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Is there an $C_2$ axis of symmetry in $\ce{Cl-CH=C=CH-Cl}$? 1,3-dichloroallene

A $C_2$ axis of symmetry means that I should be able to rotate the molecule about an axis by $180^\circ$. But I would need a composition of the following two rotations

  1. $90^\circ$ rotation about $\ce{C=C=C}$ axis
  2. $180^\circ$ about the perpendicular bisector of $\ce{C=C=C}$.

Would that count as a $C_2$ axis of rotation?

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    $\begingroup$ No, it doesn't. $\endgroup$ – orthocresol♦ Jun 10 '20 at 5:29
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    $\begingroup$ Actually... it does! $\endgroup$ – Ivan Neretin Jun 10 '20 at 6:52
  • $\begingroup$ The rule is that the molecule must be indistinguishable before and after the symmetry operation. Therefore is not the C$_2$ axis a line from the midpoint between the two Cl atoms (or H atoms) to the central C atom ? The only other operations are E and S$_4$ $\endgroup$ – porphyrin Jun 10 '20 at 8:11
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    $\begingroup$ Sometimes, the perfectly OK and preferred formula does not help. In this case it's useful to draw it with 4 stereochem. wedges insted of 2. $\endgroup$ – mykhal Jun 10 '20 at 9:17
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    $\begingroup$ Yes, there is a different $C_2$ axis; but you can't combine a $C_4$ and $C_2$ rotation about two different axes and call that a $C_2$ rotation. I guess my earlier comment was not clear enough, my bad. I was answering OP's last question, i.e. my point is that no, that composite operation does not count as a $C_2$ rotation. Judging from comment upvote counts, it seems that 3 people read the first question and 1 person read the last question. :-) $\endgroup$ – orthocresol♦ Jun 10 '20 at 12:19
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There is little to add to the comment by Ivan, a $C_2$ axis is indeed here. One can visualize symmetry elements for small molecules using, for example, Jmol. Launch the program GUI and do the following:

  1. File ā†’ Get MOL
  2. Type in an identifier, e.g. the name, 1,3-dichloropropa-1,2-diene, or CAS number, 83682-32-0.

  3. Open console (File ā†’ Console) and enter show pointgroup to list symmetry elements and draw pointgroup to add them to the picture:

    Jmol GUI

    animated rotation in 3D

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  • $\begingroup$ Note that 1,3-dichloropropa-1,2-diene is not The name (it's a redudant one). ;) $\endgroup$ – mykhal Jun 10 '20 at 9:22
  • $\begingroup$ @mykhal It looks redundant, but it's a preferred name (see IUPAC "Blue Book" (doi.org/10.1039/9781849733069), p. 64 where the name 1,3-dichloropropa-1,2-diene is given as PIN), so I went with the safest option for the name out there:) $\endgroup$ – andselisk♦ Jun 10 '20 at 9:27
  • $\begingroup$ I meant PIN as well (I (ACD obviously as well) think P-14.3.4.4 may be applied). But never mind. $\endgroup$ – mykhal Jun 10 '20 at 9:37

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