We present a quantum mechanical study of carbamoylphosphine oxide (CMPO) complexes of MX3 (M3+ = La3+, Eu3+, Yb3+; X- = Cl-, NO3-) with a systematic comparison of monodentate vs bidentate binding modes of CMPO. The per ligand interaction energies DeltaE increase from La3+, to Yb3+ and are higher with Cl- than with NO3- as counterions, as a result of steric strain in the first coordination sphere with the bidentate anions. The energy difference between monodentate (via phosphoryl oxygen) and bidentate CMPO complexes is surprisingly small, compared to DeltaE or to the binding energy of one solvent molecule. Protonation of uncomplexed CMPO takes place preferably at the phosphoryl oxygen O-P, while in the Eu(NO3)(3)CMPOH+ complex carbonyl (O-C) protonation is preferred and O-P is bonded to the metal. A comparison of uranyl and lanthanide nitrate complexes of CMPO shows that the interaction energies DeltaE of the former are lower. Finally, the effect of grafting CMPO arms at the wide rim of a calix[4]arene platform is described. The results are important for our understanding of cation binding and extraction by potentially bidentate CMPO, diamide, and diphosphoryl types of ligands.