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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)密度泛函理論新進(jìn)展及應(yīng)用楊金龍1ComputationExperimentTheoryScienceResearch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ComputationExperimentTheorySci2T/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)T/nano/IWGN.3/nano/IWGN.Research.Directions/電子結(jié)構(gòu)計(jì)算:預(yù)言材料性質(zhì)、驗(yàn)證理論猜想、理解實(shí)驗(yàn)觀測(cè)現(xiàn)象。/nano/IWGN.R/nano/IWGN.Research.Directions/動(dòng)力學(xué)模擬:預(yù)言反應(yīng)過程、驗(yàn)證理論猜想、理解實(shí)驗(yàn)觀測(cè)現(xiàn)象。/nano/IWGN.Rese5MaterialsPropertiesfromFirst-principles“Supercomputer”GiganticcomputerprogramsMaterialsPropertiesfromFirs6Top500SupercomputersintheworldA“small”PCclustertodayFourordersofmagnitudein15yearsTop500Supercomputersinthe7計(jì)算量隨體系大小急劇增長(zhǎng)計(jì)算量隨體系大小急劇增長(zhǎng)8MaterialPropertiesfromFirst-PrinciplesFromfirstprinciples!Predictnewbehaviors/propertiesofexistingmaterialsDesignmaterialswithdesiredpropertiesUnderstandandexplainmaterialsproperties√√BecomingrealityMaterialPropertiesfromFirst9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?jī)?nèi)容密度泛函理論新進(jìn)展10密度泛函理論新進(jìn)展理論體系

交換相關(guān)泛函、含時(shí)密度泛函、動(dòng)力學(xué)平均場(chǎng)、密度泛函微擾理論數(shù)值方法

基組、格點(diǎn)、線性標(biāo)度應(yīng)用

物理、化學(xué)、生物、材料、納米科學(xué)、光譜學(xué)密度泛函理論新進(jìn)展理論體系11PartI:理論體系PartI:理論體系12PerdewPRL2019+Localdensity+Densitygradient+Inexplicitoccupiedorbitalinformation

+Explicitoccupiedorbitalinformation+Unoccupiedorbitalinformation交換相關(guān)泛函jacob'sladderPerdewPRL2019+Localdensity+13LDAunderestimates

EcbutoverestimatesEx,resultinginunexpectedlygoodvaluesofExc.TheLDAhasbeenappliedin,calculationsofbandstructuresandtotalenergiesinsolid-statephysics.Inquantumchemistry,itismuchlesspopular,becauseitfailstoprovideresultsthatareaccurateenoughtopermitaquantitativediscussionofthechemicalbondinmolecules.局域密度近似(LDA)LDAunderestimatesEcbutover14Anyrealsystemisspatiallyinhomogeneous,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Anyrealsystemisspatiallyi15GGAsusedinquantumchemistrytypicallyproceedbyfittingparameterstotestsetsofselectedmolecules.NowadaysthemostpopularGGAsarePBEinphysics,andBLYPinchemistry.CurrentGGAsseemtogivereliableresultsforallmaintypesofchemicalbonds(covalent,ionic,metallicandhydrogenbridge).GGAsusedinquantumchemistry16Inadditiontothedensityanditsderivatives,Meta-GGAsdependalsoontheKohn-Shamkinetic-energydensity:SothatExccanbewrittenasExc[n(r),?n(r),τ(r)].TheadditionaldegreeoffreedomprovidedbyτisusedtosatisfyadditionalconstraintsonExc.Meta-GGAshavegivenfavorableresults,evenwhencomparedtothebestGGAs.Thefullpotentialofthistypeofapproximationisonlybeginningtobeexploredsystematically.Meta-GGAInadditiontothedensityand17CommonhybridfunctionalmixafractionofHartree-FockexchangeintotheDFTexchangefunctional.HybridFunctionals(Becke,1993)(Perdew,2019)B3PW91,B3LYPPBE0B3LYPisthemainworking-horseincomputationalchemistryCommonhybridfunctionalmixa18LDA:SlaterexchangeVosko-Wilk-Nusaircorrelation,etcGGA:Exchange:B88,PW91,PBE,OPTX,HCTH,etcCorrelations:LYP,P86,PW91,PBE,HCTH,etcHybridGGA:B3LYP,B3PW91,B3P86,PBE0,B97-1,B97-2,B98,O3LYP,etcMeta-GGA:VSXC,PKZB,TPSS,etcHybridmeta-GGA:

