Two Theorems and Important Insight on How the Preferred Mechanism of Free Radical Scavenging Cannot Be Settled

Totally ignoring that the five enthalpies of reaction --- bond dissociation enthalpy (BDE), adiabatic ionization potential (IP), proton dissociation enthalpy (PDE), proton affinity (PA), and electron transfer enthalpy (ETE) --- characterizing the three free radical scavenging mechanisms --- direct hydrogen atom transfer (HAT), sequential electron transfer proton transfer (SET-PT), and stepwise proton loss electron transfer (SPLET) --- are not independent of each other, a recent publication (Molecules, 2019, 24, 1646) on antioxidant activity of dietary vitamins compared and "found'' different quantities which should be strictly equal by virtue of energy conservation. Aiming at clarifying this point as well as at avoiding such mistakes in future studies or unraveling errors in previous literature, in the present paper we formulate two theorems that any sound results on antioxidation should obey. The first theorem states that the sums of the enthalpies characterizing the individual steps of SET-PT and SPLET are equal: IP + PDE = PA + ETE (= H2). This is a mathematical identity emerging from the fact that both the reactants and the final products of SET-PT and SPLET are chemically identical. The second theorem, which is also a mathematical identity, states that H2 - BDE = IP_H > 0, where IP_H is the ionization potential of the H atom in the medium (e.g., gas or solvent) considered. Due to their general character, these theorems may/should serve as necessary sanity tests for any results on antioxidant activity whatever the method employed in their derivation. From a more general perspective, they should be a serious word of caution to attempts of assigning the preferred free radical scavenging pathway merely based on thermochemical descriptors.