CHAPTER 10
ORBITAL HYBRIDIZATION
and
MOLECULAR ORBITALS
Problems 1-15 + all bold numbered problems
1
2
ORBITALS AND BONDING THEORIES
• There are two major theories of bonding
• The Valence Bond (VB) Theory
3
–Simple
–Explains geometry
–An extension of the Atomic Theory
–Fails to account for some paramagnetic
properties
–Fails to explain delocalized bonds
• The Molecular Orbital (MO) Theory
–More complex
–Explains magnetic properties
–Explains delocalized bonds
4
Two Theories of Bonding
• VALENCE BOND THEORY —
Linus Pauling
• valence electrons are localized
between atoms (or are lone
pairs).
• half-filled atomic orbitals
overlap to form bonds
Maximum
Attraction
Repulsion
Minimum
Attraction
5
Free atom
6
Sigma Bond
Formation by
Atomic Orbital
Overlap
H
•
Two s
orbitals
overlap
H
+
•
•

sigma bond (
•
s)
7
Sigma Bond Formation by Atomic
Orbital Overlap
Two s orbitals
overlap
Two p
atomic
orbitals
overlap
s&p
atomic
orbitals
overlap
H
+
F
HF
VALENCE BOND THEORY
8
• Bonds form when: atomic orbitals overlap,
and two electrons with opposite spin are
present.
• The resulting lower energy state is called a
covalent bond.
• If the overlapping orbitals are 1s type
orbitals, the resulting bond is called a s1s + 1s
(previous H2)
• If the overlapping orbitals are 1s and 2p type
orbitals, the resulting bond is called a s1s + 2p.
• If the overlapping orbitals are 2p type
orbitals, the resulting bond is called a s2p + 2p
9
VALENCE BOND THEORY
• VBT works well for explaining atomic
orbital overlap between 1s-1s, 2p-2p and
1s-2p to make new bonds
• What does VBT say about more complex
molecules with more then 2 atom systems
VALENCE BOND THEORY
•VBT can not account for a 109.5º angle in CH4
due to 2p orbitals constrained 90º bond angle
•AO of 90º do not correspond to 109.5º
?
10
11
A new theory is needed
Linus Pauling proposes
Hybrid Orbital Theory
Advanced Theories of
Chemical Bonding
Atomic Orbitals
Molecules
12
13
Hybrid Orbitals
• Atomic orbitals in the free atoms are “Mixed” to
make a new Hybrid Orbital for molecules with
more then 2 atoms
• An example of mixing an s and p atomic orbital to
make a NEW Hybrid sp orbital
+
•
# AO
=
# of HO
14
New HO from AO
sp2
+
s
sp3
p
p
sp2
sp2 sp2
sp3
sp3 sp3 sp3
+
s
p
p
p
+
sp3d
s
p
d
p
p
sp3d sp3d sp3d sp3d
sp3d
15
+
sp3d2
s
p
d
p
p
d
sp3d2 sp3d2sp 3dsp3d2
sp3d2 sp3d2
These new HO do two things
1. Allow the orbitals to physically rearrange in such a
fashion to adopt the 109.5º bond angle in the sp3 for
example
2. Account for 6 coordinate molecules as in the case of
sp3d2
16
Hybrid Orbitals: a “Mixing” of
AO’s
• Other possibilities
–one s with one p (just
described)
–one s with two p’s
–one s with three p’s
–one s with three p’s and one
d
–one s with three p’s and two
d’s
New Name
 sp
 sp2
 sp3
 sp3d
 sp3d2
These are the newly mixed Hybrid Orbitals
17
Hybridization of Atomic Orbitals
Sp3
• To form polyatomic molecules having three
or more atoms, it is frequently necessary
(always in the second period) to hybridize
the atomic orbitals of the central atom to
permit maximum orbital overlap and to
maximize the number of bonds formed.
• Carbon, for example, always forms four (4)
bonds.
18
Orbitals needed to hybridize
19
20
Bonding in CH4
Need to use 4 atomic
orbitals — s, px, py,
and pz — to form 4
new hybrid orbitals
pointing in the correct
direction.
109o
21
Bonding in a Tetrahedron
Formation of Hybrid Atomic
Orbitals
4 C atom orbitals
hybridize to form four
equivalent sp3 hybrid
atomic orbitals.
22
sp3
• These hybrid atomic orbitals are linear
combinations of the atomic orbitals.
• The number of hybrid orbitals produced is always
equal to the number of atomic orbitals hybridized.
23
New Linear Combination
24
Bonding in a Tetrahedron
Formation of Hybrid Atomic Orbitals
4 C atom orbitals hybridize to form
four equivalent sp3 hybrid atomic
orbitals.
25
sp3
• Hybridization for water and ammonia is
explained on page 445.
• Figures 10.8 & 10.9.
• (Examples 10.1 and 10.2 page 446.)
• Predict the hybridization and geometry for
CHCl3 and OF2. Describe the sigma bonds
in each molecule.
Figure 10.8
26
Figure 10.9
27
sp2
• If one s orbital and two p orbitals are
combined, the resulting hybrid orbitals are
called sp2 orbitals.
• The trigonal planar shape of this set of
three orbitals is consistent with the VSEPR
theory.
• Figure 10.10, page 448, and
Figure 10.8 (3rd ed.) illustrates this
concept.
• The orbital box diagrams can be used to
confirm the bonding.
• BH3 is and example (show model).
28
29
Figure
10.10
30
Using VB Theory
Bonding in BF3
•• ••
F ••
••••
F
••
B
Boron configuration
••
F ••
••


