Abstract

Information resulting from a comprehensive investigation into the intrinsic strengths of hydrated divalent magnesium clusters is useful for elucidating the role of aqueous solvents on the Mg2+ ion, which can be related to those in bulk aqueous solution. However, the intrinsic Mg–O and intermolecular hydrogen bond interactions of hydrated magnesium ion clusters have yet to be quantitatively measured. In this work, we investigated a set of 17 hydrated divalent magnesium clusters by means of local vibrational mode force constants calculated at the ωB97X-D/6-311++G(d,p) level of theory, where the nature of the ion–solvent and solvent–solvent interactions were interpreted from topological electron density analysis and natural population analysis. We found the intrinsic strength of inner shell Mg–O interactions for [Mg(H2O)n]2+ (n = 1–6) clusters to relate to the electron density at the bond critical point in Mg–O bonds. From the application of a secondary hydration shell to [Mg(H2O)n]2+ (n = 5–6) clusters, stronger Mg–O interactions were observed to correspond to larger instances of charge transfer between the lp(O) orbitals of the inner hydration shell and the unfilled valence shell of Mg. As the charge transfer between water molecules of the first and second solvent shell increased, so did the strength of their intermolecular hydrogen bonds (HBs). Cumulative local vibrational mode force constants of explicitly solvated Mg2+, having an outer hydration shell, reveal a CN of 5, rather than a CN of 6, to yield slightly more stable configurations in some instances. However, the cumulative local mode stretching force constants of implicitly solvated Mg2+ show the six-coordinated cluster to be the most stable. These results show that such intrinsic bond strength measures for Mg–O and HBs offer an effective way for determining the coordination number of hydrated magnesium ion clusters.

Highlights

  • Magnesium, being the eighth most abundant element and second most abundant alkaline earth metal, accounts for 2% of the Earth’s crust [1]

  • We investigated a set of 17 hydrated divalent magnesium clusters by means of local vibrational mode force constants calculated at the ωB97X-D/6-311++G(d,p) level of theory, where the nature of the ion–solvent and solvent–solvent interactions were interpreted from topological electron density analysis and natural population analysis

  • The cumulative local mode stretching force constants of implicitly solvated Mg2+ show the six-coordinated cluster to be the most stable. These results show that such intrinsic bond strength measures for Mg–O and hydrogen bonds (HBs) offer an effective way for determining the coordination number of hydrated magnesium ion clusters

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Summary

Introduction

Magnesium, being the eighth most abundant element and second most abundant alkaline earth metal, accounts for 2% of the Earth’s crust [1]. As the production and application of magnesium increase, the amount of magnesium waste increases [14], having been noted to pose dangerous environmental effects [15] High concentrations of such mineral-based ions have resulted in hard water where the hydration of the Mg2+ ion yields insoluble precipitates. The determination of the coordination number (CN) has been highly sought after to understand the nature of hydrated magnesium ion clusters, where such information can be related to the bulk form of the metal cation in an aqueous solvent. The XRD work of Albright and co-workers, involving hydrated divalent magnesium clusters in concentrated chloride solutions, reported a CN of 6.8 [26]. The X-ray absorption spectra of 2 and 4 M concentrations of the Mg2+ cation in chloride solution, generated by Cappa et al, revealed that a large amount of charge transfer occurs between the water molecules of the first solvent shell and the Mg2+ ion [30]

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