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Chapter 4
Chemical Bonding
Silberberg Ch 9,10,11
Atkins: Ch 2,3
A general comparison of metals and nonmetals.
Types of Chemical Bonding
1. Metal with nonmetal:
electron transfer and ionic bonding
2. Nonmetal with nonmetal:
electron sharing and covalent bonding
3. Metal with metal:
electron pooling and metallic bonding
The three models of chemical bonding.
Chemical Bonds
Energy profile for the formation of a bond in H2
Changes in electron density during the formation of H2
region of greatest electron density
region of lowest electron density
A chemical bond is formed between atoms whenever
the forces of attraction between them are sufficiently
strong that they are not pulled apart in the course of
normal interactions with their environment.
The bond length, re, is the equilibrium separation
between the nuclei in a bond, defined by the distance at
which the potential energy is a minimum.
The bond dissociation energy, D0 is energy required to
break a bond
A Lewis dot symbol consists of the symbol of an element
and one dot for each valence electron in an atom of the
element.
Valence electrons are the outer shell electrons of an
atom. The valence electrons are the electrons that
participate in chemical bonding.
Group
e- configuration
# of valence e-
1A
ns1
1
2A
ns2
2
3A
ns2np1
3
4A
ns2np2
4
5A
ns2np3
5
6A
ns2np4
6
7A
ns2np5
7
Lewis Dot Symbols for the Representative Elements &
Noble Gases
A covalent bond is a bond in which a pair of electrons are
shared by two atoms.
F
+
7e-
F
F F
7e-
8e- 8e-
Lewis structure of F2
single covalent bond
lone pairs
F
F
single covalent bond
lone pairs
F F
lone pairs
lone pairs
Lewis structure of water
H
+
O +
H
single covalent bonds
H O H
or
H
O
H
2e-8e-2eDouble bond – two atoms share two pairs of electrons
O C O
or
O
O
C
double bonds
- 8e8e- 8ebonds
double
Triple bond – two atoms share three pairs of electrons
N N
triple
bond
8e-8e
or
N
N
triple bond
Valence Bond Theory
Bonds are formed by the overlap of atomic orbitals.
 VB  N[A,1s (1)B , 1s ( 2)  B ,1s (1)  A,1s ( 2)]
 2VB
cylindrically symmetric
with respect to rotation
about bond axis
sigma (s) bond
x axis
overlap of 2px of each F atomic orbitals
s bond
overlap of 2px of F and 1s of H atomic orbitals
H
F
s bond
sign of  +
sign of  -
Multiple Bonds
Double Bonds
overlap of 2px of each O atomic orbitals
head-on overlap
O2
s bond
overlap of 2pz of each O atomic orbitals
side-on overlap
or
O
O
p bond
Triple Bonds
overlap of 2px of each N atomic orbitals
head-on overlap
N2
s bond
N
N
overlap of 2pz and 2py of each N atomic orbitals
side-on overlap
or
N
N
p bonds
Covalent radius
Bond length in AB
approximated by rA+ rB, where r is
covalent radius in pm
Bond dissociation energy, D0, (kJ mol-1)
Diatomic molecules
Polyatomic molecules
Average bond dissociation energy:
~460 kJ mol1
D0 decreases with increasing bond length
H I < H Br < H Cl < H
D0 increases with increasing bond order
triple > double > single
F
Polar covalent bonding or polar bonding is a
covalent bond with greater electron density around one
of the two atoms
electron poor
region
H
electron rich
region
F
e- poor
H
d+
e- rich
F
d-
Electronegativity is the ability of an atom to attract
toward itself the electrons in a chemical bond.
Electron Affinity – measurable in an isolated atom,
Cl is highest
X (g) + e-
X-(g)
Electronegativity – relative to an atom in a bond,
F is highest
Pauling scale (c)
1
  D0 ( AB)  [D0 ( AA)  D0 (BB)]  0
2
c A  cB  
The Electronegativities of Common Elements
Variation of Electronegativity with Atomic Number
The Pauling electronegativity (EN) scale.
