Theoretical Evaluation of pKa in Phosphoranes:  Implications for Phosphate Ester Hydrolysis

Knowledge of the pK(a) of phosphoranes is important for the interpretation of phosphate ester hydrolysis. Calculated pK(a)'s of the model phosphorane, ethylene phosphorane, are reported. The method of calculation is based on the use of dimethyl phosphate as a reference state for evaluating relative pK(a) values, and on the optimization of the oxygen and acidic hydrogen van der Waals radii to give reasonable pK(1)(a), pK(2)(a), and pK(3)(a) for phosphoric acid in solution. Density functional theory is employed to calculate the gas-phase protonation energies, and continuum dielectric methods are used to determine the solvation corrections. The calculated pK(1)(a) and p(2)(a) for the model phosphorane are 7.9 and 14.3, respectively. These values are within the range of proposed experimental values, 6.5-11.0 for pK(1)(a), and 11.3-15.0 for pK(2)(a). The mechanistic implications of the calculated pK(a)'s are discussed.