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 the Types
of Covalent Bonds
11.3 Molecular Orbital (MO)Theory and Electron
Delocalization
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The Central Themes of 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.
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. To
explain shapes of molecules, electron orbitals
that are hybrids of atomic orbitals are theorized.
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Figure 11.1
Orbital overlap and spin pairing in three
diatomic molecules
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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
Figure 11.2
atomic orbitals
hybrid orbitals
orbital box diagrams
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The sp hybrid orbitals in gaseous
BeCl2(continued)
Figure 11.2
orbital box diagrams with orbital contours
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The sp2 hybrid orbitals in BF3
Figure 11.3
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The sp3 hybrid orbitals in CH4
Figure 11.4
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The sp3 hybrid orbitals in NH3
Figure 11.5
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The sp3 hybrid orbitals in H2O
Figure 11.5
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The sp3d hybrid orbitals in PCl5
Figure 11.6
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Figure 11.7
The sp3d2 hybrid orbitals in SF6
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Figure 11.8
The conceptual steps from molecular formula to
the hybrid orbitals used in bonding.
Molecular shape and e- group arrangement
Molecular formula
Lewis structure
Hybrid orbitals
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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 also has a tetrahedral arrangement with 2
nonbonding e- pairs.
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SAMPLE PROBLEM 11.1
Postulating Hybrid Orbitals in a Molecule
continued
(b) SF4 has a seesaw shape with 4 bonding and 1
nonbonding e- pairs.
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The s bonds in ethane.
Figure 11.9
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The s and p bonds in ethylene (C2H4)
Figure 11.10
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Figure 11.11
The s and p bonds in acetylene (C2H2)
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SAMPLE PROBLEM 11.2
Describing the Bonding in Molecules with
Multiple Bonds
SOLUTION
??bond
??bonds
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Figure 11.12
Restricted rotation of p-bonded molecules
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Molecular Orbital Theory

• Involves diagramming molecular energy levels
• Used to explain magnetic and spectral properties
  of molecules
• Used to predict the existence of certain
  molecules
• Two atomic orbitals combine to form a bonding
  molecular orbital and an anti-bonding MO.
• The number of atomic orbitals combined equals the
  number of molecular orbitals formed.
• Electrons in bonding MOs stabilize a molecule
• Electrons in anti-bonding MOs destabilize a
  molecule

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The Central Themes of 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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Figure 11.14
Contours and energies of the bonding and
antibonding molecular orbitals (MOs) in H2.
The bonding MO is lower in energy than an AO The
anti- bonding MO is higher in energy than an AO
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• Bond Order 1/2( bonding e antibonding e )
• Higher bond order stronger bond
• Molecular electron configurations
• Ex H2 (?1s)2

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Figure 11.15
The MO diagram for H2
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Figure 11.16
MO diagram for He2 and He2
s1s
Energy
s1s
MO of He
MO of He2
He2 bond order 0
He2 bond order 1/2
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SAMPLE PROBLEM 11.3
Predicting Species Stability Using MO Diagrams
SOLUTION
bond order 1/2(1-0) 1/2
bond order 1/2(2-1) 1/2
H2 does exist
H2- does exist
configuration is (s1s)2(s?1s)1
MO of H2-
MO of H2
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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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Contours and energies of s and p MOs through
combinations of 2p atomic orbitals
Figure 11.18
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P orbital mixing

• Results in 1?, 1?, 2? and 2? MOs
• For atoms with gt half filled p orbitals energy
  ?2p lt 2?2p lt 1?2p lt 2?2p
• For atoms with ? half filled p orbitals energy
  2?2p lt ?2p lt 2?2p lt 1?2p

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Figure 11.19
Relative MO energy levels for Period 2
homonuclear diatomic molecules.
without 2s-2p mixing
with 2s-2p mixing
MO energy levels for O2, F2, and Ne2
MO energy levels for B2, C2, and N2
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Recall

• Paramagnetic attracted to magnetic field,
  results from unpaired electrons
• Diamagnetic unattracted or slightly repelled by
  magnetic field, results from having all
  electrons paired

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Figure 11.20
MO occupancy and molecular properties for B2
through Ne2
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Figure 11.21
The paramagnetic properties of O2
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SAMPLE PROBLEM 11.4
Using MO Theory to Explain Bond Properties
Explain these facts with diagrams that show 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
Using MO Theory to Explain Bond Properties
continued
N2
N2
O2
O2
??2p
antibonding e- lost
bonding e- lost
??2p
?2p
?2p
s?2s
s2s
bond orders
1/2(8-2)3
1/2(7-2)2.5
1/2(8-4)2
1/2(8-3)2.5
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The MO diagram for HF
Figure 11.22
Energy
MO of HF
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The MO diagram for NO
Figure 11.23
Energy
possible Lewis structures
MO of NO
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Figure 11.24
The lowest energy p-bonding MOs in benzene and
ozone.
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Figure 10.1
The steps in converting a molecular formula into
a Lewis structure.
Place atom with lowest EN in center
Molecular formula
Step 1
Atom placement
Add A-group numbers
Step 2
Sum of valence e-
Draw single bonds. Subtract 2e- for each bond.
Step 3
Give each atom 8e- (2e- for H)
Remaining valence e-
Step 4
Lewis structure
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Figure 10.12
The steps in determining a molecular shape.
See Figure 10.1
Molecular formula
Step 1
Lewis structure
Count all e- groups around central atom (A)
Step 2
Electron-group arrangement
Note lone pairs and double bonds
Step 3
Count bonding and nonbonding e- groups separately.
Bond angles
Step 4
Molecular shape (AXmEn)