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Unformatted text preview: Lecture 26 November 13, 2009 Manyelectron Wave Functions—Hartree Products Hückel Theory: Recap Molecular orbitals and energies derived using a oneelectron formalism Energy of a manyelectron system: sum of the energies of the occupied one electron orbitals Further assumption: the orbitals are invariant to the number of electrons in the π system Hamiltonian matrix elements derived from experimental quantities (ionization potentials and rotational barriers): implicitly accounts for electronelectron repulsion in some average way Such an approach, known as an effective Hamiltonian method, is rather crude Need to take a more sophisticated accounting of manyelectron effects Oneelectron Hamiltonian Schrödinger equation for a oneelectron Hamiltonian Only terms in H: the oneelectron kinetic energy and nuclear attraction terms The operator is separable (261) N total number of electrons h i is the oneelectron Hamiltonian (262) M total number of nuclei H = h i i = 1 N " h i = ! 1 2 " i 2 ! Z k r ik k = 1 M # Eigenfunctions Eigenfunctions of the oneelectron Hamiltonian must satisfy the corresponding oneelectron Schrödinger equation (263) Because the Hamiltonian is separable, its manyelectron eigenfunctions can be constructed as products of oneelectron eigenfunctions (264) h i !...
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 Fall '08
 Staff
 Schrodinger Equation, effective Hamiltonian method, Hamiltonian matrix elements, oneelectron Hamiltonian

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