Second Hydration\nShell of Mg<sup>2+</sup>: Competition\nbetween Ion–Water Interaction and Hydrogen Bonding Interaction

Hydration in Mg<sup>2+</sup> solutions is critical in\nthe chemical\nand biological industries. Researchers have identified a rigid first\nhydration shell, but the effects of ion–water and hydrogen\nbonding (HB) interactions beyond the first shell of Mg<sup>2+</sup>, especially when ion pairs form at high concentrations, remain controversial.\nOn the basis of density functional theory, machine learning molecular\ndynamics was performed to study the second shell of Mg<sup>2+</sup> in MgCl<sub>2</sub> solutions at various concentrations. At low\nconcentrations, while both SCAN and PBE+TS-vdW predict a rigid first\nshell, SCAN affords a more softened structure due to its weakened\nHB interaction. The weakened HB interaction reveals the retarding\neffect of Mg<sup>2+</sup> on the water reorientation of the second\nshell. With an increasing concentration, SCAN reproduces the decreasing\ntrend of the hydration number, which originates from Cl<sup>–</sup> entering the second shell of Mg<sup>2+</sup>. Our results highlight\nthe importance of accurately described ion–water interaction\nand HB interaction in the intermediate range.