<i>Ab Initio</i> Molecular Dynamics Study of H ₂ SO ₃ Ionization in Hydrothermal Fluids and Nanodroplets

Using ab initio molecular dynamics and thermodynamic integration calculations, we have examined the speciation and stability of H2SO3 from 25 to 350 °C in bulk liquid and water nanodroplets. H2SO3 ionization constants have been determined by using constraint force and thermodynamic integration techniques. The temperature dependence of the first ionization (yielding HSO3–) and second ionization (yielding SO32–) constants up to 350 °C is given by the following van’t Hoff equations: logK1 = −32.5686 – 0.0297·T + 6.8894·ln(T) and logK2 = −86.3360 – 0.0608·T + 16.8911·ln(T). Our calculated ionization constants are in good agreement with experimental data at 25 °C, with pK1 = 2.08 ± 0.13 (Exp. = 1.88, [Beyad, Y. Dalton Trans. 2014, 43(5), 2147–2152]) and pK2 = 8.14 ± 0.10 (Exp. = 7.12, [Millero, F. J. J. Atmos. Chem. 1989, 8, 377–389]). With increasing temperature, values of pK1 and pK2 increase to 6.93 ± 0.13 and 15.66 ± 0.16 at 350 °C, respectively, highlighting the reduced acidity of H2SO3 and HSO3–. The derived enthalpy changes (ΔH°) shift toward more exothermic values with increasing temperature from −2.67 kcal/mol at 25 °C to −33.08 kcal/mol at 350 °C, for the first ionization step, and from −1.69 kcal/mol at 25 °C to −59.90 kcal/mol at 350 °C kcal/mol for the second ionization step, the temperature-weighted entropy (TΔS°) shift from −5.50 kcal/mol (25 °C) to −52.85 kcal/mol (350 °C) and from −12.80 kcal/mol (25 °C) to −104.56 kcal/mol (350 °C) for the first and second ionization steps, respectively. Calculated values of ΔH° and ΔS° demonstrate that with increasing temperature entropic effects outweigh enthalpic contributions, giving rise to a decreased acidity of H2SO3. Vapor-phase simulations of H2SO3 at 350 °C reveal a ∼30% larger ionization free energy ΔG compared to solution phase ionization, indicating an enhanced energetic penalty for deprotonation in low-density aqueous media. Simulations in H2SO3(H2O)100 nanodroplets at 25 and 100 °C demonstrate surface-enhanced stabilization for H2SO3, with the deprotonation free energy ΔG 2.6–4.6 kcal/mol larger at surface solvation sites versus droplet interior. Finally, these molecular dynamics results reveal that at neutral pH in bulk liquid, sulfurous acid exists as the ionized HSO3– form, while aqueous hydrothermal nanodroplet surfaces and interiors favor the fully associated acid H2SO3 and the bisulfite ion HSO3–, respectively.