Predicting pK_a Values of Para-Substituted Aniline Radical Cations vs. Stable Anilinium Ions in Aqueous Media

The focus of pK_a calculations has primarily been on stable molecules, with limited studies comparing radical cations and stable cations. In this study, we comprehensively investigate models with implicit solvent and explicit water molecules, direct and indirect calculation approaches, as well as methods for calculating free energy, solvation energy, and quasi-harmonic oscillator approximation for para-substituted aniline radical cations (R-PhNH₂^•+) and anilinium cations (R-PhNH₃⁺) in the aqueous phase. Properly including and positioning explicit H₂O molecules in the models is important for reliable pK_a predictions. For R-PhNH₂^•+, precise pK_a values were obtained using models with one or two explicit H₂O molecules, resulting in a root mean square error (RMSE) of 0.563 and 0.384, respectively, for both the CBS-QB3 and M062X(D3)/ma-def2QZVP methods. Further improvement was achieved by adding H₂O near oxygen-containing substituents, leading to the lowest RMSE of 0.310. Predicting pK_a values for R-PhNH₃⁺ was more challenging. CBS-QB3 provided an RMSE of 0.349 and the M062X(D3)/ma-def2QZVP method failed to calculate pK_a accurately (RMSE > 1). However, by adopting the double-hybrid functional method and adding H₂O near the R substituent group, the calculations were significantly improved with an average absolute difference (ΔpK_a) of 0.357 between the calculated and experimental pK_a values. Our study offers efficient and reliable methods for pK_a calculations of R-PhNH₂^•+ (especially) and R-PhNH₃⁺ based on currently mature quantum chemistry software.