Elucidating and contrasting the mechanisms for Mg and Ca sulfate ion-pair formation with multi-level embedded quantum mechanics/molecular dynamics simulations

Solutions and minerals containing sulfate (SO₄²⁻), and Ca²⁺ and Mg²⁺ cations, are ubiquitous throughout the lithosphere and are significant components of seawater, thus presenting a prototypical system for the study of strong electrolytes and crystal nucleation mechanisms. However, despite their relative abundance, key questions remain unanswered about the most fundamental atomic-level steps of their mineralization pathways and aqueous dynamics. Here, we carry out enhanced sampling multi-level molecular dynamics (MD) embedded correlated wavefunction theory simulations to elucidate ion-pairing mechanisms for Mg-SO₄ and Ca-SO₄ in concentrated aqueous solution, accurately capturing effects arising from both structural dynamics and electron exchange-correlation. We predict contact-ion-pair formation to be barrierless and highly exoergic for Ca-SO₄, in agreement with its minimal solubility, whereas for Mg-SO₄, solvent-shared and contact ion pairs have similar free energies, qualitatively consistent with its higher solubility. Finally, we demonstrate that brief high-temperature pre-equilibration may be utilized to accelerate convergence of free energies in blue-moon-ensemble enhanced-sampling MD.