Rare-earth metal oxides (REMOs) exhibit distinctive properties, among which cerium oxide (CeO2) displays numerous industrial, technological, and medical applications. However, the inclusion of hafnium (Hf) at the cerium (Ce) site to form the (Ce1-ₓHfₓO2) lattice system at a concentration of x = 0.25 would have an impact on enhancing the physical properties of the simulated configuration. Density functional theory (DFT) was used to perform the calculations, supported by the Hubbard correction factor (U). The generalized gradient approximation (GGA-PBE) was employed to analyze the electronic, structural, optical, and mechanical properties at hydrostatic pressures (P = 0, 25, 50, 75, and 100 GPa). The ground state geometry of the pristine

4-(((4-hydroxy-3,5-dimethoxybenzyl)oxy)methyl)benzoic acid was synthesized from multisteps and converted to their corresponding hydrazide. The corresponding hydrazide was cyclized to their corresponding 5-amino-1,3,4-oxadizole. Newly Schiff bases (7a-7e) were synthesized from reaction the 5-amino-1,3,4-oxadizole with several substituted of 4-hydroxybenzylaldehyde. The resulting compounds were characterized based on their IR, 1H-NMR, 13C-NMR, and HRMS data. 2,2-Diphenyl-1-picrylhydrazide (DPPH) and ferric reducing antioxidant power (FRAP) assays were used to test the antioxidant properties of the synthesized compounds. Compound 7d and 7e exhibited significant free-radical scavenging ability in both assays.

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