Trivalent Ion Hydrolysis Reactions II: Analysis of Electron Density Distributions in Metal−Oxygen Bonds

Density functional theory calculations are applied to a series of trivalent hexaquo metal complexes to determine whether systematic properties exist in the electron density distribution of the metal−oxygen (M−O) bonds in relation to the proton binding energy. Bader metal ion charges, radii, and M−O bond critical point properties are computed and correlations are sought that transcend conventionally ascribed factors affecting hydrolysis behavior, such as position in the periodic table and d-orbital filling. Charge-to-radius relationships are found to be unimproved by these methods. At the M−O bond critical points, while no correlation could be established with the electron density, distinct trends in the proton binding energy are unveiled by the Laplacian, owing principally to systematics in the curvature |λ 3 | along the M−O bond path. The ellipticity of the bonds can reflect a π interaction between the metal cation and water ligands for metal cations in which the t 2g d-orbital set is asymmetrically occupied, which is found to be coupled with a symmetry-breaking rotation of the ligands. Although global correlations were not found, the trends establish quantities that can uniquely connect hydrolysis behavior across traditional classification factors.