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 for this large group of compounds varied widely, thereby possessing a high information content. These data were subjected to a Fourier analysis yielding 1- through 6-fold terms: the one-fold terms represent the change in steric energy on going from 180° to 0°, while the changes in the 2-fold terms correspond to the expected change in π-delocalization energy with structure; the 3-fold terms were significant and found to be linearly correlated to the average of the atomic charges of the atoms at the central single bond of the cis-forms, but their origins are still not clear; we propose a novel 1,4 π-interactions that may account for this phenomenon. The 4-fold terms were at times comparable in magnitude to the 3-fold terms but overall appeared to mainly modify the 3-fold terms slightly without introducing any qualitatively new features. The 5- and 6-fold terms were negligible.