Electron density distributions in H2, F2, and HF.
Boundary ranges for classifying ionic character
of chemical bonds.
3.0
EN
2.0
0.0
Percent ionic character of electronegativity difference (EN).
Milliken electronegativity scale (c)
 Eea  I 1 
c A (Milliken)  C 

 2 
where C is a proportionality constant
Results in the same predictions of bond polarity as
the Pauling scale but the Pauling scale is the one
more commonly used.
The Ionic Bond
Coulombic attraction between oppositely charged ions.
Often the combination of cations of the alkali metals,
alkaline earth metals, Al and the anions of N, O, and
the halogens.
Na + Cl
Na+ Cl 1s22s22p6
22s22p63s23p6
1s22s
1s222p
2s623s
2p163s23p
1s5[Ne][Ar]
e- +
Na
Na+ + e-
Cl
Cl -
Na+ + Cl -
Na+ Cl -
Three ways to represent the formation of Li+ and Fthrough electron transfer.
Electron configurations
Li 1s22s1
F 1s22s22p5
+
Li+ 1s2
+
F- 1s22s22p6
2s
2p
Orbital diagrams
Li+
Li
1s
2s
1s
2p
+
+ F
1s
2s
F1s
2p
2s
Lewis electron-dot symbols
Li+
+
: F: -
:
+
:
Li .
.
:F:
2p
:
The Born-Haber cycle for lithium fluoride.
Potential Energy Diagram of NaCl
For an isolated Na+ and Cl-
Vattraction  
e2
4p0 r
-560 kJ mol-1
rb= 236 pm
Two-step process to determine Edissoiation
or
-560 kJ mol-1
-I1=-495.5 kJ mol-1
Eea=349 kJ mol-1
Periodic Trends in Lattice Energy
Coulomb’s Law
charge A X charge B
electrostatic force a
distance2
energy = force X distance
therefore
charge A X charge B
electrostatic energy a
distance
cation charge X anion charge
electrostatic energy a
cation radius + anion radius
a H0lattice
The reaction between sodium and bromine.
Na(s)
Br2(l)
NaBr(l)
Electrostatic forces
and the reason ionic
compounds crack.
Electrical conductance and ion mobility.
Solid ionic
compound
Molten ionic
compound
Ionic compound
dissolved in water
Melting and Boiling Points of Some Ionic Compounds
Compound
mp (0C)
bp (0C)
CsBr
636
1300
NaI
661
1304
MgCl2
714
1412
KBr
734
1435
CaCl2
782
>1600
NaCl
801
1413
LiF
845
1676
KF
858
1505
2852
3600
MgO
Vaporizing an ionic compound.
Classification of bonds by difference in electronegativity
Difference
Bond Type
0
Covalent
2
0 < and <2
Ionic
Polar Covalent
Increasing difference in electronegativity
Covalent
Polar Covalent
share e-
partial transfer of e-
Ionic
transfer e-
Electromagnetic radiation will only affect the rotation of a
diatomic molecule if two ends of the molecule are oppositely
charged.
Writing Lewis Structures
1. Draw skeletal structure of compound showing
what atoms are bonded to each other. Put least
electronegative element in the center.
2. Count total number of valence e-. Add 1 for
each negative charge. Subtract 1 for each
positive charge.
3. Complete an octet for all atoms except
hydrogen
4. If structure contains too many electrons, form
double and triple bonds on central atom as
needed.
Write the Lewis structure of nitrogen trifluoride (NF3).
Step 1 – N is less electronegative than F, put N in center
Step 2 – Count valence electrons N - 5 (2s22p3) and F - 7 (2s22p5)
5 + (3 x 7) = 26 valence electrons
Step 3 – Draw single bonds between N and F atoms and complete
octets on N and F atoms.
Step 4 - Check, are # of e- in structure equal to number of valence e- ?
