationaboutsimilaritiesanddifferencesbetweenthereactivityofalloysextendedsurfacesandthatofsmallbimetallicparticlesthatareoftenusedascatalysts.

Itisworthpointingoutthatwiththeoptimizationgeometrystrategyjustdescribed,onedoesnotpretendtofindallthepossiblelocalminimaoftheseclustermodels.Becausethefinaloptimizationiscarriedoutwithnoconstraintsandwithnosymmetryatall,itislikelythattheminimizationalgorithmwillreachtheenergyminimuminthepotentialenergyhypersurfacethatisclosesttothestartinggeometry.

Beforeclosingthissectionitisworthpointingoutthatthepresentcalculationshaveallbeencarriedoutbydeliberatelychoosingasingledclosed-shellelectronicstructureforthedifferentclustermodels.Atfirstsight,thischoicemayseeminadequatebecauseweareconsideringadissociationprocessthat,inprinciple,leadstoanopen-shellelectronicstructure.However,wemustrecallthatthedissociationprocesstakesplaceaboveametalsurfaceandthatmetal-hydrogenbondsareformedwhilethehydrogen-hydrogenbondbreaks.Noticethatonlythefinalstructuresareofinterestandthatnoattempthasbeenmadetolocatethepossibletransitionstatescorrespondingtodissociativechemisorption.Theuseofaclosed-shellelec-tronicstructuretolocatethetransitionstatemaybemorequestionable,althoughthisisalsoacommonpracticeinperiodicdensityfunctionalcalculations.26Withrespecttothemetalclustermodelsitiswell-knownthat,althoughPdandCuarenonmagneticmetals,smallPdn41-43andCun44clustersdonotnecessarilyhaveanonmagneticgroundstate.Panasetal.45haveproposedthatcalculatedchemisorptionenergiesthatarestablewithrespecttotheclustersizecanbeobtainedbychoosingahigherspinstatefortheclustermodel.However,Ricartetal.46haveshownthatthechoiceoftheelectronicstatedoesnotlargelyaffectthebasicbondingmechanism.Becausethemodelsusedinthisworkattempttosimulateextendedalloysthatdonotpossessnetmagneticmoments,thechoiceofaclosed-shellelectronicstructureconstitutesthenaturalreference.ThischoiceisalwayspossibleforanynumberofPdatomsintheclusterbutrequirestoincludeanevennumberofCuatomsintheCunclustermodel.

J.Phys.Chem.B,Vol.105,No.9,20011819

TABLEtheFinal1:ConfigurationComparisonofofHClusterandPeriodicResultsfor2onPd(111)a⊥

BSFS

HScluster

slab26clusterslab26clusterslab26dH-H(Å)2.882.792.872.792.942.79d⊥(Å)

0.961.010.760.840.790.84Eads(kcal/mol)14.57.618.011.519.410.4orderofstab.

3

3

2

1

1

2

a

ResultsaregivenfortheH-Hdistance,dH-H,theH-surfacedistance,d⊥,andtheinteractionenergy,Eads,withrespecttothenoninteractingH2andsurfacemodel.Theorderofstabilityofthedifferentconformationsisgiveninthelastrowofthetable.