tHCTHh,TPSSh,BMK,etcLDA:Slaterexchange19L(S)DA+UMott絕緣體,Hubbard模型Anisimovetal.:StonerI-->HubbardU軌道序:Dudarevetal.:懲罰泛函L(S)DA+UMott絕緣體,Hubbard模型20PartII:數(shù)值方法PartII:數(shù)值方法21數(shù)值離散方法基組展開LCAO基組(Gaussian基組、數(shù)值基組)實(shí)空間網(wǎng)格數(shù)值離散方法基組展開22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)平面波基組:從OPW到PP平面波展開23Muffin-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,EMTOMuffin-tin勢(shì)場(chǎng)與分波方法Muffin-tin勢(shì)場(chǎng)近24平面波基組:從USPP到PAW投影綴加波(PAW)方法贗波函數(shù)空間USPPorPAW?(VASP,ABINIT,...)平面波基組:從USPP到PAW投影綴加波(PAW)方法25實(shí)空間網(wǎng)格簡(jiǎn)單直觀允許通過增加網(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)。。。)實(shí)空間網(wǎng)格簡(jiǎn)單直觀26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)有限差分從微分到差分27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題有限元變分方法28多分辨網(wǎng)格上的小波基組多分辨分析半取樣(semicardinal)基組多分辨網(wǎng)格上的小波基組多分辨分析29PartIII:應(yīng)用PartIII:應(yīng)用30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):钚物理學(xué):強(qiáng)相關(guān)體系模型哈密頓量31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:無縫的(seamless)方法GW近似密度泛函加衰減色散(DFdD)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32生命科學(xué):生物體系困難(尺寸問題、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渡(LST)二次同步過渡(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)方法生命科學(xué):生物體系困難(尺寸問題、時(shí)間尺度)33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34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)光譜學(xué):激發(fā)態(tài)和外場(chǎng)系綜密度泛函理論35石墨烯體系的第一性原理研究石墨烯體系的第一性原理研究36GrapheneIntroductiontographeneandgraphenenanoribbon(GNR)GNRbasedspintronicsNearlyfreeelectron(NFE)statesingatedGNRsuperlatticeCuttingmechanismingrapheneoxide(GO)GrapheneIntroductiontographe37Graphene:amonolayeroftwo-dimensionalcarbonatoms198519912019Graphene:amonolayeroftwo-d38CrystalstructureofgrapheneCrystalstructureofgraphene39EnergybandsKorK’EnergybandsKorK’40Siliconout,Graphenein?

RVanNoorden,

Nature

442,228(2019)

Siliconout,Graphenein?RVa41WhatareGraphenenanoribbons(GNRs)?UnlimitedLimitedZigzagGNRsWhatareGraphenenanoribbons42UnlimitedLimitedArmchairGNRsUnlimitedLimitedArmchairGNRs43ArmchairGNRsZigzagGNRsArmchairGNRsarePM.ZigzagGNRsfavorAFM.BandGapsinGNRsY.-W.Sonetal.,Phys.Rev.Lett.

