Computation of the pK_a Values of Gallic Acid and Its Anionic Forms in Aqueous Solution: A Self-Similar Transformation...

The Gibbs free energies of gallic acid (GA) and its anionic forms in aqueous solution were computed utilizing density functional theory (DFT) at the LSDA, M062X, B3LYP/QZVP levels, in conjunction with the SMD solvation model. The pK_a values corresponding to the four-step deprotonation of GA were determined through a non-linear self-similar transformation expressed as, pK_a = a⋅pK_a(the)^c which establishes a link between theoretical and experimental pK_a values. This approach replaces the previously employed linear relationship, pK_a = a⋅pK_a(the) + b. The proposed model demonstrates high accuracy in reproducing the experimental pK_a1 = 4.16 ± 0.02, pK_a2 = 8.55 ± 0.01, pK_a3 =11.40 ± 0.10, pK_a4 =12.8 ± 0.40 values of GA, with a standard error (SE) of 0.045 and a mean absolute error (MAE) of 0.019 in pK_a unit. Furthermore, it facilitates the precise determination of the Gibbs free energy of the proton hydration, yielding ∆G(H⁺)_aq = 259.4272(75) [kcal mol^-1]. This result conforms acceptably with the experimental value of ∆G(H⁺)_aq = -259.5 [kcal mol^-1].