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 (ΔE d, ΔH d) 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 ΔE d and ΔH d from the electrostatic potential at the proton, electronic relaxation, geometric relaxation, solvation, and polymerization for the neutral-charge gas-phase molecules H 2O, CH 3OH, HCOOH, SiH 3OH, Si(OH) 4, Si 2O 7H 6, H 3PO 4, P 2O 7H 4, H 2SO 3, H 2SO 4, HOCl, HClO 4, Ge(OH) 4, As(OH) 3, and AsO(OH) 3. ΔE d, gas calculated at the modest 6-31G∗ HF of theory level correlates well with experimental pK a in solution, because hydration enthalpies for the acid anions (ΔH hyd, A−) are closely proportional to ΔE d, 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 ΔE d, gas – pK a correlation to deprotonation reactions involving charged acids. Thus, stable protonated, neutral, and deprotonated species Si(OH) 3(OH 2) 1+, Si(OH) 4 0, Si(OH) 3O 1−, and Si(OH) 2O 2 2− have been characterized, and solution pK a’s for Si(OH) 3(OH 2) 1+ and Si(OH) 3O 1− were estimated, assuming that the charged species (Si(OH) 3(OH 2) 1+, Si(OH) 3O −1) fit into the same ΔE d, gas – pK a correlation as do the neutral acids. The correlation yields a negative pK a (∼ −5) for Si(OH) 3(OH 2) +1. Calculated ΔE d, gas also correlates well with the degree of O under-bonding evaluated using Brown’s bond-length based approach. ΔE d, gas increases along the series HClO 4 – 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, pK a can be correlated with underbondings or local electrostatic energies for the monomers, partially explaining the success of phenomenological models in correlating surface pK a of oxides with bond-strengths. Accurate evaluation of ΔH d, 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 pK a 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 (ΔH hyd) values, but IPCM values for the bare acid (HA) and anion (A −) give reasonable values of ΔH hyd, A − – ΔH hyd, HA values with much smaller computational expense. Polymers of silicate are used as model systems that begin to approach solid silica, known to be much more acidic than its monomer, Si(OH) 4. Polymerization of silicate or phosphate reduces their gas-phase ΔE d, gas relative to the monomers; differences in the electrostatic potential at H +, electronic relaxation and geometric relaxation energies all contribute to the effect. Internal H-bonding in the dimers results in unusually small ΔE d,gas which is partially counteracted by a reduced ΔH hyd. Accurate representation of hydration for oligomers persists as a fundamental problem in determining their solution pK a, because of the prohibitive cost involved in directly modeling interactions between many water molecules and the species of interest. Fortunately, though, the local contribution to the difference in hydration energy between the neutral polymeric acid and its anion seems to stabilize for a small number of explicit water molecules.