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Chapter 11
Theories of Covalent Bonding
11-1
Theories of Covalent Bonding
11.1 Valence bond (VB) theory and orbital hybridization
11.2 The mode of orbital overlap and types of
covalent bonds
11.3 Molecular orbital (MO) theory and electron delocalization
11-2
The three models of chemical bonding
Figure 9.2
11-3
Covalent bond
formation in H2
Figure 9.11
11-4
Key Principles
Structure dictates shape
Shape dictates function
shape = conformation
Molecules can assume more than one
shape (conformation) in solution!
11-5
The Complementary Shapes of an Enzyme and Its Substrate
11-6
Valence-shell Electron-Pair Repulsion (VSEPR) Theory
A method to predict the shapes of molecules from their
electronic structures (Lewis structures do not depict
shape)
Basic principle: each group of valence electrons around a central
atom is located as far away as possible from the others in order to
minimize repulsions
Both bonding and non-bonding valence electrons around
the central atom are considered.
AXmEn symbolism: A = central atom, X = surrounding atoms,
E = non-bonding electrons (usually a lone pair)
11-7
A periodic table of partial ground-state electron configurations
Figure 8.12
11-8
The steps in determining a molecular shape
molecular
formula
Step 1
Lewis
structure
Step 2
Count all e- groups around the
central atom A
electron-group
arrangement
Step 3
bond
angles
Figure 10.12
11-9
Note lone pairs and
double bonds
Count bonding and
Step 4 non-bonding egroups separately.
molecular
shape
(AXmEn)
Steps to convert a molecular formula into a Lewis structure
molecular
formula
Step 1
atom
placement
Place the atom with the
lowest EN in the center
Step 2
sum of
valence e-
Add A-group
numbers
Step 3
Draw single bonds and
subtract 2e- for each bond
remaining
valence eFigure 10.1
11-10
Step 4 Give each
atom 8e(2e- for H)
Lewis
structure
Electron-group repulsions and the five basic molecular shapes
Figure 10.5
Ideal bond angles are shown for each shape.
11-11
The three molecular shapes of the tetrahedral
electron-group arrangement
Examples:
CH4, SiCl4,
SO42-, ClO4-
Examples:
NH3
PF3
ClO3
H 3 O+
Figure 10.8
11-12
Examples:
H 2O
OF2
SCl2
The four molecular shapes of the trigonal bipyramidal
electron-group arrangement
Examples:
Examples:
SF4
PF5
XeO2F2
AsF5
IF4+
SOF4
IO2F2Examples:
Examples:
XeF2
ClF3
I3-
BrF3
IF2Figure 10.10
11-13
VSEPR
(Valence Shell Electron Pair RepulsionTheory)
Accounts for molecular shapes by assuming that electron
groups tend to minimize their repulsions
Does not show how shapes can be explained from
the interactions of atomic orbitals
11-14
The Central Themes of Valence
Bond (VB) Theory
Basic Principle
A covalent bond forms when the orbitals of two atoms overlap
and are occupied by a pair of electrons that have the highest
probability of being located between the nuclei.
Three Central Themes
A set of overlapping orbitals has a maximum of two electrons
that must have opposite spins.
The greater the orbital overlap, the stronger (more stable) the
bond.
The valence atomic orbitals in a molecule are different from
those in isolated atoms (hybridization).
11-15
Orbital overlap and
spin pairing in three
diatomic molecules
hydrogen, H2
hydrogen fluoride, HF
Figure 11.1
fluorine, F2
11-16
Linus Pauling
Proposed that valence atomic orbitals in the molecule are
different from those in the isolated atoms
Mixing of certain combinations of atomic orbitals
generates new atomic orbitals
Process of orbital mixing = hybridization; generates
hybrid orbitals
11-17
Hybrid Orbitals
Key Points
The number of hybrid orbitals obtained equals the number of
atomic orbitals mixed.
The type of hybrid orbitals obtained varies with the types of
atomic orbitals mixed.
