To explore the nature of electron attachment to the guanine-centered DNA fragments in the presence of a polarizable medium, theoretical investigation of electron attachment to the guanine-related DNA single-strand fragments deoxyguanosine-3'-monophosphate (dGp), deoxyguanosine-5'-monophosphate (pdG), and deoxyguanosine-3',5'-diphosphate (pdGp) were performed using density functional theory with the polarizable continuum model. The electron distributions for the radical anions of pdGp in aqueous solution are extraordinarily different from those in the gas phase. In solution, the excess electron can covalently bind either to the base (forming pdG(*-)p) or to the 3'-phosphate in the radical anion (forming pdGp(*-)). The significant electron detachment energies found for these radical anions suggest that both pdG(*-)p and pdGp(*-) are electronically stable species in aqueous solution and are expected to be initiators in electron attachment-induced DNA damage in nature. In the presence of the polarizable medium, the base-centered radical anion pdG(*-)p is more stable than the phosphate-centered structure. By comparison with electron attachment to the monophosphated nucleotide models pdG and dGp, the existence of the phosphate-centered radical pdGp(*-) in pdGp is attributed to the cooperative influence of the two phosphate groups and the polarizable medium.