The detailed mechanism of the interaction of the radical cation ABTS•+ with a number of food acids (gallic, ferulic, caffeic, vanillic, cinnamic, syringic, p-coumaric) is revealed by means of the DFT calculations. It is shown that the interaction between the neutral molecules of the studied food acids and ABTS•+ does not lead to any charge transfer from these molecules onto ABTS•+. The almost complete conversion of the ABTS radical cation into its diamagnetic derivative occurs due to the interaction of one of the sulphonic groups of ABTS•+ with the acid anions through the formation of the corresponding intermolecular hydrogen bond. The clear-cut correlation between the bond lengths SO···H and the experimental values of the antioxidant activity of the food acids under study was found. DFT calculations taking into account the solvent (ethanol), allow one to reveal the second clear-cut correlation between the studied activity and the values of the charge transfer from the anions of the studied food acids to ABTS•+.