Self-consistent reaction field calculations of aqueous Al3+, Fe3+, and Si4+:: Calculated aqueous-phase deprotonation energies correlated with experimental In(Ka) and pKa

Reaction energies for the deprotonation of Al3+.6(H2O), Fe3+.6(H2O), and Si(OH)(4) were calculated using Hartree-Fock and density functional methods with 6-311+G(d,p) (for Al3+ and Si4+) and 6-311G(d) (for Fe3+) basis sets. Theoretical energies were calculated using a supermolecule approach (i.e., explicit hydration of the solute) combined with the Integral Equation Formalism Polarized Continuum Model (IEFPCM; Cances et al., 1997, J. Chem. Phys. 107, 3032) and the Self-Consistent Isodensity Polarized Continuum Model (SCIPCM; Keith and Frisch, 1994, ACS Symp. Ser. 56, 22) in Gaussian 98. Tests on the effects of increasing the number of water molecules explicitly included in the supermolecule were also carried out. Additional water molecules in the energy minimizations of Al(OH)(3), Fe(OH)(3), and [Si(OH)(3)(OH2)](+) resulted in 5-coordinate complexes for all three species. Correlations of deprotonation energies with observed ln(K-a) values are good for individual cations. These correlations suggest that the combined supermolecule/continuum approach can give reliable pK(a) estimates, provided that the structural optimization reflects the aqueous-phase solute and that the basis set includes polarization and diffuse functions. An estimate is made of the pK(a) of the reaction-[Si(OH)(3)(OH2)](+)((aq)) <----> Si(OH)(4(aq)) + H-(aq)(+)-which has not yet been measured. A value of pK(a) approximate to -2 is predicted in this study.