lec 10 - Molecular Orbital Theory Reading: Gray: (2-5),...

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Molecular Orbital Theory Reading: Gray: (2-5), (2-6), (3-1) to (3-6) OGC: (6.1) and (6.2)
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IX - 2 Molecular Orbital Theory MO–LCAO: M olecular O rbital– L inear C ombination of A tomic O rbitals Lewis Dot Structures don’t work for excited states; sometimes they don’t even predict the ground state accurately : Example: O 2 expected Lewis Dot Structrure: O O Actually O 2 has two unpaired electrons; this cannot be predicted with Lewis Dot Structures, but it can be predicted with MO-LCAO
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IX - 3 MO-LCAO Lewis Dot Structures tell us: H 2 + H 2 - H H H H H H MO-LCAO will tell us: a. their local stabilities b. their bond orders and their trend in bond lengths c. their magnetic properties H 2
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IX - 4 Nobel Prize, Chemistry, 1966 ”For his fundamental work concerning chemical bonds and the electronic structure of molecules by the molecular orbital method" Robert S. Mullikan
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IX - 5 Energy dependence on inter-atomic distance E 0 r r 0 region where nuclei repel most likely distance for a bond (lowest energy point) electrons start being pulled to the other atom’s nucleus at r = , E = 0; the atoms don’t interact indicates the direction of dominating forces
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IX - 6 H 2 Molecule electron density in a molecular orbital r 0 equilibrium bond distance
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IX - 7 H a Ψ a r a 0 H b Ψ b r b 0 Linear Combinations of Atomic Orbitals Molecular orbitals are built up from linear combinations of atomic orbitals:
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IX - 8 Ψ H a H b + + + + + + + + + + + + + + + + The Wavefunctions of two Separate Hydrogen Atoms
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IX - 9 + + + + + + + + + + + + + + + + Orbitals Start to Overlap as Atoms Approach + + + + + + + + + + + + + + + +
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IX - 10 Ψ Bonding Orbital: Ψ (1s a + 1s b ) = 1 σ b Wavefunction of H 2 Molecule in Ground State + + + + + + + + + + + + + + + +
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IX - 11 H a Ψ a r a 0 H b Ψ b r b 0 Another Linear Combination
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IX - 12 Ψ H a H b - - - + + + + + + + - - - - - + Combined Wavefunction with the Two Atoms a Distance Apart Note: Subtracting wavefunctions is the same as adding the negative of the second
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IX - 13 Ψ Anti-Bonding Orbital: Ψ (1s a -1s b ) = 1 σ * node: Wavefunction of H 2 in Excited State + + + + + + + + - - - - - - - -
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