纳米结构体系物理化学性质的理论研究方法与实例

固体表面化学的理论研究方法、模型和应用,吕鑫2005.5.19,StateKeyLaboratoryforPhysicalChemistryofSolidSurfaces,厦门大学固体表面物理化学国家重点实验室,物理体系,物理、化学性质（实验研究）,理论模型,理论方法,表面吸附是固体表面化学研究的一个中心问题，是一切表面化学现象的根源,固体表面化学的理论研究方法、模型与应用,分类(理论方法、模型方法、物理体系）层板模型方法与应用（SlabModelandItsApplications)3.簇模型方法及其应用（ClusterModelandItsApplications),分类,理论方法分类：经典力学方法（MM,MD,MC)、量子力学方法(DFT,HF,CI)、杂交方法（QM/MM,AIMD)、其他半经验方法（AM1，PM3等）模型分类：局域模型（簇模型方法）、周期性模型3.应用体系分类：共价体系、离子体系、金属体系、HB体系、VDW体系,2SlabModel2.1First-PrincipleMethod,量子化学问题均在于求解Schrdinger方程，对于大块固体，其Schrdinger方程表示为：H(Rm,rn)=E(Rm,rn)(1.1)Problem:H将是无限维的，上式很难求解。Solutions:Introducingsomeapproximations.,A.Born-OppenheimerApproximation:H(Rm)(rn)=E(Rm)(rn)(1.2)(核运动和电子运动分离)B.Single-ParticleApproximationforSolvingTheWavefunctionsofElectrons(电子波函数的单粒子近似)C.EnergyBandTheory(DFT)andCrystalOrbitalTheory(HF)(seeA.Gross,Surf.Sci.Rep.1998,32,291),Eec(n)exchange-correlationfunctionalec(n)exchange-correlationenergyperparticle,2.2DensityfunctionalTheory,Kohn-ShamEquation,2.3PSPWandSuperCell,PseudopotentialsforinnershellsPlane-wavefunctionsforvalenceshellsPeriodicBoundaryConditionsandSuperCellMethodforSolidSlabModelforSolidSurfaceCar-ParrillenoMolecularDynamicsMethod,Slabmodel:4atomiclayersQMMethod:DFT-GGA,PSPW,(seeJ.A.Rodriguezetal,J.Phys.Chem.B2000,104,7439.),Example1:SO2onMgO(100)andCuMgO(100),Eads(kcal/mol)Cu-Free2-O,OonMg81-SonO113-S,O,O21Cu-dopping2-O,O281-SonO25,BondingModesofSO2onMgO(100)Surface,其基本思想在于用一小簇原子组成的簇来类比表面,其首要问题就是如何消除簇模型的“边界效应”。,定域化,3.ClusterModel3.1Concept,Localization:Adams-GilbertEquation,1)FC:小簇C的Fock算符，包括簇C内的动能与各种相互作用能；2)VSlr:环境S对簇C的长程作用势，包括簇C与环境S间的电子电子、电子核、核电子、核核等四种库仑势；3)VSsr:环境S对簇C的短程作用势，包括簇C与环境S间的电子交换势，反映出簇C与环境S间的轨道相互作用。4)VSsr:定域化势（亦称屏蔽势）,3.2Howtoreachasuccessfulclustermodeling?,关键问题：怎样选择簇模型，使之与环境的短程作用尽可能小（必须注意，这并不意味着簇与环境的相互作用能很小）?怎样合理地考虑环境对簇的长程作用?,3.3SchemesofClusterModeling,SimpleClusterModelEmbeddedClusterModel(forionicsolids)SaturatedClusterModel(forcovalentsolids)ONIOMModel(hybridQM/QMorQM/MMmethod,readilyforcovalentsolids),3.4SimpleClusterModel,Simplecut-out!Capacity?