密度泛函理论新进展及应用课件

密度泛函理论新进展及应用杨金龙中国科学技术大学精品ComputationExperimentTheoryScience Research计算机模算机模拟已已经与理与理论与与实验并列，成并列，成为三种基本的科学研究手段之一三种基本的科学研究手段之一精品Timehttp:/itri.loyola.edu/nano/IWGN.Research.Directions/Scientific Computationspropertiessystemsmethods空间尺度：电子机构时间尺度：动力学精品http:/itri.loyola.edu/nano/IWGN.Research.Directions/电子子结构构计算：算：预言材料性言材料性质、验证理理论猜想、理解猜想、理解实验观测现象。象。精品http:/itri.loyola.edu/nano/IWGN.Research.Directions/动力学模力学模拟：预言反言反应过程、程、验证理理论猜想、理解猜想、理解实验观测现象。象。精品Materials Properties from First-principles“Supercomputer”Gigantic computer programs精品Top 500 Supercomputers in the worldA“small”PC cluster todayFour orders of magnitudein 15 years精品计计算量随体系大小急算量随体系大小急剧剧增增长长精品Material Properties from First-PrinciplesFrom first principles!Predict new behaviors/properties of existing materialsDesign materials with desired propertiesUnderstand and explain materials propertiesBecoming reality精品内容密度泛函理论新进展石墨烯条带体系的第一性原理计算研究精品密度泛函理论新进展理论体系交换相关泛函、含时密度泛函、动力学平均场、密度泛函微扰理论数值方法基组、格点、线性标度应用物理、化学、生物、材料、纳米科学、光谱学精品Part I:理论体系精品Perdew PRL2003+Local density+Density gradient+Inexplicit occupied orbital information+Explicit occupied orbital information+Unoccupied orbital information交换相关泛函jacobs ladder精品LDA underestimates Ec but overestimates Ex,resulting in unexpectedly good values of Exc.The LDA has been applied in,calculations of band structures and total energies in solid-state physics.In quantum chemistry,it is much less popular,because it fails to provide results that are accurate enough to permit a quantitative discussion of the chemical bond in molecules.局域密度近似(LDA)精品Any real system is spatially inhomogeneous,it has a spatially varying density n(r),it would clearly be useful to also include information on the rate of this variation in the functional.In this approximation,one tries to systematically calculate gradient-corrections of general functions of n(r)and n(r)Different GGAs differ in the choice of the function f(n,n).广义梯度近似(GGA)Alex D.Becke“一切都是合法的”剑宗John P.Perdew一定的物理规律（如标度关系和渐进行为）为基础，PBE 气宗精品GGAs used in quantum chemistry typically proceed by fitting parameters to test sets of selected molecules.Nowadays the most popular GGAs are PBE in physics,and BLYP in chemistry.Current GGAs seem to give reliable results for all main types of chemical bonds(covalent,ionic,metallic and hydrogen bridge).精品In addition to the density and its derivatives,Meta-GGAs depend also on the Kohn-Sham kinetic-energy density:So that Exc can be written as Exc n(r),n(r),(r).The additional degree of freedom provided by is used to satisfy additional constraints on Exc.Meta-GGAs have given favorable results,even when compared to the best GGAs.The full potential of this type of approximation is only beginning to be explored systematically.Meta-GGA精品Common hybrid functional mix a fraction of Hartree-Fock exchange into the DFT exchange functional.Hybrid Functionals(Becke,1993)(Perdew,1998)B3PW91,B3LYPPBE0B3LYP is the main working-horse in computational chemistry精品LDA:Slater exchange Vosko-Wilk-Nusair correlation,etcGGA:Exchange:B88,PW91,PBE,OPTX,HCTH,etc Correlations:LYP,P86,PW91,PBE,HCTH,etcHybrid GGA:B3LYP,B3PW91,B3P86,PBE0,B97-1,B97-2,B98,O3LYP,etcMeta-GGA:VSXC,PKZB,TPSS,etcHybrid meta-GGA:t tHCTHh,TPSSh,BMK,etc精品L(S)DA+UMott绝缘体，Hubbard模型Anisimov et al.：Stoner I-Hubbard U轨道序：Dudarev et al.：惩罚泛函精品Part II:数值方法精品数值离散方法基组展开LCAO基组（Gaussian基组、数值基组）实空间网格精品平面波基组：从OPW到PP平面波展开正交化平面波（OPW）赝势（PP）方法经验赝势 模守恒赝势 超软赝势精品Muffin-tin势场与分波方法Muffin-tin势场近似缀加平面波（APW）格林函数方法（KKR）线性化方法LAPW LMTO分波方法的发展FP-LAPW third-generation MTO,NMTO,EMTO精品平面波基组：从USPP到PAW投影缀加波（PAW）方法 赝波函数空间USPP or PAW?(VASP,ABINIT,.)