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231Voi.23No.120052JIANGXISCIENCEFeb!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!20051001-3679200501-0001-042004-09-032004-10-1819740212018200400812211.3300272.3300130413.10481AFirst-principleswithpseudopotentialsMethodBasedontheDensityFunctionalTheoryXI0NGZhi-hua12SUNZhen-hui1LEIMin-sheng21.KeyLaboratoryofPhotoEiectronic&TeiecommunicationofJiangxiProvinceDepartmentofPhysicsJiangxiNormaiUniversityNanchangJiangxi330027PRC2.DepartmentofAppiiedPhysicsJiangxiScience&TechnoiogyNormaiUniversityNanchangJiangxi330013PRCAbstractFirst-Principiescaicuiationhassomeobviousadvantagesreiativetothehaif-empiricaimethodmoreovertheFirst-PrincipieswithPseudopotentiaismethodbasedontheDensityFunctionaiTheoryhasbeenanimportantfoundationandkeytechnoiogyofthemodernMateriaiComputationandDesign.ThepapergivesareviewoftheFirst-PrincipieswithPseudopotentiaisMethodbasedontheDensityFunctionaiTheory.KeywordsDensityFunctionaiTheoryFirst-PrincipiesPseudopotentiaisMethodFirst-Principies5m0ehckB111.1Hohenberg-kohnDFTDensityFunctionaITheo-ryEH.ThomasE.Fermi1927HohenbergKohn212E!!rHamiItonH=T+U+V1Hohenberg-KohnE!=IT+VI+!cror!r21.2kohn-ShamF!=IT+VI3IF!F!F!Hohenberg-KohnHohenberg-KohnKohnshamKohn-sham3Kohn-sham51F!F!=T!+V!4T!V!2F!=T!+12!!crcr'!r!r'Ir-r'I53#iri=12!r=Ni=1I#irI26T!=Ni=1!cr##ir-$2#ir7E!=F!+!dror!r=Ni=1!dr##ir-$2#ir+12!!drdr'!r!r'Ir-r'I+!dror!r84Exc!8E!=Ni=1!cr##ir-$2#ir+12!!crcr'!r!r'Ir-r'I+!cror!r+Exc!9Exc!Exc!5#ir$Ni=1!cr##ir-$2#ir+12!!crcr'!r!r'r-[r'$!+!cror!r+Exc!]=0102200523Kohn-sham-2+VKSPr[]ir=Eiir11VKSPr1r+dr'Pr'Ir-r'I+aExcPaPr12Pr=Ni=1ir2131.3ir12Kohn-sham11irirKohn-sham12iririr1.4Vxc=aExcPaPLDALocaIDensityAp-proximation3sIater19514D.M.CeperIeyB.L.AIderMonte-CarIo5rS=33/4PELDAxrS=-0.9164/rS14ELDAcrS=-0.2846/1+1.0529rS+0.3334rSrS1-0.0960+0.0622InrS-0.0232rS+0.0040rSInrSrS1⎧⎨⎩⎪⎪⎪⎪15LDALDA10%~20%1%6LDAGGAGeneraIizedGradientAp-proximationLDAEGGAxcP=drfxcPrIPrI16Becke7x=IPI/P4/3BEGGAx=ELDAx-BdrP4/31-0.55exp-1.65x2x2-2.40X10-4x41+6Bxsinh-1x+1.08X10-6x417LDABecke8Perdew-wang919BLYP10Meta-GGAPost-GGAVanderwaaIs112rc1rc2rcrcrc31+!######LAPWLMT0201DreizlerRMGrossEKU.DensityFunctionalTheoryM.BerlinSpringer-vertag1990.2HohenbergPKohnW.InhomogeneouselectrongasJ.PhysRev1964136B864.3KohnWShamLJ.Self-consistenteguationslncludingexchangeandcorrelationeffectsJ.PhysRev19651401133.4SlaterJC.Asimplificationofthehartree-fockmethodJ.PhysRev195181385.5PerdewTPZungerA.Self-interactioncorrectiontoden-sity-functionalapproximationsformany-electronsystemsJ.PhysRevB1981235048.6JonesR0Gunnarsson0.Thedensityfunctionalformal-ismitsapplicationsandprospectsJ.RevModPhys198961689.7BeckeAD.Density-functionalexchange-energyapproxi-mationwithcorrectasymptoticbehaviorJ.PhysRevA1988383098.8LangrethCPerdewJP.Analysisofthegradientap-proximationandageneralizationthatworksJ.PhysRevB1980215469.9PerdewJPBurkeK.Generalizedgradientapproxima-tionmadesimpleJ.PhysRevLett1996773865.10LeeCYangW.GeneralizedgradientapproximationmadesimpleJ.PhysRevB198837785.11KohnWMeirYDE.vanderwaalsenergiesindensityfunctionaltheoryJ.PhysRevLett199880!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!4153.318634200523