In this paper we present a computational study of ligand interactions with hafnium and zirconium metal complexes which occur in the liquid-liquid extraction of these metals from their aqueous solutions. Separation of Hf and Zr has been a challenge in liquid-liquid extraction technologies and the existing methodologies, namely the MIBK (methyl isobutyl ketone) process, are used to extract hafnium into the organic phase while on the contrary the TBP (tributyl phosphate) process is used to extract Zr into the organic phase. Understanding the actual interactions taking place, including an estimate of the binding energies and conformations of the guest-host system of the metal complexes and the solvents, would help us to design better and safer extractants. Recent studies in the literature have shown that the quantum chemical based DFT methods have proven to be good tools for such types of studies. Thus in this work we have carried out high-level DFT studies using the hybrid B3LYP/Lanl2dz and BLYP/TZP (with the relativistic corrections) on tetravalent Hf and Zr metal complexes interacting with neutral ligands and compared the results to the experimental observations. These studies show that at the molecular level it is the Hf complex that has larger interaction energy with the ligands, thus indicating that in the mixture of Hf and Zr complexes in solutions which are not complicated by aggregation and polymerization, Hf would be extracted preferably into the organic solvent, in agreement with the experimental observation. We conclude from this study that primary interaction energies (gas-phase stabilization) are sufficient to significantly discriminate Hf and Zr complexes and thus can be used to explain Hf and Zr separation.