Conversion of s-trans butadiene to s-cis butadiene No nodes should be introduced in the rotational interconversion between the s-trans and s-cis forms of 1,3-butadiene.


What is the explanation for that, if one of the $\pi$-systems should rotate $180^\circ$? It seems to be that two positive and negative lobes turn upside down.
During the interconversion of s-cis and s-trans 1,3-butadiene, the molecule passes through a geometry where the two ethylenic arms are rotated 90 degrees one from the other.  In this conformation the two ethylenic arms are orthogonal to each other and there is no overlap between them.  In an MO sense they can be treated as two separate ethylenes.  Rotation beyond this conformation allows overlap to reoccur and the phase of the HOMO will be correctly reestablished with only one node occurring between C2 and C3.