We report a quantum mechanical study on the complexes of lanthanide cations M3+ with bifunctional ligands L (denoted AcA, AccA, AcP, AccP, PcP and PccP) bearing amide “A” and/or phosphoryl “P” groups separated by one “c” or two “cc” CH2 connectors. The main aims are to (i) assess how strong is the chelate effect (i.e. the preference for bi- versus monodentate binding modes of L, (ii) compare the ligands as a function of their binding sites and of the chelate ring size (six vs. seven atoms), (iii) assess the role of neutralizing counterions, and (iv) compare typical cations of increasing hardness (La3+, Eu3+, Yb3+). For this purpose, we consider M·Ln3+ and MX3·L type complexes with Cl− or NO3− as counterions. The ligand basicity towards H+, M3+ and MX3 is found to increase with the number of phosphoryl groups, to be larger with a chelate ring size of 7, compared to 6, and larger with chloride than with nitrate counterions. In MX3·L complexes, the ΔEmono/bi energy preference for bi- vs. monodentate binding modes of L ranges from 14.6 kcal mol−1 for the complex between Eu(NO3)3 and the “best ligand” PccP, to 1.6 kcal mol−1 for the complex between YbCl3 and AccP. ΔEmono/bi thus generally decreases opposite to the steric crowding in the first coordination sphere, i.e. as the cation gets harder, as the chelate ring size changes from seven to six, from nitrate to chloride counterions, and from phosphoryl to amide ligands. According to an isodesmic reaction exchanging bidentate ligands L with two separate monodentate analogues, bidentate coordination is less favorable by 14 to 29 kcal mol−1, mainly because of the intraligand strain of L induced upon coordination to the metal. These data are important in the context of designing efficient ligands for selective lanthanide or actinide cation extraction.