We report a quantum mechanical study on the complexes of UO22+ with diamide ligands L of malonamide and succinamide type, respectively, forming 6- and 7-chelate rings in their bidentate coordination to uranium. The main aims are to (i) assess how strong the chelate effect is (i.e., the preference for bi- versus monodentate binding modes of L), (ii) compare these ligands as a function of the chelate ring size, and (iii) assess the role of neutralizing counterions. For this purpose, we consider UO2L2+, (UOL22+)-L-2, UO2L32+, and UO2X2L type complexes with X- = Cl- versus NO3-. Hartree-Fock and DFT calculations lead to similar trends and reveal the importance of saturation and steric repulsions ("strain") in the first coordination sphere. In the unsaturated UO2L2+, UO2L2+, and UO2Cl2L complexes, the 7-ring chelate is preferred over the 6-ring chelate, and bidentate coordination is preferred over the monodentate one. However, in the saturated UO2(NO3)(2)L complexes, the 6- and 7-chelating ligands have similar binding energies, and for a given ligand, the mono- and bidentate binding modes are quasi-isoenergetic. These conclusions are confirmed by the calculations of free energies of complexation in the gas phase. In condensed phases, the monodentate form Of UO2X2L complexes should be further stabilized by coordination of additional ligands, as well as by interactions (e.g., hydrogen bonding) of the "free" carbonyl oxygen, leading to an enthalpic preference for this form, compared to the bidentate one. We also considered an isodesmic reaction exchanging one bidentate ligand L with two monoamide analogues, which reveals that the latter are clearly preferred (by 23-14 kcal/mol at the HF level and 24-12 kcal/mol at the DFT level). Thus, in the gas phase, the studied bidentate ligands are enthalpically disfavored, compared to bis-monodentate analogues. The contrast with trends observed in solution hints at the importance of "long range" forces (e.g., second shell interactions) and entropy effects on the chelate effect in condensed phases.