CHEM6670Notes7 - Miscellaneous topics in electronic...

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Miscellaneous topics in electronic structure methods 1 CHEM 6670 Computational Chemistry & Biophysics Miscellaneous topics Feb 5, 2008 Course instructor: Dr. Jana Khandogin [email protected] Course web site: http://ccb.ou.edu/teaching.aspx Topics Review Hellmann Feynman theorem Molecular properties Poisson equation Born model Conductor like screening model 2 KS and HF equations Kohn Sham equation Hartree Fock equation N ) ( ' ' ) ' ( 2 1 2 r v r d r r r R r Z v v xc M a a i a eff i i i eff i r r r r r r r + + = = + ρ φ ε φ N j j N j M a a i a i i i i i j j j i J R r Z h K J h φ φ φ ε φ = = = + 1 ˆ 2 1 ˆ ) ) ˆ ˆ ( ˆ ( 2 r r r r 3 j i ij ij j j i j N j j j j i j P P r r K r r φ φ φ φ = = ˆ ˆ 1 ˆ r r Exchange correlation potential is unknown! Exchange operator Self interaction error. It is canceled in HF. Wave function methods 4 Martin Head Gordon, 2007
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Miscellaneous topics in electronic structure methods 2 DFT methods 5 Martin Head Gordon, 2007 Molecular properties 6 Molecular properties 7 First order energy derivative The energy to the second order of perturbation is ) ( ) ( ) ( 2 λ λ λ λ λ P P H E The first derivative is thus, 2 1 ψ ψ + + = ψ λ ψ ψ λ λ λ ψ λ 2 1 2 2 1 0 2 P P P P H E + + + + = For real wave functions, 8 ψ λ ψ ψ λ λ λ ψ λ ψ λ λ ψ 2 1 2 2 1 0 2 2 1 0 2 2 P P P P H P P H + + + + = + + +
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