The Arrangement of First- and Second-Sphere Water Molecules in Divalent Magnesium Complexes:  Results from Molecular Orbital and Density Functional Theory and from Structural Crystallography

The structures and binding enthalpies of a variety of gas-phase divalent magnesium ion hydrates containing up to 18 water molecules have been studied computationally. Second-order Møller−Plesset (MP2) perturbation theory and B3LYP hybrid density functional theory, using large basis sets containing both (multiple) polarization and diffuse functions, were employed. A comparison with experimental data is made by use of information on 36 Mg[H₂O]₆²⁺ crystal structures listed in the Cambridge Structural Database. Computational studies indicate that Mg[H₂O]₅²⁺ and Mg[H₂O]₆²⁺ complexes with all the water molecules in the inner coordination sphere are lower in energy than structures with one or two of the water molecules placed in the second coordination sphere; these energy differences are larger for MP2 than for B3LYP calculations, when the same basis set is employed. Hydrated magnesium environments in crystal structures confirm the stability of the Mg[H₂O]₆²⁺ grouping. A new model of a divalent magnesium ion complex with a total of 18 water molecules in two concentric shells of hydration is presented. In this model six water molecules are arranged octahedrally in the first coordination shell and 12 additional water molecules, hydrogen-bonded to those in the inner shell, fill the second shell. This new structure of Mg[H₂O]₆²⁺·[H₂O]₁₂ has an integrated hydrogen-bonding network in which water pentamers, composed of four second-shell water molecules and one first-shell water molecule, play a significant role. The geometry is derived from that of a pentagonal dodecahedral arrangement of water molecules enclosing an Mg[H₂O]₆²⁺ octahedron. This model has S₆ symmetry and is calculated to be lower in energy than other forms of Mg[H₂O]₆²⁺·[H₂O]₁₂ previously described in the literature (Pavlov et al. J. Phys. Chem. A. 1998, 102, 219−228; Pye and Rudolph J. Phys. Chem. A 1998, 102, 9933−9943). The structure of Mg[H₂O]₆²⁺·[H₂O]₁₂ presented here provides additional insight into the importance of the water dipole moment in controlling the orientation of the water molecules in the first coordination shell and of water−water hydrogen bonding in controlling the orientation of water molecules in the second shell. These factors are also evident in crystal structures containing the Mg[H₂O]₆²⁺ octahedron; in particular, a neutron diffraction study (Vanhouteghem, Lenstra, and Schweiss Acta Crystallogr. 1987, B43, 523−528) showed that first-shell water molecules have the magnesium ion within 10° of the plane of each water molecule.