LDA+U第一性原理方法.ppt

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LDA+U第一性原理方法.ppt

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LDAU第一性原理方法ppt整理

Introduction to LDA+U method and applications to transition-metal oxides:Importance of on-site Coulomb interaction U 鄭弘泰國家理論中心 (清華大學) 28 Aug, 2003, 東華大學 Outline DFT, LDA (LDA, LSDA, GGA) Insufficiencies of LDA How to improve LDA Self-interaction correction (SIC) LDA+U method Applications of LDA+U on various transition-metal oxides Conclusions Density Functional Theory (DFT)Hohenberg-Kohn Theorem, PR136(1964)B864 The ground-state energy of a system of identical spinless fermions is a unique functional of the particle density. This functional attains its minimum value with respect to variation of the particle density subject to the normalization condition when the density has its correct values. Local density approximation (LDA)Kohn-Sham scheme PR140(1965)A1133 Insufficiencies of LDA Poor eigenvalues, PRB23, 5048 (1981) Lack of derivative discontinuity at integer N, PRL49, 1691 (1982) Gaps too small or no gap, PRB44, 943 (1991) Spin and orbital moment too small, PRB44, 943 (1991) Especially for transition metal oxides Attempts on improving LDA Self-interaction correction (SIC) PRB23(1981)5048, PRL65(1990)1148 Hartree-Fock (HF) method, PRB48(1993)5058 GW approximation (GWA), PRB46(1992)13051, PRL74(1995)3221 LDA+Hubbard U (LDA+U) method, PRB44(1991)943, PRB48(1993)16929 Local density approximation (LDA)Kohn-Sham scheme PR140(1965)A1133 Self-interaction correction (SIC) Perdew and Zunger, PRB23(1981)5048 Basic idea of LDA+U PRB 44 (1991) 943, PRB 48 (1993) 169 Delocalized s and p electrons : LDA Localized d or f electrons : +U using on-site d-d Coulomb interaction (Hubbard-like term) UΣi≠jninj instead of averaged Coulomb energy UN(N－1)/2 When to use LDA+U Systems that LDA gives bad results Narrow band materials : U≧W Transition-metal oxides Localized electron systems Strongly correlated materials Insulators ….. How to calculate U and J PRB 39 (1989) 9028 Co