Theoretical Calculation of pKa’s of Selenols in Aqueous Solution Using an Implicit Solvation Model and Explicit Water Molecules

A practical method for calculating the pKa’s of selenols in aqueous solution has been developed by using density functional theory with the SMD solvation model and up to three explicit water molecules. The pKa’s of 30 different organoselenols, 16 with known experimental pKa’s, have been calculated by using three different functionals (ωB97XD, B3LYP, and M06-2X) and two basis sets (6-31+G­(d,p) and 6-311++G­(d,p)). Calculations using ωB97XD and B3LYP with SMD solvation without explicit waters are found to have errors of 3–6 pKa units; the errors with M06-2X are somewhat smaller. One explicit water interacting with the selenium reduces the calculated pKa’s by 1–2 pKa units along with improving the slope and intercept of the fit of the calculated pKa’s to experiment. The best results for SMD/M06-2X/6-31+G­(d,p) are with one explicit water (MSE = −0.08 ± 0.37 and MUE = 0.32 ± 0.37) whereas ωB97XD and B3LYP still have errors larger than 2 pKa units. The best results for ωB97XD and B3LYP with 6-31+G­(d,p) are obtained by using three explicit waters (MSE = 0.36 ± 0.24 and 0.34 ± 0.25, respectively) and a fit to experiment yields a slope of 1.06 with a zero intercept. The errors for M06-2X/6-31+G­(d,p) with three explicit waters are significantly larger (−3.59 ± 0.45) because it overstabilizes the anions. On the basis of the molecules studied here, M06-2X/6-31+G­(d,p) with one explicit water and ωB97XD/6-31+G­(d,p) and B3LYP/6-31+G­(d,p) with three explicit waters and the SMD solvation model can produce reliable pKa’s for the substituted selenols.