lda u第一性原理方法

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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+UmethodApplications

2、ofLDA+Uonvarioustransition-metaloxidesConclusionsDensityFunctionalTheory(DFT)Hohenberg-KohnTheorem,PR136(1964)B864Theground-stateenergyofasystemofidenticalspinlessfermionsisauniquefunctionaloftheparticledensity.Thisfunctionalattainsitsminimumvaluewit

3、hrespecttovariationoftheparticledensitysubjecttothenormalizationconditionwhenthedensityhasitscorrectvalues.Localdensityapproximation(LDA)Kohn-ShamschemePR140(1965)A1133InsufficienciesofLDAPooreigenvalues,PRB23,5048(1981)Lackofderivativediscontinuitya

4、tintegerN,PRL49,1691(1982)Gapstoosmallornogap,PRB44,943(1991)Spinandorbitalmomenttoosmall,PRB44,943(1991)EspeciallyfortransitionmetaloxidesPRB23(1981)5048PRL49(1982)1691PRB44(1991)943AttemptsonimprovingLDASelf-interactioncorrection(SIC)PRB23(1981)504

5、8,PRL65(1990)1148Hartree-Fock(HF)method,PRB48(1993)5058GWapproximation(GWA),PRB46(1992)13051,PRL74(1995)3221LDA+HubbardU(LDA+U)method,PRB44(1991)943,PRB48(1993)16929Localdensityapproximation(LDA)Kohn-ShamschemePR140(1965)A1133Self-interactioncorrecti

6、on(SIC)PerdewandZunger,PRB23(1981)5048BasicideaofLDA+UPRB44(1991)943,PRB48(1993)169Delocalizedsandpelectrons:LDALocalizeddorfelectrons:+Uusingon-sited-dCoulombinteraction(Hubbard-liketerm)UΣi≠jninjinsteadofaveragedCoulombenergyUN(N－1)/2HubbardUforloc

7、alizeddorbital:nnn+1n-1UeLDA+Uenergyfunctional:LDA+Upotential:LDA+Ueigenvalue:Foroccupiedstateni=1,Forunccupiedstateni=0,peEexact(H)=－1.0RyELDA(H)=－0.957Ry～Eexact(H)eLDA(H)=－0.538Ry<

8、yepeEexp(H-)=－1.0552RyeESIC(H-)=－1.0515RyELDA(H-):noboundstateU=E(H+)+E(H-)－2E(H)=0.9448RypeeLDA(H)=－0.538RyU=0.9448RyOccupied(H)state:eLDA+U(H)=eLDA(H)－U/2=－1.0104Ry～－1RyUnoccupied(H+)state:eLDA+U(H+)=eLDA(H)＋U/2=－0.0656Ry～0RyWhentouseLDA+USystemsth