03 - Chemistry 2000 Lecture 3: LCAO-MO theory for diatomic...

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Chemistry 2000 Lecture 3: LCAO-MO theory for diatomic molecules Marc R. Roussel
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MO theory for homonuclear diatomic molecules I We want to develop MO theory for diatomic molecules. I Initially, we will focus on homonuclear diatomic molecules, i.e. those in which both atoms are of the same element.
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LCAO of higher orbitals I In the last lecture, we combined 1s AOs to obtain sigma bonding and antibonding molecular orbitals: 1 σ σ 1 s 1 σ * σ * 1 s I We can combine higher AOs in a similar way. I σ and σ * orbitals obtained from the 2s AOs: 2 σ σ 2 s 2 σ * σ * 2 s
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2p orbitals can be combined in two different ways: 1. The 2 p z orbitals are oriented toward each other so adding them gives sigma (cylindrically symmetric) orbitals: add -→ 3 σ σ 2 p subtract -----→ 3 σ * σ * 2 p
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Note: Subtracting the 2 p z orbitals is equivalent to adding them out of phase: add -→ 3 σ * σ * 2 p
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3. The 2 p x and 2 p y orbitals are perpendicular to the bond axis. Adding them gives π orbitals: add -→ 1 π π 2 p add 1 π * π * 2 p
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Pi orbitals have a nodal plane through the bond axis. Note: There are two degenerate 1 π orbitals and degenerate 1 π * orbitals because we can combine p x or p y orbitals in this manner:
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AO energies and LCAO theory Principle: AOs of similar energies and appropriate symmetries can mix to form MOs.
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03 - Chemistry 2000 Lecture 3: LCAO-MO theory for diatomic...

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