CALCULATING THE ACIDITY OF SILANOLS AND RELATED OXYACIDS IN AQUEOUS SOLUTION

Abstract

Ab initio molecular orbital theory was used to calculate deprotonation energies and enthalpies (ΔEd, ΔHd) of oxyacid monomers and oligomers. Results were interpreted with reference to current phenomenological models for estimating metal-oxide surface acidities. The ultimate goal is to predict surface acidities using the ab initio method.We evaluated contributions to ΔEd and ΔHd from the electrostatic potential at the proton, electronic relaxation, geometric relaxation, solvation, and polymerization for the neutral-charge gas-phase molecules H2O, CH3OH, HCOOH, SiH3OH, Si(OH)4, Si2O7H6, H3PO4, P2O7H4, H2SO3, H2SO4, HOCl, HClO4, Ge(OH)4, As(OH)3, and AsO(OH)3. ΔEd, gas calculated at the modest 6-31G* HF of theory level correlates well with experimental pKa in solution, because hydration enthalpies for the acid anions (ΔHhyd, A-) are closely proportional to ΔEd, gas. That is, anion interaction energies with water in aqueous solution and with H+ in the gas phase are closely correlated.Correction for differential hydration between an acid and its conjugate base permits generalization of the ΔEd, gas - pKa correlation to deprotonation reactions involving charged acids. Thus, stable protonated, neutral, and deprotonated species Si(OH)3(OH2)1+, Si(OH)40, Si(OH)3O1-, and Si(OH)2O22- have been characterized, and solution pKa's for Si(OH)3(OH2)1+ and Si(OH)3O1- were estimated, assuming that the charged species (Si(OH)3(OH2)1+, Si(OH)3O-1) fit into the same ΔEd, gas - pKa correlation as do the neutral acids. The correlation yields a negative pKa (~ -5) for Si(OH)3(OH2)+1.Calculated ΔEd, gas also correlates well with the degree of O under-bonding evaluated using Brown's bond-length based approach. ΔEd, gas increases along the series HClO4 - Si(OH)4 mainly because of increasingly negative potential at the site of the proton, not because of differing electronic or geometric relaxation energies. Thus, pKa can be correlated with underbondings or local electrostatic energies for the monomers, partially explaining the success of phenomenological models in correlating surface pKa of oxides with bond-strengths.Accurate evaluation of ΔHd, gas requires calculations with larger basis sets, inclusion of electron correlation effects, and corrections for vibrational, rotational, and translational contributions. Density functional and 2nd-order Moller-Plesset results for deprotonation enthalpies match well against higher-level G2(MP2) calculations.Direct calculation of solution pKa without resorting to correlations is presently impossible by ab initio methods because of inaccurate methods to account for solvation. Inclusion of explicit water molecules around the monomer immersed in a self-consistent reaction field (SCRF) provides the most accurate absolute hydration enthalpy (ΔHhyd) values, but IPCM values for the bare acid (HA) and anion (A-) give reasonable values of ΔHhyd, A- - ΔHhyd, HA values with much smaller computational expense.