固体表面化学的理论研究方法、模型和应用

固体表面化学的理论研究方法、模型和应用物理体系物理、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2SlabModel

2.1First-PrincipleMethod量子化学问题均在于求解Schrödinger方程，对于大块固体，其Schrödinger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-correlationfunctional

ec(n)exchange-correlationenergyperparticle

2.2DensityfunctionalTheory,Kohn-ShamEquation2.3PSPWandSuperCellPseudopotentialsforinnershellsPlane-wavefunctionsforvalenceshellsPeriodicBoundaryConditionsandSuperCellMethodforSolidSlabModelforSolidSurfaceCar-ParrillenoMolecularDynamicsMethodSlabmodel:

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-SonO25BondingModesofSO2onMgO(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.ClusterModel

3.1ConceptLocalization:Adams-GilbertEquation1)

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)

ρVSsrρ: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?

3.3SchemesofClusterModelingSimpleClusterModelEmbeddedClusterModel(forionicsolids)SaturatedClusterModel(forcovalentsolids)ONIOMModel(hybridQM/QMorQM/MMmethod,readilyforcovalentsolids)3.4SimpleClusterModelSimplecut-out!!!!!Capacity?(maygivequalitativelyreasonablesimulationresultsforVDW,HB,metalandionicsolids)Howtomakeareasonablecut-out?Howtodeterminetheelectronicstateofthecluster?3.4.1ClusterModelforMetalSurfaceDilemma:Thelarger,themorereasonable,butmoreexpensive;thesmaller,themoreeconomicalwithhigheraccuracy,butlessreasonable.What’sthewayout?“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):1.68Å(Cr2),2.49Å(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.

1s2sp3sp3d4spa26.4711.094.553.941.40m26.4610.964.013.351.84UHF/STO-3GCalculationsM-COcluster

CO-likeCo-COCO/CoNi-COCO/Ni

MO’samUPSamUPS421.9916.6816.820.7516.4316.6116.4613.1013.215.5213.3513.6518.2712.7013.816.1412.3312.3

4-15.533.583.05-11.821.021.3X.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)-4,2Multipl.1(3)(5)7CO/Cr418.8216.8016.7417.4816.6114.6612.6612.6013.2312.6513.9111.6712.0312.68

MetallicStatePrincipleMMn MMn MGroundState Bulk MetallicStateCompositionprocess

Adiabaticdecompositionproce

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/Au21g3uBulkHOMO-7.00-5.63-5.30LUMO-4.20-5.63-5.30Te0.01.41PropertiesofAu2clusterandbulkAu(ineV)B3LYPcalculationsofNO2Au2NO2(2A1)+Au2(1g)NO2Au2(2A1)NO2(2A1)+Au2(3u)NO2Au2(2B2)2A12B2NO2/AuEtot(au)-476.02346-475.99512De(kcal/mol)4.519.3~14.0QNO20.004-0.51SpinofNO20.64-0.13Freqs.(cm-1)(ONO)742802800s(NO2)119512001178as(NO2)14061465MoreClusterModels:Au7andAu12Resultsomittedfromhere3.4.2SimpleclustermodelforionicsolidsHowtocutoutacluster?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/MgOX.Luetal.,J.Phys.Chem.B,105(2001)10024.C2O32-SurfaceSpeciesC3O42-SurfaceSpecies3.5EmbeddedClusterModelforIonicSolid

Forionicsolid,VSsr

canbereplacedby

VIsr

:Forideallyionicsolid,VIsr

wouldbenegligible:i.e.Simpleembeddedclustermodel3.5.1SimpleembeddedclustermodelAcut-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)DemeritsofsimpleembeddedclustermodelMostoftheionicsolidsarenotideallyionic.Hence,theionicchargesarealwaysfractional;theshortrangeinteractionbetweenthecut-outclusteranditssurroundingisseldomnegligible.Way-out:ChargeconsistencyMinimizetheshortrangeinteraction.ChargeConsistencebetweentheEmbeddedclusteranditsPCCsurrounding

DifferentembeddingchargeQ

givesdifferentCwithdifferentchargesatthein-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SPCEmbeddedClusterModelX.Luetal,J.Phys.Chem.B103(1999)2689.SphericalPointChargesSelf-consistencyofChargeDensityCutoutClusterSPCEmbeddingCoordinationPrinciple

StoichiometryPrincipleNuetralityPrincipleExample:SPCClusterModelsforMgOX.Luetal.,J.Phys.Chem.B,103(1999)3373.X.Luetal.,J.Phys.Chem.B,103(1999)5657.NxOx+12-(X=1,2)SpeciesFormedonMgO3.6SaturatedClusterModelforCovalentSolidsSaturatingtheradical-likedanglingbondsattheedgeofthecut-outsbyusingsuitablesaturators(e.g.Horotherpseudoatoms).Widelyemployedinthestudyofcovalentsolidsurfaces,e.g.,Silicon,Diamond,Zeoliteandsoon.ExamplesshownbelowincludeChemicalReactionsonSiliconSurfaces.Atomicarrangementsofa)X(100)-21(X=Si,Ge)andb)Si(111)-77reconstructedsurfaces.

bucklingThreemodelsdescribingthebondingwithinabuckledX=Xdimer

ReconstructionofX(100)X=C,Si,GeInthesolidstate,eachatomadoptssp3hybridizationandtetrahedralcoordination.TwowidelyusedclustermodelsforX(100)-2x1surfaceX9H12X15H16[2+2]additionofAlkeneonSi(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.)ControversyontheMechanismX.Lu,J.Am.Chem.Soc.2003,125,6384C4H4X(X=S,O)onSi(100)-2x1surfaceX.Luetal,J.Phys.Chem.B,105(2001)10069.Example:HN3reactionwithC(100)-2x1X.Luetal.,Chem.Phys.Lett.343(2001)212.1,3-DipolarCycloadditionsonC(100)-2x1X.Luetal.,1)J.Org.Chem.67(2002)515;2)J.Phys.Chem.B,106(2002)inpress.Example:NH3onSi(111)-7x7X.Luetal,Chem.Phys.Lett.355(2002)365.ProfileofEnergySurfaceOrganicfunctionalizationofSi(111)(X.Luetal,J.Am.Chem.Soc.2003,125,7923)Benzene/Si(111)Prediction:C4H2onX(100)PossiblepathwaysIsthedirect[4+2]pathwayrealistic?No!!!!ThekeypointP4onthispathwayisindeeddiradicaloid!ItsUB3LYPwavefunctionis3.4kcal/molmorestablethantheRB3LYPone!!!C4H2/Ge(100)PESIsthedirect[4+2]pathwayrealistic?No!!!!ThekeypointP4bonthispathwayisindeeddiradicaloid!ItsUB3LYPwavefunctionismorestablethantheRB3LYPone!!!C4H2/Si(111):PredictionPESouterlayerinnerlayerA(set1)B(set3)H(set2)X(set4)ModelSystem=A+HRealSystem=A+BEONIOM=Ehow(A+H)–Elow(A+H)+Elow(A+B)(K.Morokumaetal.,J.Mol.Struct.(Theochem)461-462(1999)1.)3.7ONIOMModelAdsorptionofMethanol,FormaldehydeandFormicAcidonSi(100)-21Surface

(seeX.Luetal.,Phys.Chem.Chem.Phys.3(2001)2156.)MethanolCCSD(T):B3LYPSi2H4@Si9H12formaldehydeFormic