1、密度泛函理论新进展及应用杨金龙中国科学技术大学ComputationExperimentTheoryScience Research计算机模拟已经与理论与实验并列，成为三种基本的科学研究手段之一计算机模拟已经与理论与实验并列，成为三种基本的科学研究手段之一Timeitri.loyola.edu/nano/IWGN.Research.Directions/Scientific Computationspropertiessystemsmethods 空间尺度：电子机构 时间尺度：动力学itri.loyola.edu/nano/IWGN.Research.Directions/电子结构计算：预言材
2、料性质、验证理论猜想、理解实验观测现象。电子结构计算：预言材料性质、验证理论猜想、理解实验观测现象。itri.loyola.edu/nano/IWGN.Research.Directions/动力学模拟：预言反应过程、验证理论猜想、理解实验观测现象。动力学模拟：预言反应过程、验证理论猜想、理解实验观测现象。Materials Properties from First-principles“Supercomputer”Gigantic computer programs 0 10 20 30 40 50 60 0 2 4 6 8 10.)34()3;42()14()31()12(|16)()(
3、)(21,22222dGWifvirrVVViffiiiixcextHTop 500 Supercomputers in the worldA“small”PC cluster todayFour orders of magnitudein 15 years计算量随体系大小急剧增长计算量随体系大小急剧增长Material Properties from First-PrinciplesFrom first principles!Predict new behaviors/properties of existing materialsDesign materials with desired
4、propertiesUnderstand and explain materials propertiesBecoming reality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Part I:理论体系Perdew PRL2019+Local density+Density gradient+Inexplicit occupied orbital information+Explicit occupied orbit
5、al information+Unoccupied orbital information交换相关泛函jacobs ladder 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,
6、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)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
7、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).rnrnrfdnEGGAxc,3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 GGA
8、s 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).
9、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
10、compared to the best GGAs.The full potential of this type of approximation is only beginning to be explored systematically.22()|()|2iirrmMeta-GGA Common hybrid functional mix a fraction of Hartree-Fock exchange into the DFT exchange functional.Hybrid FunctionalsB3LDAexactLDAGGAGGAEEa(EE)bcxcxcxxxcEE
11、 a0.20,b0.72,c0.81)Ea(EEEDFTxexactxDFTxc0 xc25.0a(Becke,1993)(Perdew,2019)B3PW91,B3LYPPBE0B3LYP is the main working-horse in computational chemistryLDA:Slater exchange Vosko-Wilk-Nusair correlation,etcGGA:Exchange:B88,PW91,PBE,OPTX,HCTH,etc Correlations:LYP,P86,PW91,PBE,HCTH,etcHybrid GGA:B3LYP,B3PW
12、91,B3P86,PBE0,B97-1,B97-2,B98,O3LYP,etcMeta-GGA:VSXC,PKZB,TPSS,etcHybrid meta-GGA:HCTHh,TPSSh,BMK,etcL(S)DA+U Mott绝缘体，Hubbard模型 Anisimov et al.：Stoner I-Hubbard U 轨道序：Dudarev et al.：惩罚泛函Part II:数值方法数值离散方法 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Muffin-
13、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,.)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。）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（
14、复合网格）结合赝势方法 多尺度（multiscale）或预处理（preconditioning）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 广义的本征值问题多分辨网格上的小波基组 多分辨分析 半取样（semicardinal）基组Part III:应用物理学：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
15、加衰减色散（DFdD）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
16、体和元胞自动机-连续方程的有限差分有限元求解光谱学：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，线性响应石墨烯体系的第一性原理研究石墨烯体系的第一性原理研究Graphene Introduction to graphene and graphene nanoribbon(GNR)GNR based spintronics Nearly free electron(NFE)states in gated GNR superlattice Cutting mechanism in graphene
17、oxide(GO)Graphene:a monolayer of two-dimensional carbon atoms198519912019Crystal structure of grapheneEnergy bandsK or KSilicon out,Graphene in?R Van Noorden,Nature 442,228(2019)What are Graphene nanoribbons(GNRs)?UnlimitedLimitedZigzag GNRsUnlimitedLimitedArmchair GNRsZigzag GNRs Armchair GNRs are
18、PM.Zigzag GNRs favor AFM.Band Gaps in GNRsY.-W.Son et al.,Phys.Rev.Lett.2019,97,216803Half-metallicity(HM)100%spin polarization Applications:Spin injection Spin transport Some HM materials:CrO2,NiMnSb,Fe3O4Transition Metal Encapsulated Boron Nitride Nanotubes(New J.Phys.,2019)One-Dimensional Transit
19、ion Metal-Benzene Sandwich Polymers(JACS,2019)Zigzag GNRs(ZGNRs)turn to half metal(HM)under external transverse electric field.GNRs under Electric FieldY.-W.Son et al.,Nature 2019,444,347LDAGGAB3LYPEffect of XC Functional?Effect of finite size?E.Rudberg et al.,Nano Lett.2019,7,22118-ZGNRBand Structu
20、reCrystal 03 package,B3LYP,Gaussian basis set Kan,Yang et al.,Appl.Phys.Lett.2019,91,213116ZGNRs with Different WidthsL edgeL edgeR edgeR edgeFermi LevelFermi LevelHalf MetalHalf MetalL edgeL edgeR edgeR edgeCharge PolarizedCharge PolarizedLong range Coulomb interactionL edgeL edgeR edgeR edgeSpin P
21、olarizedSpin PolarizedOn-site Coulomb interaction UCharge and Spin PolarizationsGraphene RibbonBN Sheet RibbonBreak the Edge Symmetry by a Chemical Way8-C1BNorbital hybridization between C and BNA Hybrid Nanoribbon ModelKan,Yang et al.,J.Chem.Phys.2019,129,0847128-C2BN8-C3BNEnergy Gapsn-C1BNPartial
22、Charge DensitySpin DensityCharge and Spin DensitiesBCNNCBEFCoulomb term:long rangeOn-site U term:localCompetition Between Charge and Spin PolarizationsFunctional Group ApproachKan,Yang et al.,J.Am.Chem.Soc.2019,130,4224NO2-NH2 PairNO2-H pairNO2-CH3 pair Remove the NH2 pz BandZGNR-fullZGNR-halfGibbs
23、Free Energy of FormationCCNNHHCnnnEG Relative StabilityZGNR-halfZGNR-full Band StructuresNFE States in 0D C60M.Feng et al.,Science 2019,320,359;J.Zhao et al.,ACS Nano 2009,3,853Superatom Molecular OrbitalsNFE States in 1D NanotubesY.Miyamoto et al.,Phys.Rev.Lett.2019,74,2993;S.Okada et al.,Phys.Rev.
