COVALENT BONDING:
ORBITALS
Chapter 9
Hybridization
The mixing of atomic orbitals to form
special molecular orbitals for bonding.
The atoms are responding as needed to
give the minimum energy for the
molecule.
Molecular Geometry &
Hybridization
Parent geometry determines the hybridization.
Molecular structure is the actual geometry.
Energy-level diagram showing the formation of four sp3
hybrid orbitals.
09_158
z
z
x
x
y
y
s
z
py
x
pz
x
y
z
x
y
z
Hybridization y
px
z
x
y
z
z
x
y
x
y
sp3
gives a tetrahedral
arrangement
sp3
sp3
sp3
One 2s and three 2p orbitals hybridize to form a
new set of sp3 hybrid orbitals.
sp3 hybrid orbital
• 4 effective electron pairs.
• tetrahedral geometry.
• 109.5 o bond angle.
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H1s
sp3
sp3
H1s
C
H1s
sp3
sp3
H1s
The tetrahedral set of four sp3 orbitals of the
carbon atom share one electron each with the four
hydrogen atoms to make a methane molecule.
09_162
lone pair
sp
3
sp
3
N
H1s
H1s
sp
3
sp
3
H1s
The nitrogen atom in ammonia is sp3 hybridized.
A sigma () bond centers along the
internuclear axis.
A pi () bond occupies the space above
and below the internuclear axis.
H

H
C C
H
H
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2p
Hybridization
2p
sp 2
E
2s p
Orbitals in an isolated
carbon atom
Carbon orbitals in ethylene
An orbital energy-level diagram for sp2 hybridization.
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p orbital
sp2 orbital
sp2 orbital
sp2 orbital
In sp2 hybridization one p orbital remains unchanged
and lies perpendicular to the plane of the hybrid.
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H1 s
H1 s
sp 2
sp 2
C
C
sp 2
H1 s
sp 2
sp 2
sp 2
H1 s
The shared electron pair of in ethylene occupies
the region directly between the atoms to form a
sigma () bond.
sp2 hybrid orbital
• three effective electron pairs.
• trigonal planar geometry.
• 120 o bond angle.
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p orbital
p orbital
C
C
pi bond
sigma
bond
A carbon-carbon double bond consists of a  bond and
a  bond. The  bond is formed from unhybridized p
orbitals in the space above and below the  bond.
Pi and Sigma Bonds
 bonds consist of an electron pair
shared in the area centered between
the atoms.
 bonds occupy the space above and
below a line joining the atoms.
Pi and Sigma Bonds
 bonds allow rotation.
 bonds do not allow rotation.
09_168
sp 2
H 1s
sp 2
sp 2
sp 2
H 1s
C
C
2p
sp 2
sp 2
(a)
H
H
(b)
H
C
H
C
The orbitals used to form the bonds in ethylene.
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z
z
z
z
z
Hybridization
x
y
s
x
y
px
x
y
x
y
gives a linear
arrangement
180°
x
y
Two sp orbitals are formed when one s and one p orbital
are hybridized. They are oriented at 180o to each other.
sigma bond
(1 pair of electrons)
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O
pi bond
(1 pair of
electrons)
C
O
pi bond
(1 pair of
electrons)
(a)
O
C
O
(b)
The hybrid orbitals in the CO2 molecule.
sp hybrid orbital
• two effective electron pairs.
• linear geometry.
• 180 o bond angle.
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p
sp
N
sp
p
(a)
lone pair sigma bond lone pair
N
sp
N
sp sp
sp
(b)
N
N
(c)
The nitrogen molecule forms a triple bond -- one
 and two  bonds.
dsp3 hybrid orbitals
•
•
•
•
five effective electron pairs.
trigonal bipyramidal geometry.
90 o and 120 o bond angles.
hybrid orbitals are not all equivalent
as in the other types of hybridization.
• Phosphorus pentachloride
d2sp3 hybrid orbitals
•
•
•
•
six effective electron pairs.
octahedral geometry.
90 o bond angles.
Sulfur hexafluoride.
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Number of
Effective Pairs
Arrangement
of Pairs
Hybridization
Required
180°
2
Linear
sp
3
Trigonal
planar
sp2
120°
109.5°
4
Tetrahedral
sp3
90°
5
Trigonal
bipyramidal
dsp3
120°
90°
6
Octahedral
d2sp3
90°
The relationship of the number of effective pairs,
their spatial arrangement, and the hybrid orbitals.
The Localized Electron Model
-
Draw the Lewis structure(s)
-
Determine the arrangement of electron
pairs (VSEPR model).
-
Specify the necessary hybrid orbitals.
Deficiencies of the LEM Model
• Does not adequately explain
resonance.
• Does not work for odd-electron
molecules and ions.
• Assumes that all electrons are
localized about an atom.
