Mechanisms of low-energy electron attachment to the DNA and subsequent single-strand break (SSB) formation are of crucial importance to understand the DNA damage. In the present study, we used time-dependent density functional theory (TD-BH&HLYP/6-31G*) to explore the mechanism of SSB, in detail, by calculating the lowest excited states of 5'-dTMPH radical anion considered as a model of DNA. The C-5-O-5, bond dissociation of 5'-dTMPH radical anion was considered as the reaction coordinate along the potential energy surface of 5'-dTMPH. The dissociative sigma* state, mainly localized on the phosphate of the 5'-dTMPH radical anion, is considered responsible for the SSB formation in DNA. Our work predicts that in this DNA model system there are available pi* and sigma* excited states, near 2 eV, which can couple vibronically and lead to a DNA single strand break via the dissociative sigma* surface.