Molecular geometries of the 9,10-anthraquinone (AQ) and DNA bases (Adenine, Guanine, Cytosine, and Thymine) were optimized using B3LYP/6-31G** method. Properties of isolated intercalator (9,10-anthraquinone) and their stacking interactions with adenine ⋯ thymine (AT) and guanine ⋯ cytosine (GC) nucleic acid base pairs were investigated by means of DFTB method. DFTB method, an approximate version of the DFT method, was extended to cover London dispersion energy. AQ exhibits a large charge delocalization and it has no site with dominant charge. This intercalator has a large polarizability and is a good electron acceptor, while base pairs are good electron donors. B3LYP/6-31G** stabilization energies of intercalator ⋯ base pair complexes are large (-18.83 kcal/mol for AT ⋯ AQ and -15.69 kcal/mol for GC ⋯ AQ). It is concluded that, the dispersion energy predominantly contributes to the stability of intercalator ⋯ DNA base pair complexes. Any procedure which does not cover dispersion energy is thus not suitable for studying the process of intercalation. The results showed that AQ changes the structure of DNA on bond length, bond angle, torsion angle, and charges.