When biological matter is subjected to ionizing radiation, a wealth of secondary low-energy (<20 eV) electrons are produced. These electrons propagate inelastically, losing energy to the medium until they reach energies low enough to localize in regions of high electron affinity. We have recently shown that in fully solvated DNA fragments, nucleobases are particularly attractive for such excess electrons. The next question is what is their longer-term effect on DNA. It has been advocated that they can lead to strand breaks by cleavage of the phosphodiester C(3')-O(3') bond. Here we present a first-principles study of free energy barriers for the cleavage of this bond in fully solvated nucleotides. We have found that except for dAMP, the barriers are on the order of 6 kcal/mol, suggesting that bond cleavage is a regular feature at 300 K. Such low barriers are possible only as a result of solvent and thermal fluctuations. These findings support the notion that low-energy electrons can indeed lead to strand breaks in DNA.