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1、密度泛函理论新进展及应用,杨金龙中国科学技术大学,Computation,Experiment,Theory,Science 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,Time,http:/itri.loyola.edu/nano/IWGN.Research.Directions/,Scientific Computations,properties,systems,methods,空间尺度：电子机构时间尺度：动力学,http:/itri.loyola.edu/nano/IWGN.Research.Directions/,电子结构计算：预言材料性质、验证
2、理论猜想、理解实验观测现象。,http:/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。,Materials Properties from First-principles,“Supercomputer”,Gigantic computer programs,Top 500 Supercomputers in the world,A “small” PC cluster today,Four orders of magnitudein 15 years,计算量随体系大小急剧增长,Mate
3、rial Properties from First-Principles,From first principles!,Predict new behaviors/properties of existing materials,Design materials with desired properties,Becoming 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,Per
4、dew PRL2003,+ Local density,+ Density gradient,+ Inexplicit occupied orbital information,+ Explicit occupied orbital 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,
5、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),Any real system is spatially inhomog
6、eneous, 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
7、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,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
8、GGAs seem to give reliable results for all main types of chemical bonds (covalent, ionic, metallic and hydrogen bridge).,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 degr
9、ee 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,Common hybrid functional mix a fraction of
10、 Hartree-Fock exchange into the DFT exchange functional.,Hybrid Functionals,(Becke, 1993),(Perdew,1998),B3PW91, B3LYP,PBE0,B3LYP is the main working-horse in computational chemistry,LDA: Slater exchange Vosko-Wilk-Nusair correlation, etcGGA: Exchange: B88, PW91, PBE, OPTX, HCTH, etc Correlations: LY
11、P, P86, PW91, PBE, HCTH, etcHybrid GGA: B3LYP, B3PW91, B3P86, PBE0, B97-1, B97-2, B98, O3LYP, etcMeta-GGA: VSXC, PKZB, TPSS, etcHybrid meta-GGA: tHCTHh, TPSSh, BMK, etc,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,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
12、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-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
13、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（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
14、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）,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 kin
15、eric 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,Graphene,Introduction to graphene and graphene nanoribbon (GNR)GNR based spintronicsNearly free elect
16、ron (NFE) states in gated GNR superlatticeCutting mechanism in graphene oxide (GO),Graphene: a monolayer of two-dimensional carbon atoms,1985,1991,2004,Crystal structure of graphene,Energy bands,K or K,Silicon out, Graphene in?,R Van Noorden, Nature 442, 228(2006),What are Graphene nanoribbons (GNRs
17、)?,Unlimited,Limited,Zigzag GNRs,Unlimited,Limited,Armchair GNRs,Armchair GNRs,Zigzag GNRs,Armchair GNRs are PM.Zigzag GNRs favor AFM.,Band Gaps in GNRs,Y.-W. Son et al.,Phys. Rev. Lett. 2006, 97, 216803,Half-metallicity (HM),100% spin polarizationApplications:Spin injection Spin transportSome HM ma
18、terials:CrO2, NiMnSb, Fe3O4,Transition Metal Encapsulated Boron Nitride Nanotubes (New J. Phys., 2005)One-Dimensional Transition Metal-Benzene Sandwich Polymers(JACS, 2006),Zigzag GNRs (ZGNRs) turn to half metal (HM) under external transverse electric field.,GNRs under Electric Field,Y.-W. Son et al
19、., Nature 2006, 444, 347,LDA,GGA,B3LYP,Effect of XC Functional?,Effect of finite size?,E. Rudberg et al.,Nano Lett. 2007, 7, 2211,8-ZGNR,Band Structure,Crystal 03 package, B3LYP, Gaussian basis set ,Kan, Yang et al., Appl. Phys. Lett. 2007, 91, 213116,ZGNRs with Different Widths,L edge,R edge,Fermi
20、Level,Half Metal,L edge,R edge,Charge Polarized,Long range Coulomb interaction,L edge,R edge,Spin Polarized,On-site Coulomb interaction U,Charge and Spin Polarizations,Graphene Ribbon,BN Sheet Ribbon,Break the Edge Symmetry by a Chemical Way,8-C1BN,orbital hybridization between C and BN,A Hybrid Nan
