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.
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.
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
2H
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 201
What is the Bond Order of H
2
?
H
22 0
Bond order =
= 1
2
What is the Bond Order of H
2
-
?
H
2-2 1
1
Bond order =
=
2
2
Is He
2stable?
What is the Bond Order?
He
2Bond Order
He2
No. of e in bonding orbitals No. of e in antibonding orbitals bond order =
2
bond order 220
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
2Molecule
What about the Be
2Molecule?
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
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.
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
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