Estimation of the pK(a) values of water ligands in transition metal complexes using density functional theory with polarized continuum model solvent corrections

The deprotonation energies of the water ligands in a set of 40 d-block metal complexes have been calculated using density functional theory with polarized continuum model solvent corrections. The complexes include 13 aqua ions [M(OH2)(n)](2+/3+) and a variety of aqua complexes with organic co-ligands, whose experimental pK(a) values have been reported in the literature. For comparison, the deprotonation energies of a set of 60 organic and inorganic molecules with experimental pK(a) values ranging from -25 (HSbF6) to + 52 (C2H6) have also been calculated. Three different classes of acids are identified as giving different slopes in plots of pK(a) versus deprotonation energies; namely non-hydroxy acids, hydroxy acids, and the metal complexes. The correlatio47n coefficients for the straight lines obtained for these three classes are 0.96, 0.97 and 0.92 respectively. Better correlations are found for sub-sets of the complexes, such as the 31 first row complexes (correlation coefficient 0.95). For several of the complexes, comparison of the calculated and observed pK(a) values, together with changes in the geometry upon optimization, offer new insights into the possible solution structures. It is concluded that DFT calculations incorporating solvent corrections can be used to give reasonable estimates of pK(a) values for the aqua ligands in a range of complex types.