III.InteractionofH2withPd(111)andCu(111)SurfacesTheinteractionofH2withthePd10andCu10clustermodelspermitstotesttheadequacyofthepresentcomputationalapproachbecausethosesystemshavebeenstudiedextensivelybothfromexperimentandtheoreticalpointsofview.25TheapproachofH2withafixedgeometryabovethePd10BS,FS,andHSsitesleadsalwaystoaminimumonthisparticularsectionofthepotentialenergysurfacebutwithenergyalwayshigherthanthatoftheseparated,H2,andPd10,systems.InthecaseofBSandHSsites,theminimumappearsat1.69and1.52Åabovethesurface,suggestingperhapstheexistenceofpossibleprecursorstates,especiallybecausetheminimumabovetheFSsiteisstructurallyquitedifferent,appearingat4.79Åabovethesurface.Withthisfixedgeometry,theenergyofthesystemistoohighabovetheH2+Pd10dissociationlimitby24.4,24.9,and17.3kcal/molfortheBS,HS,andFS,respectively.TheoptimizationofthepositionoftheHatomsleadstothreedifferentconfigurationswiththeHatomswellseparatedandsituatedclosetotheactivesitescorrespondingtothestartinggeometry.TheHatomsarelocatedwellwithintheclustersurfaceanditcansafelybeconcludedthattheclustermodelisabletoproperlyrepresentdissociativechemisorption.RelevantcalculatedparametersarepresentedinTable1andcomparedtothosereportedrecentlybyDongandHafner26usingperiodicslabdensityfunctionalcalculationswithinthePerdewetal.47generalizedgradientapproximation,GGA,andaplanewavebasisset.Despitethedifferentmodelsused,clustersvsslab,differentexchange-correlationfunctionals,B3LYPvsGGA,andbasissets,localatomicorbitalsvsdelocalizedplanewaves,theresultsreportedinTable1havestrongsimilarities.Bothcalculationspredictthatthedissociativechemisorptionoccursinallsites,thatfinalstructureontheBSisthelessfavored,andthatthefinalstructureswithHnearFSandHSareenergeticallysimilar.Likewise,thehydrogen-hydrogenandhydrogen-surfacedistancesfollowthesametrend,eveniftheHatomsarecompletelyfreetomoveintheclustercalculationswhiletheirpositionabovethesurfaceintheslabmodelhassomeconstraintstopreserveperiodicity.Apointthatdeservesfurthercommentconcernsthemagnitudeofthecalculatedadsorptionenergies.TheclusterB3LYPcalculatedenergiesarelargerthattheslabGGAenergies,andthismaybeeitherduetotheuseofadifferentfunctionalortoaclusteredgeeffect.Inanycase,thiswillnotaffecttheconclusionsofthepresentworkthatarebasedonthecomparisonofdifferentsubstrateswithinthesamecomputationalapproach.Similarly,thepresentcalculatedinteractionenergiesarenotcorrectedforpossiblebasissetsuperpositionerrors,BSSE,becausethemainconclu-sionsofthisworkarebasedonqualitativetrendsand,hence,accurateinteractionenergyvaluesarenotrequired.Inaddition,therelativeenergydifferencesarelargeenoughtopreservethequalitativetrendaftercorrectingthesevaluesbymeansofthe

1820J.Phys.Chem.B,Vol.105,No.9,2001Sousaetal.

Figure2.OptimizedgeometryofthePd10(a)andCu10(b)clustermodels.ForPd10theoptimumdistancesareindicated;forCu10thelackofsymmetryleadstoalargenumberofdifferentdistancesrangingfrom2.4to2.6&#http://wendang.chazidian.comrgedarkspheresrepresentPdatomsandsmalllightspheresstandforCuatoms.

counterpoisemethod.NoticethattypicallytheBSSEcorrectionsinthesesystemsareoftheorderof5kcal/molonly.

TheinteractionofH2withtheCu10clustermodelfollowsatrendverydifferentthanthatreportedaboveforPd10.WhentheH2distanceisfixedattheequilibriumvalueforthegas-phasemolecule,theinteractionwiththeCu10clusterisveryweak.Itis?0.2kcal/molandappearsatdistancesthataretoofarawayfromthesurface,?5Å,tobeconsideredasaprecursorforaphysisorbedstate.Moreover,fulloptimizationofthepositionoftheHatomsleadsalwaystostablestructuresbutwiththeHatomssituatedintheclusteredge,welloutsidethesurfaceregionoftheclustermodel.Indeed,thepositionoftheHatomsisnearlyonthesurfaceplaneanddirectlyinteractingwithtwoedgeatomsoftheclusterfirstlayerat?1.7Å.ThisgeometryissimilartothatobtainedbyTrigueroetal.48forthechemisorptionofatomichydrogenonoptimizedcopperclusters.Clearly,thisresultindicatesthatnodissociativechemisorptionoccursontheCu(111)surface,ingoodagreementwiththeexperimentalfindings.27

Finally,weconsiderthefulloptimizationoftheclustermodelandoftheclustermodelwiththeinteractingHatoms.ThefinalstructuresforPd10andCu10aresurprisinglydifferent.ForPd10,theoptimizedstructureisclosetotheinitialgeometryobtainedbycuttingaclusterfromthebulk,cf.Figure2a.TheenergygainobtainedbyrelaxingcompletelyallCartesiancoordinatesofallclusteratomsisfairlysmall,?6kcal/mol,andthedistancesarechangedbyasmuchas0.1Å,affectingmainlythefirsttosecondlayersandthesecondlayerintraatomicdistances.TheC3Vsymmetryispreserved,albeitnotimposedbythecalculation.Interestingly,thefinalgeometryofthedifferentPd10-H2clusterscorrespondingtotheinteractionofH2ontheBS,FS,andHSsitesisalsoclosetotheoneobtainedbyoptimizingonlytheHatoms.Theonlynoticeablechangesappearinthemetal-metaldistancesandalmostmaintainthegeometryoptimizedforPd10.Theadsorptionenergygainduetogeometryrelaxationisverysimilartothatofthebareclusterand,asaconsequence,theEadsvaluesforthefullyoptimizedstructuresdifferfromthosereportedinTable1by0.5to1.5kcal/mol,dependingontheactivesite.ThesecalculationssuggestthatsmallPdclustersmaycloselyresemblethebulkmetalnotonlystructurallybutalsofromthechemicalandcatalyticpointofview.

