The ligands, derived from the combination of phenanthroline and various five-membered N-heterocyclic rings, were subject to a comprehensive investigation for their potential in the extraction and separation of actinides and lanthanides. This study employed DFT methods to thoroughly explore the properties of both phenanthroline (Ph) and the diverse five-membered N-heterocyclic rings (R1-R8). Additionally, tridentate ligands RlPh (l = 1-8) and tetradentate ligands RlPhRr (l, r = 1-8) were analyzed in detail, encompassing their electrostatic potential (ESP), protonation energy, coordination bonding with the metals Am(III) and Eu(III), and the thermodynamics of extraction separation for Am(III) and Eu(III). The findings highlight that the electrostatic potential (ESP) and binding capabilities of the five-membered N-heterocyclic ring units serve as effective predictors for the properties of intricate tridentate and tetradentate ligands, as well as their coordination bonding affinity with metals. The ligands' binding energy is closely associated with their ESP, and notably, the binding energy of tridentate and tetradentate ligands correlates well with the binding energies of their constituent structural units. The computational results reveal that the R2 unit, along with its corresponding tridentate ligand R2Ph and tetradentate ligands R2PhRr, exhibits the highest ESP, superior binding energies, and the strongest coordination bonding affinity with the metals. The theoretical calculations further identify several promising extractants for the effective separation of Am(III) and Eu(III). The tridentate ligands R1Ph, R7Ph, and R4Ph, and the tetradentate ligands R4PhR4, R6PhR6, R2PhR2, R1PhR5 and R3PhR6 were identified as having excellent separation performance for Am(III) and Eu(III). This study would provide insights for the design of extractants for the separation of Am(III) and Eu(III) by use of five-membered N-heterocyclic rings as structural units.