# C₂ axis of symmetry in 1,3-dichloroallene

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

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?

• No, it doesn't. – orthocresol Jun 10 '20 at 5:29
• Actually... it does! – Ivan Neretin Jun 10 '20 at 6:52
• 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$_4$ – porphyrin Jun 10 '20 at 8:11
• 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. – mykhal Jun 10 '20 at 9:17
• 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. :-) – orthocresol Jun 10 '20 at 12:19

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. 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:

• Note that 1,3-dichloropropa-1,2-diene is not The name (it's a redudant one). ;) – mykhal Jun 10 '20 at 9:22
• @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:) – andselisk Jun 10 '20 at 9:27
• I meant PIN as well (I (ACD obviously as well) think P-14.3.4.4 may be applied). But never mind. – mykhal Jun 10 '20 at 9:37