A universal free energy relationship for both hard and soft radical addition in water

Abstract

Prioritization of (eco)toxicological risks and technological endpoints among 100,000+ potential substances, conditions and mechanisms requires computationally ‘inexpensive’ and accurate tools to ‘screen’ reactivity and identify reaction products. Such prediction tools are very scarce. Left unresolved, charge‐transfer and hydration complicate predictions. Based on experimental reaction of radicals (3O2, CH3•, CO3•− etc.) with organic substrates, we hypothesized that a universal linear free energy relationship (LFER) can rationalize these reactions to accurately predict addition rates. We calculated free energies of forming charge‐separated intermediates from explicit descriptions of addition reaction products. We combined these energies, via a thermodynamic cycle, with electron transfer energies to calculate product formation energies. All energies include consideration of hydration effects by water. We ascribe feasibilities of ‘hard’ (ionic) and ‘soft’ (covalent) mechanisms to the relevance of the charge‐separated intermediate. Analysis shows that activation energies effectively relate to a combination of product formation energies and charge‐separation energies. The relative importance of these is determined by a mixing parameter, which is mostly constant for a given radical (substrate). Via the Eyring equation, our universal LFER explains up to 94% of the variance in data for rate constants. Prediction error is a factor 5 (2 SD), only slightly larger than variation in experimentation, particularly sensitive to varying reaction conditions. Minimal parametrization ensures that our new framework for calculating reactivity of radical addition is accurate, robust and with satisfactory rational. Calculation time for 100 reactions is <1 h on a standard desktop PC. In anticipation of underpinning with an even wider range of reagents, this ‘inexpensive’ calculus can more easily assess a greater domain of structures and extrapolate to new structures. This helps to better assess and select favourable non‐toxic, environmentally friendly and technologically superior chemical (sub)structures.