Theoretical Study of p<i>K</i>_a Values for Trivalent Rare-Earth Metal Cations in Aqueous Solution

Molecular acidity of trivalent rare-earth metal cations in aqueous solution is an important factor dedicated to the efficiency of their extraction and separation processes. In this work, the aqueous acidity of these metal ions has been quantitatively investigated using a few theoretical approaches. Our computational results expressed in terms of p<i>K</i>_a values agree well with the tetrad effect of trivalent rare-earth ions extensively reported in the extraction and separation of these elements. Strong linear relationships have been observed between the acidity and quantum electronic descriptors such as the molecular electrostatic potential on the acidic nucleus and the sum of the valence natural atomic orbitals energies of the dissociating proton. Making use of the predicted p<i>K</i>_a values, we have also predicted the major ionic forms of these species in the aqueous environment with different pH values, which can be employed to rationalize the behavior difference of different rare-earth metal cations during the extraction process. Our present results should provide needed insights not only for the qualitatively understanding about the extraction and separation between yttrium and lanthanide elements but also for the prediction of novel and more efficient rare-earth metal extractants in the future