THERMOCHEMISTRY OF SILICIC ACID DEPROTONATION: COMPARISON OF GAS-PHASE AND SOLVATED DFT CALCULATIONS TO EXPERIMENT

Abstract

Theoretical approaches to the thermochemistry of silicate anions have so far focused on gas-phase molecular orbital and density functional theory (DFT) calculations. These calculations predict that in the presence of hydroxide ligands the most stable singly charged anion of the silicic acid H4SiO4 is the five-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 silicic acid in order to assess solvent effects on the thermochemistry of silicic acid deprotonation. We show that appropriate inclusion of solvation in quantum chemical calculations is critical for correct prediction of coordination and thermochemistry of silicate anions in aqueous solutions. Multiply charged anions of silicic acid are found to be electronically unstable in the gas phase and thus it is not possible to use thermodynamic cycles involving these species in thermodynamic calculations. However, a high dielectric constant solvent is sufficient to stabilize these anions, and solvated calculations can be used to directly compute their thermodynamic quantities. When we include the zero point energy (ZPE) and statistical mechanics contributions to the Gibbs free energy, we obtain accurate free energies for successive deprotonations of silicic acid in aqueous solutions. Although the pentacoordinate hydroxoanion of silicon is more stable in the gas phase than the four-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 appropriately accounted for. Solvated DFT calculations, validated here by their accurate description of silicate anions in aqueous solutions, should lead to more reliable predictions of important geochemical quantities, such as surface acidities and detailed reaction coordinates for dissolution of minerals.