A new Schiff base compound and its derivative, 3-cyclopropyl-4-(4-nitrofuran-1-yl)methyleneamino-4,5-dihydro-1H-1,2,4-triazol-5-one (3-CNM) and 1-acetly-3-cyclopropyl-4-(4-nitrofuran-1-yl)methyleneamino-4,5-dihydro-1H-1,2,4-triazol-5-one (1-ACNM), were synthesized. The structures of compounds were characterized by 13C-NMR, 1H-NMR and FT-IR spectroscopy techniques. The antioxidant capacities of the molecules were investigated by different methods (metal chelation, DPPH and reducing power). Some quantum chemical calculations are performed on the B3LYP, B3PW91, MPW1PW91 functionals with the 6-311++G(d,p) level basis set of the density functional theory (DFT). Using the optimized structures of Schiff bases, the frontier molecular orbital, the theoretical spectroscopic and the nonlinear optic (NLO) analysis, the molecular electrostatic potential (MEP) surface, the thermodynamic parameters, the dipole moment, the molecular geometric properties and the total energy were calculated. The calculation results showed that the 3-CNM compound can be used as a suitable and good nonlinear optical compound. In addition, electronegative and electropositive atoms were determined from the MEP surface map. The difference between (ΔE) the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) energies was calculated as 3.3eV and 3.4eV for 3-CNM and 1-ACNM, respectively, and these values express the chemical stability of the molecule and the orbital interactions. This work is important because it includes the synthesis of two new molecules and theoretical calculations that support their experimental properties. It can also provide significant benefits in terms of synthesis of similar Schiff base compounds and their calculated electronic, geometric and thermodynamic properties.