Types of Hybrid Orbitals
sp
11-18
sp2
sp3
sp3d
sp3d2
The sp hybrid orbitals in gaseous BeCl2
atomic
orbitals
hybrid
orbitals
Figure 11.2
11-19
orbital box diagrams
VSEPR
predicts a
linear
shape
The sp hybrid orbitals in gaseous BeCl2 (continued)
orbital box diagrams with orbital contours
Figure 11.2
11-20
The sp2 hybrid orbitals in BF3
VSEPR predicts
a trigonal planar
shape
Figure 11.3
11-21
The sp3 hybrid orbitals in CH4
Figure 11.4
11-22
VSEPR
predicts a
tetrahedral
shape
The sp3 hybrid orbitals in NH3
VSEPR predicts
a trigonal
pyramidal shape
Figure 11.5
11-23
The sp3 hybrid orbitals in H2O
VSEPR predicts
a bent (V) shape
Figure 11.5
11-24
The sp3d hybrid orbitals in PCl5
Figure 11.6
11-25
VSEPR predicts
a trigonal bipyramidal
shape
The sp3d2 hybrid orbitals in SF6
VSEPR predicts an
octahedral shape
Figure 11.7
11-26
11-27
Conceptual steps from molecular formula to the
hybrid orbitals used in bonding
Step 1
molecular
formula
Step 2
Lewis
structure
Figure 10.1
Step 3
molecular shape
and e- group
arrangement
Figure 10.12
Figure 11.8
11-28
hybrid
orbitals
Table 11.1
SAMPLE PROBLEM 11.1
PROBLEM:
Postulating Hybrid Orbitals in a Molecule
Use partial orbital diagrams to describe how the mixing of
atomic orbitals on the central atoms leads to hybrid orbitals in
each of the following molecules.
(a) methanol, CH3OH
PLAN:
Use Lewis structures to establish the arrangement of groups
and the shape of each molecule. Postulate the hybrid orbitals.
Use partial orbital box diagrams to indicate the hybrid for the
central atoms.
SOLUTION:
H
(a) CH3OH
H
11-29
(b) sulfur tetrafluoride, SF4
C O
H H
The groups around C are
arranged as a tetrahedron.
O has a tetrahedral arrangement
with two non-bonding e- pairs.
SAMPLE PROBLEM 11.1 (continued)
2p
2s
single C atom
2p
sp3
hybridized C atom
2s
single O atom
sp3
hybridized O atom
(b) SF4 has a seesaw shape with four bonding and one non-bonding e- pairs.
F
F S
F
F
distorted
trigonal
bipyramidal
3d
3p
sp3d
3s
11-30
3d
S atom
hybridized
S atom
Covalent Bonds Between Carbon Atoms - Single Bonds
s bonds in ethane, CH3-CH3
both carbons are sp3
hybridized
s-sp3 overlaps to s bonds
sp3-sp3 overlap to form a s bond
~109.5o
Figure 11.9
11-31
free rotation
relatively even
distribution of electron
density over all s
bonds
Covalent Bonds Between Carbon Atoms - Double Bonds
s and  bonds in ethylene, C2H4
overlap in one position - s
p overlap - 
hindered rotation
~120o
electron density
11-32
Figure 11.10
Covalent Bonds Between Carbon Atoms - Triple Bonds
s and  bonds in acetylene, C2H2
overlap in one position - s
p overlap - 
hindered rotation
180o
Figure 11.11
11-33
Video: Hybridization
11-34
Describing bonding in molecules with
multiple bonds
SAMPLE PROBLEM 11.2
PROBLEM:
PLAN:
Describe the types of bonds and orbitals in acetone, (CH3)2CO.
Use the Lewis structure to determine the arrangement of groups and
the shape at each central atom. Postulate the hybrid orbitals, taking
note of multiple bonds and their orbital overlaps.
SOLUTION:
sp3
sp2
hybridized
sp2
O
O
sp3 hybridized H
C
sp2
H
C
C
H H H H
sp2 hybridized
O
2
sp3
H sp
2
sp2 C sp
C
sp3 H
3
sp
H sp3
C
sp3
C
3
sp
H
3
sp 3 H
sp
s bonds
11-35
H
H3 C
CH3
bond
Restricted rotation in -bonded molecules
cis
trans
No spontaneous interconversion between
cis and trans forms (isomers) in solution at room temperature!
11-36
Figure 11.12
Limitations of VB Theory
Inadequately explains magnetic/spectral properties
Inadequately treats electron delocalization
VB theory assumes a localized bonding model
11-37
Molecular Orbital (MO) Theory
A delocalized bonding model
A quantum-mechanical treatment of molecules
similar to that used for isolated atoms
Invokes the concept of molecular orbitals (MOs)
(extension of atomic orbitals)
Exploits the wave-like properties of matter (electrons)
11-38
Central themes of molecular
orbital (MO) theory
A molecule is viewed on a quantum mechanical level as a
collection of nuclei surrounded by delocalized molecular orbitals.
Atomic wave functions are summed to obtain
molecular wave functions.
If wave functions reinforce each other, a bonding MO is formed
(region of high electron density exists between the nuclei).
If wave functions cancel each other, an antibonding MO is formed
(a node of zero electron density occurs between the nuclei).
11-39
An analogy between light waves and atomic wave functions
Amplitudes of wave
functions are added
Figure 11.13
11-40
Amplitudes of wave
functions are
subtracted
Contours and energies of the bonding and antibonding
molecular orbitals in H2
Figure 11.14
11-41
number of AOs combined = number of MOs produced
Bonding MO: lower in energy than isolated atoms
Antibonding MO: higher in energy than isolated atoms
To form MOs, AOs must have similar energy and orientation
Sigma (s) and pi () bonds are denoted as before; a star (asterick)
is used to denote antibonding MOs.
