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 Orbitals Sigma Bond Formation

p

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

Ethene

s

and

p

bonds

Ethyne

s

and

p

bonds

Atomic and Molecular Orbitals

• In molecule, electrons occupy

molecular orbitals

surround the molecule.

which • The two 1s atomic orbitals combine to form two molecular orbitals, one bonding ( s ) and one antibonding ( s *). • This is an illustration of molecular orbital diagram of H 2.

• Notice that one electron from each atom is being “shared” to form a covalent bond. This is an example of orbital mixing. http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/main.html

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. Aufbau Principle • The maximum number of electrons in each molecular orbital is two. Pauli exclusion principle • One electron goes into orbitals of equal energy, with parallel spin, before they begin to pair up. Hund's Rule

Molecular Orbital Diagram (H

2

)

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Bond Order

Bond Order = # bonding electrons 2 # antibonding electrons 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 H 2 + H 2 and exist. Determine their bond orders and electron configurations.

s bond order = 1/2(1-0) = 1/2 H 2 + does exist s bond order = 1/2(2-1) = 1/2 H 2 does exist 1s 1s AO of H s MO of H 2 + AO of H s MO of H 2 -

Figure 11.21

The paramagnetic properties of O 2

MO Diagram for O

2 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 O 2 is therefore superior to the valence-bond model, which cannot explain this property of oxygen.

Molecular Orbital Diagram (HF)

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

Molecular Orbital Diagram (CH

4

)

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 (H

2

O)

Figure 11.16

s * 1s 1s 1s AO of He s 1s MO of He + AO of He +

He 2 + bond order = 1/2 MO diagram for He 2 + and He 2

s * 1s 1s 1s AO of He s 1s MO of He 2 AO of He

He 2 He 2 bond order = 0 does not exist!

Relative MO energy levels for Period 2 diatomic molecules.

MO energy levels for O 2 , F 2 , and Ne 2 MO energy levels for B 2 , C 2 , and N 2

SAMPLE PROBLEM 11.4

continued

N 2

s 2p

Using MO Theory to Explain Bond Properties

antibonding e lost

N 2 + O 2 O 2 +

s 2p bonding e lost p 2p s 2p p 2p p 2p p 2p s 2p 1/2(8-2)=3 s 2s s 2s 1/2(7-2)=2.5

bond orders 1/2(8-4)=2 s 2s s 2s 1/2(8-3)=2.5

Figure 11.17

2s

Li 2

1s s * 2s s * 2s s 2s s * 1s 2s 2s

Bonding in s-block homonuclear diatomic molecules.

s 2s s * 1s 1s s 1s

Li 2 bond order = 1

1s 2s

Be 2

1s s 1s

Be 2 bond order = 0

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.