3 single bonds (3x2) + 10 lone pairs (10x2) = 26 valence electrons
F
N
F
F
Write the Lewis structure of the carbonate ion (CO32-).
Step 1 – C is less electronegative than O, put C in center
Step 2 – Count valence electrons C - 4 (2s22p2) and O - 6 (2s22p4)
-2 charge – 2e4 + (3 x 6) + 2 = 24 valence electrons
Step 3 – Draw single bonds between C and O atoms and complete
octet on C and O atoms.
Step 4 - Check, are # of e- in structure equal to number of valence e- ?
3 single bonds (3x2) + 10 lone pairs (10x2) = 26 valence electrons
Step 5 - Too many electrons, form double bond and re-check # of e-
O
C
O
O
2 single bonds (2x2) = 4
1 double bond = 4
8 lone pairs (8x2) = 16
Total = 24
Two possible skeletal structures of formaldehyde (CH2O)
H
C
O
H
H
C
H
O
An atom’s formal charge is the difference between the
number of valence electrons in an isolated atom and the
number of electrons assigned to that atom in a Lewis
structure.
formal charge
on an atom in
a Lewis
structure
=
total number
total number
of valence
of nonbonding
electrons in electrons
the free atom
-
1
2
(
total number
of bonding
electrons
The sum of the formal charges of the atoms in a molecule
or ion must equal the charge on the molecule or ion.
)
H
-1
+1
C
O
formal charge
on an atom in
a Lewis
structure
H
=
C – 4 eO – 6 e2H – 2x1 e12 e-
2 single bonds (2x2) = 4
1 double bond = 4
2 lone pairs (2x2) = 4
Total = 12
total number
total number
of valence
of nonbonding
electrons in electrons
the free atom
formal charge
= 4 -2 -½ x 6 = -1
on C
formal charge
= 6 -2 -½ x 6 = +1
on O
-
1
2
(
total number
of bonding
electrons
)
H
H
0
C
formal charge
on an atom in
a Lewis
structure
0
O
=
C – 4 eO – 6 e2H – 2x1 e12 e-
2 single bonds (2x2) = 4
1 double bond = 4
2 lone pairs (2x2) = 4
Total = 12
total number
total number
of valence
of nonbonding
electrons in electrons
the free atom
formal charge
= 4 - 0 -½ x 8 = 0
on C
formal charge
= 6 -4 -½ x 4 = 0
on O
-
1
2
(
total number
of bonding
electrons
)
Formal Charge and Lewis Structures
1. For neutral molecules, a Lewis structure in which there
are no formal charges is preferable to one in which
formal charges are present.
2. Lewis structures with large formal charges are less
plausible than those with small formal charges.
3. Among Lewis structures having similar distributions of
formal charges, the most plausible structure is the one in
which negative formal charges are placed on the more
electronegative atoms.
Which is the most likely Lewis structure for CH2O?
H
-1
+1
C
O
H
H
H
0
C
0
O
A resonance structure is one of two or more Lewis structures
for a single molecule that cannot be represented accurately by
only one Lewis structure.
What are the resonance structures of the carbonate
(CO32-) ion?
-
O
C
O
O
-
O
C
O
O
-
-
-
O
C
O
O
-
Additional Examples of Resonance
Ozone: O3
Bond order: 3/2
Bond lengths: 138 pm
Benzene: C6H6 an organic compound
C
C
Simplified resonance form
C bond order: 3/2
C bond length: 140 pm
Exceptions to the Octet Rule
The Incomplete Octet
BeH2
BF3
B – 3e3F – 3x7e24e-
Be – 2e2H – 2x1e4e-
F
B
F
H
F
Be
H
3 single bonds (3x2) = 6
9 lone pairs (9x2) = 18
Total = 24
Reaction of BF3 and NH3 – Lewis Representation
coordinate covalent bond – both
electrons donated by same atom.
