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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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  • $\begingroup$ 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, 2020 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, 2020 at 9:17

1 Answer 1

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A $C_2$ axis is indeed here—although not the one that you are thinking of: your suggestion of a $C_4$ then $C_2$ rotation does not qualify as a $C_2$ symmetry operation. There is a true $C_2$ axis which bisects the allene and is tilted by $45^\circ$ from both the $\ce{Cl-C-Cl}$ and $\ce{H-C-H}$ planes.

One can visualize symmetry elements for small molecules using, for example, Jmol. Launch the program GUI and do the following:

  1. FileGet 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 (FileConsole) and enter show pointgroup to list symmetry elements and draw pointgroup to add them to the picture: Jmol GUI animated rotation around C2 axis in 3D
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