Lec11 (3) - 10.675 LECTURE 11 RICK RAJTER 1. Today 2nd...

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10.675 LECTURE 11 RICK RAJTER 1. Today 2nd Hohenberg-Kohn Thereom Kinetic Energy Thomas Fermi Kohn-Sham Orbitals Spin DFT Gradient Corrected ”Non-Local” Functionals 2. 2nd Thereom Variational principle as applied to DFT, for trial density ρ T ( r ) such that ρ T ( r ) dr = N electrons E o E v [ ρ T ( r )] E v [ ρ ] = v ( r ) ρ ( r ) dr + F [ ρ ] where v ( r ) are the nuc-elec interactions, F [ ρ ] is the electron KE + elec-elec interactions F [ ρ ] = Ψ ( T + U dr Where T = KE, U = elec-elec E v T ] = Ψ T ( T + U + V T dr > E o [Ψ] 2 ρ ( r ) = | Ψ( r ) | So far, all we’ve dealt with is the ground state energy. .. Only HF can deal with excited states. E [ ρ ] = T [ ρ ] + N [ ρ ] + U [ ρ ] + ( Nuc/Nuc ) T is KE, N is Nuc-elec, U is elec-elec. T [ ρ ] is the Thomas fermi theory choose the form of T [ ρ ] to be that of a gas of free homogenous electrons. 1
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Lec11 (3) - 10.675 LECTURE 11 RICK RAJTER 1. Today 2nd...

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