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 ( )
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.
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 orbital (b1). Thus the electronic configuration is 1a121b222b221b12.
For H2, the orbital has a1 symmetry. For CO, the bonding orbital has a1 symmetry, and the 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