Theoretical predictions of hydrolysis and complex formation of group-4 elements Zr, Hf and Rf in HF and HCl solutions

Abstract

Summary Fully relativistic molecular density–functional calculations of the electronic structures of hydrated, hydrolyzed and fluoride/chloride complexes have been performed for group–4 elements Zr, Hf, and element 104, Rf. Using the electronic density distribution data, relative values of the free energy change for hydrolysis and complex formation reactions were defined. The results show the following trend for the first hydrolysis step of the cationic species: Zr > Hf > Rf in agreement with experiments. For the complex formation in HF solutions, the trend to a decrease from Zr to Hf is continued with Rf, provided no hydrolysis takes place. At pH > 0, further fluorination of hydrolyzed species or fluoro–complexes has an inversed trend in the group Rf ≥ Zr > Hf, with the difference between the elements being very small. For the complex formation in HCl solutions, the trend is continued with Rf, so that Zr > Hf > Rf independently of pH. A decisive energetic factor in hydrolysis or complex formation processes proved to be a predominant electrostatic metal–ligand interaction. Trends in the K d (distribution coefficient) values for the group–4 elements are expected to follow those of the complex formation.