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How does trans-cyclooctene exhibit chirality if there are no stereocenters?

Related follow-on questions:

  1. Are all higher cycloalkenes chiral?
  2. Do more double bonds cause a bigger number of stereoisomers in cycloalkenes?
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EJC
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  • related http://chemistry.stackexchange.com/a/31296/9961 – Mithoron Aug 25 '15 at 18:38
  • Related: http://chemistry.stackexchange.com/questions/24901/do-molecules-with-axial-chirality-have-stereogenic-units/24910#24910 – jerepierre Aug 25 '15 at 21:09
  • Especially related, since trans-cyclooctene undergoes ring flip very slowly, unlike cyclohexane: http://chemistry.stackexchange.com/questions/34475/determining-chirality-after-considering-conformational-interconversion-in-a-cycl/34480#34480 – jerepierre Aug 25 '15 at 21:12
  • http://chemistry.stackexchange.com/questions/24901/do-molecules-with-axial-chirality-have-stereogenic-units – Mithoron Aug 26 '15 at 01:23
  • I absolutely agree with Brian's comment on the answer, it would be better, if you roll back to the original question and ask a follow up question with the added ones. – Martin - マーチン Aug 26 '15 at 03:06

1 Answers1

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Very interesting question! The key word you are looking for is planar chirality. In trans-cyclooctene, the polymethylene bridge can either go "in front of" or go "behind" the plane of the double bond, assuming you fix the double bond and the two hydrogens in place.

As pointed out by @jerepierre, they are considered different molecules due to a high-energy barrier which prevents the interconversion. Cyclooctene is the first cycloalkene to have both stable cis- and trans- isomers. The chain in trans-cyclooctene is not long enough to swing over the double bond. As the chain gets longer, the energy barrier to rotation decreases.

Here are the two mirror images of trans-cyclooctene (image source: own work).

enter image description here

These two molecules are mirror images of each other but are not superimposable. Therefore trans-cyclooctene is chiral despite not having a chiral center.

Source

Edit: this is the first time I learned that a chiral molecule does not have to have a chiral center. After making some searches online, I feel a need to expand the answer to clarify the concept of chirality.

A chiral molecule is one that has a non-superimposable mirror image. Mathematically a molecule is chiral if it is not symmetric under an improper rotation. Chirality arises due to:

  1. point chirality: typically a carbon center with four different substituents;

  2. axial chirality: such as allenes with different substituents on each carbon (see this question);

  3. planar chirality: such as the case of trans-cyclooctene;

  4. inherent chirality: due to the presence of a curvature in a structure that would be devoid of symmetry axes in any bidimensional representation, such as fullerenes.

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  • Hm. Technically, though, it does have a chiral center (at the center of the ring), right? It just doesn't coincide with a nucleus. – hBy2Py Aug 25 '15 at 16:51
  • @Brian I just edited the answer for a more comprehensive view of chirality. I don't think it has a chiral center as the four carbon atoms (the two in the double bond and the two directly bonded to them) are in the same plane and do not form a tetrahedron around a point. – ℵ_ϵ Aug 25 '15 at 16:58
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    I'm probably splitting hairs, or up against a nomenclatural definition. Formally speaking, does a 'chiral center' only exist at a nucleus? If so, then the center of mass doesn't qualify as a chiral center, and my initial comment is incorrect. – hBy2Py Aug 25 '15 at 17:10
  • Thank you. I've expanded my question a little bit, because I still have some doubts. – EJC Aug 25 '15 at 18:19
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    I'd give +1/2 if I could. An additional key feature of trans-cyclooctene is that it doesn't undergo ring flip (or does so slowly). For a similar question, see: http://chemistry.stackexchange.com/questions/34475/determining-chirality-after-considering-conformational-interconversion-in-a-cycl/34480#34480 – jerepierre Aug 25 '15 at 21:14
  • @Marko I can't answer your 2nd question right now. Meanwhile you may find this question useful: http://chemistry.stackexchange.com/questions/30940/cis-trans-stability-of-cycloalkenes – ℵ_ϵ Aug 26 '15 at 01:28
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    @Brian As I was unsure myself, I consulted the goldbook, where it is explicitly stated as "an atom". In the case of planar chirality, the definition also clearly states plane. One rational about this is, that there are multiple atoms that lie in the same plane when considering enantiomers, which is not the necessarily the case for point chirality. – Martin - マーチン Aug 26 '15 at 01:34
  • @Martin-マーチン then I have a question: could the plane be one that does not pass through the atoms? The definition linked defines the chiral plane as the plane passing thru the double bond and the linked atoms (at least in cyclohexene), but are the two carbon atoms coplanar with the $\ce{HC=CH}$? – ℵ_ϵ Aug 26 '15 at 02:01
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    @Marko, your edit would possibly have been better posted as a new question, possibly even two, with crosslinks posted among them. – hBy2Py Aug 26 '15 at 02:19
  • @user2124232 They will most likely not be perfectly planar because of the strain in the small molecule, but very close to it. – Martin - マーチン Aug 26 '15 at 03:03
  • Point four would be a Moebius band. – Karl Aug 26 '15 at 14:36
  • @KarlRatzsch mind elaborating a bit? – ℵ_ϵ Aug 27 '15 at 14:22
  • A Moebius band is chiral, you can glue it together leftsided or rightsided. Upon second thought, it might also be a planar chirality. Not sure how to picture it. – Karl Aug 27 '15 at 14:33
  • I don't understand the point about fullerenes, anyway. Would that be a fullerene with three different substituents? – Karl Aug 27 '15 at 14:37
  • @KarlRatzsch now I'm imagining how a Möbius band molecule would be like. I haven't figure out fullerene yet because of its complex structure, but other examples given by wiki such as calixarene should be easier to understand. – ℵ_ϵ Aug 27 '15 at 14:47
  • https://en.wikipedia.org/wiki/Möbius_aromaticity – Karl Aug 27 '15 at 15:09
  • Some of the terminological confusion here come because the terms centre of chirality and chiral centre don't mean exactly the same thing. In normal use a chiral centre is a carbon (or other tetrahedral atom) with 4 different substituents, guaranteeing chirality if it is in a simple molecule (though more complex chiral centres can exist eg in octahedrally coordinated metals with 3 bidentate ligands). But more complex molecules like trans-cyclooctene or hexahelicene there is a centre of chirality that does not correspond to an atom. – matt_black Oct 18 '17 at 22:36