密度泛函理論新進(jìn)展及應(yīng)用課件

密度泛函理論新進(jìn)展及應(yīng)用楊金龍中國(guó)科學(xué)技術(shù)大學(xué)ComputationExperimentTheoryScienceResearch計(jì)算機(jī)模擬已經(jīng)與理論與實(shí)驗(yàn)并列，成為三種基本的科學(xué)研究手段之一Time/nano/IWGN.Research.Directions/ScientificComputationspropertiessystemsmethods空間尺度：電子機(jī)構(gòu)時(shí)間尺度：動(dòng)力學(xué)/nano/IWGN.Research.Directions/動(dòng)力學(xué)模擬：預(yù)言反應(yīng)過(guò)程、驗(yàn)證理論猜想、理解實(shí)驗(yàn)觀測(cè)現(xiàn)象。MaterialsPropertiesfromFirst-principles“Supercomputer”GiganticcomputerprogramsTop500SupercomputersintheworldA“small”PCclustertodayFourordersofmagnitudein15years計(jì)算量隨體系大小急劇增長(zhǎng)內(nèi)容密度泛函理論新進(jìn)展石墨烯條帶體系的第一性原理計(jì)算研究PartI:理論體系LDAunderestimates

EcbutoverestimatesEx,resultinginunexpectedlygoodvaluesofExc.TheLDAhasbeenappliedin,calculationsofbandstructuresandtotalenergiesinsolid-statephysics.Inquantumchemistry,itismuchlesspopular,becauseitfailstoprovideresultsthatareaccurateenoughtopermitaquantitativediscussionofthechemicalbondinmolecules.局域密度近似(LDA)Anyrealsystemisspatiallyinhomogeneous,ithasaspatiallyvaryingdensityn(r),

itwouldclearlybeusefultoalsoincludeinformationontherateofthisvariationinthefunctional.Inthisapproximation,onetriestosystematicallycalculategradient-correctionsofgeneralfunctionsofn(r)and?n(r)Different

GGAsdifferinthechoiceofthefunctionf(n,?n).廣義梯度近似(GGA)AlexD.Becke“一切都是合法的”劍宗JohnP.Perdew一定的物理規(guī)律（如標(biāo)度關(guān)系和漸進(jìn)行為）為基礎(chǔ)，PBE氣宗GGAsusedinquantumchemistrytypicallyproceedbyfittingparameterstotestsetsofselectedmolecules.NowadaysthemostpopularGGAsarePBEinphysics,andBLYPinchemistry.CurrentGGAsseemtogivereliableresultsforallmaintypesofchemicalbonds(covalent,ionic,metallicandhydrogenbridge).Inadditiontothedensityanditsderivatives,Meta-GGAsdependalsoontheKohn-Shamkinetic-energydensity:SothatExccanbewrittenasExc[n(r),?n(r),τ(r)].TheadditionaldegreeoffreedomprovidedbyτisusedtosatisfyadditionalconstraintsonExc.Meta-GGAshavegivenfavorableresults,evenwhencomparedtothebestGGAs.Thefullpotentialofthistypeofapproximationisonlybeginningtobeexploredsystematically.Meta-GGACommonhybridfunctionalmixafractionofHartree-FockexchangeintotheDFTexchangefunctional.HybridFunctionals(Becke,1993)(Perdew,1998)B3PW91,B3LYPPBE0B3LYPisthemainworking-horseincomputationalchemistryL(S)DA+UMott絕緣體，Hubbard模型Anisimovetal.：StonerI-->HubbardU軌道序：Dudarevetal.：懲罰泛函PartII:數(shù)值方法平面波基組：從OPW到PP平面波展開正交化平面波（OPW）贗勢(shì)（PP）方法經(jīng)驗(yàn)贗勢(shì)模守恒贗勢(shì)超軟贗勢(shì)Muffin-tin勢(shì)場(chǎng)與分波方法Muffin-tin勢(shì)場(chǎng)近似綴加平面波（APW）格林函數(shù)方法（KKR）線性化方法LAPWLMTO分波方法的發(fā)展FP-LAPWthird-generationMTO,NMTO,EMTO實(shí)空間網(wǎng)格簡(jiǎn)單直觀允許通過(guò)增加網(wǎng)格密度系統(tǒng)地控制計(jì)算收斂精度線性標(biāo)度可以方便的通過(guò)實(shí)空間域分解實(shí)現(xiàn)并行計(jì)算處理某些特殊體系（帶電體系、隧穿結(jié)。。。）有限差分從微分到差分提高FD方法的計(jì)算效率對(duì)網(wǎng)格進(jìn)行優(yōu)化，如曲線網(wǎng)格（適應(yīng)網(wǎng)格）和局部網(wǎng)格優(yōu)化（復(fù)合網(wǎng)格）結(jié)合贗勢(shì)方法多尺度（multiscale）或預(yù)處理（preconditioning）有限元變分方法處理復(fù)雜的邊界條件矩陣稀疏程度及帶狀結(jié)構(gòu)往往不如有限差分好廣義的本征值問(wèn)題PartIII:應(yīng)用物理學(xué)：強(qiáng)相關(guān)體系模型哈密頓量LDA++電子結(jié)構(gòu)：CrO2點(diǎn)陣動(dòng)力學(xué):钚化學(xué)：弱作用體系松散堆積的軟物質(zhì)、惰性氣體、生物分子和聚合物，物理吸附、Cl+HD反應(yīng)用傳統(tǒng)的密度泛函理論處理弱作用體系一個(gè)既能產(chǎn)生vdW相互作用系數(shù)又能產(chǎn)生總關(guān)聯(lián)能的非局域泛函：無(wú)縫的（seamless）方法GW近似密度泛函加衰減色散（DFdD）生命科學(xué)：生物體系困難（尺寸問(wèn)題、時(shí)間尺度）QM/MM方法（飽和原子法、凍結(jié)軌道法）簡(jiǎn)單勢(shì)能面方法線性同步過(guò)渡（LST）二次同步過(guò)渡（QST）完全的分子動(dòng)力學(xué)并行復(fù)制動(dòng)力學(xué)（parallelreplicadynamics）超動(dòng)力學(xué)（hyperdynamics,metadynamics）溫度加速的動(dòng)力學(xué)（temperatureaccelerateddynamics）快速蒙特卡羅（on-the-flykinericMonteCarlo）方法納米和材料科學(xué)：輸運(yùn)性質(zhì)及其他輸運(yùn)：非平衡態(tài)第一性原理模擬材料力學(xué)：運(yùn)動(dòng)學(xué)MonteCarlo（KMC）-->點(diǎn)陣氣體和元胞自動(dòng)機(jī)-->連續(xù)方程的有限差分有限元求解光譜學(xué)：激發(fā)態(tài)和外場(chǎng)系綜密度泛函理論考慮系統(tǒng)對(duì)稱性，用求和方法計(jì)算多重態(tài)激發(fā)能多體微擾理論，GW近似Bethe-Salpeter方程TDDFT，線性響應(yīng)石墨烯體系的第一性原理研究GrapheneIntroductiontographeneandgraphenenanoribbon(GNR)GNRbasedspintronicsNearlyfreeelectron(NFE)statesingatedGNRsuperlatticeCuttingmechanismingrapheneoxide(GO)Graphene:amonolayeroftwo-dimensionalcarbonatoms198519912004CrystalstructureofgrapheneEnergybandsKorK’Siliconout,Graphenein?

