Constrained Density Functional Theory Molecular Dynamics Simulation of Deprotonation in Aqueous Silicic Acid

The solubility of silicic acid in water is so low that the molecular mechanism behind the physical properties such as pK_a remains poorly understood, despite the importance in fields such as chemistry and geology. Theoretical calculations provide the molecular-level information on such a rare chemical species yet face difficulties in the selection of reaction coordinates and the rare-event sampling of proton transfers (PTs) in condensed phases. We propose a straightforward calculation scheme of pK_a with ab initio molecular dynamics (MD) simulation and the constrained density functional theory (CDFT), which provides structural and dynamical properties such as radial distribution functions, vibrational spectra, and reaction paths. The calculated reaction free energies of deprotonations agreed with experiments within a few kcal/mol. Analysis of the solvation structure shows that, after deprotonation, the hydronium ion D₃O⁺ repels away from the deprotonated silicic acid SiO(OD)₃^- without forming a stable contact-ion pair. The calculated vibrational spectra are consistent with the spectroscopic measurements, and the dynamical analysis of the reaction path quantifies the couplings of the OD stretch vibrations of silicic acid and water to the PT reaction in terms of the vertical energy-gap coordinate that includes both the solute and the solvent components.