1s
2s
2p
planar triangle
angle = 120o
31
Bonding in BF3
• How to account for 3 bonds 120o apart using a spherical s
orbital and p orbitals that are 90o apart?
• Pauling said to modify VP approach with ORBITAL
HYBRIDIZATION
• — mix available orbitals to form a new set of
orbitals — HYBRID ORBITALS — that will give the
maximum overlap in the correct geometry.
32
Bonding in BF3

2s
hydridize orbs.
2
2p
rearrange electrons
three sp
hybrid orbitals
unused p
orbital
33
Bonding in BF3

2s
hydridize orbs.
120o
2p
rearrange electrons
three sp2
hybrid orbitals
•
three
sp 2 hybrid
orbitals
unused p
orbital
• The three hybrid orbitals are made
from 1 s orbital and 2 p orbitals  3 sp2
hybrids.
• Now we have 3, half-filled HYBRID
orbitals that can be used to form B- F
sigma bonds.
34
Bonding in BF3

2s
hydridize orbs.

120o
2p
rearrange electrons
three sp2
hybrid orbitals
•
three
sp 2 hybrid
orbitals
unused p
orbital
An orbital from each F overlaps one of the
sp2 hybrids to form a B-F s bond.
F


F
B
F
35
sp
• Figure 10.11, page 448, & Figure 10.9 (3rd
ed.) illustrates the outcome of hybridizing an
s and a p orbital to produce two sp hybrid
atomic orbitals with a linear geometry.
• BeF2 is an example of this type hybridization.
• Predict the hybridization and geometry for
PF3 and BeH2. Describe the sigma bonds in
each molecule.
• We would expect the first to be sp3
hybridized, but it actually uses the 3p atomic
orbital (3rd period) instead and has
approximately 90o bond angles.
36
Figure 10.11
36
37
Orbital Hybridization
BONDS
SHAPE
HYBRID
2
linear
sp
2 p’s
3
trigonal
planar
sp2
1p
4
tetrahedral
sp3
REMAIN
none
dsp3
and
d2sp3
• These hybridizations require five (5) and six
(6) atomic orbitals respectively and produce
an equal number of hybrid atomic orbitals.
The electronic geometries are trigonalbipyramidal, and octahedral.
• Figure 10.12 provides an overview of these
cases and a review of the others. (page 450)
• Examples 10.3 & 4 cover PF5 and others.
• Describe the hybridization, bonding, and
geometry for SF4 and SF6.
38
39
Figure 10.12
40
Multiple Bonding
• The second type of covalent bond is the p
bond.
• The pi bond (p) results from the sideways
overlap of two atomic p orbitals. The electron
density is above and below the plane.
• The second bond between two atoms is
always a p bond as is the third bond in the
case of a triple bond.
• Figures 11.8 (2nd ed.) & 10.13, 10.14, 10.16 and
models.
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Figure 10.13
42
Figure 10.14
43
Figure 10.16
2 p bonds
44
Bonding in Glycine
Multiple Bonds
Consider ethylene, C2H4
H
H
120
o
C
H
sp
C
H
2
45
46
Sigma Bonds in C2H4
H
H
120
o
C
H
sp
C
H
2
47
p Bonding in C2H4
The unused p orbital on each C atom contains an
electron and this p orbital overlaps the p orbital on the
neighboring atom to form the p bond. (See Fig. 10.13)