RVanNoorden,

Nature

442,228(2006)

WhatareGraphenenanoribbons(GNRs)?UnlimitedLimitedZigzagGNRsUnlimitedLimitedArmchairGNRsArmchairGNRsZigzagGNRsArmchairGNRsarePM.ZigzagGNRsfavorAFM.BandGapsinGNRsY.-W.Sonetal.,Phys.Rev.Lett.

2006,97,216803Half-metallicity(HM)100%spinpolarizationApplications:SpininjectionSpintransportSomeHMmaterials:CrO2,NiMnSb,Fe3O4TransitionMetalEncapsulatedBoronNitrideNanotubes(NewJ.Phys.,2005)One-DimensionalTransitionMetal-BenzeneSandwichPolymers(JACS,2006)ZigzagGNRs(ZGNRs)turntohalfmetal(HM)underexternaltransverseelectricfield.GNRsunderElectricFieldY.-W.Sonetal.,

Nature

2006,444,347LDAGGAB3LYPEffectofXCFunctional?Effectoffinitesize?E.Rudbergetal.,NanoLett.

2007,7,22118-ZGNRBandStructureCrystal03package,B3LYP,Gaussianbasisset…Kan,Yangetal.,

Appl.Phys.Lett.

2007,91,213116ZGNRswithDifferentWidthsLedgeRedgeFermiLevelHalfMetalLedgeRedgeChargePolarizedLongrangeCoulombinteractionLedgeRedgeSpinPolarizedOn-siteCoulombinteractionUChargeandSpinPolarizationsGrapheneRibbonBNSheetRibbonBreaktheEdgeSymmetrybyaChemicalWay8-C1BNπorbitalhybridizationbetweenCandBNAHybridNanoribbonModelKan,Yangetal.,

J.Chem.Phys.

2008,129,0847128-C2BN8-C3BNEnergyGapsn-C1BNPartialChargeDensitySpinDensityChargeandSpinDensitiesBCNNCBEFCoulombterm:longrangeOn-siteUterm:localCompetitionBetweenChargeandSpinPolarizationsFunctionalGroupApproachKan,Yangetal.,

J.Am.Chem.Soc.

