General Quantum-Mechanical Study on the Hydrolysis Equilibria for a Tetravalent Aquaion: The Extreme Case of the Po(IV) in Water

A systematic study of the different hydrolyzed species derived from the hydrated Po(IV) in water, [Po(H2O)(n)(OH)(m)]((4-m)) for 1 <= m <= 4, and 4 <= m + n <= 9, has been carried out by means of quantum mechanical computations. The effects of outer solvation shells have been included using a polarizable continuum dielectric model. For a fixed number of hydroxyl groups, the preferred hydration number for the Po(IV) can be determined in terms of Gibbs energy. It is shown that the hydration number (n) systematically decreases with the increase in the number of hydroxyl groups (in) in such a way the total coordination number (n + m) becomes smaller, being 9 in the aquocomplex and 4 in the neutral hydroxo-complex. Free energies for the hydrolysis processes involving Po(IV) complexes and a different number of hydroxyl groups have been computed, revealing the strong tendency toward hydrolysis exhibited by these complexes. The predominant species of Po(IV) in aqueous solutions are ruled by a dynanmical equilibrium involving aggregates containing in the first coordination shell OH- groups and water molecules. Although there is not experimental information to check the theoretical predictions, theoretical computations in Solution seem to suggest that the most likely clusters are [Po(H2O)(5)(OH)(2)](2+) and [Po(H2O)(4)(OH)(2)](2+). The geometry of the different clusters is ruled by the trend of hydroxyl groups to be mutually orthogonal and to promote a strong perturbation of the water molecule in trans-position by lengthening the Po-H2O distances and tilting the corresponding bond angle. A general thermodynamic cycle is defined to compute the Gibbs free energy associated to the formation of the different hydrolyzed forms in solution. From it, the estimates of pK(a) values associated to the different protolytic equilibria are provided and discussed. Comparison of the relative values of pK(a) along a hydrolysis series with the experimental values for other tetravalent cations supports its consistency.