Prediction of the pK_a’s of Aqueous Metal Ion +2 Complexes

Aqueous metal ions play an important role in many areas of chemistry. The acidities of [Be­(H₂O)₄]²⁺, [M­(H₂O)₆]²⁺, M = Mg²⁺, Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺, Cd²⁺, and Hg²⁺, and [M­(H₂O)_n]²⁺, M = Ca²⁺ and Sr²⁺, n = 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. pK_a’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. Be²⁺ is tetracoordinated, but a second solvation shell of 8 waters is needed to predict the pK_a. The Ca²⁺ and Sr²⁺ aquo clusters have a coordination number of 7 or 8 as found in terms of the energy of the reaction M­(H₂O)₇²⁺ + H₂O → M­(H₂O)₈²⁺ and the pK_a 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 pK_a’s, and the MP2 level also provides reliable predictions. Our predictions were used to elucidate the properties of metal +2 ion complexes. The pK_a predictions provide confirmation of the size of the first solvation shell sizes. The calculations show that it is still difficult to predict pK_a’s using this cluster/implicit solvent approach to better than 1 pK_a unit.