Double helical structures of DNA and RNA are mostly determined by base pair stacking interactions, which give them the base sequence-directed features, such as small roll values for the purine–pyrimidine steps. Earlier attempts to characterize stacking interactions were mostly restricted to calculations on fiber diffraction geometries or optimized structure using ab initio calculations lacking variation in geometry to comment on rather unusual large roll values observed in AU/AU base pair step in crystal structures of RNA double helices. We have generated stacking energy hyperspace by modeling geometries with variations along the important degrees of freedom, roll, and slide, which were chosen via statistical analysis as maximally sequence dependent. Corresponding energy contours were constructed by several quantum chemical methods including dispersion corrections. This analysis established the most suitable methods for stacked base pair systems despite the limitation imparted by number of atom in a base pair step to employ very high level of theory. All the methods predict negative roll value and near-zero slide to be most favorable for the purine–pyrimidine steps, in agreement with Calladine's steric clash based rule. Successive base pairs in RNA are always linked by sugar–phosphate backbone with C3′-endo sugars and this demands C1′–C1′ distance of about 5.4 Å along the chains. Consideration of an energy penalty term for deviation of C1′–C1′ distance from the mean value, to the recent DFT-D functionals, specifically ωB97X-D appears to predict reliable energy contour for AU/AU step. Such distance-based penalty improves energy contours for the other purine–pyrimidine sequences also. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 107–120, 2014.