Computational and solubility equilibrium experimental insight into Ca2+–fluoride complexation and their dissociation behaviors in aqueous solutions: implication for the association constant measured using fluoride ion selective electrodes

Abstract

Although the Ca²⁺–F⁻ association is of great importance for aqueous environments and industrial systems containing F⁻, as well as for defluorination processes, many details of the association solvation structures and behavior remain unclear. Herein, a combination of classical/ab initio molecular dynamics simulations and density functional theory calculations was used to investigate the structure and hydration of CaF_x^2−x (x = 1, 2) and the association/dissociation behavior of Ca²⁺–F⁻ in aqueous CaF₂ solutions. The primary shell of Ca²⁺ is found to be very flexible in the association of Ca²⁺–F⁻, with coordination numbers dynamically oscillating in the range of 6–9, with 6 and 7 being the most favorable. The calculations show that for CaF(H₂O)₁₄⁺, the contact ion pair (CIP) is more favorable and occurs with no energy barrier, whereas the formation of CaF₂(aq.) must overcome a ∼3.6 kJ mol⁻¹ energy barrier; moreover, the CIP and solvent shared ion pair (SSIP) dynamically coexist for CaF₂(H₂O)₁₄ in aqueous CaF₂ solutions. Calculations for the dissociation process of CaF(H₂O)₆⁺ show a dramatic energy increase going from SSIP to free Ca²⁺ and F⁻, ascribed to the surprisingly long-range electrostatic attraction between Ca²⁺ and F⁻ rather than to special F⋯H interactions. The energy increase results in the estimated association constant of CaF⁺ being larger than that previously measured using fluoride ion selective electrodes. This is attributed to the fact that the latter value might correspond to the ligand reaction of free Ca²⁺ and F⁻ to form the Ca²⁺–F⁻ SSIP. The combination of these results with CaF_2(s) solubility measurements suggests that the higher-order Ca²⁺–F⁻ complexes are absent in aqueous CaF₂ solutions.