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Chapter 9

Molecular Orbital Theory

Molecular Orbital Theory

Lewis structures and valence bond theory fail to predict some important properties of molecules.

Paramagnetism is a result of a molecule’s electron configuration. Species that contain one or more unpairedelectrons are paramagnetic.

Paramagneticspecies are attracted to magnet fields.

The Lewis structure for O2 shows

no unpaired electrons.

O2 exhibits paramagnetism.

Molecular Orbital Theory

Lewis structures and valence bond theory fail to predict some important properties of molecules.

Species that contain paired electrons are diamagnetic.

Diamagnetic species are weakly repelled by magnetic fields.

Nitrogen, N2, is diamagnetic.

Molecular Orbital Theory

Another bonding theory is needed to describe the paramagnetism of O2.

In molecular orbital theory, the atomic orbitals combine to form new

orbitals that are the “property” of the entire molecule.

The new orbitals are called molecular orbitals.

Molecular orbitals have characteristics similar to atomic and hybrid orbitals:

specific shapes

specific energies

accommodate a maximum of 2 electrons each

electron filling follows the Pauli exclusion principle

the number of molecular orbitals obtained equals the number of orbitals combined

Bonding and Antibonding Molecular Orbitals

H2 is the simplest homonuclear diatomic molecule.

Valence bond theory:

 H2 forms when from the overlap of the 1s orbitals.

Molecular orbital theory:

 H2 forms when the 1s orbitals combine to give molecular orbitals.  Molecular orbitals result from the constructive and destructivecombination of

atomic orbitals.

Molecular Orbital Theory

Constructive combination of the two 1s orbitals gives rise to a molecular orbital that lies along the internuclear axis.

Constructive combination increases the electron density between the two nuclei.

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Bonding and Antibonding Molecular Orbitals

Destructive combination of the two 1s orbitals gives rise to a molecular orbital that lies along the internuclear axis, but does not lie between the two nuclei.

Electron density in this molecular orbital pulls the two nuclei in opposite directions.

This molecular orbital is referred to as an antibonding

molecular orbital.

Bonding and Antibonding Molecular Orbitals

Molecular orbitals that lie along the internuclear axis are referred to as σ molecular orbitals.

Examples:

σ1s bonding molecular orbital from the combination of two 1s

orbitals

σ*1s antibonding molecular orbital from the combination of two 1s

orbitals

The asterisk distinguishes an antibonding molecular orbital from a bonding orbital.

The Molecular Orbital Model

The Combination of Hydrogen 1

s

Atomic Orbitals

to Form Molecular Orbitals

Size, Shape,

and Energy

of H

2

MOs

Sigma (

s

)

MOs

MO1 MO2

bonding bonding

antibonding anti bonding

σ Molecular Orbitals

Molecular orbitals have specific energies.

Electrons in bonding molecular orbitals stabilize the molecule and are lower in energy than the isolated atomic orbitals.

Electrons in antibonding molecular orbitals destabilize the molecule and are higher in energy than the isolated atomic orbitals.

Two Types of Molecular Orbitals in H

2

• A

bonding

molecular orbital is

lower in

energy

than the atomic orbitals of which it is

composed.

– Electrons in this type of orbital favor the

molecule; that is, they

favor bonding

.

• An

antibonding

molecular

orbital is

higher

in energy

than the atomic orbitals of which it

is composed.

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Bonding

and

Antibonding

Molecular Orbitals (MOs)

bonding

antibonding

A Molecular

Orbital

Energy-Level

Diagram for

the H

2

Molecule

The Molecular Orbital

Energy-Level Diagram for H

2

-

Ion

molecules of H

How do the bond strengths in

2

and H

2-

compare?

H

2

H

2

-Bond Order

The bond order

indicates how stable a molecule is.

Larger Bond Order

Means Greater Bond Strength

No. of e in bonding orbitals No. of e in antibonding orbitals

bond order =

2

Bond Order

H2

No. of e in bonding orbitals No. of e in antibonding orbitals bond order =

2

bond order  201

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What is the Bond Order of H

2

?

H

2

2 0

Bond order =

= 1

2

What is the Bond Order of H

2

-

?

H

2

-2 1

1

Bond order =

=

2

2

Is He

2

stable?

What is the Bond Order?

He

2

Bond Order

He2

No. of e in bonding orbitals No. of e in antibonding orbitals bond order =

2

bond order  220

2 According to molecular orbital theory, HeNOT a stable molecule and does not exist. 2 is

The Molecular Orbital Energy-Level

Diagram of the Li

2

Molecule

What about the Be

2

Molecule?

π Molecular Orbitals

p atomic orbitals also form molecular orbitals by both constructive and destructive combination.