Exceptions to the Octet Rule
Odd-Electron Molecules
NO
N – 5eO – 6e11e-
N
O
The Expanded Octet (central atom with principal quantum number n > 2)
SF6
S – 6e6F – 42e48e-
F
F
F
S
F
F
F
6 single bonds (6x2) = 12
18 lone pairs (18x2) = 36
Total = 48
Molecular Structure
Valence Shell Electron Pair Repulsion Model
(VSEPR)
Molecular geometry is the three-dimensional arrangement of
atoms in a molecule
Valence shell
outermost electron-occupied shell of an atom
holds the electrons that are usually involved in chemical
bonding
VSEPR Model
accounts for the geometric arrangement of electron
pairs around the central atom
in terms of electrostatic repulsion between electron
pairs
Molecular geometry is uniquely determined from two numbers:
1. Steric Number (Ns): total number of electron pairs
around the central atom.
2. Number of lone pairs (nonbonding valence
electrons pairs) on the central atom
Valence shell electron pair repulsion (VSEPR) model:
Class
Sn
# lone
pairs on
central atom
AB2
2
0
Arrangement of
electron pairs
Molecular
Geometry
linear
linear
B
B
Linear
0 lone pairs on central atom
Cl
Be
Cl
2 atoms bonded to central atom
VSEPR
Class
AB2
AB3
Sn
2
3
# lone
pairs on
central atom
Arrangement of
electron pairs
Molecular
Geometry
0
linear
linear
0
trigonal
planar
trigonal
planar
3 atoms bonded to
central atom
0 lone pairs on central atom
VSEPR
Class
AB2
Sn
2
# lone
pairs on
central atom
Arrangement of
electron pairs
Molecular
Geometry
0
linear
linear
trigonal
planar
tetrahedral
AB3
3
0
trigonal
planar
AB4
4
0
tetrahedral
4 atoms bonded to
central atom
0 lone pairs on central
atom
VSEPR
Class
AB2
Sn
2
# lone
pairs on
central atom
Arrangement of
electron pairs
Molecular
Geometry
0
linear
linear
trigonal
planar
AB3
3
0
trigonal
planar
AB4
4
0
tetrahedral
tetrahedral
AB5
5
0
trigonal
bipyramidal
trigonal
bipyramidal
4 atoms bonded to
central atom
0 lone pairs on central
atom
VSEPR
Class
AB2
Sn
2
# lone
pairs on
central atom
Arrangement of
electron pairs
Molecular
Geometry
0
linear
linear
trigonal
planar
AB3
3
0
trigonal
planar
AB4
4
0
tetrahedral
tetrahedral
AB5
5
0
trigonal
bipyramidal
trigonal
bipyramidal
AB6
6
0
octahedral
octahedral
6 atoms bonded to
central atom
0 lone pairs on central
atom
VSEPR – Effect of lone pairs
Class
Sn
# lone
pairs on
central atom
AB3
3
0
AB2E
2
1
Arrangement of
electron pairs
trigonal
planar
trigonal
planar
Molecular
Geometry
trigonal
planar
bent
VSEPR
Class
Sn
# lone
pairs on
central atom
AB4
4
0
AB3E
3
1
Arrangement of
electron pairs
Molecular
Geometry
tetrahedral
tetrahedral
tetrahedral
trigonal
pyramidal
lone-pair vs. lone pair
lone-pair vs. bonding
bonding-pair vs. bonding
>
>
repulsion
pair repulsion
pair repulsion
VSEPR
Class
AB4
Sn
4
# lone
pairs on
central atom
0
Arrangement of
electron pairs
Molecular
Geometry
tetrahedral
tetrahedral
AB3E
3
1
tetrahedral
trigonal
pyramidal
AB2E2
2
2
tetrahedral
bent
O
H
H
VSEPR
Class
AB5
AB4E
Sn
5
4
# lone
pairs on
central atom
Arrangement of
electron pairs
Molecular
Geometry
0
trigonal
bipyramidal
trigonal
bipyramidal
1
trigonal
bipyramidal
distorted
tetrahedron
10.1
VSEPR
Class
AB5
Sn
5
# lone
pairs on
central atom
0
AB4E
4
1
AB3E2
3
2
Arrangement of
electron pairs
