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Would a [2]catenate whose each ring consist of a different number of methylene groups only, be optically active if one hydrogen atom of a random methylene group is replaced with e.g. chlorine? I think yes, but I need a second opinion.

The compounds attached seem to be enantiomers. I don't see how, by rotation, they could be super-imposable.

enter image description here

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If a molecule, or any conformation of a molecule, contains a plane of symmetry, then the molecule is not chiral (achiral).

The all hydrocarbon [2]catenane will be achiral. The molecule contains a plane of symmetry; picture a plane that contains one of the rings and bisects the other ring. In the following image, you can see that the plane of the screen contains the ring on the right and bisects the ring on the left.

A [2]catenane

You might say that if we replaced the circles with cyclohexane rings, because of their chair-like shape, the plane of symmetry is lost. That is true, but you can flatten one of the cyclohexane rings and the plane of symmetry is restored. Remember, if any thermally accessible conformation of a molecule is achiral, then the molecule is achiral.

Sometimes it helps to build a model or use a Newman projection to help with the stereochemical analysis. Here is such a projection for your chloro-[2]catenane. Note that it still possesses a plane of symmetry (a plane perpendicular to the screen).

enter image description here

If we go further and add another chlorine atom, but now to the back ring, then the molecule becomes chiral — just like 1,3-dichloroallene.

Regarding:

The compounds attached seem to be enantiomers. I don't see how by rotation they could be super-imposable.

Look at the bottom figure in my second drawing. I've taken your interlocking 5- and 6-membered catenane and rotated the 6-membered ring a bit further along (a conformational isomer; remember, as I mentioned above, if a molecule, or any conformation of a molecule, contains a plane of symmetry, then the molecule is not chiral [achiral]). The plane of the screen now contains the 5-membered ring and it bisects the cyclohexane ring. The plane of the screen also contains the methyl group. The plane of the screen is a symmetry element of this molecule; therefore this molecule is achiral.

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  • $\begingroup$ But what if the rings consist of different number of C atoms? $\endgroup$
    – EJC
    Commented Jan 9, 2015 at 16:37
  • $\begingroup$ @Marko Doesn't matter. Consider the simple case of a [2]catenane composed of a flat cyclopropane and flat cyclobutane. As discussed above, a plane exists for the all hydrocarbon case and the monochloro case - remember, you might have to rotate the ring containing the chlorine so that it (the chlorine) is contained in the plane. $\endgroup$
    – ron
    Commented Jan 9, 2015 at 16:44
  • $\begingroup$ @ron I think you should consider rotation of the substituted rings - if it can turn one isomer into other compound is optically inactive $\endgroup$
    – Mithoron
    Commented Jan 9, 2015 at 17:11
  • $\begingroup$ @Mithoron Yes, that's absolutely correct. My statement, "any conformation of a molecule" was meant to include the rotational case you're presenting. I'll mention here that a plane of symmetry is a sufficient, but not a necessary condition to make a molecule achiral. More complex catenanes without a plane of symmetry but belonging to the $\ce{S_{n}}$ point group would also be achiral. $\endgroup$
    – ron
    Commented Jan 9, 2015 at 17:24
  • $\begingroup$ It has a plane of symmetry, but because the two rings are connected, the two "enantiomers" can't inter convert. I don't see how it would be possible to do that. $\endgroup$
    – EJC
    Commented Jan 9, 2015 at 17:49

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