MO Diagrams for Diatomic Molecules Chapter 5 Friday, October 17, 2014

Homonuclear Diatomic Molecules What happens when we move to more complicated systems? Consider O 2. The Lewis dot structure famously predicts the wrong electronic structure for O 2 We can use LCAO-MO theory to get a better picture: 2sa2sa 2pa2pa 2sb2sb 2pb2pb Notice that E σ > E π, because the σ bonds have more overlap than π bonds EσEσ EπEπ

Electron Configurations and Bond Orders Just as with atoms, we can write a molecular electron configuration for O 2 σ 2 σ* 2 σ 2 π 4 π* 2 We can also calculate the O–O bond order: LCAO MO theory also predicts (correctly) that O 2 has two unpaired electrons.

Orbital Mixing Orbitals of similar but unequal energies can interact if they have the same symmetry The 2s and 2p z orbitals form MOs with the same symmetry ( σ g and σ u ). sp mixing causes the σ g and σ u MOs to be pushed apart in energy: The σ and π orbitals change order!

Orbital Mixing The size of the effect depends on the 2s-2p energy difference. small Z eff = small energy difference = large sp mixing large Z eff = large energy difference = small sp mixing order changes

MOs of Homonuclear Diatomic Molecules The MO picture of homonuclear diatomic molecules depends on the amount of sp mixing. O 2, F 2, Ne 2 Li 2, Be 2, B 2, C 2, N 2

Bond Order and Bond Distance The MO bond order is the main factor controlling the internucelar distance. B 2 σ 2 σ* 2 π 2 BO = 1 C 2 σ 2 σ* 2 π 4 BO = 2 N 2 σ 2 σ* 2 π 4 σ 2 BO = 3 O 2 σ 2 σ* 2 σ 2 π 4 π* 2 BO = 2 F 2 σ 2 σ* 2 σ 2 π 4 π* 4 BO = 1 O 2 – σ 2 σ* 2 σ 2 π 4 π* 3 BO = 1.5 O 2 + σ 2 σ* 2 σ 2 π 4 π* 1 BO = 2.5 N 2 + σ 2 σ* 2 π 4 σ 1 BO = 2.5 C 2 2– σ 2 σ* 2 π 4 σ 2 BO = 3

Relative AO Energies for MO Diagrams Photoelectron spectroscopy gives us a pretty good idea of the relative energies for AOs. H He Li Be B C N O F Ne B C N O F Na Mg Al Si P S Cl Ar Al Si P S Cl Ar 1s1s 2s2s 2p2p 3s3s 3p3p –13.6 eV –18.6 eV –40.2 eV

nb MO Diagram for HF The AO energies suggest that the 1s orbital of hydrogen interacts mostly with a 2p orbital of fluorine. The F 2s is nonbonding. H–F nb σ σ* Energy H –13.6 eV 1s1s F –18.6 eV –40.2 eV 2s2s 2p2p So H–F has one σ bond and three lone electron pairs on fluorine

Relative AO Energies for MO Diagrams H He Li Be B C N O F Ne B C N O F Na Mg Al Si P S Cl Ar Al Si P S Cl Ar 1s1s 2s2s 2p2p 3s3s 3p3p

Energy Heteronuclear Diatomic Molecules: CO In molecules with more than one type of atom, MOs are formed from AOs that have different energies. Consider CO: 2sa2sa 2pa2pa C 2sb2sb 2pb2pb O C≡O σ σ* π π* σ σ* Bonding orbitals get polarized towards oxygen Anti-bonding orbitals get polarized towards carbon HOMO is on carbon LUMO is on carbon too!

Summary MO Theory LCAO-MO Theory is a simple method for predicting the approximate electronic structure of molecules. Atomic orbitals must have the proper symmetry and energy to interact and form molecular orbitals. Photoelectron spectroscopy provides useful information on the energies of atomic orbitals. Next we’ll see that symmetry will help us treat larger molecules in the LCAO-MO theory framework.