Chapter 9
Covalent Bonding:
Orbitals
EXERCISE!
Draw the Lewis structure for methane, CH4.
– What is the shape of a methane molecule?
tetrahedral
– What are the bond angles?
109.5o
H
H C H
H
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CONCEPT CHECK!
What is the valence electron configuration of a
carbon atom?
s2p2
Why can’t the bonding orbitals for methane be
formed by an overlap of atomic orbitals?
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Bonding in Methane
• Assume that the carbon atom has four equivalent
atomic orbitals, arranged tetrahedrally.
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Hybridization
• Mixing of the native atomic orbitals to form special
orbitals for bonding.
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sp3 Hybridization
• Combination of one s and three p orbitals.
• Whenever a set of equivalent tetrahedral atomic
orbitals is required by an atom, the localized electron
model assumes that the atom adopts a set of sp3
orbitals; the atom becomes sp3 hybridized.
• The four orbitals are identical in shape.
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Hybridization – mixing of two or more atomic
orbitals to form a new set of hybrid orbitals.
1. Mix at least 2 nonequivalent atomic orbitals (e.g. s
and p). Hybrid orbitals have very different shape
from original atomic orbitals.
2. Number of hybrid orbitals is equal to number of
pure atomic orbitals used in the hybridization
process.
3. Covalent bonds are formed by:
a. Overlap of hybrid orbitals with atomic orbitals
b. Overlap of hybrid orbitals with other hybrid
orbitals
Hybrid Orbitals
• Hybrid orbitals are orbitals used to describe
bonding that are obtained by taking
combinations of atomic orbitals of an isolated
atom.
In this case, a set of hybrids are
constructed from one “s” orbital and three
“p” orbitals, so they are called sp3 hybrid
orbitals.
The four sp3 hybrid orbitals take the shape
of a tetrahedron.
An Energy-Level Diagram Showing the Formation of
Four sp3 Orbitals
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Formation of sp3 Hybrid Orbitals
SP3 Hybridization
https://www.khanacademy.org/science/organi
c-chemistry/gen-chemreview/hybridization/v/sp3-hybridizedorbitals-and-sigma-bonds
EXERCISE!
Draw the Lewis structure for C2H4 (ethylene)?
– What is the shape of an ethylene molecule?
trigonal planar around each carbon atom
– What are the approximate bond angles around the
carbon atoms?
120o
H
H
H
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C C
H
13
CONCEPT CHECK!
Why can’t sp3 hybridization account for the
ethylene molecule?
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sp2 Hybridization
• Combination of one s and two p orbitals.
• Gives a trigonal planar arrangement of atomic
orbitals.
• One p orbital is not used.
– Oriented perpendicular to the plane of the sp2
orbitals.
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Formation of sp2 Hybrid Orbitals
Sigma (Σ) Bond
• Electron pair is shared in an area centered on a line
running between the atoms.
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Pi (Π) Bond
• Forms double and triple bonds by sharing electron
pair(s) in the space above and below the σ bond.
• Uses the unhybridized p orbitals.
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Multiple Bonding
• To describe the multiple bonding in ethene,
we must first distinguish between two kinds of
bonds.
A s (sigma) bond is a “head-to-head”
overlap of orbitals with a cylindrical shape
about the bond axis. This occurs when two
“s” orbitals overlap or “p” orbitals overlap
along their axis.
A p (pi) bond is a “side-to-side” overlap of
parallel “p” orbitals, creating an electron
distribution above and below the bond axis.
Multiple Bonding
• Now imagine that the atoms of ethene move
into position.
Two of the sp2 hybrid orbitals of each
carbon overlap with the 1s orbitals of the
hydrogens.
The remaining sp2 hybrid orbital on each
carbon overlap to form a s bond.
Multiple Bonding
• The remaining “unhybridized” 2p orbitals on
each of the carbon atoms overlap side-to-side
forming a p bond.
You therefore describe the carbon-carbon
double bond as one s bond and one p
bond.
Pi bond (p) – electron density above and below plane of nuclei
of the bonding atoms
Sigma bond (s) – electron density between the 2 atoms
An Orbital Energy-Level Diagram
for sp2 Hybridization
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The Hybridization of the s, px,
and py Atomic Orbitals
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Formation of C=C Double Bond in
Ethylene
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EXERCISE!
