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Cerium oxide nanoparticles have demonstrated their effectiveness as recyclable and efficient catalysts in synthesising 2,4,5 trisubstituted imidazole derivatives. Several approaches, such as IR, 1H-NMR, 13C-NMR, and mass spectrometry techniques, characterize the structures of the obtained compounds. This synthetic method incorporates several merits, including easy operational conditions, moderate time requirements, cost-effectiveness, absence of by-products, and high yield. In this study, the optimal yield was achieved with a cerium oxide concentration of 10 mol% in an ethanol medium maintained at a temperature of 80 °C for 120 to 180 minutes. To describe the molecular geometry, global reactive descriptors, MEP, and computational analyses were carried out by the DFT method with a basis set of B3LYP/ 6–31 G (d, p). It was observed that compound 4c was found to possess a larger energy gap due to a low degree of electronic conjugation compared to the other synthesised compounds. Based on the results obtained from the study of NLO properties, it was evident that compound 4d manifested first-order hyperpolarizability 11 times more significant than the standard urea. NBO analysis confirmed that in all compounds, greater stability was achieved due to intramolecular charge transfer.
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