Quantum-mechanical calculations are used to gain insight into the ligand-metal bonding in dithiophosphinate (L = R2PS2-) complexes of trivalent lanthanides M3+. The ligands are important in the context of liquid-liquid extraction of lanthanide(III) and actinide(III) ions from aqueous solutions. Our results demonstrate the importance of cumulative interactions and steric strain in the first coordination sphere of the metal. For the [LM](2+) complexes, in the absence of competing ligands, phenyl-substituted ligands yield the highest binding energies and the order of metals is La < Eu < Yb. The sequence of the metal ligand interactions in 1:1 complexes is shown to differ from the order of the protonation energies of L. However, these results are strongly modulated if additional counterions or ligands are involved. In the [LMCl3](-) complexes alkyl-substituted ligands yield higher interaction energies than aryl-substituted ones, and generally the influence of the substituents R on the interaction energies becomes small. In the [L4M](-) complexes, the order of metals is reversed to La > Eu > Yb. The steric effect causing this reversal is stronger than all electronic effects of the substituents R on metal selectivity. The structures predicted at the Nartree-Fock level, under "gas-phase" conditions, are compared to structures predicted with correlated methods, with structures modeled in solution via the self-consistent reaction field (SCRF) method, and with experimental results.