• Gives no direct information about
bond energies.
Molecular Orbitals (MO)
Analagous to atomic orbitals for
atoms, MOs are the quantum
mechanical solutions to the
organization of valence electrons in
molecules. Electrons are considered
to be delocalized over the entire
molecule.
Types of MOs
bonding: lower in energy than the
atomic orbitals from which it is
composed.
antibonding: higher in energy than the
atomic orbitals from which it is
composed.
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Energy diagram
Electron probability distribution
HA
H2
HB
MO2
E
1s A
+
+
+
1s B
MO1
(a)
+
(b)
The molecular orbital energy diagram for the H2
molecule and the MO1 and MO2 orbitals formed.
MO1 = 1s and MO2 = 1s*.
Bond Order (BO)
Difference between the number of bonding
electrons and number of antibonding
electrons divided by two.
# bonding electrons  # antibonding electrons
BO =
2
Larger bond order means greater bond strength!
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B2
C2
N2
O2
2p*
 2p*
2p*
 2p*
2p
 2p
2p
 2p
2s*
 2s*
2s
 2s
F2
E
Magnetism
Para–
magnetic
Dia–
magnetic
Dia–
magnetic
Para–
magnetic
Dia–
magnetic
Bond order
1
2
3
2
1
Observed
bond
dissociation
energy
(kJ/mol)
290
620
942
495
154
Observed
bond
length
(pm)
159
131
110
121
143
The molecular orbital energy-level diagrams, bond orders,
bond energies, and bond lengths for diatomic molecules.
In order to participate in MOs,
atomic orbitals must overlap in
space. (Therefore, only valence
orbitals of atoms contribute
significantly to MOs.)
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Li
Li
1s
1s
2s
2s
The relative size of the lithium 1s and 2s orbitals.
The 1s orbital can be considered to be localized
and do not participate in bonding.
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B
B
(a)
(b)
(c)
(d)
The boron molecule will form one  and two 
bonds.
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*2p
Antibonding
2px
2px
(a)
2p
Bonding
*2p
Antibonding
2py
2p
2py
(b)
Bonding
The two p orbitals that overlap head on make two 
molecular orbitals -- one bonding and one antibonding.
The two p orbitals that lie parallel overlap to produce two
 molecular orbitals, one bonding and one antibonding.
Paramagnetism
- unpaired electrons
- attracted to induced magnetic field
- much stronger than diamagnetism
- B2 & O2
09_195
B2
C2
N2
O2
2p*
 2p*
2p*
 2p*
2p
 2p
2p
 2p
2s*
 2s*
2s
 2s
F2
E
Magnetism
Para–
magnetic
Dia–
magnetic
Dia–
magnetic
Para–
magnetic
Dia–
magnetic
Bond order
1
2
3
2
1
Observed
bond
dissociation
energy
(kJ/mol)
290
620
942
495
154
Observed
bond
length
(pm)
159
131
110
121
143
The molecular orbital energy-level diagrams, bond orders,
bond energies, and bond lengths for diatomic molecules.
Diamagnetism
- paired electrons
- repelled from induced magnetic field
- much weaker than paramagnetism
- C2 , N2 , & F2 .
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Balance
Glass tubing
Sample tube
Electromagnet
Apparatus used to measure the paramagnetism
of a sample. A paramagnetic sample will appear
heavier when the electromagnet is turned on.
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H
atom
HF
molecule
F
atom
*
1s
E
2p

A partial molecular orbital energy-level diagram
for the HF molecule. Bond order is 1 -- a single
bond.
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H nucleus
F nucleus
The electron probability distribution in the bonding
molecular orbital of the HF molecule.
Pi and Sigma Bonds
 bonds in a molecule are described as
being localized.
 bonds are considered to be delocalized
over the entire molecule.
NO2 Molecule
Draw the Lewis Structure, determine the
parent geometry, the actual geometry, and
the approximate bond angle.
NO+ ION
Draw the Lewis Structure, draw the
molecular orbital energy-level diagram,
determine the bond order, and the type of
magnetism for the NO+ ion.
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sp 2
H
C
H
H
C
sp 2
C
C
C
H
H
H1s
C
H
The  bonding system in the benzene molecule.
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H
H
H
H
(a)
H
H
H
H
H
H
H
H
(b)
The  molecular orbital system in benzene. The
electrons in the  orbitals are delocalized over the
ring of carbon atoms.
Outcomes of MO Model
1. As bond order increases, bond energy
increases and bond length decreases.
2. Bond order is not absolutely associated
with a particular bond energy.
3. N2 has a triple bond, and a
correspondingly high bond energy.
4. O2 is paramagnetic. This is predicted by
the MO model, not by the LE model,
which predicts diamagnetism.
Combining LE and MO
Models
 bonds can be described as being
localized.
 bonding must be treated as being
delocalized.