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The compound shown below was synthesized by Professor I M Dimm who was astonished to find that it was exceedingly stable. Prof. Dimm had expected world renown for making what he thought would be an unstable compound. Dimm reasoned that with six double bonds and a triple bond in the molecule there would be 16 π electrons and thus, no aromatic character ($4n, n=4$, not $4n+2$). Where was his reasoning wrong?

enter image description here

My reasoning so far:

Two of the electrons in the triple bond are not part of the conjugated π system. They are in a π orbital that is perpendicular to the rest of the p orbitals that make the conjugated π system. The conjugated π system thus only contains 14 electrons. $14 = 4n + 2$ for $n= 3$. So this molecule is aromatic.

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    $\begingroup$ Your answer seems correct to me. $\endgroup$ – mcocdawc Dec 2 '16 at 16:14
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    $\begingroup$ Actually, it depends on the molecular geometry; until we know it, we know just about nothing. There are two possibilities. (1) Both sides of the cycle are conjugated to the same $\pi$ component of the triple bond; then your reasoning is correct. (2) Sides of the cycle are conjugated to different $\pi$ components of the triple bond; then there is no cycle, the whole thing is effectively an equivalent of a long linear conjugated polyene, which is neither aromatic nor antiaromatic. Now, the description of the compound as "exceedingly stable" favors the first option. $\endgroup$ – Ivan Neretin Dec 2 '16 at 17:48
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    $\begingroup$ @IvanNeretin Wow … has that kind of twisted pi system been synthesised so far? I am very much intrigued! I love the idea! $\endgroup$ – Jan Dec 2 '16 at 23:58
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    $\begingroup$ Come to think of it, more twisted systems are known. $\endgroup$ – Ivan Neretin Dec 3 '16 at 6:07
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The textbook answer to this is that the triple bond consists of two orthogonal π systems whose interaction with each other is symmetry-forbidden. So as the attached figure shows, the two p-orbitals marked in red cannot participate in the aromatic system if the molecule’s structure is as drawn; thus the two electrons do not count towards the Hückel rule, thus $4n+2$ is satisfied with $n=3$ and $4n+2 = 14$.

Three-dimensional view of the pi system

However, that is not the end of the story; merely its beginning. Professor Dimm should take the time to determine the actual crystal structure of the compound he synthesised. You might want to compare this with cyclodecapenta-1,3,5,7,9-ene. While it may look like a perfect Hückel-aromatic molecule, it does not adopt a planar structure due to ‘inverse Baeyer strain’ (the flat all-cis conformation would have $144^\circ$ angles, far away from the theoretical $120^\circ$ $\mathrm{sp^2}$ angles) or steric hindrance (the (1E,3Z,5E,7Z,9Z)-confomation is not flat due to steric strain of the internal hydrogens). A similar case can be made for (1E,3Z,5E,7E,9Z,11E)-cyclotetradeca-1,3,5,7,9,11-hexaen-13-yne as can be seen in the figure below.

Scheme of the molecule with the steric interactions of the hydrogens highlighted

The hydrogens coloured in red would overlap far too much to create a stable molecule. It will adopt a non-planar configuration to relieve this steric stress which is a greater source of destabilisation than giving up an aromatic system. We can only speculate on the molecules structure until we actually saw it. Unfortunately, it is also unknown as far as SciFinder is concerned. However, two geometric isomers of dehydro[14]annulene (as the molecule is also called) have been synthesised and isolated:

two isolated isomers of dehydro[14]annulene

Interstingly, these compounds that were discovered in the 1960’s[1] show aromaticity by their chemical shifts. The internal hydrogens are shielded and display a chemical shift of approximately $-1~\mathrm{ppm}$ (symmetric isomer) and $0$ and $-1~\mathrm{ppm}$ (unsymmetric isomer). Similarly, the outer hydrogens appear as a group in the aromatic region.[2] Cresp and Sondheimer used low-temperature NMR studies to assign the correct structures.[2] And in 2013, Santander et al. performed calculations to determine the mechanism of interconversion between the two (‘by allowing a dilute ether solution to stand without protection from daylight, or, more rapidly by irradiation of a refluxing benzene solution with a $100~\mathrm{W}$ lamp.’[2]), which turns out to be via an interesting (in my opinion) Hückel-bond shift.[3]

Let’s hope that Professor Dimm actually synthesises the compound and properly reports its structure.


References:

[1]: F. Sondheimer, Proc. Roy. Soc. A, 1967, 297, 173. Taken directly from reference [2].

[2]: T. M. Cresp, F. Sondheimer, Tetrahedron Lett. 1982, 23, 1731. DOI: 10.1016/S0040-4039(00)87202-0.

[3]: M. V. Santander, M. B. Pastor, J. N. Nelson, C. Castro, W. L. Karney, J. Org. Chem. 2013, 78, 2033. DOI: 10.1021/jo302072p.

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