Molecular
Geometry
trigonal
bipyramidal
trigonal
bipyramidal
trigonal
bipyramidal
trigonal
bipyramidal
distorted
tetrahedron
T-shaped
F
F
Cl
F
10.1
VSEPR
Class
AB5
Sn
5
# lone
pairs on
central atom
0
AB4E
4
1
AB3E2
3
2
AB2E3
2
3
Arrangement of
electron pairs
Molecular
Geometry
trigonal
bipyramidal
trigonal
bipyramidal
trigonal
bipyramidal
trigonal
bipyramidal
distorted
tetrahedron
trigonal
bipyramidal
T-shaped
linear
I
I
I
VSEPR
Class
Sn
# lone
pairs on
central atom
Arrangement of
electron pairs
Molecular
Geometry
AB6
6
0
octahedral
octahedral
AB5E
5
1
octahedral
square
pyramidal
F
F
F
Br
F
F
VSEPR
Class
Sn
# lone
pairs on
central atom
Arrangement of
electron pairs
Molecular
Geometry
AB6
6
0
octahedral
octahedral
AB5E
5
1
octahedral
AB4E2
4
2
octahedral
square
pyramidal
square
planar
F
F
Xe
F
F
Guidelines for Applying the VSEPR Model
1. Draw Lewis structure for molecule.
2. Determine the steric number. Electrons in double
and triple bonds are treated as single bonding pair.
atom.
3. Use VSEPR to predict the geometry of the molecule.
What are the molecular geometries of SO2 and SF4?
O
S
AB2E
bent
F
O
F
S
F
AB4E
F
distorted
tetrahedron
4. When predicting bond angles, remember
lone-pair vs. lone pair
lone-pair vs. bonding
bonding-pair vs. bonding
>
>
repulsion
pair repulsion
pair repulsion
5. If a molecule has two or more resonance structures,
apply the VSEPR model to any one of them.
Dipole Moments and Polar Molecules
electron poor
region
electron rich
region
H
F
d
d
m=qxr
q is the charge
r is the distance between charges
1 D = 3.336 x 10-30 C m
Infrared Spectroscopy, the study of the infrared
frequencies that are absorbed by a particular material.
It provides information about molecular structure and
identity.
CO2
IR inactive – no change in dipole
fingerprinting – definitive method of identification
CH2
CHC
N
Valence Bond Theory and Hybridization
Application of VB theory to polyatomic molecules must account
for molecular geometry.
Be – 1s22s2
BeCl2
Cl – 1s22s22p33s23p5
Be – to form 2 bonds, need 2 unpaired electrons
Cl – could overlap 3s or 3p orbitals to form the bonds
to form 2 equivalent bonds requires 2 equivalent orbitals
Hybridization: the mixing of nonequivalent atomic orbitals in
an atom (usually a central atom) to generate a set of
hypothetical equivalent bonding orbitals, called hybrid
orbitals,
+
-
Cl
Be
Cl
promotion energy < energy released during bond formation
sp2 Hybridization
BF3
B – 1s22s22p1
F
F
B
F
sp3 Hybridization
CH4
C – 1s22s22p2
H
C
H
H
H
Hybridization – theoretical model to explain
bonding in polyatomic molecules
1. Mix at least 2 nonequivalent atomic orbitals (e.g. s
and p). Hybrid orbitals have very different shape
from original atomic orbitals.
2. Number of hybrid orbitals is equal to number of
pure atomic orbitals used in the hybridization
process.
3. Covalent bonds are formed by:
a. Overlap of hybrid orbitals with atomic orbitals
b. Overlap of hybrid orbitals with other hybrid
orbitals
Procedure for Hybridizing Atomic Orbitals
1. Draw the Lewis structure for the molecule.
2.
Predict the overall arrangement of the electron
pairs (both bonding pairs and lone pairs) using the
VSEPR model (see Tables 4.1 and 4.2).
