Dissolution Thermochemistry of Alkali Metal Dianion Salts (M₂X₁, M = Li⁺, Na⁺, and K⁺ with X = CO₃^2–, SO₄^2–, C₈H₈^2–, and B₁₂H₁₂^2–)

Abstract

The dissolution Gibbs free energies (Δ<i>G</i>°_diss) of salts (M₂X₁) have been calculated by density functional theory (DFT) with Conductor-like Polarizable Continuum Model (CPCM) solvation modeling. The absolute solvation free energies of the alkali metal cations (Δ<i>G</i>_solv(M⁺)) come from the literature, which coincide well with half reduction potential versus SHE data. For solvation free energies of dianions (Δ<i>G</i>_solv(X^2–)), four different DFT functionals (B3LYP, PBE, BVP86, and M05–2X) were applied with three different sets of atomic radii (UFF, UAKS, and Pauling). Lattice free energies (Δ<i>G</i>_latt) of salts were determined by three different approaches: (1) volumetric, (2) a cohesive Gibbs free energy (Δ<i>G</i>_coh) plus gaseous dissociation free energy (Δ<i>G</i>_gas), and (3) the Born–Haber cycle. The G4 level of theory, electron propagator theory, and stabilization by dielectric medium were used to calculate the second electron affinity to form the dianions CO₃^2– and SO₄^2–. Only the M05–2X/Pauling combination with the three different methods for estimating Δ<i>G</i>_latt yields the expected negative dissolution free energies (Δ<i>G</i>°_diss) of M₂SO₄. Salts with large dianions like M₂C₈H₈ and M₂B₁₂H₁₂ reveal the limitation of using static radii in the volumetric estimation of lattice energies. The value of Δ<i>E</i>_coh was very dependent on the DFT functional used.