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 4n + 2 Pi electrons
0 4(0) + 2 = 2 1 4(1) + 2 = 6 2 4(2) + 2 = 10 3 4(3) + 2 = 14 4 4(4) + 2 = 18
Which are Aromatic???
OO
N
B
N
B
N
B
H
H
H
H
H
H
O
N
NN
N
H
1
2
2
3
3
4
5
67
8
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 associatedwith 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 samedenoted β (Beta)
022222121
12121111 ESHESH
ESHESH
0
E
E
E
Benzene Structure
Benzene Pi System
Benzene Hückel Theory
0
0000
000
000
000
000
0000
E
E
E
E
E
E
)( E
x
0496 246 xxx
21 E 32 EE 54 EE 26 E
86)(4)2(2 E
Benzene Pz Wave Functions 6543211 222222
6
1zzzzzz pppppp 21 E
65322 22224
1zzzz pppp 2E
6543213 2
2
122
122
2
122
12
3
1zzzzzz pppppp 23 E
65324 22224
1zzzz pppp 4E
6543215 2
2
122
122
2
122
12
3
1zzzzzz pppppp 5E
6543216 2222226
1zzzzzz pppppp 26 E
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????