Periodic density functional theory (DFT) calculations have been performed to model the adsorption of nucleobases at clay edges as potential adsorption sites for DNA/RNA oligomerization. According to the accessibility and availability of hydroxyl groups and water molecules at clay edges, numerous adsorption conformations via H-bonding, in a similar way to the Watson–Crick base pairing in DNA strands, have been considered. It is found that guanine and cytosine are mainly adsorbed through three H-bonds with edge’s hydroxyls and water molecules, while adenine and thymine do generally engage two H-bonds. As a result, the largest adsorption energies were found for guanine and cytosine (−32 to −35 kcal mol–1) in comparison to most adsorbed modes with adenine and thymine (−22 to −24 kcal mol–1). For thymine, a three H-bond tilted adsorption mode has also been observed with an exceptionally large adsorption energy of −35 kcal mol–1. Significant stabilizing dispersive forces with the surface are present in all the explored adducts, around 30% of the total adsorption energy (−6 to −10 kcal mol–1). The stacking of an additional nucleobase and its adsorption via H-bonding on the edge surface has also been studied. The large stabilizing interactions of the complexes, arising from both H-bonding and stacking interactions, range between −44 and −66 kcal mol–1, the dispersion component accounting for around −20 kcal mol–1, while no cooperative effects are observed. A significant number of strong H-bonds (<1.6 Å) is observed in the most stable complexes. Obtained results show that a side by side nucleobase adsorption is possible at clay edges due to the availability of hydroxyl and water motifs. Finally, the adsorption of a thymine dinucleotide unit (TpT) is simulated, showing that its adsorption occurs also via H-bonding with the edges. This adsorption mechanism may be considered as a probable adsorption mode allowing for the phosphodiester bond formation leading to RNA oligomerization.