Theories of Covalent Bonding

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Chapter 11
Theories of Covalent Bonding
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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
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The three models of chemical bonding
Figure 9.2
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Covalent bond formation in H2
Figure 9.11
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Key Principles
Structure dictates shape
Shape dictates function
shape conformation
Molecules can assume more than one shape
(conformation) in solution!
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The Complementary Shapes of an Enzyme and Its
Substrate
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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)
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A periodic table of partial ground-state electron
configurations
Figure 8.12
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The steps in determining a molecular shape
molecular formula
Step 1
Count all e- groups around the central atom A
Lewis structure
Step 2
Note lone pairs and double bonds
electron-group arrangement
Step 3
Count bonding and non-bonding e- groups
separately.
bond angles
Step 4
molecular shape (AXmEn)
Figure 10.12
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Steps to convert a molecular formula into a Lewis
structure
Place the atom with the lowest EN in the center
molecular formula
Step 1
atom placement
Add A-group numbers
Step 2
Draw single bonds and subtract 2e- for each bond
sum of valence e-
Step 3
Give each atom 8e- (2e- for H)
remaining valence e-
Step 4
Figure 10.1
Lewis structure
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Electron-group repulsions and the five basic
molecular shapes
Figure 10.5
Ideal bond angles are shown for each shape.
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The three molecular shapes of the tetrahedral
electron-group arrangement
Examples CH4, SiCl4, SO42-, ClO4-
Examples H2O OF2 SCl2
Examples NH3 PF3 ClO3 H3O
Figure 10.8
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The four molecular shapes of the trigonal
bipyramidal electron-group arrangement
Examples SF4 XeO2F2 IF4 IO2F2-
Examples PF5 AsF5 SOF4
Examples XeF2 I3- IF2-
Examples ClF3 BrF3
Figure 10.10
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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
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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).
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Orbital overlap and spin pairing in three
diatomic molecules
Figure 11.1
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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
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Hybrid Orbitals
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.
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The sp hybrid orbitals in gaseous BeCl2
atomic orbitals
hybrid orbitals
VSEPR predicts a linear shape
Figure 11.2
orbital box diagrams
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The sp hybrid orbitals in gaseous BeCl2
(continued)
orbital box diagrams with orbital contours
Figure 11.2
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The sp2 hybrid orbitals in BF3
VSEPR predicts a trigonal planar shape
Figure 11.3
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The sp3 hybrid orbitals in CH4
VSEPR predicts a tetrahedral shape
Figure 11.4
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The sp3 hybrid orbitals in NH3
VSEPR predicts a trigonal pyramidal shape
Figure 11.5
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The sp3 hybrid orbitals in H2O
VSEPR predicts a bent (V) shape
Figure 11.5
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The sp3d hybrid orbitals in PCl5
VSEPR predicts a trigonal bipyramidal shape
Figure 11.6
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The sp3d2 hybrid orbitals in SF6
VSEPR predicts an octahedral shape
Figure 11.7
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Conceptual steps from molecular formula to the
hybrid orbitals used in bonding
molecular shape and e- group arrangement
molecular formula
Lewis structure
hybrid orbitals
Figure 11.8
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SAMPLE PROBLEM 11.1
Postulating Hybrid Orbitals in a Molecule
(a) methanol, CH3OH
(b) sulfur tetrafluoride, SF4
SOLUTION
(a) CH3OH
The groups around C are arranged as a tetrahedron.
O has a tetrahedral arrangement with two
non-bonding e- pairs.
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SAMPLE PROBLEM 11.1
(continued)
hybridized O atom
hybridized C atom
single C atom
single O atom
(b) SF4 has a seesaw shape with four bonding and
one non-bonding e- pairs.
distorted trigonal bipyramidal
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Covalent Bonds Between Carbon Atoms - Single Bonds
s bonds in ethane, CH3-CH3
109.5o
Figure 11.9
free rotation
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Covalent Bonds Between Carbon Atoms - Double Bonds
s and ? bonds in ethylene, C2H4
hindered rotation
120o
Figure 11.10
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Covalent Bonds Between Carbon Atoms - Triple Bonds
s and p bonds in acetylene, C2H2
hindered rotation
180o
Figure 11.11
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Video Hybridization
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Describing bonding in molecules with multiple
bonds
SAMPLE PROBLEM 11.2
SOLUTION
??bond
? bonds
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Restricted rotation in p-bonded molecules
cis
trans
No spontaneous interconversion between cis and
trans forms (isomers) in solution at room
temperature!
Figure 11.12
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Limitations of VB Theory
Inadequately explains magnetic/spectral properties
Inadequately treats electron delocalization
VB theory assumes a localized bonding model
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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)
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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).
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An analogy between light waves and atomic wave
functions
Figure 11.13
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Contours and energies of the bonding and
antibonding molecular orbitals in H2
Figure 11.14
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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 (p) bonds are denoted as before
a star (asterick) is used to denote antibonding
MOs.
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Molecular orbital diagram for the H2 molecule
MOs are filled in the same sequence as for AOs
(aufbau and exclusion principles, Hunds rule)
Figure 11.15
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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!
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MO diagrams for He2 and He2
s1s
Energy
s1s
MO of He
MO of He2
He2 bond order 1/2
He2 bond order 0
can exist!
cannot exist!
Figure 11.16
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SAMPLE PROBLEM 11.3
Predicting species stability using MO diagrams
bond order 1/2(1-0) 1/2
bond order 1/2(2-1) 1/2
SOLUTION
H2 does exist!
H2- does exist!
AO of H
MO of H2-
MO of H2

configuration is (s1s)2(s?1s)1
configuration is (s1s)1
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Figure 11.17
Bonding in s-block homonuclear diatomic molecules
Be2
Li2
Energy
Li2 bond order 1
Be2 bond order 0
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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.
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Contours and energies of s and ? MOs through
combinations of 2p atomic orbitals
end-to-end overlap
side-to-side overlap
Figure 11.18
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Relative energies
s2p lt p2p lt p2p lt s2p
More effective end-to-end interaction relative to
side-to-side in bonding MOs
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Relative MO energy levels for Period 2
homonuclear diatomic molecules
without 2s-2p mixing
with 2s-2p mixing
Figure 11.19
MO energy levels for O2, F2 and Ne2
MO energy levels for B2, C2 and N2
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MO occupancy and molecular properties for B2
through Ne2
Figure 11.20
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The paramagnetic properties of O2
Explained by MO diagram
Figure 11.21
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SAMPLE PROBLEM 11.4
Using MO theory to explain bond properties
Explain these facts with diagrams showing the
sequence and occupancy of MOs.
SOLUTION
N2 has 10 valence electrons, so N2 has 9.
O2 has 12 valence electrons, so O2 has 11.
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SAMPLE PROBLEM 11.4
(continued)
N2
N2
O2
O2
??2p
antibonding e- lost
bonding e- lost
??2p
?2p
?2p
s?2s
s2s
1/2(8-2) 3
1/2(7-2) 2.5
1/2(8-4) 2
1/2(8-3) 2.5
(weaker)
(weaker)
bond orders
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Heteronuclear Diatomic Molecules
Figure 11.22
The MO diagram for HF
Energy
nonbonding MOs
lower in energy than 1s of H!
MO of HF
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In polar covalent compounds, bonding MOs are
closer in energy to the AOs of the
more electronegative atom.
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Figure 11.23
The MO diagram for NO
bond order 2.5
Energy
possible Lewis structures
MO of NO
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The lowest energy p-bonding MOs in benzene and
ozone
resonance hybrid
Figure 11.24