Hückel Theory
Hückel’s Molecular Orbital Theory
By Sean Hanley
Overview
•
•
•
•
•
Explain Hückel’s Rule
Aromatic Compounds
Explain Molecular Orbital (MO) Theory
Hückel Theory in Quantum Sense
So What??
Hückel’s Rule
• Any conjugated monocyclic polyene that is
planar and has (4n+2)π and/or
nonbonding electrons, with n = 0,1,2, etc.,
will exhibit the special stability associated
with aromaticity. (1930)
Hückel’s Rule
• n
0
1
2
3
4
4n + 2 Pi electrons
4(0) + 2 = 2
4(1) + 2 = 6
4(2) + 2 = 10
4(3) + 2 = 14
4(4) + 2 = 18
Which are Aromatic???
3
2
1
O
O
H
5
2
H
B
N
N
B
B
H
34
H
N
8
O
H
H
N
6
7
N
N
H
N
Some Common Aromatic
Compounds
Comparison of Molecules
Benzene is Stabilized by
36 kcal/mol called the
Empirical
Resonance Energy
Molecular Orbital Theory Simplified
• Hybrid Orbitals
• The Bonding of Chemistry
• Atomic Orbitals
Shape of P and D orbitals
Atomic Orbitals to Molecular
Orbitals
Molecular Orbital Theory
Dioxygen O2
Molecular Orbital Theory
2 Bonds
Molecular Orbital Theory
Dicarbon + ion
Molecular Orbital Theory
1.5 Bonds
Overlap of Orbitals
• 2pz orbitals overlap causing stabilization a
semi bonding
• Ethene Example
– sp^2 hybridized
– 1 Double Bond
– Ψpi= c12pzA + c22pzB
Ethene Example
• Determinant associated
with Wave function
• H11=H22
• Sij set to zero unless i=j
• Sii=1
• Diagonal elements are
assumed to be the same
for all carbon atoms
denoted α (Alpha)
• Nearest neighbor carbon
atoms assumed the same
denoted β (Beta)
H11  ES11
H12  ES12
H 21  ES21
H 22  ES22
 E

0

 E
0
E   
Benzene Structure
Benzene Pi System
Benzene Hückel Theory
E

0
0
0
0

E

0
0
0
0

E

0
0
0
0
0

E

0
0
0
0

E

0
0
0
0

E
E1    2
E2  E3    
x
(  E )

x6  6x4  9x2  4  0
E4  E5    
E6    2
E  2(  2 )  4(   )  6  8
1 
Benzene
P
z Wave Functions
1
2 pz1  2 pz 2  2 pz 3  2 pz 4  2 pz 5  2 pz 6 
6
1
2 pz 2  2 pz 3  2 pz 5  2 pz 6 
2 
4
E1    2
E2    
3 
1 
1
1
1
1

2
p

2
p

2
p

2
p

2
p

2
p
 z1
z2
z3
z4
z5
z6 
2
2
2
2
3

E3    2
4 
1
2 pz 2  2 pz 3  2 pz 5  2 pz 6 
4
E4    
1 
1
1
1
1

5 
 2 p z1  2 p z 2  2 p z 3  2 p z 4  2 p z 5  2 p z 6 
2
2
2
2
3

E5    
1
2 p z1  2 p z 2  2 p z 3  2 p z 4  2 p z 5  2 p z 6 
6 
6
E6    2
MO Diagram of Benzene
Benzene MO
Aromatic Stabilization
Aromatic Stabilization
Recent Research in Aromaticity
• In 2000 chemists in Germany formulated a
rule to determine when a fullerene would
be aromatic. In particular, they found that if
there were 2(n+1)^2 π electrons
• Buckminsterfullerene (Buckyball), with 60
π electrons, is non-aromatic, since
60/2=30
Questions????