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

The focus of p 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-PhNH) and anilinium cations (R-PhNH) in the aqueous phase. Properly including and positioning explicit HO molecules in the models is important for reliable p predictions. For R-PhNH, precise p values were obtained using models with one or two explicit HO 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 HO near oxygen-containing substituents, leading to the lowest RMSE of 0.310. Predicting p values for R-PhNH was more challenging. CBS-QB3 provided an RMSE of 0.349 and the M062X(D3)/ma-def2QZVP method failed to calculate p accurately (RMSE > 1). However, by adopting the double-hybrid functional method and adding HO near the R substituent group, the calculations were significantly improved with an average absolute difference (Δp) of 0.357 between the calculated and experimental p values. Our study offers efficient and reliable methods for p calculations of R-PhNH (especially) and R-PhNH based on currently mature quantum chemistry software.