Draw the Lewis structure for CO2.
– What is the shape of a carbon dioxide molecule?
linear
– What are the bond angles?
180o
O C O
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sp Hybridization
• Combination of one s and one p orbital.
• Gives a linear arrangement of atomic orbitals.
• Two p orbitals are not used.
– Needed to form the π bonds.
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Formation of sp Hybrid Orbitals
The Orbital Energy-Level Diagram for the Formation
of sp Hybrid Orbitals on Carbon
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When One s Orbital and One p Orbital are Hybridized, a Set
of Two sp Orbitals Oriented at 180 Degrees Results
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The Orbitals for CO2
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EXERCISE!
Draw the Lewis structure for PCl5.
– What is the shape of a phosphorus pentachloride
molecule?
trigonal bipyramidal
– What are the bond angles?
Cl Cl
o
o
90 and 120
Cl
P
Cl
Cl
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dsp3 Hybridization
• Combination of one d, one s, and three p orbitals.
• Gives a trigonal bipyramidal arrangement of five
equivalent hybrid orbitals.
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The Orbitals Used to Form the
Bonds in PCl5
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EXERCISE!
Draw the Lewis structure for XeF4.
– What is the shape of a xenon tetrafluoride
molecule?
octahedral
– What are the bond angles?
F
90o and 180o
F Xe
F
F
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d2sp3 Hybridization
• Combination of two d, one s, and three p orbitals.
• Gives an octahedral arrangement of six equivalent
hybrid orbitals.
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How is the Xenon Atom in XeF4
Hybridized?
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CONCEPT CHECK!
Draw the Lewis structure for HCN.
Which hybrid orbitals are used?
Draw HCN:
– Showing all bonds between atoms.
– Labeling each bond as σ or π.
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CONCEPT CHECK!
Determine the bond angle and expected
hybridization of the central atom for each of the
following molecules:
NH3
SO2
KrF2
CO2
ICl5
NH3 – 109.5o, sp3
SO2 – 120o, sp2
KrF2 – 90o, 120o, dsp3
CO2 – 180o, sp
ICl5 – 90o, 180o, d2sp3
How do I predict the hybridization of the central atom?
1. Draw the Lewis structure of the molecule.
2. Count the number of lone pairs AND the number of
atoms bonded to the central atom
# of Lone Pairs
+
# of Bonded Atoms
Hybridization
Examples
2
sp
BeCl2
3
sp2
BF3
4
sp3
CH4, NH3, H2O
5
sp3d
PCl5
6
sp3d2
SF6
Hybrid Orbitals
Hybrid
Geometric
Orbitals
Arrangements
sp
Linear
Number of Example
Orbitals
2
Be in BeF2
sp2
Trigonal planar
3
B in BF3
sp3
Tetrahedral
4
C in CH4
sp3d
Trigonal bipyramidal
5
P in PCl5
sp3d2
Octahedral
6
S in SF6
Using the Localized Electron
Model
• Draw the Lewis structure(s).
• Determine the arrangement of electron pairs using
the VSEPR model.
• Specify the hybrid orbitals needed to accommodate
the electron pairs.
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• Regards a molecule as a collection of nuclei and
electrons, where the electrons are assumed to
occupy orbitals much as they do in atoms, but
having the orbitals extend over the entire
molecule.
• The electrons are assumed to be delocalized
rather than always located between a given pair
of atoms.
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• The electron probability of both molecular
orbitals is centered along the line passing through
the two nuclei.
– Sigma (σ) molecular orbitals (MOs)
• In the molecule only the molecular orbitals are
available for occupation by electrons.
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Molecular Orbital Theory
• Molecular orbital theory is a theory of the
electronic structure of molecules in terms of
molecular orbitals, which may spread over
several atoms or the entire molecule.
As atoms approach each other and their
atomic orbitals overlap, molecular orbitals
are formed.
In the quantum mechanical view, both a
bonding and an antibonding molecular
orbital are formed.
Molecular Orbital Theory
• https://www.khanacademy.org/science/organi
c-chemistry/conjugation-diels-alder-motheory/molecular-orbital-theory/v/intro-tomolecular-orbital-mo-theory
Molecular Orbital Theory
• For example, when two hydrogen atoms bond,
a s1s (bonding) molecular orbital is formed
as well as a s1s* (antibonding) molecular
orbital.
