Limitations
How to draw
Lewis structures of Benzene?
1
Limitations – Bonding in Benzene
• Six carbon atoms arranged on
a hexagonal plane
• Bond angle of 120 degrees
• Carbon-carbon bonds in
benzene are of equal length
2
• Each carbon is sp2 hybridized
with remaining p-orbital
perpendicular to the molecular
plane
C
• Network of s-bonds formed
about the ring in the plane of the
molecule by sp2 hybrid orbitals
sp2
• 3 pairs of overlapping p-orbitals
gives alternate double bonds
pi
C
C
C
sigma bonds
H
3
• Valence bond theory explains the in-plane s bonds well.
• However, it is known that the p bonds are delocalized.
VB theory does not do a good job in describing the p bonds
4
we need concept of‘resonance’ to explain the
p bonding in Benzene and other compounds
with alternate double bonds
5
Lewis structures of N2 and O2?
6
Pros and cons of VB theory
Pros
• Visual and intuitive
• Useful in describing structure, properties and reactions in
organic chemistry
Cons
• Principle of electron pair localized between two atoms too
restrictive: cannot explain delocalized pi-bonding
• Unable to predict certain properties in molecules.
eg. paramagnetism in oxygen
7
Molecular Orbital Theory
Quantum
Chemistry
Mulliken
(1896-1986)
Nobel prize 1966
Hund
(1896-1997)
8
Key Words in this PART
Molecular Orbital Theory
HOMO and LUMO
Bonding & antibonding
Diatomic Molecule
LCAO Approximation
- homonuclear
- heteronuclear
MO diagram
Bond Order
Hybridization + MO approach
9
10
Possible bonding interactions
s+s
p+p
p+p
p+s
s+p
p+p
11
Basic concept of MO theory
s
s
AO
AO
ss
MO
12
Features
VB theory
• A molecule as a group of atoms bonded
through localized overlapping of valence-shell
atomic and/or hybrid orbitals occupied by
electrons.
MO theory
• A molecule as a collection of nuclei with orbitals
delocalized over the whole molecule and
occupied by electrons
View whole molecule
Symmetry & Energy level & distance
13
To understand readily, at first….
s
+
or
+
p
or
+
or
or
=
•
=
The different shadings of the lobes represent different
sign of the wave function .
14
How Bonding and Anti-bonding MO`s are formed
• In 1926 and 1927, Schrödinger and Heisenberg published papers
on wave mechanics, descriptions of the wave properties of electrons
in atoms. Schrödinger equation describes the wave properties of an
electron in terms of its position, mass, total energy, and potential
energy.
Erwin Rudolf Josef Alexander
Schrödinger (1887 - 1961)
Werner Karl Heisenberg
(1901 - 1976)
15
• Each atomic orbital is associated with a wave function AO
[Solving Schrödinger's equation for an atom results in a series of
wave functions (electron probability distributions) and associated
energy levels. These wave functions are orbitals]
H = the Hamiltonian operator
 = the wave function
E = energy of the electron
h = Planck constant
m = mass of the particle (electron)
e = charge of the electron
Z = charge of the nucleus
4p0 = permittivity of a vacuum
n = quantum numbers
a = wavelength
(for one-dimensional particle)
=
||2 = probability density (to find electron)
16
-LCAO Approximation • LCAO- Linear Combination of Atomic Orbitals
• Approximate solutions to molecular Schrödinger's equation can be
constructed from linear combination of atomic orbitals, the sums and
differences of the atomic wave functions.
= c11 + c22 + c33 +… + cnn
c = adjustable coefficients
17
Three conditions need to be met for effective overlap
• 1)
must be such that regions with same sign
[+ and + (or – and -) or red and red (or blue and blue)] for
wave function overlap.
