Why 5-member rings prefer being cis-fused?

Question

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?

Answer 1

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.

cis Isomer

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.