24、B 2000,62,7634;B.Yan et al.,J.Am.Chem.Soc.2009,130,17012NFE States in 1D Nanotubesspxpydx2-y2dxyAtomic character of NFE states in nanotubeHu,Yang et al.,unpublishedNFE States in2D Graphene Systemband structure of graphenethe nearly free surface state in graphite monolayerS.M.Posternak et al.,Phys.Re
25、v.Lett.1983,50,761;Phys.Rev.Lett.1984,52,863.What the NFE States Look Like in GNRs?Periodic boundary condition Edges of all nanoribbons were saturated by H atomsIndividual GNR-0.8896-0.8316-0.7729-0.7092-0.5938XE-FermiE-vacE-Evac3.26423.32223.38093.44463.5599E-EfermiNFE States in GNR SuperlatticeThe
26、re 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 1.1meElectrostatic Potential&1D Kronig-Penney Modelx-y plane avera
27、ged potential1D Kronig-Penney model potentialtwo series of special solutionsElectron Doping to ZGNR Superlattice Light DopingHeavy DopingEnergy of the Lowest NFE StateDownshift of NFE states show similar behavior for armchair and zigzag GNRs when the NFE state is colse to Fermi levelGated GNR Superl
28、attice as FETEffect 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.Ideal FET Device Clean transport channel,high mobility,high on-off ratio
29、.Ideal FET!Prepare Graphene on Large Scale?Chemical vapor deposition(1970)Micromechanical exfoliation(Scotch tape)Epitaxial growth on SiC surface Oxidation and reduction in solutionGraphite Oxide Brodie:HNO3+NaClO3,gives GO bright in color,stable with a low contamination,and with smallest interlayer
30、 distance(1860)Staudemaier:H2SO4+HNO3+KClO3,slowest,gives the lightest colored GO(1898)Hummers-Offeman:H2SO4+KMnO4,fastest,gives a brownish GO(1958)Oxidative Cutting Graphite flakes breaks down into GO flakes,and the final size does not depend on the initial size.CNT:from nearly endless,highly tangl
31、ed ropes into short,open-ended pipesJ.Liu et al.,Science 2019,280,1253;M.J.McAllister et al.,Chem.Mater 2019,19,4386Unzipping Mechanism Epoxy groups prefer to align in a line Hoping barrier for epoxy groups on graphene surface is not too highJ.L.Li et al.,Phys.Rev.Lett.2019,96,176101Epoxy line is en
32、ough?an epoxy line defect only weakens the fracture stress of the sheet by approximately 16%J.T.Paci et al.,J.Phys.Chem.C 2019,111,18099Whats the Whole Story about Unzipping?Epoxy ChainEpoxy PairsCarbonyl PairsLi,Yang et al.,J.Am.Chem.Soc.2009,131,6320Epoxy Pair The energy of the epoxy-pair structur
33、e is 2.71 eV lower than an additional isolated epoxy group The additional energy gain for the second epoxy pair is 0.78 eV larger than isolated EP For a short epoxy chain,forming an epoxy pair or adding an epoxy group to extend the chain is comparable in energyThe Cutting Process0.76-0.480.26-1.09Li
34、,Yang et al.,J.Am.Chem.Soc.2009,131,6320Unzipping or Tearing?Go Inward?new edge carbon bonds are easier to be attacked than those inside an existing carbonyl paircpprcpEEEE)(212Li,Yang et al.,J.Am.Chem.Soc.2009,131,6320Structure of GOHofmann(1939)Ruess(1946)Scholz(1969)Nakajima(1988)Lerf(2019)Szabo(
35、2019)XPS of GOH.-K.Jeong et al.,J.Am.Chem.Soc.2019,130,1362T.Szabo et al.,Chem.Mater.2019,18,2740C 1s Binding Energy Simulation The 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 chemi
36、cal shift(R-CCS)with respect to the epoxide group.C-epoxide and C-OH are difficult to be resolved in a XPS spectrumThe Large Ribbon Model To consider both inner and edge species,a large ribbon model is adopted.All functional groups are put in a single systemBinding 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 COOOZhang,Carravetta,Li,Luo,and Yang,J.Chem.Phys.131,244505(2009)Thanks!Dr.Hongjun Xiang Dr.Er-jun Kan Dr.Shuanglin Hu Dr.Wenhua Zhang Dr.Zhenyu Li Prof.Yi Luo NFSC MOE CAS MOST