精品实空间网格简单直观 允许通过增加网格密度系统地控制计算收敛精度线性标度 可以方便的通过实空间域分解实现并行计算处理某些特殊体系（带电体系、隧穿结。）精品有限差分从微分到差分提高FD方法的计算效率对网格进行优化，如曲线网格（适应网格）和局部网格优化（复合网格）结合赝势方法 多尺度（multiscale）或预处理（preconditioning）精品有限元变分方法 处理复杂的边界条件矩阵稀疏程度及带状结构往往不如有限差分好 广义的本征值问题精品多分辨网格上的小波基组多分辨分析半取样（semicardinal）基组精品Part III:应用精品物理学：强相关体系模型哈密顿量 LDA+电子结构：CrO2点阵动力学:钚精品化学：弱作用体系松散堆积的软物质、惰性气体、生物分子和聚合物，物理吸附、Cl+HD反应用传统的密度泛函理论处理弱作用体系一个既能产生vdW相互作用系数又能产生总关联能的非局域泛函：无缝的（seamless）方法GW近似 密度泛函加衰减色散（DFdD）精品生命科学：生物体系困难（尺寸问题、时间尺度）QM/MM方法（饱和原子法、冻结轨道法）简单势能面方法线性同步过渡（LST）二次同步过渡（QST）完全的分子动力学并行复制动力学（parallel replica dynamics）超动力学（hyperdynamics,metadynamics）温度加速的动力学（temperature accelerated dynamics）快速蒙特卡罗（on-the-fly kineric Monte Carlo）方法精品纳米和材料科学：输运性质及其他输运：非平衡态第一性原理模拟 材料力学：运动学Monte Carlo（KMC）-点阵气体和元胞自动机-连续方程的有限差分有限元求解精品光谱学：激发态和外场系综密度泛函理论 考虑系统对称性，用求和方法计算多重态激发能多体微扰理论，GW近似Bethe-Salpeter方程 TDDFT，线性响应精品石墨石墨烯烯体系的第一性原理研究体系的第一性原理研究精品GrapheneIntroduction to graphene and graphene nanoribbon(GNR)GNR based spintronicsNearly free electron(NFE)states in gated GNR superlatticeCutting mechanism in graphene oxide(GO)精品Graphene:a monolayer of two-dimensional carbon atoms198519912004精品Crystal structure of graphene精品Energy bandsK or K精品Silicon out,Graphene in?R Van Noorden,Nature 442,228(2006)精品What are Graphene nanoribbons(GNRs)?UnlimitedLimitedZigzag GNRs精品UnlimitedLimitedArmchair GNRs精品Armchair GNRsArmchair GNRsZigzag GNRsArmchair GNRs are PM.Zigzag GNRs favor AFM.Band Gaps in GNRsY.-W.Son et al.,Phys.Rev.Lett.2006,97,216803精品Half-metallicity(HM)100%spin polarizationApplications:Spin injection Spin transportSome HM materials:CrO2,NiMnSb,Fe3O4Transition Metal Encapsulated Boron Nitride Nanotubes(New J.Phys.,2005)One-Dimensional Transition Metal-Benzene Sandwich Polymers(JACS,2006)精品Zigzag GNRs(ZGNRs)turn to half metal(HM)under external transverse electric field.GNRs under Electric FieldY.-W.Son et al.,Nature 2006,444,347精品LDAGGAB3LYPEffect of XC Functional?Effect of finite size?E.Rudberg et al.,Nano Lett.2007,7,2211精品8-ZGNRBand StructureCrystal 03 package,B3LYP,Gaussian basis set Kan,Yang et al.,Appl.Phys.Lett.2007,91,213116精品ZGNRs with Different Widths精品LedgeRedgeFermiLevelHalfMetalLedgeRedgeChargePolarizedLong range Coulomb interactionLedgeRedgeSpinPolarizedOn-site Coulomb interaction UCharge and Spin Polarizations精品Graphene RibbonBN Sheet RibbonBreak the Edge Symmetry by a Chemical Way精品8-C1BNorbital hybridization between C and BNA Hybrid Nanoribbon ModelKan,Yang et al.,J.Chem.Phys.2008,129,084712精品8-C2BN8-C3BNEnergy Gaps精品n-C1BNPartial Charge DensitySpin DensityCharge and Spin Densities精品BCNNCBEFCoulomb term:long rangeOn-site U term:localCompetition Between Charge and Spin Polarizations精品Functional Group ApproachKan,Yang et al.,J.Am.Chem.Soc.2008,130,4224精品NO2-NH2 Pair精品NO2-H pairNO2-CH3 pair Remove the NH2 pz Band精品ZGNR-fullZGNR-halfGibbs Free Energy of Formation Relative Stability精品ZGNR-halfZGNR-full Band Structures精品NFE States in 0D C60M.Feng et al.,Science 2008,320,359;J.Zhao et al.,ACS Nano 2009,3,853Superatom Molecular Orbitals精品NFE States in 1D NanotubesY.Miyamoto et al.,Phys.Rev.Lett.1995,74,2993;S.Okada et al.,Phys.Rev.B 2000,62,7634;B.Yan et al.,J.Am.Chem.Soc.2009,130,17012精品NFE States in 1D Nanotubesspxpydx2-y2dxyAtomic character of NFE states in nanotubeHu,Yang et al.,unpublished精品NFE States in2D Graphene Systemband structure of graphenethe nearly free surface state in graphite monolayerS.M.Posternak et al.,Phys.Rev.Lett.1983,50,761;Phys.Rev.Lett.1984,52,863.