Symmetry and the Woodward-Hoffmann Rules  Contents -  Huckel Theory using Symmetry

The Valence-Bond description of Benzene

We use sp² hybrids for the $\sigma$ bonds. sp² hybrids are constructed in terms of (2s_C,2p_yC,2p_zC) atomic orbitals and they are directional
   
Hence we can construct $\sigma$ valence-bond pairs as indicated.
For the $\pi$ electrons, there are two possible (`Kekule') structures $\psi_1=\{\pi_A\pi_F\}\{\pi_E\pi_D\}\{\pi_B\pi_C\}$
   
$\psi_2=\{\pi_A\pi_B\}\{\pi_C\pi_D\}\{\pi_E\pi_F\}$
both written in terms of valence-bond pairs. There are also three `Dewar' structures

with corresponding wavefunctions $\psi_3,\psi_4,\psi_5$.
On constructing a $5\times 5$ secular matrix, the resulting wavefunction is
$\Psi=0.6(\psi_1+\psi_2)+0.26(\psi_3+\psi_4+\psi_5)$
with energy
$E=Q+2.61\gamma$
where one Kekule structure has energy $E=Q+1.50\gamma$. The resonance energy, defined as
E(C₆H₆)-3*E(C₂H₄) is thus 1.11$\gamma$.
Valence Bond and Molecular Orbital theories may be compared in the following table for resonance energies (in kcal mol^-1, 1kcal mol^-1=4.2 kJmol^-1)
 

	Expt	VB	$\gamma$	MO	$\beta$
C6H6	39	1.11$\gamma$	35	2.00$\beta$	20
C10H10	75	2.04$\gamma$	37	3.68$\beta$	20
C14H14	105	3.09$\gamma$	34	5.32$\beta$	20

 
Both are successful! 

  
 Symmetry and the Woodward-Hoffmann Rules  Contents -  Huckel Theory using Symmetry

1998-09-23