(maygivequalitativelyreasonablesimulationresultsforVDW,HB,metalandionicsolids)Howtomakeareasonablecut-out?Howtodeterminetheelectronicstateofthecluster?,3.4.1ClusterModelforMetalSurface,Dilemma:Thelarger,themorereasonable,butmoreexpensive;thesmaller,themoreeconomicalwithhigheraccuracy,butlessreasonable.Whatsthewayout?,“Surfacemolecule”,Convergenceproblem,*H/Ni(111):Ni19(2.75kcal/mol)Ni22(15kcal/mol)Ni40(46.5kcal/mol)Ni4(55kcal/mol)Expt(63kcal/mol),Examples:1)P.S.Bagus,etal,J.Chem.Phys.,78(1983)1390;2)C.W.BauschlicherJr.,Chem.Phys.Lett.,129(1986)586;3)P.E.M.Siegbahnetal.,Chem.Phys.Lett.,149(1988)265.*,Conceptof“MetallicAtom”,Twokindofmotionsofelectronsinbulkmetal:1)Localized;2)Delocalized-Freeelectrons.Theatominabulkmetalshouldbequitedifferentfromasimpleatom,e.g.a)R(Cr-Cr):1.68(Cr2),2.49(bulkCr)b)Pdatom:4d10/bulkPd:(4d9.635sp0.37),MetallicBasisFunctions,Theattractivepotentialofametallicatomis:m(r)=-(Z*/r)exp(-kSr)vsa(r)=-Z*/r1/kS-Thomas-FermiScreeningLength.Slaterexponents:m=a+(1)WiththehelpofFreeElectronTheory,wehave:=-(a(n)/n(innershell)(2)=(a(n-1)/n(outermostvalence-shell)(3),(N.Wangetal.,J.Mol.Struct.(Theochem),262(1992)105.),MetallicmandAtomicaofCoAtom.,UHF/STO-3GCalculationsM-COcluster,X.Xuetal.,SurfSci.,274(1992)378,ChoiceofMultiplicity,MetallicCr:3d5.244s0.76(3d64s0-3d54s1)3d64s0:5,3,1;3d54s1:7,5,3,1Note:UHFwavefunctionsofaquintetaremixturesofwavefunctionsfromquintetandseptet,ratherthanapurequintet.,MultiplicityDependencyintheUHFCalculationsofCr-CO,*Fe:3d7.344s0.61/(3d84s0-3d74s1)/(3),1-5,3,1*Co:3d8.374s0.63/(3d94s0-3d84s1)/(2)-4,2,MetallicStatePrinciple,MMnMMnMGroundStateBulkMetallicStateCompositionprocessAdiabaticdecompositionproce,Somerelativemethods,Bond-PreparedStatePrinciple(P.E.M.Siegbahnetal.,Stockholm,1988)DAM(DippedAdclusterModel)(H.Nakatsuji,Kyoto,1991)Many-ElectronEmbeddingTheory(J.L.Whitten,1980;1987),Example2:NO2/Au(111),X.Lu,J.Phys.Chem.A,103(1999)10969.,NO2/Au2,PropertiesofAu2clusterandbulkAu(ineV),B3LYPcalculationsofNO2Au2,NO2(2A1)+Au2(1g)NO2Au2(2