Semibullvalene is an unsettling molecule. Whilst it has a classical structure describable by a combination of Lewis-style two electron and four electron bonds, its NMR behaviour reveals it to be highly fluxional. This means that even at low temperatures, the position of these two-electron bonds rapidly shifts in the equilibrium shown below. Nevertheless, this dynamic behaviour can be frozen out at sufficiently low temperatures. But the barrier was sufficiently low that a challenge was set; could one achieve a system in which the barrier was removed entirely, to freeze out the coordinates of the molecule into a structure where the transition state (shown at the top) became instead a true minimum (bottom)? A similar challenge had been set for freezing out the transition state for the Sn2 reaction into a minimum, the topic also of a more recent post here. Here I explore how close we might be to achieving inversion of the semibullvalene [3,3] sigmatropic potential.
Why might such a frozen transition state be interesting? Well, all transition states for allowed thermal pericyclic reactions can be described as aromatic. If one were able to transmogrify such a transition state into a minimum, then it too would be expected to be aromatic, but a most unusual type of aromatic. The C-C bonds which represent the breaking and forming bonds in a [3,3] sigmatropic rearrangement would in effect be two-centre 1-electron bonds, and those electrons would be part of the aromatic sextet. Such bonds are normally referred to as homoaromatic, examples of which are pretty rare. In my previous post, I had noted a crystal structure that apparently sustains two equal C-C bonds of length 1.99Å. However, a calculation at this geometry reveals it in fact to be a transition state (above, top), with an imaginary mode of 275i cm-1. So the challenge (computationally at least) is to find a system where this imaginary mode is changed to become real rather than imaginary.
My effort to achieve this involved augmenting CAZFUE with a further two cyano groups. This did indeed reduce the imaginary mode to 74i cm-1; we are getting close!
The next step was to read a recent article in which replacing the key C-C bond with a C-N bond was observed to reduce the barrier for the rearrangement to ~ 4 kcal/mol. So I immediately computed the tetra-azo system, in which the two key C-C bonds are now replaced by N-N bonds in order to extend this effect.
It was gratifying to observe that the [3,3] sigmatropic vibration, imaginary (i.e. corresponding to a transition state) in the previous examples, became +ve (+238 cm-1) in this system. The two N-N bonds are however not completely symmetric (2.06 and 2.17Å), but they are in effect essentially frozen at the half-way stage of the equilibrium.
The final step in this path is to combine the two effects above, by exploring the di-cyano-diaza derivative.
This now has C2 (chiral) exact two-fold symmetry, with C-N distances of 2.139Å. The [3,3] sigmatropic vibrational mode is again real, with a value of 255 cm-1. A real candidate for synthesis perhaps?
Finally, is it aromatic? The wavefunction for this system is stable (which means no triplet state lower in energy can be found), so it stands a good chance of being so. I will report back on this aspect in a later post.
Postscript: The above calculation for the last system was done at the B3LYP/6-311G(d,p)/SCRF=thf level. A similar result is obtained at e.g. a MP2/6-311G(d,p)/SCRF=thf level; the [3,3] vibrational mode has the real value of 318 cm-1.
- L.M. Jackman, A. Benesi, A. Mayer, H. Quast, E.M. Peters, K. Peters, and H.G. Von Schnering, "The Cope rearrangement of 1,5-dimethylsemibullvalene-2,6- and 3,7-dicarbonitriles in the solid state", Journal of the American Chemical Society, vol. 111, pp. 1512-1513, 1989. http://dx.doi.org/10.1021/ja00186a064
- S. Zhang, J. Wei, M. Zhan, Q. Luo, C. Wang, W. Zhang, and Z. Xi, "2,6-Diazasemibullvalenes: Synthesis, Structural Characterization, Reaction Chemistry, and Theoretical Analysis", Journal of the American Chemical Society, vol. 134, pp. 11964-11967, 2012. http://dx.doi.org/10.1021/ja305581f