Transcription of 5.4 紧束缚模型 (tight-binding model) - USTC
1 (tight- binding model).. p189.. p75.. xB.. xC. xs=a(xB+xC).. xs2.. xA=a(xB-xC). xA2.. - Linear combination of atomic orbitals (LCAO).. 2 2. H i [ VAi VBi ] i i i 2m . i Ci A (ri ) i B (ri ) . 1. H dr *. 2C 2 ( H aa H ab ). C ( A B ). dr *. C ( A B ). H dr *. 2C 2 ( H aa H abb ). dr *. H dr *. 2C 2 ( H aa H ab ) .. *. d dr Bonding orbital H dr *. 2C 2 ( H aa H ab ) .. *. dr Anti-bonding orbital H aa *A H A dr B* H B dr 0. H ab *A H B dr 0. H ab .. LCAO . tight- binding ) . Slater Gaussian . Slater .. Splitting of 1s State of Six Atoms Splitting of Atomic Levels in Sodium Tight- binding Na.
2 Occupation of Bands Sodium Splitting of Atomic Levels in Carbon Tight- binding g g C . 1 . Rs a E (k ) s J 0 2 J1 cos ka . k 0 k . a 1. k (r ) . N.. m j (r Rm ). k (r ) . 1. ( 1) m 1. j (r Rm ). N m k=0. s . k= / a p . p J1<1. 2. 3. tight- binding ( J0 . Hamiltonian Eigenvalues: E1=E0. H= E0. Eigenvalues: g H E0 J1. H= E1=E0+ J1. J1 E0 E2=E0 J1. E0 J1 J1 Eigenvalues: H= J E0 J1 E1=E0 2J1. 1. J1 J1 E0 E2=E0 + J1. E3=E0+ J1. J1 is the orbital interaction between the nearest neighbours J1 . 2 2. 1 . 2. 0 (r1 ) . 2. 0 (r2 ) 2 0 (r1 ) 0 (r2 ). 2 2 2 2. E1 E0 J1 E1 E0 J1. 3 3 3 2 2 1 1 2. 1 0 (r1 ) 0 (r2 ) 0 (r3 ) 2 0 (r1 ) 0 (r2 ) 3 0 (r1 ) 0 (r2 ) 0 (r3 ).)
3 3 3 3 2 2 6 6 6. E1 E0 2J. 2 J1 E1 E0 J1 E1 E0 J1. J1 .. bond bond bond Walter Ashley Harrison (1989). Electronic Structure and the Properties of Solids. 4 4 4. , , 5 6.
