Prediction of the p<i>K</i><sub>a</sub>’s of Aqueous Metal Ion +2 Complexes

Aqueous metal ions play an important role in many areas of chemistry. The acidities of [Be­(H<sub>2</sub>O)<sub>4</sub>]<sup>2+</sup>, [M­(H<sub>2</sub>O)<sub>6</sub>]<sup>2+</sup>, M = Mg<sup>2+</sup>, Mn<sup>2+</sup>, Fe<sup>2+</sup>, Co<sup>2+</sup>, Ni<sup>2+</sup>, Cu<sup>2+</sup>, Zn<sup>2+</sup>, Cd<sup>2+</sup>, and Hg<sup>2+</sup>, and [M­(H<sub>2</sub>O)<sub><i>n</i></sub>]<sup>2+</sup>, M = Ca<sup>2+</sup> and Sr<sup>2+</sup>, <i>n</i> = 7 and 8, complexes have been predicted using density functional theory, second-order Møller–Plesset perturbation theory (MP2), and coupled cluster CCSD­(T) theory in the gas phase. p<i>K</i><sub>a</sub>’s in aqueous solution were predicted by using self-consistent reaction field (SCRF) calculations with different solvation models. The most common binding motif of the majority of the metal +2 complexes is coordination number (CN) 6, with each hexaaquo cluster having reasonably high symmetry for the best arrangement of the water molecules in the first solvation shell. Be<sup>2+</sup> is tetracoordinated, but a second solvation shell of 8 waters is needed to predict the p<i>K</i><sub>a</sub>. The Ca<sup>2+</sup> and Sr<sup>2+</sup> aquo clusters have a coordination number of 7 or 8 as found in terms of the energy of the reaction M­(H<sub>2</sub>O)<sub>7</sub><sup>2+</sup> + H<sub>2</sub>O → M­(H<sub>2</sub>O)<sub>8</sub><sup>2+</sup> and the p<i>K</i><sub>a</sub> values. The calculated geometries are in reasonable agreement with experiment. The SCRF calculations with the conductor-like screening model (COSMO), and the conductor polarized continuum model (CPCM) using COSMO-RS radii, consistently agree best with experiment at the MP2/aug-cc-pVDZ and CCSD­(T)/aug-cc-pVDZ levels of theory. The CCSD­(T) level provides the most accurate p<i>K</i><sub>a</sub>’s, and the MP2 level also provides reliable predictions. Our predictions were used to elucidate the properties of metal +2 ion complexes. The p<i>K</i><sub>a</sub> predictions provide confirmation of the size of the first solvation shell sizes. The calculations show that it is still difficult to predict p<i>K</i><sub>a</sub>’s using this cluster/implicit solvent approach to better than 1 p<i>K</i><sub>a</sub> unit.