Trying to come up with examples of (hypothetical) molecules/shapes that have $D_4$ and $C_{9h}$ point groups.

For $D_4$, I thought a cyclobutane structure, but with 4 substituents coming off of the ring all pointing in the same direction. However, I'm not sure if this is $D_4$ because in a book I am reading it says that all the $D_n$ point groups show chirality, which this molecule does not.

For $C_{9h}$, I really can't think of any shape/structure that doesn't just end up being $D_{9h}$. $C_9$ would be a 9-bladed propellor shape, although I'm not really sure how to draw this, and I don't see how I could alter that to get $C_{9h}$.



For nearly any point group which is actually feasible (including $D_4$), look up the Symmetry gallery. Your all-cis tetra-substituted cyclobutane would be $C_{4v}$, BTW.

As for $C_{9h}$... well, I don't quite believe this is possible, but probably we may come up with something that would look almost realistic.

A substituted nanotube fragment will do, I think. C9h molecule

Surely it is hypothetical, so what? Cyclo-$\ce{C18}$ is hypothetical as well, and in my opinion, has lower chances to be stable. Also, its symmetry is kinda dubious.

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    $\begingroup$ why is cyclo-C18 hypothetical? wasn't it first observed in 1989? science.sciencemag.org/content/245/4922/1088 $\endgroup$ – DavePhD Sep 16 '16 at 16:41
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    $\begingroup$ No, it was not. These guys made some calculations, then prepared some precursors, then saw in the mass spectra some $\ce{C18}$ which is probably cyclic, though nobody knows for sure. That's a circumstantial evidence at best. $\endgroup$ – Ivan Neretin Sep 18 '16 at 1:05
  • $\begingroup$ @iopscience.iop.org/article/10.1086/500110/pdf maybe you will be more convinced by this 2006 gas phase spectrum, although these author say it is a cumulene ring with alternating bond angles, D9h. $\endgroup$ – DavePhD Sep 18 '16 at 12:10
  • $\begingroup$ a 2011 book says "With this correction, the minimum is the cyclo-polyacetylene C9h. However, there is a tendency for HF as well as BLYP to artificially yielding lower symmetry structures. Thus, the most stable structure of the cyclic C18 is still debatable" books.google.com/… $\endgroup$ – DavePhD Sep 18 '16 at 12:22
  • $\begingroup$ OK, well, so this thing does exist, after all. It is its exact geometry (and consequently symmetry) that is hypothetical. $\endgroup$ – Ivan Neretin Sep 19 '16 at 13:07

The cyclo-C18 polyyne is $C_{9h}$ according Carbon Rich Compounds II: Oligoacetylenes at page 46

The molecule is a planar 18-carbon ring with alternating short and long bonds (triple and single bonds) and bond angles alternating between 157 and 163 degrees.

  • $\begingroup$ Isn't it $\ce{D}_{9\ce{h}}$? Forgive me if I am wrong. $\endgroup$ – DHMO Sep 16 '16 at 15:08
  • $\begingroup$ You might want to attach this image. $\endgroup$ – DHMO Sep 16 '16 at 15:14
  • $\begingroup$ Now that's what I call a stretch. We'll have to tell the difference between $C_{9h}$, $D_{9h}$, and probably other options, based on some minuscule, nearly invisible deviations. In the absence of other options, though, this might do. $\endgroup$ – Ivan Neretin Sep 16 '16 at 15:14
  • $\begingroup$ @user34388 it that accurate, or is like scheme 8.4 here: books.google.com/… $\endgroup$ – DavePhD Sep 16 '16 at 15:15
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    $\begingroup$ @IvanNeretin C9h is 0.3 kcal/mol lower than D9h, has alternating bond angles of 157 and 163 degrees pubs.acs.org/doi/abs/10.1021/ja00120a026 $\endgroup$ – DavePhD Sep 16 '16 at 15:37

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