Symmetry and the Woodward-Hoffmann Rules

butadiene-cyclobutene

Is a reaction forbidden or allowed?. Symmetry can often answer this question. Consider the butadiene $\leftarrow\rightarrow$ cyclobutene reaction. If we consider the ring opening of cyclobutene, there are two pathways, conrotatory or disrotatory. The diagram shows these paths by considering two possible rotations of the CH₂ groups.  

Conrotatory motion maintains C₂ symmetry, and disrotatory motion maintains C_s symmetry. We may therefore draw an orbital energy correlation diagram, in which the orbitals of butadiene are classified under C_s symmetry (a^',a^'',a^',a^''), on the lhs, and under C₂ symmetry (b,a,b,a), on the rhs. The bonds of cyclobutene which are involved ( $\sigma,\pi,\pi^*,\sigma^*$) are shown in the middle. Lines are then drawn connecting the cyclobutene orbitals under C_s symmetry (a^',a^',a^'',a^''), and under C₂ symmetry (a,b,a,b).
The diagram clearly shows that the disrotatory path is favoured photochemically and the conrotatory path is favoured thermally.
 
 

   

Dissociation of Formaldehyde

We shall consider the dissociation of H₂CO $\rightarrow$H₂+CO.

We shall use C_2v symmetry with the axes as shown.
For H₂CO, we can form CH bonding orbitals (a₁ and b₂), the O lone pair (2p_yO=b₂) and the CO $\pi$ orbital (b₁). Thus the electronic configuration is 1a₁²1b₂²2b₂²1b₁².
For H₂, the $\sigma_g$ orbital has a₁ symmetry. For CO, the $\sigma$ bonding orbital has a₁ symmetry, and the $\pi$ orbitals have b₁+b₂ symmetry. Thus the separated molecules have electronic configuration 1a₁²2a₁²1b₂²1b₁². This is different to the molecule, and therefore there will be an orbital crossing, and the transition state will have a lower symmetry.
 
 

   
 

Indeed the b₂ and a₁ orbitals must have the same symmetry, and this happens in C_s, where there is only a plane of symmetry. The transition state is shown below, and there is a very high barrier (75 kcal mol^-1)

 

The above arguments, entirely based on symmetry, which predict whether their is a barrier in a reaction, form the basis of the Woodward-Hoffmann rules, examples of which are discussed in a Part III Organic Chemistry course.
 

1998-09-23