[Ben Bob2]

I'm looking at the reaction of furan with a generic dienophile with heat initiation.

There are four pi electrons in furan, so the molecular orbitals will fill according to the picture I've posted below.

I know that the diene and dienophile orbitals must overlap to react.

According to the Woodward-Hoffmann rule, a thermally-initiated 4pi system will undergo a conrotatory change to achieve proper overlapping as I also show in the picture.

Finally, products of this reaction are shown with the ether bridge intact.

So here's my question: if conrotation occurs, then the bonds to the ether must go in opposite directions. How then does the ether not break? Or does it break and reform in another step? Or have I just had a total brain fart of some sort?

Thanks.

[Dan]

My pericyclic chemistry is rusty, but I think you are confusing some things here.

For a thermal D-A cycloaddition, you need to look at the HOMO-LUMO interaction between the two coupling partners. You have drawn the HOMO of both coupling partners, which is why it appears to be disallowed.

[Ben Bob2]

Yup, that explains it.
Thank you!

[Irlanur]

Also:

a thermally-initiated 4pi system will undergo a conrotatory change to achieve proper overlapping

Is pretty irrelevant for cycloadditions like the D-A. The con/dis-rotatory is important for electrocyclic reactions (which is, "in principle", possible here, but this would lead to an epoxidized cyclobutene, which is probably not thermodynamically favoured;) )