ContrarytothatofPd10,thefinaloptimizedstructureofCu10iscompletelydifferentfromthatobtainedbycuttingaclusterfromthebulk.Thereareseveralarbitrarywaystodescribethegeometryofthisoptimizedcluster.Forinstance,itmaybeseenasbeingcomposedoffourlayers,eachhavingthestructureofthecorrespondingCuclusterwiththesamenumberofatoms.Thesecondlayercontainsfivemetalatomsandadoptsanearlyplanarstructureformingthreetriangles,thisispreciselytheoptimizedstructureofCu5asreportedbydifferentauthors.48,49Thethirdlayercontainsthreeatomsinatriangularshape,andthefirstandfourthcontainasingleatomontopofatriangle,thusformingtetrahedralunits.Despitethehugestructuralmodification,theenergyrelaxationisrathermodest,?21kcal/mol.BecausethefinaloptimizedgeometryofthisCu10clusterbearsnoresemblancetotheinitialstructure,theinteractionofH2withthisclusterhasnotbeenconsidered.

IV.InteractionofH2withPdCu(111)BimetallicSurfacesTheresultsobtainedfromthepresentclustermodelcalcula-tionssuggestthat,asexpected,theresponseofbimetallicsurfacestothepresenceofmolecularhydrogenisverydifferentthanthatofthesinglemetalsurfacesdescribedintheprevioussection.Becauseforsinglemetalsurfacesthepredictionsarisingfromthepresentcomputationalapproachareinagreementwithexperimentandwithpreviousavailablecalculations,itisexpectedthatthedescriptionobtainedforthebimetallicsurfaceswillbeofsimilarquality.

ForthePd4Cu6clustermodel,theinteractionofanH2moleculewiththeinternucleardistancefixedat0.742Å,asinthegasphase,alreadyresultsinaconstrainedlocalminimumthatisstableby4.4kcal/molandisplacedat1.94Åabovethesurface.ThisisatvariancewiththecorrespondingsituationpredictedbythePd10modelofPd(111)wheretheinteractionisratherendothermicandalsodifferentfromtheveryweakinteractionpredictedfortheinteractionwithCu(111).Thisresultsuggeststheexistenceofaprecursorformolecularhydrogendissociationonthisbimetallicsurfacesite.Here,thegeometryoptimizationprocedurepermitstoidentifysuchprecursorstate.Infact,enablingthepositionoftheHatomstooptimizeabovethePd4Cu6clustermodelwithnoconstraintsledtotwodifferentminima;bothclosetotheBSsite.Nootherminimawere

found,

H2InteractionwithPdCu(111)BimetallicSurfacesJ.Phys.Chem.B,Vol.105,No.9,20011821

Figure3.OptimizedgeometryofthePd4Cu6(a)andPdCu12(b)clustermodels.ForPd4Cu6theoptimumdistancesareindicated;forPdCu12thelackofsymmetryleadstoalargenumberofdifferentdistancesrangingfrom2.4to2.9Å.PdatomsarerepresentedbydarklargesphereswhereasCuatomsarerepresentedbysmalllightspheres.

