Lec12 (2) - 10.675 LECTURE 12 RICK RAJTER 1. Today LSD...

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± ± ± V 10.675 LECTURE 12 RICK RAJTER 1. Today LSD Functionals Correlation Methods CI, Partial CI G1, G2, G3 Coupled Cluster, CCD, CCSD, QCISD 2. LSD - Local Spin DFT Thomas Fermi is too hard to correct wave function, as T T F [ ρ ] would completely change it. LSD - Electrons can be unpaired here, as opposed to ground state paired methods. ρ α , ρ β densities of the α, β spins, either +/- 1/2. In the following derivations, σ is means either the α or β spin. ± 2 ρ σ 1 2 [ ρ α , ρ β ] = φ σ n ρ σ Ψ ρ σ ( b ( r ) ρ β ) dr dr + J [ ρ α + ρ β ] + E xc [ ρ α , ρ β ] + v ( r )( ρ α E ρ β ) dr + β e b ( r ) ρ α β e Where b ( r ) is the magnetic ±eld. set n ρ α ’s to 1 for the lowest KS orbitals w/normalization. Solve 2 KS equations 1 2 1 2 α 2 + V ef f rho α ( = ± ρ α Ψ ρ α β 2 + V ef f rho β ( For q = ± ρ β Ψ ρ β = 1,2,3,4 . .. N ρ ( r ) dr + δE xc [ ρ α β ] α = V ( r ) + ef f
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Lec12 (2) - 10.675 LECTURE 12 RICK RAJTER 1. Today LSD...

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