CHEM6670Notes7 - Miscellaneous topics in electronic...

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Unformatted text preview: Miscellaneous topics in electronic structure methods 1 CHEM 6670 omputational Chemistry & Biophysics 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 ellmann eynman theorem • Hellmann ‐ Feynman theorem • Molecular properties • Poisson equation • Born model • Conductor ‐ like screening model 2 KS and HF equations Kohn ‐ Sham equation Hartree ‐ Fock equation ) ( ' ' ) ' ( 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 N M a a i a i i i i i N 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 j i j j j P P r r K r r φ φ φ φ = − = − ∑ ∑ ∑ ˆ ˆ 1 ˆ r r 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 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 • The first derivative is thus, ) ( ) ( ) ( 2 2 1 λ ψ λ λ λ ψ λ P P H E + + = ψ λ ψ ψ λ λ λ ψ λ 2 1 2 2 1 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 2 2 1 2 2 P P P P H P P H + + + + ∂ ∂ = ∂ ∂ + + + Miscellaneous topics in electronic structure methods 3 First ‐ order energy derivative • Let the perturbation go to zero, • The wavefunction depends on the MO expansion coefficien...
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This note was uploaded on 04/29/2008 for the course CHEM 6670 taught by Professor Janakhandogin during the Spring '08 term at The University of Oklahoma.

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CHEM6670Notes7 - Miscellaneous topics in electronic...

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