Molecular Orbital Theory

Molecular Orbital Theory - Molecular Orbital Theory I...

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1 Molecular Orbital Theory I. Introduction. A. Ideas. 1. Start with nuclei at their equilibrium positions. 2. Construct a set of orbitals that cover the complete nuclear framework, called molecular orbitals (MO's) .3. Use the rules of quantum mechanics to arrange the molecular orbitals in order of increasing energy and add the electrons. 4. Fill the MO's with the molecule's electrons. a. Lowest energy MO's filled first. b. No more than two electrons in the same MO with their spins paired. c. Half fill a degenerate set with spins parallel before pairing up in the same MO. 5. Start with the atomic orbitals (AO’s). Can construct the MO's by taking Linear Combinations of the Atomic Orbitals using at least one AO from each atom (LCAO method). 6. Most of the time the only electrons that need be considered are the valence electrons and the AO's used in the linear combinations are the valence orbitals 7. Arrange the molecular orbitals in order of increasing energy and add the electrons. a. Lowest energy MO's filled first. b. No more than two electrons in the same MO with their spins paired. c. Half fill a degenerate set with spins parallel before pairing up in the same MO. B. Lowest energy states of homonuclear diatomic molecules. 1. Get the two lowest energy MO's by taking linear combinations of the lowest energy atomic orbitals, the 1s atomic orbitals. There are two ways to combine, can add them together or subtract them. The resulting MO's are sketched below.
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2 ! 1s A "# 1s " 1s ! 1s B ! 1s A ! 1s A ! 1s B ! 1s B + Atom A Atom B a. Ψ 1s is a spherical function that is positive in all regions in space. When two 1s functions are added the resulting wave function, labeled σ 1s , is also positive in all regions. (A sketch of σ 1s is shown above.) On the other hand, when the two 1s atomic orbital functions are subtracted, the resulting function, σ * 1s , is positive around nucleus A, negative around nucleus B, and is equal to zero halfway between the two nuclei (see above). The wave function is said to have a nodal point between the two nuclei. b. The σ designation indicates that the wave function is symmetric with respect to the inter-nuclear axis. That is, the wave function does not change sign as one goes above or below the internuclear line. The subscript, 1s, tells the atomic orbitals that are involved in the molecular orbital. 3. The relative energies of the orbitals. a. The molecular orbital energy diagram.
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3 !" 1s ! 1s # 1s A # 1s B Atom A Atom B AB Molecule $ $ Energy b. The σ 1s orbital is lower in energy than the atomic orbitals by an amount β . Occupation of this orbital will tend to stabilize the molecule and promote bonding between the two atoms. The molecular orbital is said to be a bonding molecular orbital . c. The σ * 1s orbital is higher in energy (less stable) than the atomic orbitals by an amount β . Occupation of this orbital will tend to destabilize the molecule and detract from bonding. It is called an antibonding molecular orbital .
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