宏剑培训密度泛函理论新进展及应用课件

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1、宏剑培训密度泛函理论新进展及应用密度泛函理论新进展及应用杨金龙中国科学技术大学宏剑培训密度泛函理论新进展及应用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宏剑培训密度泛函理论新进展及应用TimeScientific Computationspropertiessystemsmethods 空间尺度：电子机构 时间尺度：动力学宏剑培训密度泛函理论新进展及应用电子结构计算：预言材料性质、验证理论猜想、理解实验观测现象。电子结构计算：预

2、言材料性质、验证理论猜想、理解实验观测现象。宏剑培训密度泛函理论新进展及应用动力学模拟：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。宏剑培训密度泛函理论新进展及应用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)()()(21,22222dGWifvirrVVViffiiiixcextH宏剑培

3、训密度泛函理论新进展及应用Top 500 Supercomputers in the worldA “small” PC cluster todayFour orders of magnitudein 15 years宏剑培训密度泛函理论新进展及应用计算量随体系大小急剧增长计算量随体系大小急剧增长宏剑培训密度泛函理论新进展及应用Material Properties from First-PrinciplesFrom first principles!Predict new behaviors/properties of existing materialsDesign materials w

4、ith desired propertiesUnderstand and explain materials propertiesBecoming reality宏剑培训密度泛函理论新进展及应用内容 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宏剑培训密度泛函理论新进展及应用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、光谱学宏剑培训密度泛函理论新进展及应用Part I: 理论体系宏剑培训密度泛函理论新进展及应用Perdew PRL2003+ Local density+ D

5、ensity gradient+ Inexplicit occupied orbital information + Explicit occupied orbital information+Unoccupied orbital information交换相关泛函jacobs ladder宏剑培训密度泛函理论新进展及应用 LDA underestimates Ec but overestimates Ex, resulting in unexpectedly good values of Exc. The LDA has been applied in, calculations of ba

6、nd 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)宏剑培训密度泛函理论新进展及应用 Any real system is spatially inhomogen

7、eous, 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

8、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 气宗宏剑培训密度泛函理论新进展及应用 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

9、, and BLYP in chemistry. Current GGAs seem to give reliable results for all main types of chemical bonds (covalent, ionic, metallic and hydrogen bridge).宏剑培训密度泛函理论新进展及应用 In addition to the density and its derivatives, Meta-GGAs depend also on the Kohn-Sham kinetic-energy density: So that Exc can be

10、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.

11、22( )|( )|2iirrmMeta-GGA宏剑培训密度泛函理论新进展及应用 Common hybrid functional mix a fraction of Hartree-Fock exchange into the DFT exchange functional.Hybrid FunctionalsB3LDAexactLDAGGAGGAEEa(EE)bcxcxcxxxcEE a0.20,b0.72,c0.81)Ea(EEEDFTxexactxDFTxc0 xc25. 0a (Becke, 1993)(Perdew,1998)B3PW91, B3LYPPBE0B3LYP is th

12、e main working-horse in computational chemistry宏剑培训密度泛函理论新进展及应用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,

13、TPSS, etcHybrid meta-GGA: HCTHh, TPSSh, BMK, etc宏剑培训密度泛函理论新进展及应用L(S)DA+U Mott绝缘体，Hubbard模型 Anisimov et al.： Stoner I -Hubbard U 轨道序： Dudarev et al.：惩罚泛函宏剑培训密度泛函理论新进展及应用Part II:数值方法宏剑培训密度泛函理论新进展及应用数值离散方法 基组展开 LCAO基组（Gaussian基组、数值基组） 实空间网格宏剑培训密度泛函理论新进展及应用平面波基组：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

14、守恒赝势 超软赝势宏剑培训密度泛函理论新进展及应用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宏剑培训密度泛函理论新进展及应用平面波基组：从USPP到PAW 投影缀加波（PAW）方法 赝波函数空间 USPP or PAW? (VASP, ABINIT, .)宏剑培训密度泛函理论新进展及应用实空间网格 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

15、 处理某些特殊体系（带电体系、隧穿结。）宏剑培训密度泛函理论新进展及应用有限差分 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）宏剑培训密度泛函理论新进展及应用有限元 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 广义的本征值问题宏剑培训密度泛函理论新进展及应用多分辨网格上的小波基组 多分辨分析 半取样（semicardinal）基组宏剑培训密度泛函理论新进展及应用Part III:应用宏剑培训密度泛函理论新进展及应用物理学：

16、强相关体系 模型哈密顿量 LDA+ 电子结构：CrO2 点阵动力学: 钚宏剑培训密度泛函理论新进展及应用化学：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）宏剑培训密度泛函理论新进展及应用生命科学：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（paralle

