# Point group of cis- and trans-decalin

What is the point group of of cis- and trans-decalin?

I watched a video saying that it is $$C_\mathrm{2h}$$ for cis-isomer, but my friend says it is $$D_\mathrm{2h}.$$ I'm so confused.

• D2h should contain quite a few mirror planes. Where are they? – Ivan Neretin Sep 5 '19 at 8:04
• This video gets it right: youtube.com/watch?v=GERJoub3LVo – Karsten Theis Sep 5 '19 at 16:02

cis-Decalin

Here is a view of cis-decalin with the bridging C-C bond in the plane of the paper:

(It was made using the Jmol software, e.g. at https://chemapps.stolaf.edu/jmol/jsmol/simple.htm using the "Load by name" button and entering "cis-decalin".) At https://www.chemtube3d.com/stdecalinflips/, you can see that this can flip into the mirror image (much like a cylcohexane chair flip).

What is the point group of of cis-decalin?

I see a two-fold axis (perpendicular to the paper). I don't see a center of inversion or any mirror planes; the molecule looks chiral (the flip mentioned above changes it to its mirror image). So maybe C2?

trans-Decalin

Here is a view of trans-decalin with 5 carbons closer to us and 5 further away from us:

I see a center of inversion, a mirror plane (left:right swap), and a two-fold horizontally in the plane of view. I guess that's C2h.

• Related: Does trans-decalin really have a plane of symmetry? Trigger warning: You might be watching the gif forever... – Martin - マーチン Sep 5 '19 at 14:11
• I have run some conformational checks on the structures. The maximum point group for cis-decalin is as you propose C2. For trans-decalin, we do indeed find C2h as already stated. There are other (higher-energy) conformations with twist-boat rings in their conformations, which (mostly) would be of C1 symmetry. – Martin - マーチン Sep 6 '19 at 9:25