The following slide illustrates the relative
energies of the molecular orbitals compared
to the original atomic orbitals.
Because the energy of the two electrons is
lower than the energy of the individual atoms,
the molecule is stable.
H atom
H2 molecule
H atom
s1s*
1s
1s
s1s
Energy levels of bonding and antibonding molecular
orbitals in hydrogen (H2).
A bonding molecular orbital has lower energy and greater
stability than the atomic orbitals from which it was formed.
An antibonding molecular orbital has higher energy and
lower stability than the atomic orbitals from which it was
formed.
Two Possible Interactions Between Two Equivalent p Orbitals
The arrows
show the
occupation of
molecular
orbitals by the
valence
electrons in N2.
Molecular Orbital (MO) Configurations
1. The number of molecular orbitals (MOs) formed is always
equal to the number of atomic orbitals combined.
2. The more stable the bonding MO, the less stable the
corresponding antibonding MO.
3. The filling of MOs proceeds from low to high energies.
4. Each MO can accommodate up to two electrons.
5. Use Hund’s rule when adding electrons to MOs of the
same energy.
6. The number of electrons in the MOs is equal to the sum of
all the electrons on the bonding atoms.
Sigma Bonding and Antibonding
Orbitals
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Bond Order
• Larger bond order means greater bond strength.
# of bonding e   # of antibonding e 
Bond order =
2
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Example: H2
2  0
Bond order =
=1
2
Example: H2–
2  1 1
Bond order =
=
2
2
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Homonuclear Diatomic
Molecules
• Composed of 2 identical atoms.
• Only the valence orbitals of the atoms contribute
significantly to the molecular orbitals of a
particular molecule.
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Pi Bonding and Antibonding
Orbitals
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Paramagnetism
• Paramagnetism – substance is attracted into the
inducing magnetic field.
– Unpaired electrons (O2)
• Diamagnetism – substance is repelled from the
inducing magnetic field.
– Paired electrons (N2)
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Apparatus
Used to
Measure the
Paramagneti
sm of a
Sample
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Molecular Orbital Summary of Second Row Diatomic
Molecules
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Heteronuclear Diatomic
Molecules
• Composed of 2 different atoms.
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Heteronuclear Diatomic
Molecule: HF
• The 2p orbital of fluorine is at a lower energy than
the 1s orbital of hydrogen because fluorine binds
its valence electrons more tightly.
– Electrons prefer to be closer to the fluorine
atom.
• Thus the 2p electron on a free fluorine atom is at
a lower energy than the 1s electron on a free
hydrogen atom.
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Orbital Energy-Level Diagram for
the HF Molecule
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Heteronuclear Diatomic
Molecule: HF
• The diagram predicts that the HF molecule should
be stable because both electrons are lowered in
energy relative to their energy in the free
hydrogen and fluorine atoms, which is the driving
force for bond formation.
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The Electron Probability Distribution in the Bonding
Molecular Orbital of the HF Molecule
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Heteronuclear Diatomic
Molecule: HF
• The σ molecular orbital containing the bonding
electron pair shows greater electron probability
close to the fluorine.
• The electron pair is not shared equally.
• This causes the fluorine atom to have a slight
excess of negative charge and leaves the
hydrogen atom partially positive.
• This is exactly the bond polarity observed for HF.
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Delocalization
• Describes molecules that require resonance.
• In molecules that require resonance, it is the π
bonding that is most clearly delocalized, the σ
bonds are localized.
• p orbitals perpendicular to the plane of the
molecule are used to form π molecular orbitals.
• The electrons in the π molecular orbitals are
delocalized above and below the plane of the
molecule.
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Resonance in Benzene
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The Sigma System for Benzene
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The Pi System for Benzene
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Delocalized molecular orbitals are not confined between
two adjacent bonding atoms, but actually extend over three
or more atoms.
Electron density above and below the plane of the
benzene molecule.
Pi Bonding in the Nitrate Ion
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• Can be used to determine the relative energies of
electrons in individual atoms and molecules.
• High-energy photons are directed at the sample, and
the kinetic energies of the ejected electrons are
measured.
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