17、l 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）方法宏剑培训密度泛函理论新进展及应用纳米和材料科学：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宏剑培训密度泛函理论新进展及应用光谱学：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

18、理论，GW近似Bethe-Salpeter方程 TDDFT，线性响应宏剑培训密度泛函理论新进展及应用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宏剑培训密度泛函理论新进展及应用Graphene Introduction to graphene and graphene nanoribbon (GNR) GNR based spintronics Nearly free electron (NFE) states in gated GNR superlattice Cutting mechanism in graphene oxide (GO)宏剑培训密度泛函理论新进展及应用Graphe

19、ne: a monolayer of two-dimensional carbon atoms198519912004宏剑培训密度泛函理论新进展及应用Crystal structure of graphene宏剑培训密度泛函理论新进展及应用Energy bandsK or K宏剑培训密度泛函理论新进展及应用Silicon out, Graphene in? R Van Noorden, Nature 442, 228(2006) 宏剑培训密度泛函理论新进展及应用What are Graphene nanoribbons (GNRs)?UnlimitedLimitedZigzag GNRs宏剑培

20、训密度泛函理论新进展及应用UnlimitedLimitedArmchair GNRs宏剑培训密度泛函理论新进展及应用Zigzag GNRs Armchair GNRs are PM. Zigzag GNRs favor AFM.Band Gaps in GNRsY.-W. Son et al.,Phys. Rev. Lett. 2006, 97, 216803宏剑培训密度泛函理论新进展及应用Half-metallicity (HM) 100% spin polarization Applications:Spin injection Spin transport Some HM materia

21、ls:CrO2, NiMnSb, Fe3O4Transition Metal Encapsulated Boron Nitride Nanotubes (New J. Phys., 2005)One-Dimensional Transition Metal-Benzene Sandwich Polymers(JACS, 2006)宏剑培训密度泛函理论新进展及应用 Zigzag GNRs (ZGNRs) turn to half metal (HM) under external transverse electric field.GNRs under Electric FieldY.-W. S

22、on et al., Nature 2006, 444, 347宏剑培训密度泛函理论新进展及应用LDAGGAB3LYPEffect of XC Functional?Effect of finite size?E. Rudberg et al.,Nano Lett. 2007, 7, 2211宏剑培训密度泛函理论新进展及应用8-ZGNRBand StructureCrystal 03 package, B3LYP, Gaussian basis set Kan, Yang et al., Appl. Phys. Lett. 2007, 91, 213116宏剑培训密度泛函理论新进展及应用ZGN

23、Rs with Different Widths宏剑培训密度泛函理论新进展及应用L edgeL edgeR edgeR edgeFermi LevelFermi LevelHalf MetalHalf MetalL edgeL edgeR edgeR edgeCharge PolarizedCharge PolarizedLong range Coulomb interactionL edgeL edgeR edgeR edgeSpin PolarizedSpin PolarizedOn-site Coulomb interaction UCharge and Spin Polarizatio

24、ns宏剑培训密度泛函理论新进展及应用Graphene RibbonBN Sheet RibbonBreak the Edge Symmetry by a Chemical Way宏剑培训密度泛函理论新进展及应用8-C1BNorbital hybridization between C and BNA Hybrid Nanoribbon ModelKan, Yang et al., J. Chem. Phys. 2008, 129, 084712宏剑培训密度泛函理论新进展及应用8-C2BN8-C3BNEnergy Gaps宏剑培训密度泛函理论新进展及应用n-C1BNPartial Charge

25、DensitySpin DensityCharge and Spin Densities宏剑培训密度泛函理论新进展及应用BCNNCBEFCoulomb term: long rangeOn-site U term: localCompetition Between Charge and Spin Polarizations宏剑培训密度泛函理论新进展及应用Functional Group ApproachKan, Yang et al., J. Am. Chem. Soc. 2008, 130, 4224宏剑培训密度泛函理论新进展及应用NO2-NH2 Pair宏剑培训密度泛函理论新进展及应用NO

26、2-H pairNO2-CH3 pair Remove the NH2 pz Band宏剑培训密度泛函理论新进展及应用ZGNR-fullZGNR-halfGibbs Free Energy of FormationCCNNHHCnnnEG Relative Stability宏剑培训密度泛函理论新进展及应用ZGNR-halfZGNR-full Band Structures宏剑培训密度泛函理论新进展及应用NFE States in 0D C60M. Feng et al., Science 2008, 320, 359;J. Zhao et al., ACS Nano 2009, 3, 853

