Beyond Single Structures: The Role of Structural Ensembles in Discrete-Continuum Modeling of Highly Charged Metal Ions.

Metal ions play critical roles in chemical, biochemical, and materials systems. The discrete-continuum model has been widely used for modeling metal ions in the aqueous phase due to its excellent balance of accuracy and efficiency. Previously, we demonstrated that a discrete-continuum model combining B3LYP-D3/def2-QZVP for the first solvation shell with the SMD implicit solvent model for outer shells accurately predicts hydration free energies (HFEs) of divalent, trivalent, and tetravalent ions. However, those results relied on single optimized geometries. Here, we extend this approach by incorporating molecular dynamics (MD) simulations to enhance conformational sampling for nine metal ions with charges from +2 to +4: the alkaline earth metal ions (Be2+, Mg2+, Ca2+, Sr2+, Ba2+), Al3+, Ce3+, Zr4+, and Hf4+. MD trajectories were filtered through quantum mechanical geometry optimization to identify representative structures, from which Boltzmann-weighted HFE values were calculated. Our results reveal that larger alkaline earth metal ions access more local minima, with the number of representative structures increasing as surface charge density decreases. Remarkably, these local minima exhibit fundamentally different electronic structures and chemical bonding patterns, as revealed by ETS-NOCV analysis. For ions with van der Waals surface charge densities below 0.1 e/Å2, accounting for multiple minima through Boltzmann weighting substantially improves agreement between discrete-continuum predictions and experimental HFEs. We propose this threshold as a practical criterion for determining when enhanced sampling is necessary in discrete-continuum models. These findings establish that rigorous conformational sampling is essential for accurate HFE predictions of soft metal ions, while the single-frame protocol remains adequate for rigid ions with high surface charge densities.