2019,97,216803ArmchairGNRsZigzagGNRsArmcha44Half-metallicity(HM)100%spinpolarizationApplications:SpininjectionSpintransportSomeHMmaterials:CrO2,NiMnSb,Fe3O4TransitionMetalEncapsulatedBoronNitrideNanotubes(NewJ.Phys.,2019)One-DimensionalTransitionMetal-BenzeneSandwichPolymers(JACS,2019)Half-metallicity(HM)100%spin45ZigzagGNRs(ZGNRs)turntohalfmetal(HM)underexternaltransverseelectricfield.GNRsunderElectricFieldY.-W.Sonetal.,

Nature

2019,444,347ZigzagGNRs(ZGNRs)turntoha46LDAGGAB3LYPEffectofXCFunctional?Effectoffinitesize?E.Rudbergetal.,NanoLett.

2019,7,2211LDAGGAB3LYPEffectofXCFuncti478-ZGNRBandStructureCrystal03package,B3LYP,Gaussianbasisset…Kan,Yangetal.,

Appl.Phys.Lett.

2019,91,2131168-ZGNRBandStructureCrystal0348ZGNRswithDifferentWidthsZGNRswithDifferentWidths49LedgeRedgeFermiLevelHalfMetalLedgeRedgeChargePolarizedLongrangeCoulombinteractionLedgeRedgeSpinPolarizedOn-siteCoulombinteractionUChargeandSpinPolarizationsLedgeRedgeFermiLevelHalfMe50GrapheneRibbonBNSheetRibbonBreaktheEdgeSymmetrybyaChemicalWayGrapheneRibbonBNSheetRibbon518-C1BNπorbitalhybridizationbetweenCandBNAHybridNanoribbonModelKan,Yangetal.,

J.Chem.Phys.

2019,129,0847128-C1BNπorbitalhybridizationb528-C2BN8-C3BNEnergyGaps8-C2BN8-C3BNEnergyGaps53n-C1BNPartialChargeDensitySpinDensityChargeandSpinDensitiesn-C1BNPartialChargeDensitySp54BCNNCBEFCoulombterm:longrangeOn-siteUterm:localCompetitionBetweenChargeandSpinPolarizationsBCNNCBEFCoulombterm:longran55FunctionalGroupApproachKan,Yangetal.,

J.Am.Chem.Soc.

2019,130,4224FunctionalGroupApproachKan,56NO2-NH2PairNO2-NH2Pair57NO2-HpairNO2-CH3pair

RemovetheNH2

pzBandNO2-HpairNO2-CH3pairRemove58ZGNR-fullZGNR-halfGibbsFreeEnergyofFormation

RelativeStabilityZGNR-fullZGNR-halfGibbsFreeE59ZGNR-halfZGNR-full

BandStructuresZGNR-halfZGNR-fullBandStruct60NFEStatesin0DC60M.Fengetal.,

Science

2019,320,359;J.Zhaoetal.,ACSNano

2009,3,853SuperatomMolecularOrbitalsNFEStatesin0DC60M.Fenget61NFEStatesin1DNanotubesY.Miyamotoetal.,

Phys.Rev.Lett.

2019,74,2993;S.Okadaetal.,Phys.Rev.B2000,62,7634;B.Yanetal.,

J.Am.Chem.Soc.

2009,130,17012NFEStatesin1DNanotubesY.M62NFEStatesin1DNanotubesspxpydx2-y2dxyAtomiccharacterofNFEstatesinnanotubeHu,Yangetal.,

unpublishedNFEStatesin1DNanotubesspxp63NFEStatesin

2DGrapheneSystembandstructureofgraphenethenearlyfreesurfacestateingraphitemonolayerS.M.Posternaketal.,

Phys.Rev.Lett.

