Mechanisms of low-energy electron (LEE) attachment and subsequent single-strand break (SSB) formation are investigated by density functional theory treatment of a simple model for DNA, i.e., the nucleotide, 5'-thymidine monophosphate (5'-dTMPH). In the present study, the C-5'-O-5' bond dissociation due to LEE attachment has been followed along the adiabatic as well as on the vertical (electron attached to the optimized geometry of the neutral molecule) anionic surfaces using B3LYP functional and 6-31G* and 6-31++G** basis sets. Surprisingly, it is found that the PES of C-5'-O-5' bond dissociation in the anion radicals have approximately the same barrier for both adiabatic and vertical pathways. These results provide support for the hypothesis that transiently bound electrons (shape resonances) to the virtual molecular orbitals of the neutral molecule likely play a key role in the cleavage of the sugar-phosphate C-5'-O-5' bond in DNA resulting in the direct formation of single strand breaks without significant molecular relaxation. To take into account the solvation effects, we considered the neutral and anion radical of 5'-dTMP surrounded by 5 or 11 water molecules with Na+ as a counterion. These structures were optimized using the B3LYP/6-31G** level of theory. We find the barrier height for adiabatic C-5'-O-5' bond dissociation of 5'-dTMP anion radical in aqueous environment is so substantially higher than in the gas phase that the adiabatic route will not contribute to DNA strand cleavage in aqueous systems. This result is in agreement with experiment.