资源描述：
《LDA+U第一性原理方法.ppt》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、IntroductiontoLDA+Umethodandapplicationstotransition-metaloxides:Importanceofon-siteCoulombinteractionU鄭弘泰國家理論中心(清華大學)28Aug,2003,東華大學OutlineDFT,LDA(LDA,LSDA,GGA)InsufficienciesofLDAHowtoimproveLDASelf-interactioncorrection(SIC)LDA+UmethodApplicationsofLDA+Uonvarioustran
2、sition-metaloxidesConclusionsDensityFunctionalTheory(DFT)Hohenberg-KohnTheorem,PR136(1964)B864Theground-stateenergyofasystemofidenticalspinlessfermionsisauniquefunctionaloftheparticledensity.Thisfunctionalattainsitsminimumvaluewithrespecttovariationoftheparticledensitys
3、ubjecttothenormalizationconditionwhenthedensityhasitscorrectvalues.Localdensityapproximation(LDA)Kohn-ShamschemePR140(1965)A1133InsufficienciesofLDAPooreigenvalues,PRB23,5048(1981)LackofderivativediscontinuityatintegerN,PRL49,1691(1982)Gapstoosmallornogap,PRB44,943(1991
4、)Spinandorbitalmomenttoosmall,PRB44,943(1991)EspeciallyfortransitionmetaloxidesPRB23(1981)5048PRL49(1982)1691PRB44(1991)943AttemptsonimprovingLDASelf-interactioncorrection(SIC)PRB23(1981)5048,PRL65(1990)1148Hartree-Fock(HF)method,PRB48(1993)5058GWapproximation(GWA),PRB4
5、6(1992)13051,PRL74(1995)3221LDA+HubbardU(LDA+U)method,PRB44(1991)943,PRB48(1993)16929Localdensityapproximation(LDA)Kohn-ShamschemePR140(1965)A1133Self-interactioncorrection(SIC)PerdewandZunger,PRB23(1981)5048BasicideaofLDA+UPRB44(1991)943,PRB48(1993)169Delocalizedsandpe
6、lectrons:LDALocalizeddorfelectrons:+Uusingon-sited-dCoulombinteraction(Hubbard-liketerm)UΣi≠jninjinsteadofaveragedCoulombenergyUN(N－1)/2HubbardUforlocalizeddorbital:nnn+1n-1UeLDA+Uenergyfunctional:LDA+Upotential:LDA+Ueigenvalue:Foroccupiedstateni=1,Forunccupiedstateni=0
7、,peEexact(H)=－1.0RyELDA(H)=－0.957Ry～Eexact(H)eLDA(H)=－0.538Ry<8、U(H)=eLDA(H)－U/2=－1.0104Ry～－1RyUnoccupied(H+)state:eLDA+U(H+)=eLDA(H)＋U/2=－0.0656Ry～0RyWhentouseLDA+USystemsth
