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Molecular Orbital Theory. LCAO-MO = linear combination of atomic orbitals. ψ 1 = c 1 φ 1 + c 2 φ 2 ψ 2 = c 1 φ 1 - c 2 φ 2. Add and subtract amplitudes of atomic orbitals to make molecular orbitals Just like making hybrid orbitals, but AO’s come from different atoms

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## ψ 1 = c 1 φ 1 + c 2 φ 2 ψ 2 = c 1 φ 1 - c 2 φ 2

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**Molecular Orbital Theory**LCAO-MO = linear combination of atomic orbitals ψ1 = c1φ1 + c2φ2 ψ2 = c1φ1 - c2φ2 Add and subtract amplitudes of atomic orbitals to make molecular orbitals Just like making hybrid orbitals, but AO’s come from different atoms Bonding orbitals: Electrons have high probability of being between nuclei (lower energy)**Orbital overlap determines bonding energy**Weak overlap => weak interaction (bonding & antibonding MO energy same as AO’s Strong overlap => lowers energy of bonding MO, raises energy of antibonding MO**Bonding and antibonding orbital energies in H2**We typically draw MO energy level diagrams at the equilibrium bond distance**MO energy level diagram for H2 (H2+, HHe, He2, …)**α = Coulomb integral => ionization energy of electron in atomic orbital, e.g., H1s β = Exchange integral => energy difference between AO and bonding orbital S = Overlap integral, S12 = ∫φ1*φ2dτ**MO diagram for a polar bond (e.g., in HCl)**α values are different because of electronegativity difference between H and Cl Larger difference between bonding and antibonding orbital energies Bonding orbital closer in energy to Cl 3pz AO = > bond has more “Cl character”**MO diagram for an ionic bond (e.g., in Na+F-)**Larger energy difference Bonding electron pair is localized on the F atom Excited state is Na0F0**Summary of MO theory so far:**• Add and subtract AO wavefunctions to make MOs. # of AOs = # of MOs. • More nodes → higher energy MO • Bond order = ½ ( # of bonding electrons - # of antibonding electrons) • Bond polarity emerges in the MO picture as orbital “character.” • AOs that are far apart in energy do not interact much when they combine to make MOs.**Orbital Symmetry**AO’s of different symmetries (in the point group of the molecule) do not interact Greatly simplifies the problem of constructing MO’s for complex molecules**MO diagram for HCl molecule**Cl 2px and 2py orbitals have π symmetry – no interaction with σ symmetry orbitals Cl 3s is too low in energy to interact => nonbonding electron pair 8 electrons => 1 bond + 3 lone pairs (same result as valence bond picture)**σ, π, and δ orbitals in inorganic compounds**Face-to-face overlap of d-orbitals => δ bond e.g., in [Re2Cl8]2−**σ and π bonding in metal d-orbital complexes**Early transition metal Empty d-orbital Late transition metal Filled d-orbital Ligand acts as a σ donor (= Lewis base), empty d-orbital is σ acceptor (Lewis acid) Ligands can also act as π donors or π acceptors**MO diagram for 2nd row diatomic molecules**Li2, Be2, B2, C2, N2 O2, F2 Fill up MOs in Aufbau order O2 = 12 e = double bond, 2 unpaired electrons (paramagnetic) B2, C2?**π-bonding: 2nd row vs. 3rd (4th, 5th, 6th) rows**Ethylene: Stable molecule, doesn't polymerize without a catalyst. Silylene: Never isolated, spontaneously polymerizes. The large Ne core of Si atoms inhibits sideways overlap of 3p orbitals → weak π-bond N can make π-bonds, so N2 has a very strong triple bond and is a relatively inert diatomic gas “RTV” silicone polymer (4 single bonds to Si) vs. acetone (C=O double bond)

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