Table indicates the median r 2 for each fit across both acyclic and ring patterns, comparing the correlation of relative probabilities at each torsion angle between the fit and the underlying histogram. Note that since the cosine fits in this work allow the phase shift parameter to vary, the results are improved over the published ETKDG fits. We speculate that the fixed phases in the previous ETKDG fits are insufficiently physical, and while it may be useful conceptually to consider these distributions as arising from a typical cosine series potential energy function, this assumption does not fit the present data well.