We report a quantum mechanical study on the interaction of M3+ cations (La3+, Eu3+, Yb3+) with bidentate model ligands L of the malonamide type L-OO and their thia analogues L-OS and L-SS. The chelate effect is analyzed, first by comparing the bidentate vs monodentate binding modes of the ligands in MCl3L complexes, which indicates a surprisingly small preference for the former, and second, by an isodesmic reaction involving MCl3L type complexes, which shows that two monodentate amide-like ligands bind better than one bidentate analogue, because of avoided strain induced upon metal binding. The role of counterions and stoichiometry is investigated by a comparison of the charged ML3+ complexes with the neutral MCl3L and MCl3L2 ones. In all systems, the order of ligand binding energies is L-OO > L-OS > L-SS for a given metal, following the order of calculated basicities. For a given ligand, the interaction energies increase in the order La3+ < Eu3+ less than or equal to Yb3+ in the ML3+ and MCl3L complexes. With higher coordination numbers (bidentate MCl3L2 complexes), the cation selectivity inverts to La3+ > Eu3+ > Yb3+, as a result of "steric crowding" in the first coordination sphere, which penalizes binding to the smaller cations. The results are important in the context of modeling complexes of lanthanide and actinides, and for the design of selective ligands for metal separation.