Covalent Bonding:
Orbitals
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
•These overlapping orbitals can have up to two electrons
that must have opposite spins (Pauli principle).
•The valence orbitals in a molecule are different from those
in isolated atoms.
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14a–2
Figure 12.18: Three representations
of the hydrogen 1s
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14a–3
Figure 13.1: (a) The interaction of two hydrogen atoms
(b) Energy profile as a function of the distance
between the nuclei of the hydrogen atoms.
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14a–4
Figure 13.1: (a) The interaction of two hydrogen atoms
(b) Energy profile as a function of the distance
between the nuclei of the hydrogen atoms.
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14a–5
Figure 12.19b: Representation of
the 2p orbitals.
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14a–6
3 WAYS TO FORM σ MOLECULAR ORBITALS
Hydrogen, H2
Hydrogen fluoride, HF
Fluorine, F2
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What about
The other 2
Atomic
p orbitals?
14a–7
Figure 14.1: (a) Lewis structure of the methane
molecule (b) the tetrahedral molecular geometry
of the methane molecule.
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14a–8
Figure 14.2: valence orbitals on a free
carbon atom
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14a–9
Figure 14.1: (a) Lewis structure of the methane
molecule (b) the tetrahedral molecular geometry
of the methane molecule.
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14a–10
Figure 14.3: native 2s and three 2p atomic orbitals
characteristic of a free carbon atome are combined to
form a new set of four sp3 orbitals.
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14a–11
Carbon
1s22s22p2
Carbon could only make two bonds
if no hybridization occurs. However,
carbon can make four equivalent bonds.
B
A
B
B
Energy
hybrid orbitals
px
py
B
pz
s
Brown, LeMay, Bursten, Chemistry The Central Science, 2000, page 321
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sp3
sp3
C atom of CH4 orbital diagram
14a–12
Figure 14.4: Cross section of an sp3 orbital
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14a–13
The four sp3 hybrid orbitals in CH4
Promotion
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14a–14
Figure 11.9
The s bonds in ethane.
both C are sp3 hybridized
s-sp3 overlaps to s bonds
sp3-sp3 overlap to form a s bond
Rotation about C-C
bond allowed.
s (Greek sigma) bonds
have axial symmetry and
good overlap
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relatively even
distribution of electron
density over all s
bonds
14a–15
Figure 14.6: Tetrahedral set of four sp3
orbitals on the carbon atom
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14a–16
Figure 14.7: The nitrogen atom in ammonia
is sp3 hybridized.
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14a–17
The four sp3 hybrid orbitals in CH4
Promotion
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14a–18
The four sp3 hybrid orbitals in CH4
Promotion
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14a–19
The four sp3 hybrid orbitals in NH3
Promotion
N
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14a–20
The four sp3 hybrid orbitals in NH3
Promotion
N
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14a–21
Figure 11.5
The sp3 hybrid orbitals in H2O
Lone pairs
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14a–22
Diamond - sp3 hybridized C
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14a–23
Figure 14.8: The hybridization of the s, px, and
py atomic orbitals results in the formation of three
sp2 orbitals centered in the xy plane.
NB: The remaining p orbital can be empty or serve another function
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14a–24
The three sp2 hybrid orbitals in
BF3
Promotion
Note the single left over
Unhybridized p orbital on B
Region of overlap
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14a–25
Hybrid Orbitals
Ground-state B atom
2s
2p
B atom with one electron “promoted”
2s
2p
Energy
hybrid orbitals
px
py
pz
sp2
sp2
s
2p
B atom of BH3 orbital diagram
H
hybridize
B
s orbital
H
p orbitals
three sps hybrid orbitals
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sp2
hybrid orbitals shown together
(large lobes only)
H
14a–26
Figure 14.10: When one s and two p oribitals are mixed to form a
set of three sp2 orbitals, one p orbital remains unchanged and
is perpendicular to the plane of the hybrid orbitals.
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14a–27
Figure 14.13: (a) The orbitals used to form the bonds in
ethylene. (b) The Lewis structure for ethylene.
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14a–28
The plastics shown here were
manufactured with ethylene.
Source: Comstock - Mountainside, NJ
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14a–29
Figure 14.11: The σ bonds in ethylene.
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14a–30
Figure 14.12: A carbon-carbon double bond
consists of a σ bond and a π bond.
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14a–31
Figure 14.48: The benzene molecule consists of a ring
of six carbon atoms with one hydrogen atom bound to
each carbon; all atoms are in the same plane.
• Sp2 hybridized
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14a–32
FIGURE 14.49: Sigma Bonding
System in Benzene
FIGURE 14.50: (a) Pi MO System in Benzene,
(b) Delocalized Pi MO Over Entire Ring of C
Atoms
O
O
O
O
N
N
N
O
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O
O
O
O
14a–35
FIGURE 14.51: (a) Pi Bonding
System in NO3-, (b) Delocalized Electrons
in the pi MO System of NO3- Ion
Graphite – sp2 hybridized C
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14a–37
Fullerene-C60 and Fullerene-C70
What hybridization of C describes the structures?
