A thermodynamic investigation has been performed to study the complexation of trivalent metal (M) ions (M = Am(III), Eu(III)) with tetradentate ligands (L), 6,6'-bis(5,6-dialkyl-1,2,4-triazin-3-yl)-2,2'-bipyridines (BTBPs), by using relativistic quantum mechanical calculations. The structures and stabilities of the inner-sphere BTBPs complexes were explored in the presence of various counterions such as NO(3)(-), Cl(-), and ClO(4)(-). According to our calculations, Am(III) and Eu(III) can chelate eight or nine water molecules at most, whereas more stable species like M(NO(3))(3)(H(2)O)(4) tend to be formed in the presence of nitrate ions. The inner sphere of the BTBPs complexes can accommodate four water molecules or three nitrate ions based on our calculations, forming species such as [ML(H(2)O)(4)](3+) and ML(NO(3))(3). Compared with Eu(III) complexes, the Am(III) counterparts have obviously lower binding, energies in both the gas phase and solution. In addition, the solvent effect significantly decreases the binding energies of the BTBPs complexes. It has been found that the complexing reactions, in which products and reactants possess the same or close number of nitrate ions, are more favorable for formation of the BTBPs complexes. In short, the reactions of M(NO(3)(-))(3)(H(2)O)(4) -> ML(NO(3))(3) and [M(NO(3))(H(2)O)(7)](2+) -> [ML(2)(NO(3))](2+) are probably the dominant ones in the Am(III)/Eu(III) separation process.