What question did this study set out to answer?

This research aims to elucidate the underlying mechanisms of hydration structure and stability in alkaline-earth metal ion clusters.

July 3, 2026Open Access

Structural Evolution of Hydrated Alkaline-Earth Metal Ion Clusters via Molecular Face Theory with Kohn–Sham One-Electron Potential

Key Points

This research aims to elucidate the underlying mechanisms of hydration structure and stability in alkaline-earth metal ion clusters.
Applied Molecular Face Theory (MFT) using Kohn–Sham one-electron potential for analysis.
Investigated gas-phase hydrated clusters M[(H2O)n]2+ for M = Be, Mg, Ca, Sr, Ba and n = 1–15.
Analyzed electron density, charge transfer, and steric effects associated with hydration.
Total water binding energy decreases with increasing ionic radius (Be2+ > Mg2+ > Ca2+ > Sr2+ > Ba2+).
Strong correlations established between KSpot depth, bond length (R = 0.98), and binding energy (R = 0.99).
Transition from monolayer to bilayer hydration occurs with seven to eight water molecules, influenced by steric and electrostatic interactions.

Abstract

High Resolution Image Download MS PowerPoint Slide Alkaline-earth metal ions exhibit distinct hydration behaviors that evolve with coordination number and govern their chemical reactivity, transport properties, and biological functions, yet a unified description linking hydration structure, electronic effects, and steric hindrance remains incomplete. In this work, the Molecular Face Theory (MFT) based on the Kohn–Sham one-electron potential (KSpot) was applied to systematically investigate the structural evolution of gas-phase hydrated clusters M(H 2 O) n 2+ (M = Be, Mg, Ca, Sr, and Ba, n = 1–15). In addition, KSpot was employed to quantify electron density distribution, atomic partitioning, charge transfer, and steric effects during hydration. Across the series, the total water binding energy decreases monotonically with increasing ionic radius (Be 2+ > Mg 2+ > Ca 2+ > Sr 2+ > Ba 2+ ), reflecting the dominant role of ionic charge density. The depth of the KSpot at the saddle point along a chemical bond ( D pb ) for the metal–oxygen coordination bond exhibits a strong negative correlation with bond length ( R = 0.98) and a positive correlation with binding energy ( R = 0.99), establishing it as a quantitative descriptor of coordination stability. With the increasing hydration number, the first ionization potential decreases continuously, while the molecular face surface areas and volumes display clear inflection points at n = 6–8, elucidating saturation of the first hydration shell. Charge distribution analysis reveals efficient electrostatic screening by the first-shell water molecules, followed by a pronounced saturation behavior upon shell completion. Stereoselective analysis of calcium ion clusters indicates that seven to eight water molecules mark the structural transition from a monolayer to bilayer hydration, where steric hindrance and electrostatic interactions jointly determine conformational stability and promote second-shell formation. These results provide a unified electronic and stereoselective perspective on alkaline-earth metal ion hydration and its shell-by-shell structural evolution.

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