The orientations of px, py, and pz give rise to two different types of

molecular orbitals:

σ molecular orbitals – electron density along the internuclear axis

px orbitals point towards each other bonding and antibonding σ

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π Molecular Orbitals

p atomic orbitals also form molecular orbitals by both constructive and destructive combination.

π molecular orbitals – electron density above and below the internuclear axis

Molecular Orbital Theory

Molecular orbitals resulting from the combination of p atomic orbitals are higher than those resulting from the combination of s atomic orbitals.

This order of orbital energies assumes no mixing of s and p orbitals.

s orbitals only interact with s orbitals

p orbitals only interact with p orbitals

This is found in O2, Fe2, Ne2.

Molecular Orbital Theory

Molecular orbitals resulting from the combination of p atomic orbitals are higher than those resulting from the combination of s atomic orbitals.

This order of orbital energies assumes some mixing of s and p orbitals.

This arrangement of orbitals is found in Li2, B2, C2 and N2.

Molecular Orbital Diagrams

Filling molecular orbital diagrams follows the same rules as the filling of atomic orbitals.

1) Lower energy orbitals fill first.

2) Each orbital can accommodate a maximum of two electrons with

opposite spin.

3) Hund’s rule is obeyed.

Molecular Orbital Diagrams

Molecular orbital diagrams for second-period homonuclear diatomic molecules.

Worked Example 7.8

Strategy Start with the molecular orbital diagram for O2 and add an

electron to the lowest-energy molecular orbital available.

The superoxide ion (O2-) has been implicated in a number of degenerative

conditions, including aging and Alzheimer’s disease. Using molecular orbital

theory, determine whether (O2-) is paramagnetic or diamagnetic, and then

calculate its bond order.

Solution In this case, either of the two singly occupied π*2p

orbitals can accommodate an additional electron. This gives a molecular orbital diagram in which there is one unpaired electron,

making (O2-) paramagnetic. The new diagram has six electrons in

bonding molecular orbitals and three in antibonding molecular orbitals. We can ignore the electrons in the σ2s and σ*2s orbitals

because their contributions to the bond order cancel each other. The bond order is (6 – 3)/2 = 1.5.

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Lewis Theory

Strength:

 qualitative prediction of bond strength and bond length Weakness:

 two dimensional model, real molecules are three dimensional

 fails to explain why bonds form

Valence-Shell Electron-Pair Repulsion Model

Strength:

 predict the shape of many molecules and polyatomic ions Weakness:

 fails to explain why bonds form (based on Lewis theory)

Bonding Theories and Descriptions of Molecules

with Delocalized Bonding Bonding Theories and Descriptions of Molecules with Delocalized Bonding

Valence Bond Theory

Strength:

covalent bonds form when atomic orbitals overlap Weakness:

fails to explain the bonding in many molecules

Hybridization of Atomic Orbitals

Strength:

an extension of valence bond theory. Using hybrid orbitals it is possible to explain the bonding and geometry of more molecules

Weakness:

fails to predict some important properties, such as magnetism

Bonding Theories and Descriptions of Molecules with Delocalized Bonding

Molecular Orbital Theory

Strength:

 accurately predict the magnetic and other properties of molecules Weakness:

 complex

Bonding Theories and Descriptions of Molecules with Delocalized Bonding

Some molecules are best described using a combination of models.

Benzene, C6H6, is represented with two resonance structures:

The π bonds in benzene are delocalized-- spread out over the entire

molecule.

Bonding Theories and Descriptions of Molecules with Delocalized Bonding

The π bonds in benzene are delocalized-- spread out over the entire

molecule.

Worked Example 7.9

Strategy The Lewis structure of the carbonate ion shows three electron domains

around the central C atom, so the carbon must be sp2 hybridized.

It takes three resonance structures to represent the carbonate ion CO32-:

None of the three, though, is a completely accurate description. As with benzene, the bonds that are shown in the Lewis structure as one double and two single are actually three equivalent bonds. Use a combination of valence bond theory and

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Worked Example 7.9 (cont.)

Solution Each of the sp2 hybrid orbitals on the C atom overlaps with a singly

occupied p orbital on an O atom, forming three σ bonds. Each O atom has an

additional, singly occupied p orbital perpendicular to the one involved in σ

bonding. The unhybridized p orbital on C overlaps with the p orbitals on O to

form π bonds, which have electron densities above and below the plane of the

molecule. Because the species can be represented by resonance structures, we

know that the π bonds are delocalized.

Think About It Although the Lewis structure of CO32- shows three electron

domains on one of the O atoms, we generally do not treat terminal atoms (those

References

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