2s
2p
3 sp 2
hybrid
orbitals
p
orb.
for p
bond
48
Multiple Bonding
in C2H4
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Consequences of Multiple Bonding
Restricted rotation around C=C bond.
50
Multiple Bonding
• Describe the hybridization, bonding, and
geometry for H2CO and HCN. Also do a
valence bond bonding diagram for each.
• Figure 10.15 for H2CO bonding.
• O3, ozone, is an excellent example of pi
resonance and a need for a better theory,
the delocalized molecular theory.
51
Figure 10.15
52
Isomers Resulting from p Bonding
• Since the pi bond is not free to rotate, two
isomer are created, the cis and the trans.
• See page 457 and Figure 10.18.
• The cis structure has the same atoms on the
same side of the double bond.
• The trans isomer has the atoms across the
double bond diagonally.
• There is a third possible isomer which has
both terminal atoms on the same central
atom, but this is a structural isomer.
• Illustrate with C2H2Br2.
53
Figure 10.18
54
Isomers of C2H2Br2
Trans
Cis
55
Two Theories of Bonding
• MOLECULAR
ORBITAL THEORY —
Robert Mullikan
(1896-1986)
• valence electrons are
delocalized
• valence electrons are
in orbitals (called
molecular orbitals)
spread over entire
molecule.
56
Benzene
• The bonding p in benzene, C6H6, can be
explained using resonance, but that
explanation leaves as many questions as
answers.
• A theory involving delocalization of
bonding p electrons is needed:
The M.O. Theory.
• Figure 10.19 and 3rd ed.
57
Figure 10.19
57
58
10.3 MOLECULAR ORBITAL THEORY
• Instead of considering atomic orbitals or
hybrid atomic orbitals localized on a single
atom, we consider a set of orbitals
common to the whole molecule, delocalized
M.O. theory.
• In the case of localized M.O. theory, the
orbitals are common to the two atoms
being bonded.
• This new theory is needed to explain the
paramagnetic property of oxygen and
certain other diatomic molecules.
• Paramagnetic species have one or more
unpaired electrons.
• Diamagnetic species have no unpaired
electrons.
59
Paramagnetic/diamagnetic
60
MOLECULAR ORBITAL THEORY
• Molecular orbitals, like atomic orbitals, are
assigned electrons according to the Pauli
principle and Hund's rule.
• The electrons fill the lowest energy orbitals
first with out pairing, then pair.
• Once these orbitals are filled, electrons are
assigned to the next highest energy
orbitals.
There are four principles in the M. O. T.
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1)
The number of molecular orbitals is always
equal to the number of atomic orbitals for the
atoms forming the molecule (or ion). For every
bonding molecular orbital there is a
corresponding antibonding orbital.
• Figure 10.21, page 461.
• In this case we see a sb and a s*. The bonding
orbitals result from an in phase combination of
the atomic orbitals, and the antibonding
orbitals result from an out of phase
combination to the atomic orbitals.
Figure 10.21
62
63
There are four principles in the M. O. T.
2)
The bonding molecular orbital is
always lower in energy than the parent
atomic orbitals and stabilizes the
molecule. The antibonding orbital is
always higher in energy that the parent
atomic orbitals and destabilizes the
molecule.
• Figure 10.22, page 461.
–This figure illustrates the bonding for H2.
64
Figure 10.22
64
65
There are four principles in the M. O. T.
