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Unformatted text preview: Chem 120A MO-LCAO and approximations, esp. H¨uckel theory 05/04/07 Spring 2007 Lecture 41 READING: Ratner/Schatz Ch. 12 MO-LCAO and bond localized pictures Molecular orbital theory is based on the zeroth order description of single electron molecular orbitals exp- resed as linear combinations of atomic orbitals: ψ MO = c 1 φ 1 + c 2 φ 2 + ... (1) For example, for the hydrogen molecule we had φ 1 = 1 s A ( 1 ) + 1 s B ( 1 ) , φ 2 = 1 s A ( 1 ) = 1 s B ( 1 ) ,... Adding spin to these spatial orbitals and taking account of the required antisymmetry of the electrons with respect to pairwise permutations (exchange) gives Slater determinants of one-electron spin-space orbitals. The secular equation resulting from these is known as the Hartree-Fock equation and its solutions can give accurate molecular orbitals. Usually one includes only the Slater determinant corresponding to the ground state electron configuration at the Hartree-Fock level. The resulting molecular orbitals are the best (variation- ally) effective single electron orbitals. Adding multiple Slater determinants corresponding to excited state electron configurations is known as configuration interaction and can in principle give exact results if one includes all possible configurations. See notes in lecture 39 and Ratner/Schatz Ch. 11 or Atkins/Friedman Ch. 9.1-9.12. The Hartree-Fock method and its extensions constitute a powerful set of methods that are widely applied in chemistry, but they are somewhat expensive and so it is still attractive to use other less exact methods for molecules whose electronic states can be suitably represented using some approximation. The molecular orbital approach yields orbitals that are delocalized over all or large parts of the molecule, as the name suggests. Molecular orbitals can be constructed with the assistance of group theory, which allows construction of symmetry-adapted molecular orbitals (Atkins/Friedman Ch. 8.8). An alternative approach that provides useful insight into the geometry of polyatomic molecules is the bond-localized de- scription (also known as valence bond or atoms-in-molecules). Note that this is however not quantitative for molecular energies. An example of this is the use of atomic hybrid orbitals to describe the geometry of molecules with simple rules such as maximizing the distance between lone pairs, then lone pair-bond...
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