精品What the NFE States Look Like in GNRs?Periodic boundary conditionEdges of all nanoribbons were saturated by H atoms精品Individual GNR-0.8896-0.8316-0.7729-0.7092-0.5938XE-FermiE-vacE-Evac3.26423.32223.38093.44463.5599E-Efermi精品NFE States in GNR SuperlatticeThere are many NFE states above 3eV from the Fermi energy,and they can be classified to two types:One mainly distributes on the ribbonThe other mainly in the vacuum between ribbons.Along the ribbon direction,the effective mass is around 1.1me精品Electrostatic Potential&1D Kronig-Penney Modelx-y plane averaged potential1D Kronig-Penney model potentialtwo series of special solutions精品Electron Doping to ZGNR Superlattice 精品Light Doping精品Heavy Doping精品Energy of the Lowest NFE StateDownshift of NFE states show similar behavior for armchair and zigzag GNRs when the NFE state is colse to Fermi level精品Gated GNR Superlattice as FET精品Effect of Ribbon and Vacuum Widths The minimum electron doping concentration to move the lowest NFE state to Fermi level in ZGNR superlattice decrease with the increase of ribbon width.It increase with Vacuum width.精品Ideal FET Device Clean transport channel,high mobility,high on-off ratio.Ideal FET!精品Prepare Graphene on Large Scale?Chemical vapor deposition(1970)Micromechanical exfoliation(Scotch tape)Epitaxial growth on SiC surfaceOxidation and reduction in solution精品Graphite OxideBrodie:HNO3+NaClO3,gives GO bright in color,stable with a low contamination,and with smallest interlayer distance(1860)Staudemaier:H2SO4+HNO3+KClO3,slowest,gives the lightest colored GO(1898)Hummers-Offeman:H2SO4+KMnO4,fastest,gives a brownish GO(1958)精品Oxidative CuttingGraphite flakes breaks down into GO flakes,and the final size does not depend on the initial size.CNT:from nearly endless,highly tangled ropes into short,open-ended pipesJ.Liu et al.,Science 1998,280,1253;M.J.McAllister et al.,Chem.Mater 2007,19,4386精品Unzipping MechanismEpoxy groups prefer to align in a lineHoping barrier for epoxy groups on graphene surface is not too highJ.L.Li et al.,Phys.Rev.Lett.2006,96,176101精品Epoxy line is enough?an epoxy line defect only weakens the fracture stress of the sheet by approximately 16%J.T.Paci et al.,J.Phys.Chem.C 2007,111,18099精品Whats the Whole Story about Unzipping?Epoxy ChainEpoxy PairsCarbonyl PairsLi,Yang et al.,J.Am.Chem.Soc.2009,131,6320精品Epoxy PairThe energy of the epoxy-pair structure is 2.71 eV lower than an additional isolated epoxy groupThe additional energy gain for the second epoxy pair is 0.78 eV larger than isolated EPFor a short epoxy chain,forming an epoxy pair or adding an epoxy group to extend the chain is comparable in energy精品The Cutting Process0.76-0.480.26-1.09Li,Yang et al.,J.Am.Chem.Soc.2009,131,6320精品Unzipping or Tearing?精品Go Inward?new edge carbon bonds are easier to be attacked than those inside an existing carbonyl pairLi,Yang et al.,J.Am.Chem.Soc.2009,131,6320精品Structure of GOHofmann(1939)Ruess(1946)Scholz(1969)Nakajima(1988)Lerf(1998)Szabo(2006)精品XPS of GOH.-K.Jeong et al.,J.Am.Chem.Soc.2008,130,1362T.Szabo et al.,Chem.Mater.2006,18,2740精品C 1s Binding Energy SimulationThe binding energy of C 1s orbital is calculated as the energy difference between the ground state and core-excited state with one core electron removed.Relative core chemical shift(R-CCS)with respect to the epoxide group.C-epoxide and C-OH are difficult to be resolved in a XPS spectrum精品精品The Large Ribbon ModelTo consider both inner and edge species,a large ribbon model is adopted.All functional groups are put in a single system精品Binding Energiessp2 C-C edge groups(such as C=O,C-OH,C-epoxide in epoxide chain)C-OH-inner and C-epoxide C-EP,COOH COOO精品Zhang,Carravetta,Li,Luo,and Yang,J.Chem.Phys.131,244505(2009)精品Thanks!Dr.Hongjun XiangDr.Er-jun KanDr.Shuanglin HuDr.Wenhua ZhangDr.Zhenyu LiProf.Yi LuoNFSCMOECASMOST精品