密度泛函理論新進展及應(yīng)用課件

密度泛函理論新進展及應(yīng)用楊金龍中國科學技術(shù)大學ComputationExperimentTheoryScienceResearch計算機模擬已經(jīng)與理論與實驗并列，成為三種基本的科學研究手段之一Time/nano/IWGN.Research.Directions/ScientificComputationspropertiessystemsmethods空間尺度：電子機構(gòu)時間尺度：動力學/nano/IWGN.Research.Directions/動力學模擬：預(yù)言反應(yīng)過程、驗證理論猜想、理解實驗觀測現(xiàn)象。MaterialsPropertiesfromFirst-principles“Supercomputer”GiganticcomputerprogramsTop500SupercomputersintheworldA“small”PCclustertodayFourordersofmagnitudein15years計算量隨體系大小急劇增長內(nèi)容密度泛函理論新進展石墨烯條帶體系的第一性原理計算研究PartI:理論體系LDAunderestimates

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

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

GGAsdifferinthechoiceofthefunctionf(n,?n).廣義梯度近似(GGA)AlexD.Becke“一切都是合法的”劍宗JohnP.Perdew一定的物理規(guī)律（如標度關(guān)系和漸進行為）為基礎(chǔ)，PBE氣宗GGAsusedinquantumchemistrytypicallyproceedbyfittingparameterstotestsetsofselectedmolecules.NowadaysthemostpopularGGAsarePBEinphysics,andBLYPinchemistry.CurrentGGAsseemtogivereliableresultsforallmaintypesofchemicalbonds(covalent,ionic,metallicandhydrogenbridge).Inadditiontothedensityanditsderivatives,Meta-GGAsdependalsoontheKohn-Shamkinetic-energydensity:SothatExccanbewrittenasExc[n(r),?n(r),τ(r)].TheadditionaldegreeoffreedomprovidedbyτisusedtosatisfyadditionalconstraintsonExc.Meta-GGAshavegivenfavorableresults,evenwhencomparedtothebestGGAs.Thefullpotentialofthistypeofapproximationisonlybeginningtobeexploredsystematically.Meta-GGACommonhybridfunctionalmixafractionofHartree-FockexchangeintotheDFTexchangefunctional.HybridFunctionals(Becke,1993)(Perdew,1998)B3PW91,B3LYPPBE0B3LYPisthemainworking-horseincomputationalchemistryL(S)DA+UMott絕緣體，Hubbard模型Anisimovetal.：StonerI-->HubbardU軌道序：Dudarevetal.：懲罰泛函PartII:數(shù)值方法平面波基組：從OPW到PP平面波展開正交化平面波（OPW）贗勢（PP）方法經(jīng)驗贗勢模守恒贗勢超軟贗勢Muffin-tin勢場與分波方法Muffin-tin勢場近似綴加平面波（APW）格林函數(shù)方法（KKR）線性化方法LAPWLMTO分波方法的發(fā)展FP-LAPWthird-generationMTO,NMTO,EMTO實空間網(wǎng)格簡單直觀允許通過增加網(wǎng)格密度系統(tǒng)地控制計算收斂精度線性標度可以方便的通過實空間域分解實現(xiàn)并行計算處理某些特殊體系（帶電體系、隧穿結(jié)。。。）有限差分從微分到差分提高FD方法的計算效率對網(wǎng)格進行優(yōu)化，如曲線網(wǎng)格（適應(yīng)網(wǎng)格）和局部網(wǎng)格優(yōu)化（復(fù)合網(wǎng)格）結(jié)合贗勢方法多尺度（multiscale）或預(yù)處理（preconditioning）有限元變分方法處理復(fù)雜的邊界條件矩陣稀疏程度及帶狀結(jié)構(gòu)往往不如有限差分好廣義的本征值問題PartIII:應(yīng)用物理學：強相關(guān)體系模型哈密頓量LDA++電子結(jié)構(gòu)：CrO2點陣動力學:钚化學：弱作用體系松散堆積的軟物質(zhì)、惰性氣體、生物分子和聚合物，物理吸附、Cl+HD反應(yīng)用傳統(tǒng)的密度泛函理論處理弱作用體系一個既能產(chǎn)生vdW相互作用系數(shù)又能產(chǎn)生總關(guān)聯(lián)能的非局域泛函：無縫的（seamless）方法GW近似密度泛函加衰減色散（DFdD）生命科學：生物體系困難（尺寸問題、時間尺度）QM/MM方法（飽和原子法、凍結(jié)軌道法）簡單勢能面方法線性同步過渡（LST）二次同步過渡（QST）完全的分子動力學并行復(fù)制動力學（parallelreplicadynamics）超動力學（hyperdynamics,metadynamics）溫度加速的動力學（temperatureaccelerateddynamics）快速蒙特卡羅（on-the-flykinericMonteCarlo）方法納米和材料科學：輸運性質(zhì)及其他輸運：非平衡態(tài)第一性原理模擬材料力學：運動學MonteCarlo（KMC）-->點陣氣體和元胞自動機-->連續(xù)方程的有限差分有限元求解光譜學：激發(fā)態(tài)和外場系綜密度泛函理論考慮系統(tǒng)對稱性，用求和方法計算多重態(tài)激發(fā)能多體微擾理論，GW近似Bethe-Salpeter方程TDDFT，線性響應(yīng)石墨烯體系的第一性原理研究GrapheneIntroductiontographeneandgraphenenanoribbon(GNR)GNRbasedspintronicsNearlyfreeelectron(NFE)statesingatedGNRsuperlatticeCuttingmechanismingrapheneoxide(GO)Graphene:amonolayeroftwo-dimensionalcarbonatoms198519912004CrystalstructureofgrapheneEnergybandsKorK’Siliconout,Graphenein?

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