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

1984,52,863.NFEStatesin

2DGrapheneSyst64WhattheNFEStatesLookLikeinGNRs?PeriodicboundaryconditionEdgesofallnanoribbonsweresaturatedbyHatomsWhattheNFEStatesLookLike65IndividualGNR-0.8896-0.8316-0.7729-0.7092-0.5938XE-FermiE-vacE-Evac3.26423.32223.38093.44463.5599E-EfermiIndividualGNR-0.8896-0.8316-066NFEStatesinGNRSuperlatticeTherearemanyNFEstatesabove3eVfromtheFermienergy,andtheycanbeclassifiedtotwotypes:OnemainlydistributesontheribbonTheothermainlyinthevacuumbetweenribbons.Alongtheribbondirection,theeffectivemassisaround1.1meNFEStatesinGNRSuperlattice67ElectrostaticPotential&

1DKronig-PenneyModelx-yplaneaveragedpotential1DKronig-PenneymodelpotentialtwoseriesofspecialsolutionsElectrostaticPotential&

1D68ElectronDopingtoZGNRSuperlattice

ElectronDopingtoZGNRSuperl69LightDopingLightDoping70HeavyDopingHeavyDoping71EnergyoftheLowestNFEStateDownshiftofNFEstatesshowsimilarbehaviorforarmchairandzigzagGNRswhentheNFEstateiscolsetoFermilevelEnergyoftheLowestNFEState72GatedGNRSuperlatticeasFETGatedGNRSuperlatticeasFET73EffectofRibbonandVacuumWidths

TheminimumelectrondopingconcentrationtomovethelowestNFEstatetoFermilevelinZGNRsuperlatticedecreasewiththeincreaseofribbonwidth.ItincreasewithVacuumwidth.EffectofRibbonandVacuumWi74IdealFETDevice

Cleantransportchannel,highmobility,highon-offratio.

IdealFET!IdealFETDeviceCleantransp75PrepareGrapheneonLargeScale?Chemicalvapordeposition(1970)Micromechanicalexfoliation(Scotchtape)EpitaxialgrowthonSiCsurfaceOxidationandreductioninsolutionPrepareGrapheneonLargeScal76GraphiteOxideBrodie:HNO3+NaClO3,givesGObrightincolor,stablewithalowcontamination,andwithsmallestinterlayerdistance(1860)Staudemaier:H2SO4+HNO3+KClO3,slowest,givesthelightestcoloredGO(1898)Hummers-Offeman:H2SO4+KMnO4,fastest,givesabrownishGO(1958)GraphiteOxideBrodie:HNO3+NaC77OxidativeCuttingGraphiteflakesbreaksdownintoGOflakes,andthefinalsizedoesnotdependontheinitialsize.CNT:fromnearlyendless,highlytangledropesintoshort,open-endedpipesJ.Liuetal.,

Science

2019,280,1253;M.J.McAllisteretal.,

Chem.Mater

2019,19,4386OxidativeCuttingGraphiteflak78UnzippingMechanismEpoxygroupsprefertoaligninalineHopingbarrierforepoxygroupsongraphenesurfaceisnottoohighJ.L.Lietal.,,

Phys.Rev.Lett.

2019,96,176101UnzippingMechanismEpoxygroup79Epoxylineisenough?anepoxylinedefectonlyweakensthefracturestressofthesheetbyapproximately16%J.T.Pacietal.,J.Phys.Chem.C

2019,111,18099Epoxylineisenough?anepoxy80What’stheWholeStoryaboutUnzipping?EpoxyChainEpoxyPairsCarbonylPairsLi,Yangetal.,J.Am.Chem.Soc.

2009,131,6320What’stheWholeStoryaboutU81EpoxyPairTheenergyoftheepoxy-pairstructureis2.71eVlowerthananadditionalisolatedepoxygroupTheadditionalenergygainforthesecondepoxypairis0.78eVlargerthanisolatedEPForashortepoxychain,forminganepoxypairoraddinganepoxygrouptoextendthechainiscomparableinenergyEpoxyPairTheenergyoftheep82TheCuttingProcess0.76-0.480.26-1.09Li,Yangetal.,J.Am.Chem.Soc.

2009,131,6320TheCuttingProcess0.76-0.480.83UnzippingorTearing?UnzippingorTearing?84GoInward?newedgecarbonbondsareeasiertobeattackedthanthoseinsideanexistingcarbonylpair?Li,Yangetal.,J.Am.Chem.Soc.

