lecture26_umn

lecture26_umn - Lecture 26 November 13, 2009 Many-electron...

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Unformatted text preview: Lecture 26 November 13, 2009 Many-electron Wave FunctionsHartree Products Hckel Theory: Recap Molecular orbitals and energies derived using a one-electron formalism Energy of a many-electron system: sum of the energies of the occupied one- electron orbitals Further assumption: the orbitals are invariant to the number of electrons in the system Hamiltonian matrix elements derived from experimental quantities (ionization potentials and rotational barriers): implicitly accounts for electron-electron 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 many-electron effects One-electron Hamiltonian Schrdinger equation for a one-electron Hamiltonian Only terms in H: the one-electron kinetic energy and nuclear attraction terms The operator is separable (26-1) N total number of electrons h i is the one-electron Hamiltonian (26-2) 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 one-electron Hamiltonian must satisfy the corresponding one-electron Schrdinger equation (26-3) Because the Hamiltonian is separable, its many-electron eigenfunctions can be constructed as products of one-electron eigenfunctions (26-4) h i !...
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lecture26_umn - Lecture 26 November 13, 2009 Many-electron...

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