An 8 ns molecular dynamics (MD) simulation has been carried out on an oligomeric DNA duplex in a minimal salt sodium aqueous solution in order to study the magnetic relaxation process of Na-23. The explicit modeling of the solvent and the time length of the simulation allow study of the fast and, to some extent, the slow components of the relaxation. In agreement with experimental studies of the quadrupolar relaxation of monatomic cations in oligomeric DNA solution, the relaxation displays a multiexponential decay. According to the simulation, the slow components originate from ions directly bound to the DNA surface. The effects of the binding of the cations to DNA on the static and dynamical relaxation parameters have been studied in different binding sites either in the grooves or in the backbone. This study reveals that the quadrupolar coupling constant and the spectral densities vary largely from site to site, the fastest relaxation occurring for the ion directly bound to the minor groove. The combination of MD results with quadrupolar relaxation experimental data suggests that the occupancy of the binding sites in the minor groove of uninterrupted adenine sequences is relatively low.