Transcript No Slide Title

Advanced Theories of
Chemical Bonding
Chapter 10
Atomic Orbitals
Molecules
1
Two Theories of Bonding
• MOLECULAR
ORBITAL THEORY —
Robert Mullikan (18961986)
• valence electrons are
delocalized
• valence electrons are
in orbitals (called
molecular orbitals)
spread over entire
molecule.
2
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.
• See Screen 10.3 and Figures 10.1
and 10.2.
3
Sigma Bond Formation by
Orbital Overlap
Two s orbitals
overlap
4
Sigma Bond Formation
Two s
orbitals
overlap
Two p
orbitals
overlap
5
6
Using VB Theory
Bonding in BF3
•• ••
F ••
Boron configuration
B

 
•••
••••
F
F• 1s
2p
2s
••
••
planar triangle
angle = 120o
7
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 VB 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. (See Screen 10.6)
8
Bonding in BF3
2p
2s
hydridize orbs.
2
rearrange electrons
three sp
hybrid orbitals
unused p
orbital
See Figure 10.9 and Screen 10.6
9
Bonding in BF3
•
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.
10
Bonding in BF3

An orbital from each F overlaps one of the
sp2 hybrids to form a B-F  bond.
F


F
B
F
11
Bonding in CH4
How do we account for 4
C—H sigma bonds
109o apart?
Need to use 4 atomic
orbitals — s, px, py, and
pz — to form 4 new
hybrid orbitals
pointing in the correct
direction.
109o
Bonding in a Tetrahedron —
Formation of Hybrid Atomic Orbitals
4 C atom orbitals
hybridize to form
four equivalent sp3
hybrid atomic
orbitals.
12
Bonding in a Tetrahedron —
Formation of Hybrid Atomic Orbitals
4 C atom orbitals
hybridize to form
four equivalent sp3
hybrid atomic
orbitals.
13
14
Bonding in CH4
Figure 10.6
15
Orbital Hybridization
Figure 10.5
BONDS
SHAPE
HYBRID REMAIN
2
linear
sp
2 p’s
3
trigonal
planar
sp2
1p
4
tetrahedral sp3
none
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17
Bonding in
Glycine
sp
3
H
O
C
H H
C
••
H N
sp
3
sp
2
••
O H
••
sp
3
18
Bonding in
Glycine
sp
3
H
O
C
H H
C
••
H N
sp
3
sp
2
••
O H
••
sp
3
19
Bonding in
Glycine
sp
3
H
O
C
H H
C
••
H N
sp
3
sp
2
••
O H
••
sp
3
20
Bonding in
Glycine
sp
3
H
O
C
H H
C
••
H N
sp
3
sp
2
••
O H
••
sp
3
21
Bonding in
Glycine
sp
3
H
O
C
H H
C
••
H N
sp
3
sp
2
••
O H
••
sp
3
22
Multiple Bonds
Consider ethylene, C2H4
H
H
120Þ
C
H
sp
C
H
2
23
Sigma Bonds in C2H4
H
H
120Þ
C
H
sp
C
H
2
24
π 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 π bond. (See Fig.
10.9)

2s
 
2p

 
2
3 sp
hybrid
orbitals

p
orb.
for š
bond
25
π 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
π bond. (See Fig. 10.9)
26
Multiple Bonding
in C2H4
27
 and π Bonding in C2H4
Figure 10.11
28
 and π Bonding in CH2O
Figure 10.12
29
 and π Bonding in C2H2
Figure 10.13
Consequences of Multiple
Bonding
There is restricted rotation around C=C bond.
Figure 10.14
30
Consequences of Multiple
Bonding
Restricted rotation around C=C bond.
See Butene.Map in ENER_MAP in CAChe models.
31
32
Double Bonds and Vision
See Screen 10.13, Molecular Orbitals and Vision
See also Chapter Focus 10, page 380
33
Molecular Orbital Theory
• Valence electrons are delocalized
• Valence electrons are in orbitals
(called molecular orbitals) spread
over entire molecule.
The Paramagnetism of O2
34
Molecular Orbital Theory
• Bonding and antibonding sigma MO’s are formed from 1s
orbitals on adjacent orbitals.
35
36
Molecular Orbital Theory
Figure 10.17
1. No. of MO’s = no. of
atomic orbitals used.
2. Bonding MO is
lower in energy than
atomic orbitals.
Antibonding MO is
higher.
3. Electrons assigned
to MO’s of higher and
higher energy.
37
Dihelium Molecule
Bond order = 1/2 [# e- in bonding MOs
- # e- in antibonding MOs]
38
Sigma Bonding from p Orbitals
39
π Bonding from p Orbitals
Sideways overlap of atomic 2p orbitals that lie in the same
direction in space give π bonding and antibonding MOs.
40
 & π Bonding from p Orbitals
41
42
MO Theory of Metals &
Semiconductors
• Can explain
– Luster
– Electrical and thermal conductivity
– Malleability
• All explanations come down to electron mobility
43
MO Theory of Metals &
Semiconductors
• Electrical conductivity
– Metals — conductivity decreases with temperature
– Semiconductors — increases with T
– Insulator — very low conductivity
44
MO Theory of Metals &
Semiconductors
• Band theory-The central idea underlying the
description of the electronic structure of solids is
that valence electrons donated by atoms are
spread over the entire structure.
MO Theory of Metals & Semiconductors
C ompl e te ly
fil le d ban d
for m an y
atoms
s orbitals
of 2 Be
atoms
3 Be
atoms
45
46
MO Theory of Metals & Semiconductors
Fermi
level
s orbitals
of 2 Na
atoms
3 Na
atoms
Only 1/2 of the levels are filled.
1/2 bond per atom.
Be Metal and MOs
47
2000 MOs
Empty
1500 MOs p  š*
empty
1500 MOs
p š
500 MOs
*
500 MOs

