Thus famously wrote Woodward and Hoffmann (WH) in their classic monograph about the conservation of orbital symmetry in pericyclic reactions. But they also note that the “fantastic” hydrocarbon (number 85 in their review) shown below presents a situation of great interest in having a half life of ~30 minutes at 353K (a free energy barrier of ~ 26.2 kcal/mol). Here I investigate if it might actually be such a violation.
I should first note that WH expect that violating reactions are likely to comport themselves via a non-concerted reaction path involving discrete intermediates.1 Which in the above case would be a biradical. But why is it an interesting example? Because, as a 4n (n=2) electron electrocyclic reaction (involving the bonds shown in red above), it must involve one antarafacial component. This is apparently rendered impossible (so WH claim) by the very rigid geometry of the system. However, an alternative, and geometrically more viable reaction involving only suprafacial components would indeed be be a violation according to their definition, if it were to be concerted, without (biradical) intermediates. So if a concerted pathway with no antarafacial components could be found, it would constitute a violation.
To model this system, the benzo groups (blue) are first removed. A transition state for the reaction is found [ωB97XD/6-311g(d)] with ΔG† 21.5 kcal/mol and an intrinsic reaction coordinate (IRC) that shows a concerted profile, albeit one with quite unusual features revealed in the gradient norm along the IRC.
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WH argued that violations of their rules would be avoided by the reacting system adopting a stepwise, non-concerted pathway. It may be that the dynamics of reactions would also allow avoidance to occur by adopting concerted, but asynchronous geometrical distortions such as those seen here.2
1 “When I use a word,” Humpty Dumpty said in rather a scornful tone, “it means just what I choose it to mean – neither more nor less.” I add this quote, since the WH approach is based on an orbital picture deriving from a single determinantal SCF solution of the Schroedinger equation. In so-called multi-configurational treatments (MCSCF), molecular orbitals for a single configuration no longer occupy such a central position in the theory.
2 For example, it could be argued that a violation of the WH rules for 2πs + 2πs thermal cycloadditions can be avoided by a trapezoidal distortion, DOI: 10.1039/A805668D.
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