- Surprising features in a recently published high-level calculation of the rotational profile of butadiene led us to compare butadiene with a set of 17 heterodienes. The rotational profiles of this large group of compounds varied widely, thereby possessing a high information content. These data were subjected to a Fourier analysis yielding one through six-fold terms: the one-fold terms represent the change in steric energy on going from 180 deg to 0 deg, while the changes in the two-fold terms correspond to the expected change in pi-delocalization energy with structure; the three-fold were significant and found to be linearly correlated to the average of the atomic charges at the central single bond of the cis-forms, but their origins are still not clear- we propose a novel 1,4 pi interaction that may account for this phenomenon. The four-fold terms were at times comparable in magnitude to the three-fold terms, but overall appeared to mainly modify the three-fold terms slightly without introducing any qualitatively new features. The fifth- and six-fold terms were negligible.