The influence of hydrogen bonds in model intercalated systems between guanine‐cytosine and adenine‐thymine DNA base pairs (bps) was analyzed with the popular intercalator 1,10‐phenanthroline (phen) and derivatives obtained by substitution with OH and NH2 groups in positions 4 and 7. Semiempirical and Density Functional Theory (DFT) methods were used both including dispersion effects: PM6‐DH2, M06‐2X and B3LYP‐D3 along with the recently developed near linear‐scaling coupled cluster method DLPNO‐CCSD(T) for benchmark calculations. Our results given by QTAIM and non‐covalent interaction analysis confirmed the existence of hydrogen bonds created by OH and NH2. The trends in the energy decomposition analysis for the interaction energy, ΔEint, showed that the ΔEelstat contributions are equal or even a little bit higher than the values for ΔEdisp. Such important ΔEelstat attractive contribution comes mainly from the conventional hydrogen bonds formed by OH and NH2 functional groups with DNA not only with bps but specially with the sugar and phosphate backbone. This behavior is very different from that of phen and other classical intercalators that cannot form conventional hydrogen bonds, where the ΔEdisp is the most important attractive contribution to the ΔEint. The inclusion of explicit water molecules in molecular dynamics simulations showed, as a general trend, that the hydrogen bonds with the bps disappear during the simulations but those with the sugar and phosphate backbone remain in time, which highlights the important role of the sugar and phosphate backbone in the stabilization of these systems.