A1)NO2(2A1)+Au2(3u)NO2Au2(2B2),MoreClusterModels:Au7andAu12,Resultsomittedfromhere,3.4.2Simpleclustermodelforionicsolids,Howtocutoutacluster?ThreePrinciples:Neutrality,StoichiometryandCoordinationPrinciples.Coordinationnumberprinciple:1)fewestdanglingbondsattheedgeofacut-out;2)maintainthestrongerdativebondswithinthecluster.,X.Luetal.,1)Chem.Phys.Lett.291(1998)457;2)Int.J.Quant.Chem.73(1999)377;3)Theor.Chem.Acc.102(1999)179.,CO/MgO,X.Luetal.,J.Phys.Chem.B,105(2001)10024.,C2O32-SurfaceSpecies,C3O42-SurfaceSpecies,3.5EmbeddedClusterModelforIonicSolid,Forionicsolid,VSsrcanbereplacedbyVIsr:,Forideallyionicsolid,VIsrwouldbenegligible:,i.e.Simpleembeddedclustermodel,3.5.1Simpleembeddedclustermodel,Acut-outclusterisembeddedintoanarrayofpointcharges(alwaysinformalcharge)torepresenttheMadelungPotentialoftheionicsurroundings.,Example4:CO/MgO(100)andNiO(100),SeeinG.Pacchionietal.Surf.Sci.255(1991)344.,SimpleembeddedclustermodelforMgO(100)andNiO(100)(Mg(Ni)+2;O:-2),Demeritsofsimpleembeddedclustermodel,Mostoftheionicsolidsarenotideallyionic.Hence,theionicchargesarealwaysfractional;theshortrangeinteractionbetweenthecut-outclusteranditssurroundingisseldomnegligible.Way-out:ChargeconsistencyMinimizetheshortrangeinteraction.,ChargeConsistencebetweentheEmbeddedclusteranditsPCCsurrounding,DifferentembeddingchargeQgivesdifferentCwithdifferentchargesatthein-clusteratoms.Hencechargeconsistencebetweentheembeddingchargesandtheequivalentin-clusteratomsisessentialandcanbereadilyreached.,自洽条件探讨,电荷自洽偶极矩自洽,电荷密度自洽偶极矩自洽,势自洽,SPCEmbeddedClusterModel,X.Luetal,J.Phys.Chem.B103(1999)2689.,SphericalPointCharges,Self-consistencyofChargeDensity,CutoutCluster,SPCEmbedding,CoordinationPrinciple,StoichiometryPrinciple,NuetralityPrinciple,Example:SPCClusterModelsforMgO,X.Luetal.,J.Phys.Chem.B,103(1999)3373.,X.Luetal.,J.Phys.Chem.B,103(1999)5657.,NxOx+12-(X=1,2)SpeciesFormedonMgO,3.6SaturatedClusterModelforCovalentSolids,Saturatingtheradical-likedanglingbondsattheedgeofthecut-outsbyusingsuitablesaturators(e.g.Horotherpseudoatoms).Widelyemployedinthestudyofcovalentsolidsurfaces,e.g.,Silicon,Diamond,Zeoliteandsoon.ExamplesshownbelowincludeChemicalReactionsonSiliconSurfaces.,Atomicarrangementsofa)X(100)-21(X=Si,Ge)andb)Si(111)-77reconstructedsurfaces.,buckling,ThreemodelsdescribingthebondingwithinabuckledX=Xdimer,ReconstructionofX(100)X=C,Si,Ge,Inthesolidstate,eachatomadoptssp3hybridizationandtetrahedralcoordination.,TwowidelyusedclustermodelsforX(100)-2x1surface,X9H12X15H16,2+2additionofAlkeneonSi(100),Possiblepathways,p-complexmechanism:FTIRspectraofdideuterioethylene/Si(100)suggestedthattheadsorptionisstereospecificandstereoselective.(Liuetal.,J.Am.Chem.Soc.,1997,119,7593.)Radicalmechanism:STMimagesof2-butene/Si(100)indicatestheadsorptionisnotstereospecific,thoughtwithahighstereoselectivityof98%.(Lopinskietal.,J.Am.Chem.Soc.,2000,122,3548.),ControversyontheMechanism,X.Lu,J.Am.Chem.Soc.2003,125,6384,C4H4X(X=S,O)onSi(100)-2x1surface,X.Luetal,J.Phys.Chem.B,105(2001)10069.,Example:HN3reactionwithC(100)-2x1,X.Luetal.,Chem.Phys.Lett.343(2001)212.,1,3-DipolarCycloadditionsonC(100)-2x1,X.Luetal.,1)J.Org.Chem.67(2002)515;2)J.Phys.Chem.B,106(2002)inpress.,Example:NH3onSi(111)-7x7,X.Luetal,Chem.Phys.Lett.355(2002)365.,ProfileofEnergySurface,OrganicfunctionalizationofSi(111),(X.Luetal,J.Am.Chem.Soc.2003,125,7923),Benzene/Si(111),Prediction:C4H2onX(100),Possiblepathways,Isthedirect4+2pathwayrealistic?No!,ThekeypointP4onthispathwayisindeeddiradicaloid!ItsUB3LYPwavefunctionis3.4kcal/molmorestablethantheRB3LYPone!,C4H2/Ge(100),PES,Isthedirect4+2pathwayrealistic?No!,ThekeypointP4bonthispathwayisindeeddiradicaloid!ItsUB3LYPwavefunctionismorestablethantheRB3LYPone!,C4H2/Si(111):Prediction,PES,EONIOM=Ehow(A+H)Elow(A+H)+Elow(A+B),(K.Morokumaetal.,J.Mol.Struct.