# Point Groups - University of California, Irvine

MO Diagrams for Diatomic Molecules Chapter 5 Friday, October 9, 2015 Homonuclear Diatomic Molecules What happens when we move to more complicated systems? Consider O2. The Lewis dot structure famously predicts the wrong electronic structure for O2 We can use LCAO-MO theory to get a better picture: Notice that E > E, because the bonds have more overlap than bonds E 2pa 2sa

E 2pb 2sb Electron Configurations and Bond Orders Just as with atoms, we can write a molecular electron configuration for O2 2*224*2 We can also calculate the OO bond order: 1 BO # bonding e # anti-bonding e 2 1 8 4 2 2 LCAO MO theory also predicts (correctly) that O2 has two unpaired electrons. Orbital Mixing Orbitals of similar but unequal energies can interact if they have the same symmetry The 2s and 2pz orbitals form MOs with the same symmetry (g and u). sp mixing causes the g and u MOs to be pushed apart in energy:

The and orbitals change order! Orbital Mixing The size of the effect depends on the 2s2p energy difference . small Zeff = small energy difference = large sp mixing order changes large Zeff = large energy difference = small sp mixing MOs of Homonuclear Diatomic Molecules The MO picture of homonuclear diatomic molecules depends on the amount of sp mixing.

Li2, Be2, B2, C2, N2 O2, F2, Ne2 Bond Order and Bond Distance The MO bond order is the main factor controlling the internucelar distance. B2 2*22 BO = 1 F2 2*224*4 BO = 1 O2 2*224*3 BO = 1.5 C2 2*24 BO = 2 C22 2*242 BO = 3 N2 + 2*241 BO = 2.5 N2 2*242 BO = 3

O2 2*224*2 BO = 2 O 2+ 2*224*1 BO = 2.5 Relative AO Energies for MO Diagrams Photoelectron spectroscopy gives us a pretty good idea of the relative energies for AOs. B Li H Al Na C Be N 13.6 eV 1s He

B 2p C O 18.6 eV Ne 2s P Mg Al F Si Si S 3p 3s P S

N O F 40.2 eV Ne Cl Cl Ar Ar 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. * 13.6 eV 1s Energy nb H

2p 18.6 eV So HF has one bond and three lone electron pairs on fluorine nb 2s HF F 40.2 eV Relative AO Energies for MO Diagrams Photoelectron spectroscopy gives us a pretty good idea of the relative energies for AOs. Al B Li C

Be H 1s He Na 10.7 eV N B 19.4 eV 2p C O 15.8 eV F Ne 2s P Mg Al

Si S 3p 3s O F Ne Cl P S N 32.4 eV Si Cl Ar Ar Heteronuclear Diatomic Molecules: CO In molecules with more than one type of atom, MOs are formed from AOs that have different energies. Consider CO:

* LUMO is on carbon too! Energy * HOMO is on carbon 2pa 2pb Anti-bonding orbitals get polarized towards carbon * 2sa 2sb C CO

O Bonding orbitals get polarized towards oxygen 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 well see that symmetry will help us treat larger molecules in the LCAO-MO theory framework.

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