27、Superatom Molecular Orbitals宏剑培训密度泛函理论新进展及应用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宏剑培训密度泛函理论新进展及应用NFE States in 1D Nanotubesspxpydx2-y2dxyAtomic character of NFE stat

28、es in nanotubeHu, Yang et al., unpublished宏剑培训密度泛函理论新进展及应用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.宏剑培训密度泛函理论新进展及应用What the NFE States Look Like i

29、n GNRs? Periodic boundary condition Edges of all nanoribbons were saturated by H atoms宏剑培训密度泛函理论新进展及应用Individual GNR-0.8896-0.8316-0.7729-0.7092-0.5938XE-FermiE-vacE-Evac3.26423.32223.38093.44463.5599E-Efermi宏剑培训密度泛函理论新进展及应用NFE States in GNR SuperlatticeThere are many NFE states above 3eV from the F

30、ermi 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宏剑培训密度泛函理论新进展及应用Electrostatic Potential & 1D Kronig-Penney Modelx-y plane averaged potential1D Kronig-

31、Penney model potentialtwo series of special solutions宏剑培训密度泛函理论新进展及应用Electron Doping to ZGNR Superlattice 宏剑培训密度泛函理论新进展及应用Light Doping宏剑培训密度泛函理论新进展及应用Heavy Doping宏剑培训密度泛函理论新进展及应用Energy of the Lowest NFE StateDownshift of NFE states show similar behavior for armchair and zigzag GNRs when the NFE stat

32、e is colse to Fermi level宏剑培训密度泛函理论新进展及应用Gated GNR Superlattice as FET宏剑培训密度泛函理论新进展及应用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 widt

33、h.宏剑培训密度泛函理论新进展及应用Ideal FET Device Clean transport channel, high mobility, high on-off ratio. Ideal FET !宏剑培训密度泛函理论新进展及应用Prepare Graphene on Large Scale? Chemical vapor deposition (1970) Micromechanical exfoliation (Scotch tape) Epitaxial growth on SiC surface Oxidation and reduction in solution宏剑培训

34、密度泛函理论新进展及应用Graphite Oxide Brodie: 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)宏剑培训密度

35、泛函理论新进展及应用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 tangled ropes into short, open-ended pipesJ. Liu et al., Science 1998, 280, 1253; M.J. McAllister et al., Chem. Mater 2007, 19, 4386宏剑培训密度泛

36、函理论新进展及应用Unzipping 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. 2006, 96, 176101宏剑培训密度泛函理论新进展及应用Epoxy line is enough? an epoxy line defect only weakens the fracture stress of the sheet by approxim

37、ately 16%J.T. Paci et al.,J. Phys. Chem. C 2007, 111, 18099宏剑培训密度泛函理论新进展及应用Whats the Whole Story about Unzipping?Epoxy ChainEpoxy PairsCarbonyl PairsLi, Yang et al., J. Am. Chem. Soc. 2009, 131, 6320宏剑培训密度泛函理论新进展及应用Epoxy Pair The energy of the epoxy-pair structure is 2.71 eV lower than an additional

38、 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 energy宏剑培训密度泛函理论新进展及应用The Cutting Process0.76-0.480.26-1.09Li, Yang et al., J. Am

39、. Chem. Soc. 2009, 131, 6320宏剑培训密度泛函理论新进展及应用Unzipping or Tearing?宏剑培训密度泛函理论新进展及应用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, 6320宏剑培训密度泛函理论新进展及应用Structure of GOHofmann (1939)Ruess (

40、1946)Scholz (1969)Nakajima (1988)Lerf (1998)Szabo (2006)宏剑培训密度泛函理论新进展及应用XPS of GOH.-K. Jeong et al., J. Am. Chem. Soc. 2008, 130, 1362T. Szabo et al., Chem. Mater. 2006, 18, 2740宏剑培训密度泛函理论新进展及应用C 1s Binding Energy Simulation The binding energy of C 1s orbital is calculated as the energy difference b

41、etween 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宏剑培训密度泛函理论新进展及应用宏剑培训密度泛函理论新进展及应用The Large Ribbon Model To consider both inner and ed

42、ge species, a large ribbon model is adopted. All functional groups are put in a single system宏剑培训密度泛函理论新进展及应用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宏剑培训密度泛函理论新进展及应用Zhang, Carravetta, Li, Luo, and Yang, J. Chem. Phys. 131, 244505 (2009)宏剑培训密度泛函理论新进展及应用Thanks! Dr. Hongjun Xiang Dr. Er-jun Kan Dr. Shuanglin Hu Dr. Wenhua Zhang Dr. Zhenyu Li Prof. Yi Luo NFSC MOE CAS MOST