2009,131,6320GoInward?newedgecarbonbond85StructureofGOHofmann(1939)Ruess(1946)Scholz(1969)Nakajima(1988)Lerf(2019)Szabo(2019)StructureofGOHofmann(1939)R86XPSofGOH.-K.Jeongetal.,

J.Am.Chem.Soc.

2019,130,1362T.Szaboetal.,

Chem.Mater.

2019,18,2740XPSofGOH.-K.Jeongetal.,J87C1sBindingEnergySimulationThebindingenergyofC1sorbitaliscalculatedastheenergydifferencebetweenthegroundstateandcore-excitedstatewithonecoreelectronremoved.Relativecorechemicalshift(R-CCS)withrespecttotheepoxidegroup.C-epoxideandC-OHaredifficulttoberesolvedinaXPSspectrumC1sBindingEnergySimulation88宏劍培訓(xùn)密度泛函理論新進(jìn)展及應(yīng)用-課件89TheLargeRibbonModelToconsiderbothinnerandedgespecies,alargeribbonmodelisadopted.AllfunctionalgroupsareputinasinglesystemTheLargeRibbonModelToconsi90BindingEnergiessp2C-C<edgegroups(suchasC=O,C-OH,C-epoxideinepoxidechain)<C-OH-innerandC-epoxide<C-EP,COOH<COOOBindingEnergiessp2C-C<edge91Zhang,Carravetta,Li,Luo,andYang,J.Chem.Phys.131,244505(2009)Zhang,Carravetta,Li,Luo,an92Thanks!Dr.HongjunXiangDr.Er-junKanDr.ShuanglinHuDr.WenhuaZhangDr.ZhenyuLiProf.YiLuoNFSCMOECASMOSTThanks!Dr.HongjunXiang93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)密度泛函理論新進(jìn)展及應(yīng)用楊金龍94ComputationExperimentTheoryScienceResearch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ComputationExperimentTheorySci95T/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)T/nano/IWGN.96/nano/IWGN.Research.Directions/電子結(jié)構(gòu)計(jì)算:預(yù)言材料性質(zhì)、驗(yàn)證理論猜想、理解實(shí)驗(yàn)觀測(cè)現(xiàn)象。/nano/IWGN.R/nano/IWGN.Research.Directions/動(dòng)力學(xué)模擬:預(yù)言反應(yīng)過程、驗(yàn)證理論猜想、理解實(shí)驗(yàn)觀測(cè)現(xiàn)象。/nano/IWGN.Rese98MaterialsPropertiesfromFirst-principles“Supercomputer”GiganticcomputerprogramsMaterialsPropertiesfromFirs99Top500SupercomputersintheworldA“small”PCclustertodayFourordersofmagnitudein15yearsTop500Supercomputersinthe100計(jì)算量隨體系大小急劇增長(zhǎng)計(jì)算量隨體系大小急劇增長(zhǎng)101MaterialPropertiesfromFirst-PrinciplesFromfirstprinciples!Predictnewbehaviors/propertiesofexistingmaterialsDesignmaterialswithdesiredpropertiesUnderstandandexplainmaterialsproperties√√BecomingrealityMaterialPropertiesfromFirst102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?jī)?nèi)容密度泛函理論新進(jìn)展103密度泛函理論新進(jìn)展理論體系

交換相關(guān)泛函、含時(shí)密度泛函、動(dòng)力學(xué)平均場(chǎng)、密度泛函微擾理論數(shù)值方法

基組、格點(diǎn)、線性標(biāo)度應(yīng)用

物理、化學(xué)、生物、材料、納米科學(xué)、光譜學(xué)密度泛函理論新進(jìn)展理論體系104PartI:理論體系PartI:理論體系105PerdewPRL2019+Localdensity+Densitygradient+Inexplicitoccupiedorbitalinformation