althoughthegeometrysearchwasstartedfromquitealargenumberofgeometries,includingthosewiththehydrogenatomsabovetheFSandHSsites.Inthefirstminimum,thehydrogen-hydrogendistanceisonlyslightlyelongatedwithrespecttothegas-phasevalue,0.798vs0.742Å,theperpendiculardistanceoftheHatomstothesurfaceis1.87Å,andthetotalenergyislowerthatthatofthenoninteractingsystemsby5.1kcal/mol.Thesecondminimumcorrespondstothesamesitebutherethehydrogen-hydrogendistanceismuchlargerthatinthepreviouscase,2.20Å,andthehydrogen-surfacedistancebecomes1.23Å.Inthiscase,thehydrogen-hydrogendistanceisthreetimestheinternucleardistanceforthegas-phasemoleculeandtheHatomsareclosertothesurface.Therefore,thesecondminimumcorrespondstoadissociativechemisorptionprocess.However,thetotalenergyofthisminimumisslightlyabove,3.7kcal/mol,thatcorrespondingtothenoninteractingsystems.Theabsolutevaluesofthechemisorptionenergiesmaybesomehowaffectedbytheclustersize,butitisveryunlikelythatchoosingalargermodelwillchangetheoveralldescriptionoftheprocess.Anindirectproofthatthisispreciselythecasecanbeobtainedbyallowingthegeometryofthewholesystemtorelax.ThefinalgeometryofPd4Cu6,Figure3a,isnotverydifferentfromtheonechosenasmodelwiththedistancetakenfromthePd40Cu60alloy.30Theenergyrecoveredbyallowingthesurfaceclustermodeltorelaxis?18kcal/mol,largerthanthatreportedaboveforPd10.Thisdifferencereflectsthefactthatsomeofthemetal-metaldistancesintheoptimizedgeometryofthebimetallicclusterarequitechangedwithrespecttotheinitialvalue.Thisfinalgeometryisalmostunchangeduponinteractionwithmolecularhydrogen.Thetwominimafoundforthefrozensubstratearealsopresentinthefinaltotallyrelaxedsurfaceclustermodel.However,theinteractionenergyofmolecularhydrogencalculatedwithrespecttotherelaxedsurfaceappearstobechangedby+0.9and-0.5kcal/molonlyforthephysisorbedprecursoranddissociativelychemisorbedstructures,respectively.Therefore,thereisnofurthersubstraterelaxationinducedbythepresenceofmolecularhydrogeninthesurfaceoftheoptimizedPd4Cu6cluster.

TheinteractionofmolecularhydrogenwiththePdCu12clustermodelhaslittleresemblancewiththeonedescribedaboveforPd4Cu6.Freezingthehydrogen-hydrogendistanceat0.742Åresultsinaconstrainedminimumquitefarawayfromthesurface,2.47Å,and,consequentlywithaveryweakinteractionenergy,?1kcal/mol,withrespecttothenoninteractingsystems.Thelargedistancetothesurfaceandthesmallvalueoftheinteractingenergypointtowardthenonexistenceofanyphys-isorbedspecies.Inaddition,releasingtheconstraintsonthe

positionofthehydrogenatomsabovethesurfacedoesalwaysresultinafinalgeometrywiththehydrogenatomswelloutsidetheclustermodelandinteractingwithtwoedgeCuatoms.ThissituationiscomparabletothatdescribedfortheCu10modelofCu(111)andindicatesthat,contrarytoPd4Cu6,thesinglesurfacePdatomofthePdCu12isnotabletochangethepropertiesofthelargecomponentinthealloy.Thisisameaningfulpointbecauseitshowstheimportanceoftheelectronicorligandeffects.ToclosethediscussionaboutthePdCu12clustermodelwecommentonthestructureobtainedwhenthegeometryoptimizationoftheclustermodeliscarriedoutwithnorestrictions.AsinthecaseofCu10,thefinalgeometryofPdCu12islargelydistortedfromtheinitialstructure,Figure3b.Themaindistortioncorrespondstoamotionoftheatomsintheclusterthirdlayer,resultinginaratherflatcluster.However,thePdatompreservesitspositionandthecorrespondingsurfaceisreminiscenttothatoftheoriginalcluster.Asexpected,thereactivitytowardmolecularhydrogenisnotchangedandtheonlystablestructurescorrespondtosituationswiththehydrogenatomsintheclusteredge.

Tosummarize,resultsinthissectionshowthatthetwobimetallicsurfaceclustermodelsrepresentativeofdifferentcompositionshavearatherdifferentchemicalreactivitytowardmolecularhydrogen.AveryimportantpointisthatpresentresultssuggestthatasinglePdatomonthesurfaceofaPdCualloyisabletotrapandtodissociatemolecularhydrogen,ingoodagreementwithexperimentalfindings.28However,toexhibitthisparticularchemicalreactivity,thissinglesurfacePdatomneedsaproperelectronicenvironmentthatcanbeprovidedbyotherPdatomsinthesecondmetallayerbutthatisnotatallprovidedbyCuatoms.Inotherwords,itseemsthatthereactivityofthedifferentPdCualloystowardH2dissociationisenhancedbythepresenceofPdmicroclustersinthealloy.V.Conclusions

InthisworkadensityfunctionalclustermodelapproachhasbeenappliedtothestudyoftheinteractionofmolecularhydrogenwithtwodifferentclustermodelsofthePdCu(111)surface.BothmodelscorrespondtoadifferentformalalloycompositionbutwithasinglePdatominthesurface.Forcomparison,theinteractionofH2withPd(111)andCu(111)hasbeenstudiedusingthesametheoreticaltechniques.Thepresentcomputationalapproachproperlypredictsthedissocia-tivecharacteroftheH2chemisorptiononPd(111)andthelowreactivityofCu(111)towardthesamemolecule.Moreover,

the