DFT - Density Functional Theory N LCAO approach: a = cia i...

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Colby College Density Functional Theory LCAO approach: Ψ a = i=1 N c ia φ i Ψ a = one-electron molecular orbital φ i = atomic orbitals for N orbitals (Slater or Gaussian) c ia = orbital coefficients -- variational parameters Variation Theorem: vary c ia ’s to find the lowest energy: Hartree-Fock Equations: f 1 Ψ a (1) σ(1) = ε a Ψ a (1) σ(1) ε a = one-electron orbital energy for MO a, b, c, … f 1 = h 1 + j=1 n/2 {2J j (1) - K j (1) } j = all the other filled orbitals for electron 1, 2, 3, … core Hamiltonian: h 1 = h 2 2m 2 1 - k=1 m Z k e 2 4 π ε o r k 1 k = all nuclei HF electron-electron repulsion: Coulomb operator: J j (1) Exchange operator: K j (1)
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This document was uploaded on 02/22/2012.

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