The experimentally observed extraction complexes of trivalent lanthanide Eu-III and actinide Am-III/Cm-III cations with purified Cyanex301 [bis(2,4,4-trimethylpentyl)dithiophosphinic acid, HBTMPDTP denoted as HL], i.e., ML3 (M = Eu, Am, Cm) as well as the postulated complexes HAmL4 and HEuL4(H2O) have been studied by using energy-consistent 4f- and 5f-in-core pseudopotentials for trivalent f elements, combined with density functional theory and second-order Moller-Plesset perturbation theory. Special attention was paid to explaining the high selectivity of Cyanex301 for Am-III/Cm-III over Eu-III. It is shown that the neutral complexes ML3, where L acts as a bidentate ligand and the metal cation is coordinated by six S atoms, are most likely the most stable extraction complexes. The calculated metal-sulfur bond distances for ML3 do reflect the cation employed: i.e., the larger the cation, the longer the metal-sulfur bond distances. The calculated M-S and M-P bond lengths agree very well with the available experimental data. The obtained changes of the Gibbs free energies in the extraction reactions M3+ + 3HL -> ML3 + 3H(+) agree with the thermodynamical priority for Am3+ and Cm3+. Moreover, the ionic metal-ligand dissociation energies of the extraction complexes ML3 show that, although EuL3 is the most stable complex in the gas phase, it is the least stable in aqueous solution.