Time-dependent motions of 32 deoxyribodinucleoside and ribodinucleoside monophosphate anions in aqueous solution at 310 K were monitored during 40 ns using classical molecular dynamics (MD). In all studied molecules, spontaneous stacking/unstacking transitions occured on a time-scale of 10 ns. To facilitate the structural analysis of the sampled configurations we defined a reaction coordinate for the nucleobase stacking that considers both the angle between the planes of the two nucleobases and the distance between their mass-centers. Additionally, we proposed a physically meaningful transient point on this coordinate that separates the stacked and unstacked states. We applied this definition to calculate free energies for stacking of all pairwise combinations of adenine, thymine (uracil), cytosine and guanine moieties embedded in studied dinucleosides monophosphate anions. The stacking equilibrium constants decreased in the order 5’-AG-3’ > GA ~ GG ~ AA > GT ~ TG ~ AT ~ GC ~ AC > CG ~ TA > CA ~ TC ~ TT ~ CT ~ CC. The stacked conformations of AG occurred ten-times more frequently than its unstacked conformations. On the other hand, the last five base combinations showed a greater preference for the unstacked than the stacked state. The presence of an additional 2’-OH group in the RNA–based dinucleoside monophosphates increased the fraction of stacked complexes but decreased the compactness of the stacked state. The calculated MD trajectories were also used to reveal prevailing mutual orientation of the nucleobase dipoles in the stacked state.