# Why 5-member rings prefer being cis-fused?

It always bothers me how whenever I am doing practice problems I never got a proper explanation as to why 5-member rings prefer(thermodynamically) being cis- rather than trans-fused( as opposed to decalins where the cis-fused rings are more stable due to gauche and 1,3-diaxial interactions). They seem to never give an explanation about the phenomenon besides "it is how it is".

I don't see an immediate reason why the cis fused would be stable. The cyclohexane would be happier having two equatorial substituents so it must have something to do with the 5-member ring.

Also on the topic, the equatorial and axial positions on a cyclopentane are also very confusing:

It seems that it was to equatorial positions on the same side of the ring and next to each other( the two right-most). How do you choose which substituents to put where and where does the bulk go- I cannot see a clear factor to decide?

• Inner angle of a regular pentagon is $108°$. Tetrahedron angle is $109.47°$. These two values are not very different. At room temperature, the molecular vibrations may be sufficient to continuously pass from cis- to trans-cyclopentane Apr 15, 2022 at 18:53

tldr; I think it's pretty close between the two forms - at least for unsubstituted hydrocarbons

Since we just worked on a project to understand ring puckering conformations, I was curious about this.

So I created the two hydrocarbons you indicated in your question and searched for the lowest-energy conformations using the GFN2 semi-empirical method. (It's quite good for ranking conformers in our recent benchmark.)

For the un-substituted framework, the calculations come to ~0.18 kcal/mol difference with trans slightly more stable .. and I'd guess the method has at least a ~1 kcal/mol error. So they're roughly the same at least with this theoretical method.

## trans Isomer

Both cyclohexanes seem free of ring strain, and all the torsions are close to ideal.

If I were to judge the various interactions, I'd say it's close. Perhaps the cis form has interactions between the 5-membered ring and the "bottom" axial hydrogens.

• Thank you for your comment. I guess that if substituents are added to the ring, the situation in terms of stability would be more clear cut. Apr 16, 2022 at 15:47