3. Predict the overall arrangement of the electron
pairs (both bonding pairs and lone pairs) using the
VSEPR model (see Tables 4.1 and 4.2).
Hybridization Using d Atomic Orbitals
SF6
S – [Ne]3s23p4
Hybridization in Double and Triple Bonds
Double Bonds:
H
H
C C
H
unhybridized
hybridzied
H
C2H4
Another View:
Triple Bonds:
H
C C
H
C2H2
Another View:
Isomers
Structural Isomers: Same molecular formula but
different bond connectivity
C4H10
Steroisomers: Same molecular formula, identical
bond connectivity but different three-dimensional
structures
Geometric isomers: stereisomers that differ in the
spatial arrangement of the atoms relative to one
another
Optical isomers or enantiomers: nonsuperimposable
mirror images
CHFBr
chiral molecule
chiral center
achiral
chiral
24.2
Cis-Trans Isomerization in the Vision Process
24.2
Operation of a Polarimeter
Molecular orbital theory
Bonds are formed from interaction of atomic orbitals
to form molecular orbitals.
O
O
No unpaired e-
Should be diamagnetic
Experiments show O2 is paramagnetic
H2+: The Simplest Molecule
V (rA , rB ; R) 
e2
4p0 rA

e2
4p0 rB
Electron-nuclear
attraction
Born-Oppenheimer approximation
set of wavefunctions,
(x,y,z;R), describing the
quantum state of the electron
called molecular orbitals

e2
4p0 R
internuclear
repulsion
Linear Combinations of Atomic Orbitals
LCAO
 MO ( A, B)  c AA, 1s  cBB ,1s

2
MO
( A, B)  
2
MO
(B, A)
which implies
 MO ( A, B)   MO (B, A)
because cA=cB or cA=-cB, there are only two possible
molecular orbitals. Orbitals are conserved.
1
 A,1s B,1s 
 
2
lower energy
s (sigma)
1
 A,1s B,1s 
 
2
higher energy
Energy as a Function of Internuclear Separation
higher energy
Molecular orbital energy-level diagram
(MO diagram)
H2+: one electron
H2: two electrons
H
2
1
 A,1s(1)  B,1s(1)  A,1s(2)  B,1s(2)
 s 1s (1)  s 1s ( 2) 
2
Molecular Orbital (MO) Configurations
1. The number of molecular orbitals (MOs) formed is always
equal to the number of atomic orbitals combined.
2. The more stable the bonding MO, the less stable the
corresponding antibonding MO.
3. The filling of MOs proceeds from low to high energies.
4. Each MO can accommodate up to two electrons.
5. Use Hund’s rule when adding electrons to MOs of the
same energy.
6. The number of electrons in the MOs is equal to the sum of
all the electrons on the bonding atoms.
Molecular Orbitals from LCAO of 2s atomic orbitals
Molecular Orbitals from LCAO of 2p atomic orbitals
Two Possible Interactions Between Two Equivalent p Orbitals
Assume x is the internuclear axis
1. head-on overlap of the 2px orbitals
2. side-on overlap of the 2py or 2pz orbitals
Two pairs of p orbitals at 90o from each other.
Generalized Molecular Orbitals Diagrams for
Homonuclear Diatomic Molecules of Period 2.
Li2 through N2
LCAO for 1s orbitals omitted.
O2 and F2
Homonuclear Diatomic Molecules of First- and
Second-Period Elements
HF
CO
C
O
MO Theory for Heteronuclear Diatomics
• MO’s will no longer contain equal contributions from
each AO.
– AO’s interact if symmetries are compatible.
– AO’s interact if energies are close.
– No interaction will occur if energies are too far apart. A
nonbonding orbital will form.
YX makes a
greater
contribution to
the Y*MO
YY makes a greater
contribution to the
YMO
Example HF
• The F (2s) is much lower in
energy than the H (1s) so they
do not mix.
– The F (2s) orbital makes a nonbonding MO.
