Recent reports of the successful incorporation of unnatural base pairs (UBPs), such as d5SICS-dNaM, in the gene sequence and replication with DNA is an important milestone in synthetic biology. Followed by this, several other UBPs, such as dTPT3-dNaM, dTPT3-dFIMO, dTPT3-IMO, dTPT3-FEMO, FTPT3-NaM, FTPT3-FIMO, FTPT3-IMO, and FTPT3-FEMO, have demonstrated similar or better retention and fidelity inside cells. Of these base pairs, dNaM-dTPT3 has been optimized to be a better fit inside a pAIO plasmid. Based on both implicit and explicit dispersion-corrected density functional theory (DFT) calculations, we show that although this set of UBPs is significantly diverse in elemental and structural configuration, the members do share a common trait of favoring a slipped parallel stacked dimer arrangement. Unlike the natural bases (A, T, G, C, and U), this set of UBPs has a negligible affinity for a Watson-Crick (WC)-type planar structure because they are invariably more stable within slipped parallel stacked orientations. We also observed that all the UBPs have either similar or higher binding energies with the natural bases in similar stacked orientations. When arranged between two natural base pairs, the UBPs exhibited a binding energy similar to that of three-base sequences of natural bases. Our computational data show that the most promising base pairs are 5SICS-NaM, TPT3-NaM, and TPT3-FEMO. These results are consistent with recent progress on experimental research into UBPs along with our previous calculations on the d5SICS-dNaM pair and, therefore, strengthen the hypothesis that hydrogen bonding might not be absolutely essential and that interbase stacking dispersion interactions play a key role in the stabilization of genetic materials.