Theoretical simulations are particularly well suited to investigate, at a molecular level, direct and indirect effects of ionising radiations in DNA, as in the particular case of irradiation by swift heavy ions such as those used in hadron therapy. In the past recent years, we have developed the modeling at the microscopic level of the early stages of the Coulomb explosion of DNA molecules immersed in liquid water that follows the irradiation by swift heavy ions. To that end, Time-Dependent Density Functional Theory molecular dynamics simulations (TD-DFT MD) have been developed where localised Wannier orbitals are propagated. This latter enables to separate molecular orbitals of each water molecule from the molecular orbitals of the biomolecule. Our main objective is to demonstrate that the double ionisation of one molecule of the liquid sample, either one water molecule from the solvent or the biomolecule, may be in some cases responsible for the formation of an atomic oxygen as a direct consequence of the molecule Coulomb explosion. Our hypothesis is that the molecular double ionisation arising from irradiation by swift heavy ions (about 10% of ionisation events by ions whose velocity is about the third of speed of light), as a primary event, though maybe less probable than other events resulting from the electronic cascading (for instance, electronic excitations, electron attachments), may be systematically more damageable (and more lethal), as supported by experiments that have been carried out in our group in the 1990s (in studies of damages created by K holes in DNA). The chemical reactivity of the produced atomic oxygen with other radicals present in the medium will ultimately lead to chemical products that are harmful to DNA. In the present paper, we review our theoretical methodology in an attempt that the community be familiar with our new approach. Results on the production of atomic oxygen as a result of the double ionisation of water or as a result of the double ionisation of the Uracil RNA base will be presented.