All possible X-H (where X can be C, N, O or S) bond dissociation energies (BDEs) of glutathione (γ-L-glutamyl-L-cysteinyl-glycine, GSH) and its fragments have been calculated by first principle methods, and the antioxidant potential of GSH was revealed to be higher than expected in earlier studies. Electron delocalization was found to have an important influence on the antioxidant potential. All structures were optimized and their harmonic vibrational frequencies were calculated in the gas phase at the B3LYP/6-31G(d) level of theory. Solvent effects were taken into account for optimizations at the same level of theory by applying the conductor-like polarizable continuum model (CPCM). Hydrogen cleavage from glutathione proved that the G3MP2B3 composite method provides results consistent with the experimental values for bond dissociation enthalpies (DH(298)) of S-H, O-H, C-H, and N-H bonds. In order to replace the G3MP2B3 energies with accurate single point calculations, six density functionals, namely, MPWKCIS, MPWKCIS1K, M06, TPSS1KCIS, TPSSh, and B3LYP, were tested against G3MP2B3 for obtaining accurate bond dissociation energies. The MPWKCIS1K/6-311++G(3df,2p)//B3LYP/6-31G(d) level of theory provides the best correlation with the G3MP2B3 method for BDEs in both phases, and therefore, it is recommended for similar calculations. Gas phase results showed that the O-H bond was the weakest, while in aqueous phase the N-H bond in the ammonium group proved to have the smallest BDE value in the studied system. In both cases, the cleavage of the X-H bond was followed by decarboxylation which was responsible for the energetic preference of these processes over the S-H dissociation, which was regarded as the most favorable one until now. The calculated BDE values showed that in aqueous phase the most preferred H-abstraction site is at the weakest N-H bond (BDE(aq) = 349.3 kJ mol(-1)) in the glutamine fragment near the α-carbon. In water, the formation of N-centered radicals compared to S-centered ones (BDE(aq) = 351.7 kJ mol(-1)) is more endothermic by 2.54 kJ mol(-1), due to decarboxylation. Hydrogen dissociation energies from the α-carbons are also comparable in energy with those of the thiol hydrogen, within computational error. The higher stability of the radicals--except the S-centered ones--is due to various degrees of electron delocalization. In aqueous phase, four quasi-equivalent stable radical centers (the α-carbons, the N-centered radical of the NH(2) group, and the S-centered radical) were found which provide the antioxidant behavior of glutathione.