We report the structure, bonding, energetic, and thermodynamic parameters of Eu3+ and Am3+ with diglycolamic acid functionalized CNTs at BP86 and B3LYP functional level of theory using SVP and TZVP basis set. The free energy of extraction, Delta G(ext), of Eu3+ and Am3+ was computed using standard thermodynamical procedure in conjunction with COSMO (conductor like screening model) model. The value of Delta G(ext) for Eu3+ ion was found to be higher than that of Am3+ as observed in the extraction experiments. The HOMO-LUMO analysis indicates that Eu3+ ion is harder than Am3+ ion leading to stronger interaction with hard donor based DGA-CNT.