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ComputationExperimentTheoryScienceResearch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精品Time/nano/IWGN.Research.Directions/ScientificComputationspropertiessystemsmethods空间尺度：电子机构时间尺度：动力学精品/nano/IWGN.Research.Directions/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。精品/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。精品MaterialsPropertiesfromFirst-principles“Supercomputer”Giganticcomputerprograms精品Top500SupercomputersintheworldA“small”PCclustertodayFourordersofmagnitudein15years精品计算量随体系大小急剧增长精品MaterialPropertiesfromFirst-PrinciplesFromfirstprinciples!Predictnewbehaviors/propertiesofexistingmaterialsDesignmaterialswithdesiredpropertiesUnderstandandexplainmaterialsproperties√√Becomingreality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PartI:理论体系精品PerdewPRL2003+Localdensity+Densitygradient+Inexplicitoccupiedorbitalinformation

+Explicitoccupiedorbitalinformation+Unoccupiedorbitalinformation交换相关泛函jacob'sladder精品LDAunderestimates

EcbutoverestimatesEx,resultinginunexpectedlygoodvaluesofExc.TheLDAhasbeenappliedin,calculationsofbandstructuresandtotalenergiesinsolid-statephysics.Inquantumchemistry,itismuchlesspopular,becauseitfailstoprovideresultsthatareaccurateenoughtopermitaquantitativediscussionofthechemicalbondinmolecules.局域密度近似(LDA)精品Anyrealsystemisspatiallyinhomogeneous,ithasaspatiallyvaryingdensityn(r),

itwouldclearlybeusefultoalsoincludeinformationontherateofthisvariationinthefunctional.Inthisapproximation,onetriestosystematicallycalculategradient-correctionsofgeneralfunctionsofn(r)and∇n(r)Different

GGAsdifferinthechoiceofthefunctionf(n,∇n).广义梯度近似(GGA)AlexD.Becke“一切都是合法的”剑宗JohnP.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GGAsusedinquantumchemistrytypicallyproceedbyfittingparameterstotestsetsofselectedmolecules.NowadaysthemostpopularGGAsarePBEinphysics,andBLYPinchemistry.CurrentGGAsseemtogivereliableresultsforallmaintypesofchemicalbonds(covalent,ionic,metallicandhydrogenbridge).精品Inadditiontothedensityanditsderivatives,Meta-GGAsdependalsoontheKohn-Shamkinetic-energydensity:SothatExccanbewrittenasExc[n(r),∇n(r),τ(r)].TheadditionaldegreeoffreedomprovidedbyτisusedtosatisfyadditionalconstraintsonExc.Meta-GGAshavegivenfavorableresults,evenwhencomparedtothebestGGAs.Thefullpotentialofthistypeofapproximationisonlybeginningtobeexploredsystematically.Meta-GGA精品CommonhybridfunctionalmixafractionofHartree-FockexchangeintotheDFTexchangefunctional.HybridFunctionals(Becke,1993)(Perdew,1998)B3PW91,B3LYPPBE0B3LYPisthemainworking-horseincomputationalchemistry精品LDA: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,etc精品L(S)DA+UMott绝缘体，Hubbard模型Anisimovetal.：StonerI-->HubbardU轨道序：Dudarevetal.：惩罚泛函精品PartII: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LAPWLMTO分波方法的发展FP-LAPWthird-generationMTO,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USPPorPAW?(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PartIII: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（parallelreplicadynamics）超动力学（hyperdynamics,metadynamics）温度加速的动力学（temperatureaccelerateddynamics）快速蒙特卡罗（on-the-flykinericMonteCarlo）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MonteCarlo（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，线性响应精品石墨烯体系的第一性原理研究精品GrapheneIntroductiontographeneandgraphenenanoribbon(GNR)GNRbasedspintronicsNearlyfreeelectron(NFE)statesingatedGNRsuperlatticeCuttingmechanismingrapheneoxide(GO)精品Graphene:amonolayeroftwo-dimensionalcarbonatoms198519912004精品Crystalstructureofgraphene精品EnergybandsKorK’精品Siliconout,Graphenein?

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