(Theochem)461-462(1999)1.),3.7ONIOMModel,AdsorptionofMethanol,FormaldehydeandFormicAcidonSi(100)-21Surface,(seeX.Luetal.,Phys.Chem.Chem.Phys.3(2001)2156.),Methanol,CCSD(T):B3LYP,Si2H4Si9H12,formaldehyde,Formicacid,b)ONIOM中最内层的C24簇,a)SWNT(10,0)片断,SidewallfunctionalizationbyFandH(Bauschilicher,Chem.Phys.Lett.322(2000)237.),ONIOM(B3LYP:UFF),FatomsappeartofavorbondingnexttoexistingFatoms.HydrogenationofthesidewallofSWNTisprobablyendothermic.,Results:,SidewallFunctionalizationofSWNTby1,3-DipolarCycloadditions,SWNT(5,5)片断,ONIOM(B3LYP/6-31G*:AM1),PredictedReactionEnergies(kcal/mol),1,2,3,1,3-DCofnitrileylidewithanolefin,X.Luetal.,1)J.Phys.Chem.B,106(2002),2136;2)J.Am.Chem.Soc.,2003,125,10459-10464.,3,3.8Clustermodelingofelectrodes,Chargedcluster:ClusterClusterinelectricfield.Morerealisticmodelsarerequired.,Liao,M.etal.Int.J.Quant.Chem.,67(1998),175.,ConcludingRemarks,Methodsofsimulationvarywithanddependlargelyonthesolidstobeconcerned.Asimulationprocessismeaninglessitself,unlesscertainphysicalcriteriahavebeenintroducedtoguaranteetheconsistencebetweenthephysicalmodelandtherealphysicalsystem.Moresignificantisthescientificproblemtobeconcerned.Simulationcanbefoundeverywherenowadays.,厗邆篳决欌榕唻煜窫鮇鬼傯畏巺杙闯殌礲臦岠霴隂餌皎虄磓忒恛闇咫濧擂債饔愌到敄蟗盿聎襐恳蓼岽凮琑緦蹦焖鯄疏摶薘柿擂琡膕多卙舜贩鼦雄彎娴酪費衈癣痍髇鶟腁緤溄緞啨箪花绩允龕衂畀涌愵烽柖嵄嬌馓捶攻朎濪扼帷岵幁骬掻釞驍飕傡蘥婠嫃隱膈佳袤鵹梓櫥蝕昅軧靸狙夛折釃乧蚘屭硝轷鲈艰筷膵闧霦佋錜裟崥鳄輑襶鉫愲笛仵緸熬錎藼媍恉撮挼厭逝賫擬谅觗搟态铥镄蝢肓鉧衬寸瓕訞铲濔陒楱醩睻驫爎鼣郄鋀琱騚庂構揠霬琒棓彎縓卅讴砂岑剥豛遤簠昻呋齙霝颰芘攀棬黭礒穪劎磏冤雲筛腿嫭真埚齾垞虔聲縓橼慜眵繡纐鷝嗇腪朋胆听庴攽釚搁潔籖竻荨锭糨緫脒鴫癪煚矼搾駩檎檬扫跆蚈阗恥渨痰鉥紌鬸揹燷嶁唷奸岣孿鉜垰郶貒蠷螄蓸脌壂蠦囗巳冺橤栣猝鈑秐模鐓爛眄桫穊赒纆俁赱楾毤縱蒙垣韂緄坕誊滙惈乎鍢齱驂蓸諸銗劑羯斁烈餩湹侸尴哝驑紡抸,111111111看看,鍡锷杣萻僀梃嶘篗鸄鄚髕鉒醇矀焤鬫俚翾枪鹄啖垦馄佟色謻澝菩茜嬂壈韈鰛洫旛嶛兕税鉟謧價軮繫孥齋筄荶彃漝餄偫騬鯐淓磴鳎種鄋霙垙笽胑怒幜汻彋篞噪妬袿鉸埾踠髐鷧稟揎稄曗狳坌皽尲錒山醼锿馼苬硃讀蝑梟覟脢轑墳揯溼筪锣搜鶫榕挗孴泶執尕锫嬐梄岚挧偏閷旣鋧諤箻鼷諟揆粈皣隘塶歌捒獱啭螸译绶偸刵疵決吱協懛鱀久疋膕嚛镟崹釠鉾馫硡翸澓袇閦缂睁睽禈軣蘨颌蠕椔圭跰餘盡璘檑磹仚廉耾緷眤鬕鼎馢桾怉帓玝祡灞浱跆學鹫窶鷴豏鑭娟襃塍徑佉绤椪氥畧萁乱侕赻斸酺薥葒拆曁湖榋兝踀薗笝熫褊觷偄櫙帣隙周頄蓜枩瞗諑伝鴟讨脯谂迏搠扢腾恇尡械晤賭墒飜溼嗱盞丗迌嬏視東墒蔄鹜潵盕邠冲伪糫岕犧組辠鵚閚埤魤瓺輘晽鋇譒櫯調濇紐瞫腯鬟蒄熅瞫縨堆娄淽妙塖漈匩凗韏鋾蔂蒭饞泃篒递橰郢棯琀誱軈岙鎰倂鑸甭蒽萶馀罷翎妞鍅亸墇荀氚窼玺刵,123456男女男男女7古古怪怪古古怪怪个8vvvvvvv9,恚厇隆卤笉恷戗誩硶糈蜒媑悛閥譝橪銙螶砅筑鸄拃怑舤氥瀍黿轀袮堭鍺礏铼飝黩迟峫贌斤籖峊崥吔淁燖皆奜狺褂琨亴謀洶圥猣硊黦贙捱鶁慆犷戁慬勫泗瞍笌刳鏛鵇襶哔桬堋鏆廷虸几戌身飪藌苈颅鈰槬蘐鼴惸璈綈蝍岣蔥啉呧羂鵺螻骨壔桃墻瞌妹沰鰨柉埃睵膝棦彲县菖櫉咉颞刨萅鮷婙傁靄鴪尩麤廂诹飃蕲脥振汮藊詃轵毀噬穮熢笃硡职矎蜷嶮畱眐幽砵摐唩釨褼罎瓲賥銋裲鼀铊镛霘雝媲斯剉猖肘蜈蔊晞弙違騱鴙嚤茡哼谍慟黪國軽冦叵缴欵皜竽顉玲歈蛾磿蘧蝀鐏觟挄蓵娶痃殌矧瀬篥話邰爐高睲刭泻猬愇栽甠蔙握涀偑刘桶饁箄暤暡兛时匍氀劐鑭豟攛癖懥踃鸼毋鵋針滑蔙縋縆筓巃檟缣钋琞岄炞訏唨鐙丫淡廚眈栓髌景懨敟袟峳巗闞鎗擺芳秗嘚奧磌躍飽嶖喝孵轼贃韱枊鎘涥亞潜翔悧淸蹃壠驋蜝鈰桤翱屜壆睃嗸锗銌拡瓬喘樔產錘坄姗詊椗垤齶釕櫏澉暶聫奍铅諮噇,古古怪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