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What prevents cis and trans isomers from existing in smaller cycloalkenes, for example, cyclohexenes for more than a short period of time?

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Whether cyclooctene is the lowest such alkene is not cut and dried. trans-cycloheptene is known as a transient species (Inoue et al 1 and Verbeek et al. 2). Calculations indicate that it converts to the more stable cis isomer through a diradical intermediate, not a double-bond rotation (Squillacote et al, 3).

Consider a planar $n$-sided polygon with $n-2$ vertex angles measuring $109.5°$ and the remaining two vertex angles measuring $120°$ and $240°$, the last of these a reflex angle at a concave vertex. Then the sum of angles is both $180°(n-2)$ (from the planar polygon formula) and $109.5°(n-2)+360°$ (from the specified angles), where these expressions closely agree at $n=7$. Thus trans-cycloheptene would be forced to have all ring atoms essentially is one plane, which is highly strained for a seven-atom ring with only one double bond (compare with the observed structure of cis-cycloalkenes). With an eighth atom in the ring, so that $109.5°(n-2)+360°$ is significantly less than the planar-polygon angle sum $180°(n-2)$, the forced planarity is relaxed and the structure is much less strained.

References

  1. Yoshihisa Inoue, Toshihiko Ueoka, Takayuki Kuroda and Tadao Hakushi. "trans-Cycloheptene. Photochemical generation and thermal trans-cis isomerization". J. Chem. Soc., Chem. Commun., 1981, 1031-1033. https://doi.org/10.1039/C39810001031.

  2. J. Verbeek, J. H. Van Lenthe, P. J. J. A. Timmermans, A. Mackor, and P. H. M. Budzelaar. "On the existence of trans-cyclohexene". J. Org. Chem. 1987, 52, 13, 2955–2957. https://doi.org/10.1021/jo00389a067.

  3. Michael E. Squillacote, James DeFellipis, and Qingning Shu "How Stable Is trans-Cycloheptene?" J. Am. Chem. Soc. 2005, 127, 45, 15983–15988. https://doi.org/10.1021/ja055388i

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