3)
Electrons in the molecule are assigned
to orbitals of successively higher energy
according to the Pauli principle and
Hund's rule.
Bonding orbitals stabilize and antibonding
orbitals destabilize the molecule.
4)
Atomic orbitals combine most
effectively to form molecular orbitals when
the atomic orbitals have similar energies.
66
Bond order
• Bond order is defined as the number of net
bonding electrons divided by two.
B.O. = (# bonding e- - # antibonding e-)/2.
• The bond order can be fractional, but is never
negative.
• A bond order of zero indicates that the
molecule (ion) is not stable.
• Example 10.7 and Exercise 10.7.
67
Continued
• Do a molecular orbital diagram and
molecular orbital configuration for:
• H2- and He2+.
• Figure 10.24, page 463, illustrates the
bonding for Li2.
• Do a molecular orbital diagram and
molecular orbital configuration for: He2and Be2+.
• Example 10.8 and Exercise 10.8.
68
Figure 10.24
Molecular Orbitals for Homonuclear Diatomic
Molecules
• P orbitals can be used for both s molecular
orbitals and p molecular orbitals. Figure 10.25
and 10.26, pages 464.
• This gives rise to a new form of molecular
orbital diagram.
• Figure 10.27, page 465.
• Notice the differences with the p bonding
orbitals lower in energy than the s2p bonding
orbitals, but the reverse order for the
antibonding orbitals.
69
70
Figure 10.25
Figure 10.26
71
Figure 10.27
72
Molecular Orbitals for Homonuclear Diatomic Molecules
73
• O.H. Table 10.1 page 466 for the second
period molecules. Examples and Exercises 10.9.
• For heteronuclear diatomic ions and
molecules, the element with the higher
electronegativity always has the lower
energy atomic orbitals, and receives the
additional electrons if the ion is an anion.
• Do a molecular orbital diagram and molecular
orbital configuration for: NO, OF-, and CN+. Give
the bond order and magnetic properties for
each.
74
Delocalized Molecular Theory
• O3 is an excellent example.
• Figure 10.28 page 469.
• The molecule has one p bond and two
bonding sites.
• The bond order is 1.5, with 1 sigma bond
between each oxygen atom and one p
bond spread between the three atoms.
• The other pair of electrons is in a p
nonbonding orbital.
• The molecule is diamagnetic.
75
Figure 10.28
0 e-
2 eSee the M.O. diagram page
468.
2 e-
76
Figure 10.19
Benzene
Delocalize
d electrons
Figure 10.29
77
Benzene
M.O. diagram
78
79
10.4 METALS AND SEMICONDUCTORS
• The atomic orbitals of metals form
delocalized, conducting bands.
• Figure 10.30, page 470.
• In the case of metals with s and p orbitals,
these bands overlap.
• This is called the Band theory.
• Use the Band theory to show how Mg and Al
are conductors.
80
Figure 10.30
Sodium as a
conductor
81
Lithium, a metal conductor
82
METALS AND SEMICONDUCTORS
• Nonmetals hybridize first and then form
two bands, the valence band and the
conduction band, with a gap between
them. See Figure 10.32, page 471.
• If the gap is small as in Si and Ge which
are semiconductors, the electrons are
easily promoted from one band the other
allowing for conduction.
83
Doping Si with Al
84
METALS AND SEMICONDUCTORS
• Use the Band theory to show how C and Ge
behave.
• If Si and Ge are doped with atoms having 3
or 5 valence electrons, p and n type
semiconductors are created.
• Figure 10.34, page 472.
85
Figure 10.34
85