Calculating the acidity of silanols and related oxyacids in aqueous solution

Ab initio molecular orbital theory was used to calculate deprotonation ener gies and enthalpies (DeltaE(d), DeltaH(d)) of oxyacid monomers and oligomer s. Results were interpreted with reference to current phenomenological mode ls for estimating metal-oxide surface acidities. The ultimate goal is to pr edict surface acidities using the ab initio method. We evaluated contributions to DeltaE(d) and DeltaH(d) from the electrostati c potential at the proton, electronic relaxation, geometric relaxation, sol vation, 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). DeltaE(d), (gas) calculated at the modest 6-31G* HF of theory level correlates well with experimental p K(a) in solution, because hydration enthalpies for the acid anions (DeltaH( hyd, A-)) are closely proportional to DeltaE(d), gas. That is, anion intera ction 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 bas e permits generalization of the DeltaE(d,gas) - pK(a) correlation to deprot onation reactions involving charged acids. Thus, stable protonated, neutral , and deprotonated species Si(OH)(3)(OH2)(1+), Si(OH)(4)(0), Si(OH)(3)O1-, and Si(OH)(2)O-2(2-) have been characterized, and solution pK(a)'s for Si(O H)(3)(OH2)(1+) and Si(OH)(3)O1- were estimated, assuming that the charged s pecies (Si(OH)(3)(OH2)(1+), Si(OH)(3)O-1) fit into the same DeltaE(d), (gas ) - pK(a) correlation as do the neutral acids. The correlation yields a neg ative pK(a) (similar to -5) for Si(OH)(3)(OH2)(+1). Calculated DeltaE(d), (gas) also correlates well with the degree of O under -bonding evaluated using Brown's bond-length based approach. DeltaE(d), (ga s) increases along the series HClO4 - Si(OH)(4) mainly because of increasin gly 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, partia lly explaining the success of phenomenological models in correlating surfac e pK(a) of oxides with bond-strengths. Accurate evaluation of DeltaH(d), (gas) requires calculations with larger b asis sets, inclusion of electron correlation effects, and corrections for v ibrational, rotational, and translational contributions. Density functional and 2nd-order Moller-Plesset results for deprotonation enthalpies match we ll against higher-level G2(MP2) calculations. Direct calculation of solution pK(a) without resorting to correlations is p resently impossible by ab initio methods because of inaccurate methods to a ccount for solvation. Inclusion of explicit water molecules around the mono mer immersed in a self-consistent reaction field (SCRF) provides the most a ccurate absolute hydration enthalpy (DeltaH(hyd)) values, but IPCM Values f or the bare acid (HA) and anion (A(-)) give reasonable values of DeltaH(hyd ,) (A)- - DeltaH(hyd), (HA) values with much smaller computational expense. Polymers delicate are used as model systems that begin to approach solid si lica, known to be much more acidic than its monomer, Si(OH)(4). Polymerizat ion of silicate or phosphate reduces their gas-phase DeltaE(d), (gas) relat ive to the monomers; differences in the electrostatic potential at H+, elec tronic relaxation and geometric relaxation energies all contribute to the e ffect. Internal H-bonding in the dimers results in unusually small DeltaE(d ),(gas) which is partially counteracted by a reduced DeltaH(hyd). Accurate representation of hydration for oligomers persists as a Fundamental problem in determining their solution pK(a), because of the prohibitive cost invol ved in directly modeling interactions between many water molecules and the species of interest. Fortunately, though, the local contribution to the dif ference in hydration energy between the neutral polymeric acid and its anio n seems to stabilize for a small number of explicit water molecules. Copyri ght (C) 2000 Elsevier Science Ltd.