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Symmetry and the Woodward-Hoffmann Rules


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 Cs symmetry. We may therefore draw an orbital energy correlation diagram, in which the orbitals of butadiene are classified under Cs 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 Cs 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 C2v symmetry with the axes as shown.
For H2CO, we can form CH bonding orbitals (a1 and b2), the O lone pair (2pyO=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 Cs, 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.

next up previous
Next: Cyclic Hydrocarbons Up: Contents - Previous: The Valence-Bond description of Benzene
Nicholas Handy