+Explicitoccupiedorbitalinformation+Unoccupiedorbitalinformation交換相關(guān)泛函jacob'sladderPerdewPRL2019+Localdensity+106LDAunderestimates

EcbutoverestimatesEx,resultinginunexpectedlygoodvaluesofExc.TheLDAhasbeenappliedin,calculationsofbandstructuresandtotalenergiesinsolid-statephysics.Inquantumchemistry,itismuchlesspopular,becauseitfailstoprovideresultsthatareaccurateenoughtopermitaquantitativediscussionofthechemicalbondinmolecules.局域密度近似(LDA)LDAunderestimatesEcbutover107Anyrealsystemisspatiallyinhomogeneous,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Anyrealsystemisspatiallyi108GGAsusedinquantumchemistrytypicallyproceedbyfittingparameterstotestsetsofselectedmolecules.NowadaysthemostpopularGGAsarePBEinphysics,andBLYPinchemistry.CurrentGGAsseemtogivereliableresultsforallmaintypesofchemicalbonds(covalent,ionic,metallicandhydrogenbridge).GGAsusedinquantumchemistry109Inadditiontothedensityanditsderivatives,Meta-GGAsdependalsoontheKohn-Shamkinetic-energydensity:SothatExccanbewrittenasExc[n(r),?n(r),τ(r)].TheadditionaldegreeoffreedomprovidedbyτisusedtosatisfyadditionalconstraintsonExc.Meta-GGAshavegivenfavorableresults,evenwhencomparedtothebestGGAs.Thefullpotentialofthistypeofapproximationisonlybeginningtobeexploredsystematically.Meta-GGAInadditiontothedensityand110CommonhybridfunctionalmixafractionofHartree-FockexchangeintotheDFTexchangefunctional.HybridFunctionals(Becke,1993)(Perdew,2019)B3PW91,B3LYPPBE0B3LYPisthemainworking-horseincomputationalchemistryCommonhybridfunctionalmixa111LDA:SlaterexchangeVosko-Wilk-Nusaircorrelation,etcGGA:Exchange:B88,PW91,PBE,OPTX,HCTH,etcCorrelations:LYP,P86,PW91,PBE,HCTH,etcHybridGGA:B3LYP,B3PW91,B3P86,PBE0,B97-1,B97-2,B98,O3LYP,etcMeta-GGA:VSXC,PKZB,TPSS,etcHybridmeta-GGA:

tHCTHh,TPSSh,BMK,etcLDA:Slaterexchange112L(S)DA+UMott絕緣體,Hubbard模型Anisimovetal.:StonerI-->HubbardU軌道序:Dudarevetal.:懲罰泛函L(S)DA+UMott絕緣體,Hubbard模型113PartII:數(shù)值方法PartII:數(shù)值方法114數(shù)值離散方法基組展開LCAO基組(Gaussian基組、數(shù)值基組)實(shí)空間網(wǎng)格數(shù)值離散方法基組展開115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)平面波基組:從OPW到PP平面波展開116Muffin-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,EMTOMuffin-tin勢(shì)場(chǎng)與分波方法Muffin-tin勢(shì)場(chǎng)近117平面波基組:從USPP到PAW投影綴加波(PAW)方法贗波函數(shù)空間USPPorPAW?(VASP,ABINIT,...)平面波基組:從USPP到PAW投影綴加波(PAW)方法118實(shí)空間網(wǎng)格簡(jiǎn)單直觀允許通過增加網(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)。。。)實(shí)空間網(wǎng)格簡(jiǎn)單直觀119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)有限差分從微分到差分120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題有限元變分方法121多分辨網(wǎng)格上的小波基組多分辨分析半取樣(semicardinal)基組多分辨網(wǎng)格上的小波基組多分辨分析122PartIII:應(yīng)用PartIII:應(yīng)用123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):钚物理學(xué):強(qiáng)相關(guān)體系模型哈密頓量124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:無縫的(seamless)方法GW近似密度泛函加衰減色散(DFdD)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125生命科學(xué):生物體系困難(尺寸問題、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渡(LST)二次同步過渡(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)方法生命科學(xué):生物體系困難(尺寸問題、時(shí)間尺度)126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127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)光譜學(xué):激發(fā)態(tài)和外場(chǎng)系綜密度泛函理論128石墨烯體系的第一性原理研究石墨烯體系的第一性原理研究129GrapheneIntroductiontographeneandgraphenenanoribbon(GNR)GNRbasedspintronicsNearlyfreeelectron(NFE)statesingatedGNRsuperlatticeCuttingmechanismingrapheneoxide(GO)GrapheneIntroductiontographe130Graphene:amonolayeroftwo-dimensionalcarbonatoms198519912019Graphene:amonolayeroftwo-d131CrystalstructureofgrapheneCrystalstructureofgraphene132EnergybandsKorK’EnergybandsKorK’133Siliconout,Graphenein?

