First-Principles\nInsights into the Selective Separation\nof MoS<sub>4</sub><sup>2–</sup> and WO<sub>4</sub><sup>2–</sup>: Crucial Role of Hydration Structures

The selective separation of MoS<sub>4</sub><sup>2–</sup> and WO<sub>4</sub><sup>2–</sup> using quaternary ammonium\nsalt through solvent extraction or ion exchange methods has been well-established\nin the metallurgical industry. However, the conventional electrostatic\nadsorption theory falls short in explaining the separation mechanism.\nThrough first-principles density functional theory (DFT) calculations\nand newly self-developed deep potential molecular dynamics (DPMD)\nsimulation method, our work first reveals that the disparity in hydration\nstructures of MoS<sub>4</sub><sup>2–</sup> and WO<sub>4</sub><sup>2–</sup> plays a crucial role in their selective separation.\nIt is proposed that MoS<sub>4</sub><sup>2–</sup> and WO<sub>4</sub><sup>2–</sup> anions undergo hydration to form [MoS<sub>4</sub>(H<sub>2</sub>O)<i><sub>n</sub></i>]<sup>2–</sup> and [WO<sub>4</sub>(H<sub>2</sub>O)<i><sub>n</sub></i>]<sup>2–</sup>, respectively, facilitated by hydrogen bond\n(H-bond) interactions. Emphasis is placed on the discrepancy between\nMoS<sub>4</sub><sup>2–</sup> and WO<sub>4</sub><sup>2–</sup> in hydration structures by the hydration energy, Hirshfeld charge,\nevaluation of weak interactions, hydration radius, hydration coordination\nnumber, and H-bonds distribution. MoS<sub>4</sub><sup>2–</sup> presents a larger first hydration radius and a lower first hydration\ncoordination number due to weaker interactions with H<sub>2</sub>O,\nwhile WO<sub>4</sub><sup>2–</sup> is subjected to enhanced\nhydration shielding, resulting in MoS<sub>4</sub><sup>2–</sup> anions being more susceptible to be selectively separated by a quaternary\nammonium salt. This insight paves the way for the selective separation\nof MoS<sub>4</sub><sup>2–</sup> and WO<sub>4</sub><sup>2–</sup>, further bridging the gap between theory and industry applications.