PII S0016-7037(01)00739-6Thermochemistry of silicic acid deprotonation: Comparison of gas-phase and solvated DFTcalculations to experimentJ. SEFCIK1and W. A. GODDARD III2,*1Laboratorium fu¨r Technische Chemie, ETH Zu¨rich, Universita¨tstr. 6, CH-8092 Zu¨rich, Switzerland2Materials and Process Simulation Center, Beckman Institute, 139-74, California Institute of Technology, Pasadena, CA 91125, USA(Received October 23, 2000; accepted in revised form June 8, 2001)Abstract—Theoretical approaches to the thermochemistry of silicate anions have so far focused on gas-phasemolecular orbital and density functional theory (DFT) calculations. These calculations predict that in thepresence of hydroxide ligands the most stable singly charged anion of the silicic acid H4SiO4is thefive-coordinated anion H5SiO5⫺. However, experimental evidence from in situ nuclear magnetic resonance(NMR) experiments clearly shows that deprotonated silicic acid in alkaline aqueous solutions is four-coordinated, H3SiO4⫺. We compare gas-phase and solvated DFT calculations of monomeric anions of silicicacid in order to assess solvent effects on the thermochemistry of silicic acid deprotonation. We show thatappropriate inclusion of solvation in quantum chemical calculations is critical for correct prediction ofcoordination and thermochemistry of silicate anions in aqueous solutions. Multiply charged anions of silicicacid are found to be electronically unstable in the gas phase and thus it is not possible to use thermodynamiccycles involving these species in thermodynamic calculations. However, a high dielectric constant solvent issufficient to stabilize these anions, and solvated calculations can be used to directly compute their thermo-dynamic quantities. When we include the zero point energy (ZPE) and statistical mechanics contributions tothe Gibbs free energy, we obtain accurate free energies for successive deprotonations of silicic acid in aqueoussolutions. Although the pentacoordinate hydroxoanion of silicon is more stable in the gas phase than thefour-coordinated one (by 18 and 5 kcal/mol in the self-consistent field (SCF) energy and the Gibbs free energy,respectively), it is less stable by 5 kcal/mol in the Gibbs free energy when hydration effects are appropriatelyaccounted for. Solvated DFT calculations, validated here by their accurate description of silicate anions inaqueous solutions, should lead to more reliable predictions of important geochemical quantities, such assurface acidities and detailed reaction coordinates for dissolution of minerals. Copyright © 2001 ElsevierScience Ltd1. INTRODUCTIONSilicate anions play an important role in processes of growthand dissolution of minerals and synthetic materials, such aszeolites and their siliceous analogs. Anions of silicic acid andof its oligomers are prevalent species in alkaline aqueoussolutions of silicates at pH ⬎ 10 (Iler, 1979) from whichzeolites are typically synthesized (Barrer, 1982). Even at pH ⬍9, where most of the soluble silica is in the form of neutralmonomers and dimers, silicate anions play the role of reactivespecies in silicic acid condensation via nucleophilic substitu-tion (Iler, 1979; Brinker and Scherer, 1990; Sefcik and McCor-mick, 1997a) at pH above the isoelectric point of reactingsilanols (pH ⫽ 2 for surface silanols and pH ⫽ 4to5formonomeric silicic acid).Although there are reliable experimental data for the Gibbsfree energy of the first two deprotonations of silicic acid in theaqueous phase (Sefcik and McCormick, 1997b), there are nofurther experimental thermochemical data for either gas-phaseor solvated silicates to which theoretical calculations could becompared. Unavailable experimental data are then substitutedby appropriate calculations. Numerous molecular orbital calcu-lations at ever increasing levels of theory have been performedfor neutral silicate oligomers. Silicic acid monomer and dimergeometries, energetics, and vibrational spectra were studied ingreat detail (Teppen et al., 1994; Kubicki and Sykes, 1995).More recent calculations focused on neutral species up tooctamers, mainly rings and cages, believed to play a role ofintermediates in the synthesis of amorphous and crystallinesilica solids (Moravetski et al., 1996; Lewis et al., 1997; Catlowet al., 1998; Tossell and Sahai, 2000). Most of these calcula-tions did correspond to gas-phase conditions, although associ-ation energies for monomer or dimer with one or few watermolecules have been calculated (Lasaga and Gibbs, 1990; Xiaoand Lasaga, 1994; Moravetski et al., 1996). Catlow et al. (1998)estimated solvation energies of neutral oligomers using both asimple group contribution method for the hydrogen bondingand the COSMO model of the solvent continuum.There were fewer studies of silicate anions, though. Interac-tions between H4SiO4and the hydroxide anion were studied bysemiempirical methods (Davis and Burggraf, 1988; Burggraf etal., 1992), and a stable pentacoordinate anion H5SiO5⫺has beenpredicted. Gas-phase ab initio calculations predicted the same,and it has been argued that H5SiO5⫺might be a stable silicateanion in alkaline aqueous solutions (Kubicki et al., 1993;Ermoshin et al., 1997) from which zeolites are crystallized. Agas-phase ab initio study by Xiao and Lasaga (1996) showedthat four- and five-coordinated anions of the silicic acid dimerhave similar potential energies. Geometry and energetics of thesingly deprotonated silicic acid H3SiO4⫺(De Almeida andO’Malley, 1992; Kubicki et al., 1995; Rustad et al., 2000) and* Author to whom correspondence should be addressed ([email protected]).PergamonGeochimica et Cosmochimica Acta, Vol. 65, No. 24, pp. 4435–4443, 2001Copyright © 2001 Elsevier Science LtdPrinted in the USA. All rights reserved0016-7037/01 $20.00 ⫹ .004435also the doubly charged anion (Tossell, 1991; Rustad et al.,2000) were studied in detail, but solvent effects were includedonly up to few explicit water molecules (Kubicki et al., 1993;Moravetski et al., 1996; Tossell and Sahai, 2000). Moleculardynamics studies of hydrated H4SiO4and H3SiO4⫺have alsobeen carried out with various force fields (Rustad and Hay,1995; Lewis et al., 1997).There is both theoretical and experimental evidence of five-coordinate silicon in melts, glasses, and certain minerals (Xueet al., 1989; Kubicki and Lasaga, 1990; Stebbins, 1991; Poe etal., 1992; Angel et al., 1996) and in organometallic siliconcompounds (Damrauer, 1988; Holmes, 1990;