Keywords: Zirconium / Hafnium / Phosphate ligands / Free energy of extraction / Density functional calculations Density Functional theory (DFT) has been used to optimize the structures of Cyanex925 [bis(2,4,4-trimethylpentyl)octylphosphine oxide], tributyl phosphate (TBP), and their complexes with Hf and Zr oxycations by employing the triplezeta valence plus polarization (TZVP) basis set. The effect of noncovalent interactions was examined by using the TPSSH and M06-2X density functionals. The free energy of extraction ΔG ext from the aqueous to organic phase was calculated by using the standard thermodynamic procedure in conjunction with the conductor-like screening model (COSMO). The calculated ΔG ext , either with an implicit or explicit solvation model, fails to capture the experimentally reported preferential selectivity of ZrO 2+ ions over HfO 2+ ions in the absence