Solid State Physics

Solid State Physics - 223 (1) abinit www.abinit.org abinit...

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Unformatted text preview: 223 (1) abinit www.abinit.org abinit ab initio Density Functional Theory DFT GNU General Public Licence www.abinit.org abinit (2) CASTEP (www.tcm.phy.cam.ac.uk/castep/) CASTEP(CAmbridge Sequential Total Energy Package) LDA GGA Ultrasoft norm-conserving Ecut-off FFT mesh (LCAO) (Self-Consistent Field SCF) CASTEP CASTEP CASTEP (3) VASP (cms.mpi.univie.ac.at/vasp/) (Vienna Abinitio Simulation Package) Vienna CASTEP 1989 abinit VASP CASTEP Rydberg 13.6eV — 224 30-2 ( ) V a ( ) b ψ ( ) ps V c ( ) ps d ψ (1) (2) 30-2 | φ V 〉 | φ c 〉 H E V E c V V V H E φ φ = (30.14) c c c H E φ φ = (30.15) V φ ps V V c V c c φ ψ µ φ = + ∑ (30.16) | φ c 〉 | ψ V PS 〉 〈 φ c | φ V 〉 =0 ps cV c V µ φ ψ = − (30.17) H − E V | ψ V PS 〉 225 ( ) ( ) ( ) ( ) ps ps V V V V c c V c ps ps V c c V V c c V c c H E H E H E H E ψ φ φ φ ψ φ φ ψ φ φ ψ − = − + = − = − ∑ ∑ ∑ (30.18) ( ) ps V c c V V c H H E E φ φ ψ + − − = ∑ (30.19) H T V = + (30.20) ( ) ps V c c c V V H E φ φ = + − ∑ (30.21) ps ps V V T V E ψ + − = (30.22) V PS (30.22) V ( ) V c c c H E φ φ − ∑ | ψ V PS 〉 E V V L PS V NL PS ( r,r’ ) ( ) ( ) ( ) ps ps ps L N L , ' ' , ' V V V δ = − + r r r r r r (30.23) ( ) ( ) ( ) ( ) ( ) ps NL NL , , ' , , ; ', ', ' Y , , ' Y ', ' l l lm lm l l m V r r r r υ θ ϕ θ ϕ θ ϕ υ θ ϕ ∗ = = ∑ ∑ r r (30.24) υ l ( ) ( ) ( ) , ' ' l l r r r r r υ υ δ = − (30.25) l ( ) ( ) ( ) ( ) ( ) ps NL , , , ' Y , , ' Y ', ' l l lm lm l m l m V r r r lm lm θ ϕ υ θ ϕ υ ∗ = = ∑ ∑ r r (30.30) (1) Kohn-Sham 30-3 r < r c V ψ V ps ψ PS 226 D. R. Hamann (norm conserving pseudopotential, NCPP) r c ( ) r c 30-3 (1) V ( r ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 1 2 2 l l l l l d u r dV r u r l l du M V u r M dr dr r dr r α ε + − − − + + − = (30.27) M = 1 − 0.5 α 2 ( V − ε l ) α u l ( r ) ε l (2) r c l r c l r c l f ( ) ( ) c c exp l l f r r r r λ = − (30.28) λ 3.5 (3) V ( r ) ( ) ( ) ( ) ( ) 1 c c 1 l l l l V r f r r V r c f r r = − + (30.29) l c w 1 l ( r ) ( γ l ) r >r cl u l ( r ) r >r cl ( ) ( ) 1 l l l w r u r γ → (30.30) (4) w 2 l ( r ) ( ) ( ) ( ) 1 2 1 c l l l l l l w r w r r f r r γ δ + = + (30.31) δ l w 2 l ( r ) 2 2 1 l R l drw = ∫ (30.32) R l (30.27) R l ~2.5 r cl (5) w 2 l ( r ) V 2 l ( r ) ( ) ( ) ( ) ( ) ( ) ( ) 2 1 2 c 2 1 1 2 2 2 c c 2 1 2 2 2 l l l l l l l l l l l r f r r l r r V r V r V r w r r r r r λ λ γ δ λ λ λ λ ε + + + = + − + −...
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This note was uploaded on 05/05/2010 for the course PHYSICS 111 taught by Professor Zhengxiang during the Spring '08 term at Peking Uni..

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Solid State Physics - 223 (1) abinit www.abinit.org abinit...

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