Molecular Orbital Theory

The goal of molecular orbital theory is to describe molecules in a similar way to how we describe atoms, that is, in terms of orbitals, orbital diagrams, and electron configurations.

Atomic Orbitals• Orbital Mixing

– When atoms share electrons to form a bond, their atomic orbitals mix to form molecular bonds. In order for these orbitals to mix they must:

• Have similar energy levels.• Overlap well.• Be close together.

This is an example of orbital mixing. The two atoms share one electron each from there outer shell. In this case both 1s orbitals overlap and share their valence electrons.

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Molecular OrbitalsSigma Bond Formation

p atomic orbitals overlap to form sigma () and pi () molecular orbitals

Ethene and bonds

Ethyne and bonds

Atomic and Molecular Orbitals• In molecule, electrons occupy molecular orbitals which

surround the molecule.• The two 1s atomic orbitals combine to form two

molecular orbitals, one bonding () and one antibonding (*).

http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/main.html

• This is an illustration of molecular orbital diagram of H2.• Notice that one electron from each atom is being “shared” to form a covalent bond. This is an example of orbital mixing.

Molecular Orbital Theory

• Each line in the diagram represents an orbital.

• The molecular orbital volume encompasses the whole molecule.

• The electrons fill the molecular orbitals of molecules like electrons fill atomic orbitals in atoms.

Molecular Orbital and Valence Bond Theory

• Electrons go into the lowest energy orbital available.

• The maximum number of electrons in each molecular orbital is two.

• One electron goes into orbitals of equal energy, with parallel spin, before they begin to pair up.

Aufbau Principle

Pauli exclusion principle

Hund's Rule

Molecular Orbital Diagram (H2)

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Bond Order

# bonding - # antibonding electrons electrons

Bond Order =

2

The bond order is an indication of bond strength

Greater bond order = Greater bond strength

The bond order equals the number of bonds formed in the molecule

Predicting Species Stability Using MO Diagrams

PROBLEM: Use MO diagrams to predict whether H2+ and

H2- exist. Determine their bond orders and

electron configurations.

1s1s

AO of HAO of H

1s1s

AO of HAO of H

MO of HMO of H22++

bond order = 1/2(1-0) = 1/2

HH22++ does exist does exist

MO of HMO of H22--

bond order = 1/2(2-1) = 1/2

H2- does exist

Figure 11.21

The paramagnetic properties of O2

MO Diagram for O2

http://www.chem.uncc.edu/faculty/murphy/1251/slides/C19b/sld027.htm

MO vs. VB

• Atoms or molecules in which the electrons are paired are diamagnetic.

• Those that have one or more unpaired electrons are paramagnetic, attracted to a magnetic field.

• Liquid oxygen is attracted to a magnetic field and can actually bridge the gap between the poles of a horseshoe magnet.

• The molecular orbital model of O2 is therefore superior to the valence-bond model, which cannot explain this property of oxygen.

Molecular Orbital Diagram (HF)

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Molecular Orbital Diagram (CH4)

So far, we have only look at molecules with two atoms. MO diagrams can also be used for larger molecules.

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Molecular Orbital Diagram (H2O)

Figure 11.16 MO diagram for He2+ and He2

En

erg

y

MO of He+

*1s

1s

AO of He+

1s

MO of He2

AO of He

1s

AO of He

1s

*1s

1s

En

erg

y

He2+ bond order = 1/2 He2 bond order = 0

AO of He

1s

He2 does not exist!

Relative MO energy levels for Period 2 diatomic molecules.

MO energy levels for O2, F2, and Ne2

MO energy levels for B2, C2, and N2

SAMPLE PROBLEM 11.4 Using MO Theory to Explain Bond Properties

continued

2s

2s

2p

2p

2p

2p

N2 N2+ O2 O2

+

bond orders

1/2(8-2)=3 1/2(7-2)=2.5 1/2(8-4)=2 1/2(8-3)=2.5

2s

2s

2p

2p

2p

2p

bonding e- lost

antibonding e- lost

*2s

2s

2s2s

1s

*1s

1s

1s

Figure 11.17

1s

*1s

1s

1s

2s 2s

*2s

2s

Li2 bond order = 1 Be2 bond order = 0

Bonding in s-block homonuclear

diatomic molecules.

En

erg

y

Li2Be2

Conclusions

• Bonding electrons are localized between atoms.

• Atomic orbitals overlap to form bonds.• Two electrons of opposite spin can occupy

the overlapping orbitals.• Bonding increases the probability of

finding electrons in between atoms.• It is also possible for atoms to form ionic

and metallic bonds.