A systematic analysis of the electrostatic interaction between 27 natural DNA base pairs was carried out, based on ab initio correlated wave functions and the topology of the electron density. Using high rank multipole moments we show that the atomic partitioning of the interaction energy contains many substantial contributions between distant atoms. Profiles of cumulative energy versus internuclear distance show large fluctuations and provide an electrostatic fingerprint of the partitioning of interaction energy in a complex. A quantified comparison between each pair of energy profiles, one for each base pair, makes clear that there is no correlation between the total base pair interaction energy and the shape of the profile. In other words, base pairs with similar interaction energy are not stable for the same reasons in terms of atomic partitioning. In summary, simple rules to rationalize the pattern of energetic stability of naturally occurring base pairs in terms of subsets of atoms are elusive. Our work cautions against inappropriate use of Jorgensen's secondary interaction hypothesis.