RVanNoorden,

Nature

442,228(2019)

Siliconout,Graphenein?RVa134WhatareGraphenenanoribbons(GNRs)?UnlimitedLimitedZigzagGNRsWhatareGraphenenanoribbons135UnlimitedLimitedArmchairGNRsUnlimitedLimitedArmchairGNRs136ArmchairGNRsZigzagGNRsArmchairGNRsarePM.ZigzagGNRsfavorAFM.BandGapsinGNRsY.-W.Sonetal.,Phys.Rev.Lett.

2019,97,216803ArmchairGNRsZigzagGNRsArmcha137Half-metallicity(HM)100%spinpolarizationApplications:SpininjectionSpintransportSomeHMmaterials:CrO2,NiMnSb,Fe3O4TransitionMetalEncapsulatedBoronNitrideNanotubes(NewJ.Phys.,2019)One-DimensionalTransitionMetal-BenzeneSandwichPolymers(JACS,2019)Half-metallicity(HM)100%spin138ZigzagGNRs(ZGNRs)turntohalfmetal(HM)underexternaltransverseelectricfield.GNRsunderElectricFieldY.-W.Sonetal.,

Nature

2019,444,347ZigzagGNRs(ZGNRs)turntoha139LDAGGAB3LYPEffectofXCFunctional?Effectoffinitesize?E.Rudbergetal.,NanoLett.

2019,7,2211LDAGGAB3LYPEffectofXCFuncti1408-ZGNRBandStructureCrystal03package,B3LYP,Gaussianbasisset…Kan,Yangetal.,

Appl.Phys.Lett.

2019,91,2131168-ZGNRBandStructureCrystal03141ZGNRswithDifferentWidthsZGNRswithDifferentWidths142LedgeRedgeFermiLevelHalfMetalLedgeRedgeChargePolarizedLongrangeCoulombinteractionLedgeRedgeSpinPolarizedOn-siteCoulombinteractionUChargeandSpinPolarizationsLedgeRedgeFermiLevelHalfMe143GrapheneRibbonBNSheetRibbonBreaktheEdgeSymmetrybyaChemicalWayGrapheneRibbonBNSheetRibbon1448-C1BNπorbitalhybridizationbetweenCandBNAHybridNanoribbonModelKan,Yangetal.,

J.Chem.Phys.

2019,129,0847128-C1BNπorbitalhybridizationb1458-C2BN8-C3BNEnergyGaps8-C2BN8-C3BNEnergyGaps146n-C1BNPartialChargeDensitySpinDensityChargeandSpinDensitiesn-C1BNPartialChargeDensitySp147BCNNCBEFCoulombterm:longrangeOn-siteUterm:localCompetitionBetweenChargeandSpinPolarizationsBCNNCBEFCoulombterm:longran148FunctionalGroupApproachKan,Yangetal.,

J.Am.Chem.Soc.