filled
1000 Be atoms -->
1000 MOs from s
and
3000 MOs from p
1000 e- pairs
Bonding MOs
blend and
antibonding MOs
blend.
2000 MOs
1/2 filled
This gives 1 bond
per Be atom
Al Metal and MOs
Use 1000 Al atoms and get
4000 MOs
2000 MOs
Have 3000 e- or 1500 pairs
This fills the bottom levels 3/4
of the way.
2000 MOs
1.5 pairs per Al atom
This gives 3/2 bond
per Al atom
48
Silicon and MOs
Have 1000 Si atoms
49
2000 MOs
4000 e- or 2000 pairs
2 pairs per Si atom
2000 MOs
Band is completely filled
This gives 2 bond
per Si atom
Heat of Atomization
•
∆H of vaporization (or atomization) is a good
measure of bonding in solids.
•
M(s) ---> M(g)
•
Energy change = ∆Hvap
•
High ∆H values for transition metals indicate d
orbital participation.
50
51
Heat of Vaporization
Fermi Level
52
•
•
•
•
Band gap
In metals
antibonding
and bonding
levels
merge and
band gap
vanishes
Fermi
level
The HOMO at T = 0 is the Fermi level.
At temp > 0, electrons near Fermi level
can be promoted to nearby empty
levels.
These promoted e- are mobile and
move under electric field.
Promotion gives e- in higher levels and
“hole” in lower levels. Therefore, 2
mobile e-.
Electrical Conductivity
Conduction band
Empty
levels
Add
energy
e+
Filled
levels
Valence band
53
Empty
levels
Filled
levels
•
•
•
•
•
Add
energy
e+
Electrical Conductivity
54
Metal conductivity DECREASES with increase in T.
Contrary to expectation. Would expect increased electron promotion.
Ability of e- to travel smoothly thru the solid in a conduction band depends on
uniformity of atom arrangement.
An atom vibrating vigorously at a site is equivalent to an impurity that disrupts
the orbitals.
Thus, higher T means lower conductivity.
Insulators
• Very few e- from the
valence band have
sufficient energy to move
to the conduction band.
6 eV in diamond
Valence
band is full
55
Semiconductors
• Group 4A elements
– C (diamond) is an insulator
– Si, Ge, and gray Sn are semiconductors
» all of the above have the diamond
structure, which appears especially
favorable to semiconductor behavior
– White Sn and Pb are metals
56
Semiconductors
• Many inorganic compounds are
semiconductors.
• Best known are “III-V”
compounds
• GaAs = “Ge”
• InSb = “Sn”
• Have ZnS or zinc blende
structure.
57
Band Theory & Semiconductors
• Semiconductors have a band structure similar to
insulators but band gap is small
• Band gap = 0.5 to 3.0 eV
• At least a few electrons have sufficient thermal energy
to be promoted to an empty band.
58
Band Theory & Semiconductors
Conduction band
e-
e-
e-
Small band gap
+
+
+
Valence band
59
• Semiconductors have a band
structure similar to insulators but
have a small band gap
• Electrons can be promoted
thermally.
• The higher the temperature the
more electrons are promoted.
Intrinsic Semiconductors
Group 4A
Conduction
band
e-
e-
e-
Small band gap
+
+
+
Band gap (eV)
C
6.0
Si
1.1
Ge
0.7
Gray Sn (>13 ˚C)
0.1
White Sn (<13 ˚C)
0
Lead
0
Valence band
These are called INTRINSIC semiconductors
60
61
Extrinsic Semiconductors
• Conductivity controlled by a trace of dopant such as
Ga (or Al) or As
• The dopant atom takes the place of a Si atom.
• Dopant atom has one fewer electrons than Si (= Ga
or Al) or one more electron than Si (= As).
Add Group 3A Atom
--> p-type Semiconductor
62
• If Ga conc. is small, acceptor levels are
“discrete” — not extended over the
lattice.
• Positive holes left in valence band can
move.
• Si + Ga (or Al) is a positive hole or p-
type semiconductor.
p-Type Semiconductor
Conduction band
e-
e-
e-
1.1 eV
Acceptor level
+
+
+
Valence band
• Acceptor level is slightly
higher in energy than
Fermi level.
• Electrons readily
promoted into acceptor
level.
63
n-Type Semiconductor
Conduction band
e1.1 eV
e-
e-
Donor level
Valence band
• Add As — has 5e- and so
adds extra e-.
• Donor level has electrons.
• Electrons promoted from
donor level to conduction
band.
• Negative electrons are
charge carriers and so
called n-type.
64
Summary
• Conductivity of extrinsic >> intrinsic
semiconductors.
• Conductivity of extrinsic semiconductors can
be accurately controlled.
• Intrinsic semiconductors are very dependent
on T and on stray impurities.
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