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????