2008,130,4224NO2-NH2PairNO2-HpairNO2-CH3pair

RemovetheNH2

pzBandZGNR-fullZGNR-halfGibbsFreeEnergyofFormation

RelativeStabilityZGNR-halfZGNR-full

BandStructuresNFEStatesin0DC60M.Fengetal.,

Science

2008,320,359;J.Zhaoetal.,ACSNano

2009,3,853SuperatomMolecularOrbitalsNFEStatesin1DNanotubesY.Miyamotoetal.,

Phys.Rev.Lett.

1995,74,2993;S.Okadaetal.,Phys.Rev.B2000,62,7634;B.Yanetal.,

J.Am.Chem.Soc.

2009,130,17012NFEStatesin1DNanotubesspxpydx2-y2dxyAtomiccharacterofNFEstatesinnanotubeHu,Yangetal.,

unpublishedNFEStatesin

2DGrapheneSystembandstructureofgraphenethenearlyfreesurfacestateingraphitemonolayerS.M.Posternaketal.,

Phys.Rev.Lett.

1983,50,761;Phys.Rev.Lett.

1984,52,863.WhattheNFEStatesLookLikeinGNRs?PeriodicboundaryconditionEdgesofallnanoribbonsweresaturatedbyHatomsIndividualGNR-0.8896-0.8316-0.7729-0.7092-0.5938XE-FermiE-vacE-Evac3.26423.32223.38093.44463.5599E-EfermiNFEStatesinGNRSuperlatticeTherearemanyNFEstatesabove3eVfromtheFermienergy,andtheycanbeclassifiedtotwotypes:OnemainlydistributesontheribbonTheothermainlyinthevacuumbetweenribbons.Alongtheribbondirection,theeffectivemassisaround1.1meElectrostaticPotential&

1DKronig-PenneyModelx-yplaneaveragedpotential1DKronig-PenneymodelpotentialtwoseriesofspecialsolutionsElectronDopingtoZGNRSuperlattice

LightDopingHeavyDopingEnergyoftheLowestNFEStateDownshiftofNFEstatesshowsimilarbehaviorforarmchairandzigzagGNRswhentheNFEstateiscolsetoFermilevelGatedGNRSuperlatticeasFETEffectofRibbonandVacuumWidths

TheminimumelectrondopingconcentrationtomovethelowestNFEstatetoFermilevelinZGNRsuperlatticedecreasewiththeincreaseofribbonwidth.ItincreasewithVacuumwidth.IdealFETDevice

Cleantransportchannel,highmobility,highon-offratio.

IdealFET!PrepareGrapheneonLargeScale?Chemicalvapordeposition(1970)Micromechanicalexfoliation(Scotchtape)EpitaxialgrowthonSiCsurfaceOxidationandreductioninsolutionGraphiteOxideBrodie:HNO3+NaClO3,givesGObrightincolor,stablewithalowcontamination,andwithsmallestinterlayerdistance(1860)Staudemaier:H2SO4+HNO3+KClO3,slowest,givesthelightestcoloredGO(1898)Hummers-Offeman:H2SO4+KMnO4,fastest,givesabrownishGO(1958)OxidativeCuttingGraphiteflakesbreaksdownintoGOflakes,andthefinalsizedoesnotdependontheinitialsize.CNT:fromnearlyendless,highlytangledropesintoshort,open-endedpipesJ.Liuetal.,

Science

1998,280,1253;M.J.McAllisteretal.,

Chem.Mater

2007,19,4386UnzippingMechanismEpoxygroupsprefertoaligninalineHopingbarrierforepoxygroupsongraphenesurfaceisnottoohighJ.L.Lietal.,,

Phys.Rev.Lett.

2006,96,176101Epoxylineisenough?anepoxylinedefectonlyweakensthefracturestressofthesheetbyapproximately16%J.T.Pacietal.,J.Phys.Chem.C

2007,111,18099What’stheWholeStoryaboutUnzipping?EpoxyChainEpoxyPairsCarbonylPairsLi,Yangetal.,J.Am.Chem.Soc.

2009,131,6320EpoxyPairTheenergyoftheepoxy-pairstructureis2.71eVlowerthananadditionalisolatedepoxygroupTheadditionalenergygainforthesecondepoxypairis0.78eVlargerthanisolatedEPForashortepoxychain,forminganepoxypairoraddinganepoxygrouptoextendthechainiscomparableinenergyTheCuttingProcess0.76-0.480.26-1.09Li,Yangetal.,J.Am.Chem.Soc.

2009,131,6320UnzippingorTearing?GoInward?newedgecarbonbondsareeasiertobeattackedthanthoseinsideanexistingcarbonylpair?Li,Yangetal.,J.