21、oribbon Model,Kan, Yang et al., J. Chem. Phys. 2008, 129, 084712,8-C2BN,8-C3BN,Energy Gaps,n-C1BN,Partial Charge Density,Spin Density,Charge and Spin Densities,B,CN,N,CB,EF,Coulomb term: long rangeOn-site U term: local,Competition Between Charge and Spin Polarizations,Functional Group Approach,Kan,
22、Yang et al., J. Am. Chem. Soc. 2008, 130, 4224,NO2-NH2 Pair,NO2-H pair,NO2-CH3 pair,Remove the NH2 pz Band,ZGNR-full,ZGNR-half,Gibbs Free Energy of Formation,Relative Stability,ZGNR-half,ZGNR-full,Band Structures,NFE States in 0D C60,M. Feng et al., Science 2008, 320, 359;J. Zhao et al., ACS Nano 20
23、09, 3, 853,Superatom Molecular Orbitals,NFE States in 1D Nanotubes,Y. 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,NFE States in 1D Nanotubes,s,px,py,dx2-y2,dxy,Atomic character of NFE states in nanotu
24、be,Hu, Yang et al., unpublished,NFE States in2D Graphene System,band structure of graphene,the nearly free surface state in graphite monolayer,S. M. Posternak et al., Phys. Rev. Lett. 1983, 50, 761; Phys. Rev. Lett. 1984, 52, 863.,What the NFE States Look Like in GNRs?,Periodic boundary conditionEdg
25、es of all nanoribbons were saturated by H atoms,Individual GNR,-0.8896,-0.8316,-0.7729,-0.7092,-0.5938,X,E-Fermi,E-vac,E-Evac,3.2642,3.3222,3.3809,3.4446,3.5599,E-Efermi,NFE States in GNR Superlattice,There are many NFE states above 3eV from the Fermi energy, and they can be classified to two types:
26、One mainly distributes on the ribbonThe other mainly in the vacuum between ribbons.Along the ribbon direction, the effective mass is around 1.1me,Electrostatic Potential & 1D Kronig-Penney Model,x-y plane averaged potential,1D Kronig-Penney model potential,two series of special solutions,Electron Do
27、ping to ZGNR Superlattice,Light Doping,Heavy Doping,Energy of the Lowest NFE State,Downshift of NFE states show similar behavior for armchair and zigzag GNRs when the NFE state is colse to Fermi level,Gated GNR Superlattice as FET,Effect of Ribbon and Vacuum Widths,The minimum electron doping concen
28、tration 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.,Ideal FET !,Prepare Graphene on Large Scale?,Chemical vapor deposition (1970
29、)Micromechanical exfoliation (Scotch tape)Epitaxial growth on SiC surfaceOxidation and reduction in solution,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 li
30、ghtest 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 tangled ropes into short, open-ended pipes,J. Liu et al., Sc
31、ience 1998, 280, 1253; M.J. McAllister et al., Chem. Mater 2007, 19, 4386,Unzipping Mechanism,Epoxy groups prefer to align in a lineHoping barrier for epoxy groups on graphene surface is not too high,J.L. Li et al., Phys. Rev. Lett. 2006, 96, 176101,Epoxy line is enough?,an epoxy line defect only we
32、akens the fracture stress of the sheet by approximately 16%,J.T. Paci et al.,J. Phys. Chem. C 2007, 111, 18099,Whats the Whole Story about Unzipping?,Epoxy Chain,Carbonyl Pairs,Li, Yang et al., J. Am. Chem. Soc. 2009, 131, 6320,Epoxy Pair,The energy of the epoxy-pair structure is 2.71 eV lower than
33、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,The Cutting Process,0.76,-0.48,0.26,-1.09,Li, Yang et al., J. A
34、m. Chem. Soc. 2009, 131, 6320,Unzipping or Tearing?,Go Inward?,new edge carbon bonds are easier to be attacked than those inside an existing carbonyl pair,?,Li, Yang et al., J. Am. Chem. Soc. 2009, 131, 6320,Structure of GO,Hofmann (1939),Ruess (1946),Scholz (1969),Nakajima (1988),Lerf (1998),Szabo
35、(2006),XPS of GO,H.-K. Jeong et al., J. Am. Chem. Soc. 2008, 130, 1362,T. Szabo et al., Chem. Mater. 2006, 18, 2740,C 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.
36、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,The Large Ribbon Model,To consider both inner and edge species, a large ribbon model is adopted.All functional groups are put in a single system,Binding Energies,sp2 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,Zhang, Carravetta, Li, Luo, and Yang, J. Chem. Phys. 131, 244505 (2009),Thanks!,Dr. Hongjun XiangDr. Er-jun KanDr. Shuanglin HuDr. Wenhua ZhangDr. Zhenyu LiProf. Yi LuoNFSCMOECASMOST,