11-42
Molecular orbital diagram for
the H2 molecule
MOs are filled
in the same
sequence
as for AOs
(aufbau and
exclusion
principles, Hund’s
rule)
Figure 11.15
11-43
The MO bond order
[1/2 (no. of e- in bonding MOs) - (no. of e- in antibonding MOs)]
higher bond order = stronger bond
Has predictive power!
11-44
MO diagrams for He2+ and He2
s*1s
1s
1s
Energy
Energy
s*1s
1s
1s
s1s
AO of
He
MO of
He+
s1s
AO of
He+
AO of
He
He2+ bond order = 1/2
AO of
He
He2 bond order = 0
can exist!
11-45
MO of
He2
cannot exist!
Figure 11.16
SAMPLE PROBLEM 11.3
PROBLEM:
PLAN:
Predicting species stability using MO diagrams
Use MO diagrams to predict whether H2+ and H2- can exist.
Determine their bond orders and electron configurations.
Use H2 as a model and accommodate the number of electrons in
bonding and antibonding orbitals. Calculate the bond order.
SOLUTION:
s
1s
bond order
= 1/2(1-0)
= 1/2
s
H2+ does exist!
1s
1s
AO of H
bond order
= 1/2(2-1)
= 1/2
AO of
s
MO of H2+
configuration is (s1s)1
11-46
H+
H2- does exist!
1s
AO of H-
AO of H
s
MO of H2configuration is (s1s)2(s1s)1
Figure 11.17
s*2s
s*2s
2s
Energy
2s
Li2
s2s
Bonding in s-block
homonuclear
diatomic molecules
1s
1s
s1s
Li2 bond order = 1
s2s
Be2
s*1s
s*1s
11-47
2s
2s
1s
1s
s1s
Be2 bond order = 0
Bonding and antibonding MOs for core
electrons cancel = no net contribution to bonding
Only MO diagrams showing MOs created by
combining valence-electron AOs are important.
11-48
Contours and energies of s and  MOs through
combinations of 2p atomic orbitals
end-to-end
overlap
side-to-side
overlap
Figure 11.18
11-49
Relative energies
s2p < 2p < *2p < s*2p
More effective end-to-end interaction
relative to side-to-side in bonding MOs
11-50
Relative MO energy levels for Period 2 homonuclear
diatomic molecules
without 2s-2p
mixing
Figure 11.19
11-51
MO energy levels
for O2, F2 and Ne2
with 2s-2p
mixing
MO energy levels
for B2, C2 and N2
MO occupancy
and molecular
properties for B2
through Ne2
Figure 11.20
11-52
The paramagnetic
properties of O2
Explained by
MO diagram
Figure 11.21
11-53
SAMPLE PROBLEM 11.4
PROBLEM:
Using MO theory to explain bond properties
As the following data show, removing an electron from N2 forms
an ion with a weaker, longer bond than in the parent molecule,
whereas the ion formed from O2 has a stronger, shorter bond.
N2
N2+
O2
O2+
bond energy (kJ/mol)
945
841
498
623
bond length (pm)
110
112
121
112
Explain these facts with diagrams showing the sequence and
occupancy of MOs.
PLAN:
Find the number of valence electrons for each species, draw the MO
diagrams, calculate bond orders, and compare the results.
SOLUTION:
N2 has 10 valence electrons, so N2+ has 9.
O2 has 12 valence electrons, so O2+ has 11.
11-54
SAMPLE PROBLEM 11.4
N2+
N2
bonding e- lost
1/2(8-2) = 3
(continued)
s2p
s2p
2p
2p
s2p
2p
2p
s2p
s2s
s2s
s2s
s2s
1/2(7-2) = 2.5
(weaker)
1/2(8-4) = 2
(weaker)
bond orders
11-55
O2+
O2
antibonding
e- lost
1/2(8-3) = 2.5
Heteronuclear Diatomic
Molecules
Figure 11.22
Energy
s
The MO diagram for HF
1s
nonbonding MOs
2px 2py
2p
lower in energy
than 1s of H!
s
AO
of H
11-56
MO of
HF
AO
of F
In polar covalent compounds, bonding MOs
are closer in energy to the AOs of the more
electronegative atom.
11-57
Figure 11.23
s*2s
The MO diagram for NO
bond order = 2.5
Energy
*2p
2p
s2p
2p
2p
possible Lewis
structures
s*2s
2s
2s
AO of N
s2s
MO of NO
11-58
AO of O
0
0
N
O
-1
+1
N
O
The lowest energy -bonding MOs in benzene and ozone
O
O
O
resonance hybrid
Figure 11.24
11-59