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“Hückel Molecular Orbitals for Aromatic and Unsaturated Hydrocarbons” Kamil Walczak Department of Chemistry and Physical Sciences, Pace University, 1 Pace Plaza, New York, NY 10038 INTRODUCTION

Ethylene (Ethene)

1,3-Butadiene

Benzene Molecule

We present semi-empirical Hückel method used to determine stability, energy levels, and approximated molecular orbitals of delocalized “pi” electrons in aromatic and unsaturated hydrocarbons. Molecular orbitals contain all the information about the system under consideration from quantum mechanical point of view. Ions may be created by adding or removing a specific p-shaped atomic orbital from a hybrid of Hückel molecular orbital. Extension of Hückel method onto “sigma” electrons, ligands and heteroatoms is quite straightforward and may be used to examine large complexes of organometallic and inorganic compounds as well as large biological systems.

Secular equation for ethylene:

Secular equation for 1,3-butadiene:

Secular equation for benzene ring:

  c A   0  E           E    c B   0  

 0 0  c A   0  E          c E    0 0     B         0  cC  E  0      0  E    c D   0   0

 0 0 0   c A   0  E          c E    0 0 0 0     B    0  E  0 0  c C   0        0  E  0  c D   0   0 c     0  0 0  E   E  0      0 0 0  E    c F   0   

Hückel Method

Allyl Anion

Sigma-pi separability – since “sigma” and “pi” orbitals in planar molecules are orthogonal, both subsystems are separable.

Secular equation for allyl anion:

Negligence of sigma electrons – since only “pi”-type electrons determine most properties of organic molecules, skeleton electrons of “sigma”-bonds may be neglected.

 0  c A   0  E          E    c  0     B    0  E    c C   0 

Linear Combination of Atomic Orbitals (LCAO) – where one electron described by “2pz” per carbon atom is included.

   c n n

where

n  2p z (rn )

Polycyclic Aromatic Hydrocarbons

n

H n ,n    6.6 eV

and

H n ,n 1  H n 1,n    2.4 eV

Orbital Hybridization Orbital hybridization – mixture of atomic orbitals to form new hybrid orbitals suitable for qualitative description of atomic bonding and explanation of the shape of molecular orbitals.

Fullerene C60

CLOSING REMARK

HOMO 6.0 eV

LUMO  3.1 eV

Using Hückel method, we evaluate energy levels of “pi”-type electronic system by making secular determinant equal to zero and the corresponding molecular orbitals by solving a homogeneous set of linear equations for specific expansion coefficients. In particular, the superposition of p-type atomic orbitals and quantum interference effects create bonding, non-bonding and anti-bonding molecular orbitals.