°
can overlap
cannot overlap
18
• 2)
of the orbitals (AOs) must be similar
E
19
• 3)
between atoms must be short enough to provide good
overlap, long enough to prevent excessive repulsive forces
°
20
Rules on MO theory
• MOs are constructed by symmetry allowed linear
combination of AOs
• AOs of similar energy combine more effectively to give
MOs than AOs of vastly different energy
• Distance between atoms must be short enough to
provide good overlap
• No. of MO = total no. of AOs contributed
• Bonding MOs lower in energy than anti-bonding MOs
• Electrons are assigned to successive higher energy MOs
21
• If Ψ is the wave function of the MO`s obtained from two atomic
orbitals of two atoms A and B, they can combine in two ways
AO

MO
AO

Ψ
or
Math Operation – physical significance
Addition
– attraction
Subtraction – repulsion
22
Constructive interference
When two wave functions (orbitals) on different atoms add
constructively, they produce a new MO that promotes
bonding given by:
atomic orbitals
new Molecular Orbital
(1s)H(1) + (1s)H(2) 
+
b(H-H)
=
increased amplitude
When two waves add, the amplitude increases
23
Destructive interference
When two wave functions (orbitals) on different atoms add
destructively, they produce a new MO that decreases
bonding given by:
atomic orbitals
new Molecular Orbital
(1s)H(1) - (1s)H(2)
+
=
(1s)
ab(H-H)
H(1) + (- (1s)H(2) )
=
no amplitude (a node)
When two waves subtract, the amplitude decreases
24
When two waves add (overlap as red↑ & blue↑) ,
the amplitude (white) increases (↑)
When two waves subtract (overlap as red ↑ & blue↓),
the amplitude (white) decreases (zero)
25
Antibonding Orbitals
Subtraction of AOs forms an antibonding MO, which has a
node, or region of zero electron density, between the nuclei.
E ΨA – ΨB gives rise to Anti-Bonding MO`s
ABMO
BMO
ΨA + ΨB gives rise to Bonding MO`s
Addition of AOs forms a bonding MO, which has a region26of
high electron density between the nuclei.
Contours and energies of the bonding and
antibonding molecular orbitals (MOs) in H2
Amplitudes of wave functions
The bonding MO is lower in energy and the antibonding MO is
higher in energy than the AOs that combined to form them. 27
Why are BMO`s lower in energy than ABMO`s ?
ΨA – ΨB gives rise to Anti-Bonding MO`s
E
ABMO
BMO
ΨA + ΨB gives rise to Bonding MO`s
28
Why are BMO`s lower in energy than ABMO`s ?
We have to analyze electronic charge distribution
For ΨA , electronic charge density is given by ΨA2
So for BMO (Ψb)2 = (ΨA + ΨB )2
= ΨA2 + ΨB 2 + 2 ΨAΨB
Which tells us that electronic density of the BMO is greater than
the sum of the electron densities of the individual atoms A and B
by a factor of 2 ΨAΨB
(Ψab)2 = (ΨA - ΨB )2
= ΨA2 + ΨB 2 - 2 ΨAΨB
Similarly for the ABMO, electron density is less
by a factor of -2 ΨAΨB
Greater electron density means greater overlap,
Greater the overlap → the greater stability
Greater stability means lesser is the energy associated with it
29
ΨA2 + ΨB 2 + 2 ΨAΨB
ΨA2 + ΨB 2 - 2 ΨAΨB
30
MO diagram for H2
energy
high
unstable
lose energy
(unhappy)
(1s)1
(1s)1
H
H
bond strength
436 kJ/mol
low
stable
gain energy
(happy)
H H
s-bond
An electron always prefers to go to a lower energy orbital. 31
(Unless forced by energy considerations and space constraints)
MO diagram for H2
s*s
* stands for anti-bonding MO
The asterisk (*) is called a Star
1s
1s
sbs
atomic
orbital A
molecular atomic
orbital B
orbital
s orbitals in sigma bonding
(head-on overlap)
superscript b stands for bonding MO
32
p orbital scenario
y
x
z
• Side-on overlap of two corresponding p atomic orbitals on
different atoms (say 2py with 2py or 2pz with 2pz) produces:
1.
2.
p2py
p*2py
(or p2pz)
(or p*2pz)
(both are bonding orbitals)
(both are antibonding orbitals)
33
p orbital scenario
y
x
z
• The head-on overlap of two corresponding p atomic orbitals on
different atoms, say 2px with 2px produces:
1. s2px bonding orbital
2. s*2px antibonding orbital
34
Constructing MO diagrams
y
y
y
2p-orbitals
y
y
x
y
z
x
z
2px
z
x
z
x
z
2py
x
y
x
z
y
y
2pz
x
z
x
z
2px
x
z
2py
2pz
s-orbital
y
y
x
z
y
x
z
x
z
35
Constructing MO diagrams
s*2px
p*2py
y
y
y
y
p*2pz
2p
x
z
x
z
2px
x
x
p2pz
z
2py
y
z
2pz p
2py
x
z
2px
y
x
z
2py
2pz
s2px
s*2s
2s
2s
s2s
s*1s
1s
1s
s1s
36
2p