Quantum chemical benchmarking, validation, and prediction of acidity constants for substituted pyridinium ions and pyridinyl radicals

Sensibly modeling (photo)electrocatalytic reactions involving proton and electron transfer with computational quantum chemistry requires accurate descriptions of protonated, deprotonated, and radical species in solution. Procedures to do this are generally nontrivial, especially in cases that involve radical anions that are unstable in the gas phase. Recently, pyridinium and the corresponding reduced neutral radical have been postulated as key catalysts in the reduction of CO ₂ to methanol. To assess practical methodologies to describe the acid/base chemistry of these species, we employed density functional theory (DFT) in tandem with implicit solvation models to calculate acidity constants for 22 substituted pyridinium cations and their corresponding pyridinyl radicals in water solvent. We first benchmarked our calculations against experimental pyridinium deprotonation energies in both gas and aqueous phases. DFT with hybrid exchange-correlation functionals provide chemical accuracy for gas-phase data and allow absolute prediction of experimental pK _as with unsigned errors under 1 pK _a unit. The accuracy of this economical pK _a calculation approach was further verified by benchmarking against highly accurate (but very expensive) CCSD(T)-F12 calculations. We compare the relative importance and sensitivity of these energies to selection of solvation model, solvation energy definitions, implicit solvation cavity definition, basis sets, electron densities, model geometries, and mixed implicit/explicit models. After determining the most accurate model to reproduce experimentally-known pK _as from first principles, we apply the same approach to predict pK _as for radical pyridinyl species that have been proposed relevant under electrochemical conditions. This work provides considerable insight into the pitfalls using continuum solvation models, particularly when used for radical species.