Lecture_22_SCF_Method_1

Lecture_22_SCF_Method_1 - Hartree-Fock SCF Method For the...

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Hartree-Fock SCF Method For the Hartree method, the many-electron wavefunction Ψ is taken as a product of one-electron orbitals Ψ= s s n n 1 1 ( ) . .. ( ) where the starting set of orbitals is ss n 1 ,..., . An orbital is in turn a product of a radial function and a spherical harmonic sr hrY l m 11 1 1 () , = θφ . Now e- #1 feels an average potential of Vr e o i n s i r i d j Ze o r 11 1 1 2 4 2 2 1 2 4 1 ,, πε τ = = , where the first term represents the e-e repulsion of e- #1 with the (n-1) other e-’s and the second term represents the nucleus-e- #1 attraction
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The Schrödinger equation for e- #1 is −∇ + = h 2 2 1 2 11 1 1 11 1 m Vr t t (, , ) θφ ε Where t 1 is an improved orbital for e- #1 and 1 is the orbital energy corresponding to the orbital t 1 .
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This note was uploaded on 01/23/2012 for the course CHM 341 taught by Professor Klier during the Fall '08 term at Lehigh University .

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Lecture_22_SCF_Method_1 - Hartree-Fock SCF Method For the...

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