宏剑培训密度泛函理论新进展及应用

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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Timehttp://itri.loyola.edu/nano/IWGN.Research.Directions/ScientificComputationspropertiessystemsmethods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、验证理论猜想、理解实验观测现

2、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。MaterialsPropertiesfromFirst-principles“Supercomputer”GiganticcomputerprogramsTop500SupercomputersintheworldA“small”PCclustertodayFourordersofmagnitudein15years计算量随体系大小急剧增长MaterialPropertiesfromFirst-PrinciplesFro

3、mfirstprinciples!Predictnewbehaviors/propertiesofexistingmaterialsDesignmaterialswithdesiredpropertiesUnderstandandexplainmaterialsproperties√√Becomingreality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PartI:理论体系PerdewPRL2003+Localdens

4、ity+Densitygradient+Inexplicitoccupiedorbitalinformation+Explicitoccupiedorbitalinformation+Unoccupiedorbitalinformation交换相关泛函jacob'sladderLDAunderestimatesEcbutoverestimatesEx,resultinginunexpectedlygoodvaluesofExc.TheLDAhasbeenappliedin,calculationsofbandstructuresandtotalenergiesinsolid-statep

5、hysics.Inquantumchemistry,itismuchlesspopular,becauseitfailstoprovideresultsthatareaccurateenoughtopermitaquantitativediscussionofthechemicalbondinmolecules.局域密度近似(LDA)Anyrealsystemisspatiallyinhomogeneous,ithasaspatiallyvaryingdensityn(r),itwouldclearlybeusefultoalsoincludeinformationontherateof

6、thisvariationinthefunctional.Inthisapproximation,onetriestosystematicallycalculategradient-correctionsofgeneralfunctionsofn(r)and∇n(r)DifferentGGAsdifferinthechoiceofthefunctionf(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GGAsusedinquantumchemistrytypicallyproc

7、eedbyfittingparameterstotestsetsofselectedmolecules.NowadaysthemostpopularGGAsarePBEinphysics,andBLYPinchemistry.CurrentGGAsseemtogivereliableresultsforallmaintypesofchemicalbonds(covalent,ionic,metallicandhydrogenbrid