A procedure based on density functional theory is used for the calculation of the gas-phase bond dissociation enthalpy (BDE) and ionization potential for molecules belonging to the class of phenolic antioxidants. We show that use of locally dense basis sets (LDBS) vs full basis sets gives very similar results for monosubstituted phenols, and that the LDBS procedure gives good agreement with the change in experimental BDE values for highly substituted phenols in benzene solvent. Procedures for estimating the O--H BDE based on group additivity rules are given and tested. Several interesting classes of phenolic antioxidants are studied with these methods, including commercial antioxidants used as food additives, compounds related to Vitamin E, flavonoids in tea, aminophenols, stilbenes related to resveratrol, and sterically hindered phenols. On the basis of these results we are able to interpret relative rates for the reaction of antioxidants with free radicals, including a comparison of both H-atom-transfer and single-electron-transfer mechanisms, and conclude that in most cases H-atom transfer will be dominant.