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14a–38
Figure 14.14: 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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14a–39
The sp hybrid orbitals in gaseous BeCl2
Promote to
create two
half filled
orbitals that
participate in
bond
formation
Promotion
Filled 2s orbital
can’t bond to Cl
Why are sp hybrids invoked? Because if Be made one bond with its
2s and one bond with a 2p orbital, then the two Be-Cl bonds would
have different strengths & lengths. But both bonds are identical.
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14a–40
The two sp hybrid orbitals in gaseous BeCl2
Note the two “leftover” p orbitals of Be
Region of overlap
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14a–41
Figure 14.15: The hybrid orbitals in the
CO2 molecule
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14a–42
Figure 14.16: orbital energy level diagram for
the formation of sp hybrid orbitals of carbon.
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14a–43
Figure 14.17: Orbitals of an sp hybridized
carbon atom
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14a–44
sp2 hybridization of an oxygen atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
1 trigonal
Bond with
2 lone pairs
+ 1 for a pi bond
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sp2
px
sp2
px
14a–45
Figure 14.18: Orbital arrangement for an sp2
hybridized oxygen atom
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14a–46
Figure 14.19: (a) Orbitals predicted by the LE model to
describe (b) The Lewis structure for carbon dioxide
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14a–47
Hybrid Orbitals
Types of Hybrid Orbitals
sp
Shapes: linear
# orbitals: 2
sp2
triangular
3
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sp3
sp3d
sp3d2
tetrahedral trig. bipyram. Octahedral
4
5
6
14a–48
The four sp3 hybrid orbitals in NH3
Promotion
N
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14a–49
The four sp3 hybrid orbitals in NH3
Promotion
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14a–50
Figure 14.20: (a) An sp hybridized nitrogen atom
(b) The s bond in the N2 molecule (c) the two p bonds
in N2 are formed
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14a–51
The conceptual steps from molecular formula to the hybrid orbitals
used in bonding.
Step 1
Molecular
formula
Step 2
Lewis
structure
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Step 3
Molecular shape
and e- group
arrangement
Hybrid
orbitals
14a–52
sp3 hybridization of a carbon atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
sp3
4 tetrahedral
bonds
sp3
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14a–53
sp3 hybridization of a carbon atom
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14a–54
sp3 hybridization of a nitrogen atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
sp3
3 tetrahedral
bonds with
1 lone pair
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sp3
14a–55
sp3 hybridization of a nitrogen atom
N
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14a–56
sp3 hybridization of a oxygen atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
sp3
2 tetrahedral
bonds with
2 lone pairs
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sp3
14a–57
sp3 hybridization of a oxygen atom
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14a–58
sp2 hybridization of a carbon atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
3 trigonal
Bonds
+ 1 for a pi bond
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sp2
px
sp2
px
14a–59
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14a–60
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14a–61
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14a–62
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14a–63
sp2 hybridization of an oxygen atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
1 trigonal
Bond with
2 lone pairs
+ 1 for a pi bond
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sp2
px
sp2
px
14a–64
Figure 14.19: (a) Orbitals predicted by the LE model to
describe (b) The Lewis structure for carbon dioxide
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14a–65
sp hybridization of a carbon atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
2 linear
bonds
+ 2 for pi bonds
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sp
px
py
sp
px
py
14a–66
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14a–67
sp hybridization of an nitrogen atom
4 atomic
orbitals
s
p
4 hybridized
orbitals
1 linear
Bonds with
1 lone pair
+ 2 for pi bonds
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sp
px
py
sp
px
py
14a–68
Figure 14.20: (a) An sp hybridized nitrogen atom
(b) The s bond in the N2 molecule (c) the two p bonds
in N2 are formed
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14a–69
Figure 14.21: A set of dsp3 hybrid orbitals
on a phosphorous atom
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14a–70
Hybridization Involving d Orbitals
promote
3s
3p
3d
unhybridized P atom
P = [Ne]3s23p3
3s
3p
3d
vacant d orbitals
hybridize
Ba
F
Be
F
P
five sp3d orbitals
F
3d
Be
F
Be
F
Ba
degenerate
orbitals
(all EQUAL)
Trigonal bipyramidal
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14a–71
Figure 11.6
The five sp3d hybrid orbitals in PCl5
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14a–72
Figure 14.22: The orbitals used to form the
bonds in the PCL5 molecule
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14a–73
Figure 14.23: An octahedral set of d2sp3
orbitals on a sulfur atom
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14a–74
Figure 11.7
The six sp3d2 hybrid orbitals in SF6
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14a–75
Figure 14.24: The relationship among the number
of effective pairs, their spatial arrangement,
and the hybrid orbital set required
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14a–76
Figure 14.24: The relationship among the number
of effective pairs, their spatial arrangement,
and the hybrid orbital set required (cont’d)
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14a–77
Figure 11.8
The 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
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Hybrid
orbitals
Table 11.1
14a–78