Theoretical study on the acidities of chiral phosphoric acids in dimethyl sulfoxide: hints for organocatalysis.

The pKa values of 41 chiral phosphoric acid-family catalysts in DMSO were predicted using the SMD/M06-2x/6-311++G(2df,2p)//B3LYP/6-31+G(d) method for the first time. The study showed that the calculated pKa's range from -4.23 to 6.16 for absolute pKa values and from -4.21 to 6.38 for relative pKa values. Excellent agreement between the calculated and experimental pKa's was achieved for the few available cases (to a precision of around 0.4 pKa unit), indicating that this strategy may be suitable for calculating highly accurate pKa's. A good linear correlation between the pKa's for 3 and 3' disubstituted phenyl BINOL phosphoric acids and the Hammett constants was obtained. The relationship between the acidities of phosphoric acid catalysts and their reaction activity and selectivity was also discussed. Knowledge of the pKa values of phosphoric acids should be of great value for the understanding of chiral Brønsted acid-catalyzed reactions and may aid in future catalyst design.