The relationships between electronic structure particularities and antioxidant activity of some chemical compounds are considered on the basis of the density functional theory (DFT) calculations of reactions between some natural phenolic antioxidants (gallic, caffeic, p-coumaric, and other acids), as well as dihydroxyfumaric acid, and the stable radicals ABTS•+ and DPPH• in water, ethanol, and methanol. Particular attention is paid to the processes of the primary proton transfer between neutral molecules of the above antioxidants and molecules of these solvents. The important factors are also considered: the formation of the charge transfer complexes (CTC) between the anionic forms of these antioxidants and the radicals, and possible tautomeric effects essentially changing the pre-reactional structures of the investigated antioxidant molecules and their anions. The quantitative relationships between the electronic structure parameters and the antioxidant activity of some short chain n-alkanes with radicals OH• and NO3• are also discussed.