Modeling pK(a) of the Brønsted Bases as an Approach to the Gibbs Energy of the Proton in Acetonitrile

A simple but efficient computational approach to calculate pK(a) in acetonitrile for a set of phosphorus, nitrogen, and carbon bases was established. A linear function that describes relations between the calculated ΔG’(a.sol)(BH(+)) and pK(a) values was determined for each group of bases. The best model was obtained through the variations in the basis set, in the level of theory (density functionals or MP2), and in the continuum solvation model (IPCM, CPCM, or SMD). The combination of the IPCM/B3LYP/6-311+G(d,p) solvation approach with MP2/6-311+G(2df,p)//B3LYP/6-31G(d) gas-phase energies provided very good results for all three groups of bases with R(2) values close to or above 0.99. Interestingly, the slopes and the intercepts of the obtained linear functions showed significant deviations from the theoretical values. We made a linear plot utilizing all the conducted calculations and all the structural variations and employed methods to prove the systematic nature of the intercept/slope dependence. The interpolation of the intercept to the ideal slope value enabled us to determine the Gibbs energy of the proton in acetonitrile, which amounted to −258.8 kcal mol(−1). The obtained value was in excellent agreement with previously published results.