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

Abstract

A practical method for calculating the pK_a'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 pK_a's of 30 different organoselenols, 16 with known experimental pK_a'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 pK_a units; the errors with M06-2X are somewhat smaller. One explicit water interacting with the selenium reduces the calculated pK_a's by 1-2 pK_a units along with improving the slope and intercept of the fit of the calculated pK_a'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 pK_a 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 pK_a's for the substituted selenols.