– We certainly don’t have to
worry about the F (1s) because
is MUCH lower in energy.
• The H (1s) and F (2p)’s are
close in energy and do interact.
– The 2px and 2py don’t have the
appropriate symmetry though
and therefore form nonbonding
MO’S
– Only the 2pz and 1s mix.
The MO diagram for HF
Energy
s*
1s
2px 2py
2p
s
AO
of H
MO of
HF
AO
of F
Energy
s*
2p
The MO diagram for NO
s
p*
p
s
p
p
s*
2p
possible Lewis
structures
p
s
2s
2s
AO of N
AO of O
s
s
MO of NO
0
0
N
O
-1
+1
N
O
Molecular Orbital Theory
Remember that the closer to AO’s of appropriate symmetry are in energy, the more they interact
with one another and the more stable the bonding MO that will be formed. This means that as the
difference in electronegativity between two atoms increases, the stabilization provided by covalent
bonding decreases (and the polarity of the bond increases). If the difference in energy of the
orbitals is sufficiently large, then covalent bonding will not stabilize the interaction of the atoms. In
that situation, the less electronegative atom will lose an electron to the more electronegative atom
and two ions will be formed.
AO(1)
AO(1)
AO(1)
AO(1)
AO(2)
AO(2)
AO(2)
AO(2)
Most covalent
Polar Covalent
Ionic
MO Theory and Polyatomic Molecules
• MO diagrams are complicated for polyatomics.
– For example, CO2 requires drawing a diagram with four sets of
orbitals (3 AO’s and 1 MO).
• To simplify the problem we use the ligand group orbital
approach (LGO)
Ligand Group Orbital (LGO) Approach to MO’s
•
•
Consider XH2, a linear molecule, oriented along the z-axis. Let X have 2s
and 2p orbitals.
The 1s orbitals on H have two possible phases.
– Take the two H’s as a group to make LGO’s.
– Draw MO diagram.
– The MO’s will look like:
•
NOTE: The s-bonding character in orbitals Y1 and Y2 is spread over all
three atoms indicating the bond character is delocalized.
A bent triatomic H2O
How do we know which orbitals interact?
Answer: Only orbitals with the same symmetry
label can interact.
MO diagram for H2O
MO and VB compared
Valence Bond Theory
Molecular orbital theory
•
•
•
•
•
•
•
•
Separate atoms are brought
together to form molecules.
The electrons in the molecule pair
to accumulate density in the
internuclear region.
The accumulated electron density
“holds” the molecule together.
Electrons are localized (belong to
specific bonds).
Basis of Lewis structures,
resonance, and hybridization.
Very poor theory for obtaining
quantitative bond dissocation
energies.
Good theory for predicting
molecular structure.
•
•
•
•
Molecular orbitals are formed by
the overlap and interaction of
atomic orbitals.
Electrons then fill the molecular
orbitals according to the aufbau
principle.
Electrons are delocalized (don’t
belong to particular bonds, but are
spread throughout the molecule).
Can give accurate bond
dissociation energies if the model
combines enough atomic orbitals
to form molecular orbitals.
Model is complex and requires
powerful computers for even
simple molecules.
Photoelectron Spectroscopy – a tool for finding the
energy of AO’s and MO’s
• An atom or molecule is irradiated with light having energy hn.
• If the hn is large enough to overcome the binding energy of the
electrons then electrons will be ejected from the system.
• The KE of the ejected electrons is measured.
KE = hn – (binding energy of the electron)
• Koopman’s theorem – the binding energy of the electron is equal to
the energy of the AO or MO in which it resides.
Molecular Orbital Theory and Polyatomic Molecules
O3
LCAO
Delocalized Molecular Orbitals
Delocalized molecular orbitals are not confined between
two adjacent bonding atoms, but actually extend over three
or more atoms.
lowest unoccupied molecular orbital - LUMO
highest occupied molecular orbital - HOMO
C6H6 - Benzene
Bonding in Metals (Band Theory)
• Construct an MO diagram for lithium metal, Lin.
