Conversion of s-trans butadiene to s-cis butadiene
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.