Violations. There are none! Part 2.

I left the story of the molecule below on the precipice of a cliff. I had shaved off the four benzo groups (blue) in the time honoured computational tradition of clearing away distractions. Unfortunately, it became clear as the story unfolded that the benzo groups had a distractingly critical role to play, and so its time to start adding them back again, but in stages.

To recapitulate, this reaction (with four benzo groups)  has a half life of ~30 minutes at 353K, giving it a a free energy barrier of ~26.2 kcal/mol. According to Woodward and  Hoffmann, it is a “forbidden” reaction (4n, n=2, electrons require an antarafacial component from somewhere). Shorn of the benzo groups, such a component developed in one of the forming phenyl rings (forming a Möbius benzene). But, by adding two benzo groups back to this phenyl ring (turning it into an anthracene),  we will stop this process in its tracks.

The first thing to note is that with two benzo groups in place, the predicted free energy barrier ΔG is 29.6 kcal/mol. This gives us a sense of whether modelling the reaction with a closed shell model (actually wB97XD/6-311G(d,p)  is realistic. You see,  the reaction could proceed via biradicals, which would require an open shell model. If the closed shell calculated barrier was way higher than that observed, this might be a strong hint that biradicals were indeed involved.  But the match above does not cry biradicals to us (although it does not eliminate them either of course) so we will continue.

The opening of the molecule proceeds as above, resulting in a transition state, which an IRC shows as leading to the formation of a strange intermediate show below, being some 12 kcal/mol higher in energy than the starting point. Of possible significance is the hydrogen ringed in orange in this intermediate. This lies slightly above in the plane of the central ring, and hence is  cis with respect to the phenyl group para to it, but on the cusp of being trans to it.

Intermediate in ring opening. Click for 3D

This intermediate is however in a very shallow potential,  only a tiny barrier separating it from the formation of  a Dewar benzene as shown by the  IRC below.  The transition state vibrational mode (click below) shows mostly motion only of the hydrogen ringed in orange. The product of this reaction is  ~25 kcal/mol lower in energy than the starting point of this odyssey.

"Final" product, a Dewar benzene biphenyl. Click for TS

Note we have not yet observed the antarafacial component required by a 4n-electron pericyclic thermal reaction. The Dewar benzene however can only convert to benzene by another 4n-electron conrotatory electrocyclic ring opening, which requires that antarafacial component (which for the cis-Dewar benzene would again form a Möbius benzene). The reaction has in effect put off the antarafacial element until the last possible instant.

So to summarise. In part 1, we found the ring opening to incorporate an antarafacial component by directly forming one Möbius benzene ring. Prevented from doing so by the presence of benzo groups (anthranyl), the reaction now proceeds as far as a Dewar benzene, thus delaying the antarafaciality. So the urge to avoid violation again results in some impressive gymnastics!

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One Response to “Violations. There are none! Part 2.”

  1. [...] and Hoffmann’s “symmetry-forbidden” reactions, which have been the subject of several posts here already. But in the section on nobel gas chemistry, the same Hoffmann is reported as having [...]

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