– There will be n MOs arising from taking linear combinations of n 2s
AO’s.
• Result:
– Delocalized metal-metal bonding.
– In the presence of an electric field, the electrons can move into vacant
MO’s (because the energy spacing is small).
– And since the MO’s are delocalized the promoted electrons can move
from one Li to another => electrical conductivity.
Electrical conductivity is a characteristic property of partially filled
bands of MO’s.
Electrical Conductivity in Metals
•
•
If the nuclei are arranged in a perfectly ordered lattice then there should be
no resistance to oppose the flow of current.
Also, increase T increases the thermal population of the higher levels and
should increase the electrical conductance.
• BUT, thermal vibrations of the nuclei increase electrical resistance so
conductivity actually decreases with temperature.
The uppermost filled molecular orbital
becomes known as the Fermi energy.
Semi-conductor
Metallic conductor
Metallic conductor
• If the 2s and 2p band overlap
then you have a conductor.
• A large separation (band gap)
between a fully occupied band
and an empty band 
insulator.
• A partially occupied band 
metallic conductor.
• Overlap of an occupied and a
vacant band  metallic
conductor.
• Small band gap 
semiconductor.
Insulator
Band Theory
Band Theory (A better model)
• Beryllium is a conductor, but the model as we have
described it predicts Be to be an insulator  because all
the MO’s are filled.
– Must consider the 2p AO’s which gives another band.
Fermi Level
• The HOMO (highest occupied
molecular orbital) in the metal at
absolute zero is defined as the
Fermi Level.
– As temperature increases,
electrons thermally populated
MOs above the fermi level.
• Thermal populations in a metal
cannot be described by the
Boltzmann distribution.
– Instead they are described by
the Fermi-Dirac distribution
which is a modified Boltzmann
distribution that accounts for the
Pauli principle.
Fermi-Dirac Distribution
@ temperatures greater than 0 K,
the occupation of the molecular
orbitals tails into the empty bands
above the Fermi energy. This
indicates that the electrons close to
the Fermi level are very mobile and
can move relatively freely through
the solid. At much higher energies,
it is found that the occupation of the
empty levels follows a Boltzmann
distribution.
The density of states (DOS)
• The density of states describes the energy levels per unit
energy increment.
• The density of states in a band is found to be nonuniform across the band.
• The reason for this is that the levels are packed more
closely together at some energies than others as a result
of overlap of the molecular orbitals.
Semi-conductors (intrinsic)
• Semi-conductors arise when we have
a fully occupied band separated from
an unoccupied band by a small band
gap.
– Sufficient energy (heat) can thermally
populated the unoccupied band.
– Electrons present in the upper
conduction band act as charge
carriers.
– Positive holes in the lower valence
band also act as charge carriers.
– Conductance increases with
temperature.
Semi-conductors (extrinsic)
• Semi-conducting can be enhanced if a dopant
is added to the crystal lattice.
• For example, replace a few Si (group 14) sites
with a few Gallium (group 13) atoms.
– Makes electron deficient sites and leads to a
discrete (if the concentration of dopant is small)
unoccupied level in the band structure.
– Electrons can then populate the acceptor level,
leaving positive holes in the lower band  ptype conductor (positive charge flow).
Semi-conductors (extrinsic)
• Semi-conducting can be enhanced if a dopant
is added to the crystal lattice.
• For example, replace a few Si (group 14) sites
with a few Arsenic (group 15) atoms.
– Makes electron rich sites and leads to a
discrete (if the concentration of dopant is small)
occupied level in the band structure.
– Electrons in the donor level can thermally
populate the conduction band where they are
free to move  n-type conductor (negative
charge flow).
– Phosphorous (group 15) can also be used as a
dopant in Si to get an n-type conductor.
• Silicon semi-conductors are only efficient if
they are made from ultra-high purity Si, which
is extracted from SiO2 (naturally occurring)
The reason metals deform.
metal is deformed