2019,130,4224FunctionalGroupApproachKan,149NO2-NH2PairNO2-NH2Pair150NO2-HpairNO2-CH3pair

RemovetheNH2

pzBandNO2-HpairNO2-CH3pairRemove151ZGNR-fullZGNR-halfGibbsFreeEnergyofFormation

RelativeStabilityZGNR-fullZGNR-halfGibbsFreeE152ZGNR-halfZGNR-full

BandStructuresZGNR-halfZGNR-fullBandStruct153NFEStatesin0DC60M.Fengetal.,

Science

2019,320,359;J.Zhaoetal.,ACSNano

2009,3,853SuperatomMolecularOrbitalsNFEStatesin0DC60M.Fenget154NFEStatesin1DNanotubesY.Miyamotoetal.,

Phys.Rev.Lett.

2019,74,2993;S.Okadaetal.,Phys.Rev.B2000,62,7634;B.Yanetal.,

J.Am.Chem.Soc.

2009,130,17012NFEStatesin1DNanotubesY.M155NFEStatesin1DNanotubesspxpydx2-y2dxyAtomiccharacterofNFEstatesinnanotubeHu,Yangetal.,

unpublishedNFEStatesin1DNanotubesspxp156NFEStatesin

2DGrapheneSystembandstructureofgraphenethenearlyfreesurfacestateingraphitemonolayerS.M.Posternaketal.,

Phys.Rev.Lett.

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

1984,52,863.NFEStatesin

2DGrapheneSyst157WhattheNFEStatesLookLikeinGNRs?PeriodicboundaryconditionEdgesofallnanoribbonsweresaturatedbyHatomsWhattheNFEStatesLookLike158IndividualGNR-0.8896-0.8316-0.7729-0.7092-0.5938XE-FermiE-vacE-Evac3.26423.32223.38093.44463.5599E-EfermiIndividualGNR-0.8896-0.8316-0159NFEStatesinGNRSuperlatticeTherearemanyNFEstatesabove3eVfromtheFermienergy,andtheycanbeclassifiedtotwotypes:OnemainlydistributesontheribbonTheothermainlyinthevacuumbetweenribbons.Alongtheribbondirection,theeffectivemassisaround1.1meNFEStatesinGNRSuperlattice160ElectrostaticPotential&

1DKronig-PenneyModelx-yplaneaveragedpotential1DKronig-PenneymodelpotentialtwoseriesofspecialsolutionsElectrostaticPotential&

1D161ElectronDopingtoZGNRSuperlattice

ElectronDopingtoZGNRSuperl162LightDopingLightDoping163HeavyDopingHeavyDoping164EnergyoftheLowestNFEStateDownshiftofNFEstatesshowsimilarbehaviorforarmchairandzigzagGNRswhentheNFEstateiscolsetoFermilevelEnergyoftheLowestNFEState165GatedGNRSuperlatticeasFETGatedGNRSuperlatticeasFET166EffectofRibbonandVacuumWidths

TheminimumelectrondopingconcentrationtomovethelowestNFEstatetoFermilevelinZGNRsuperlatticedecreasewiththeincreaseofribbonwidth.ItincreasewithVacuumwidth.EffectofRibbonandVacuumWi167IdealFETDevice

Cleantransportchannel,highmobility,highon-offratio.

IdealFET!IdealFETDeviceCleantransp168PrepareGrapheneonLargeScale?Chemicalvapordeposition(1970)Micromechanicalexfoliation(Scotchtape)EpitaxialgrowthonSiCsurfaceOxidationandreductioninsolutionPrepareGrapheneonLargeScal169GraphiteOxideBrodie:HNO3+NaClO3,givesGObrightincolor,stablewithalowcontamination,andwithsmallestinterlayerdistance(1860)Staudemaier:H2SO4+HNO3+KClO3,slowest,givesthelightestcoloredGO(1898)Hummers-Offeman:H2SO4+KMnO4,fastest,givesabrownishGO(1958)GraphiteOxideBrodie:HNO3+NaC170OxidativeCuttingGraphitefl

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