Theoretical and experimental study on (E)-N'-(2-hydroxy-5-(thiophen-3-yl)benzylidene)benzohydrazide compound: Its optimization with DFT and Fuzzy logic approach (FLA), structural and spectroscopic investigation, HOMO-LUMO, MEP, atomic charge, and NBO analysis

•(E)-N'-(2-hydroxy-5-(thiophen-3-yl)benzylidene)benzohydrazide (TBH) was successfully synthesized and characterized.•Optimization of molecular structure was performed by Fuzzy Logic Approach (FLA) and Density Functional Theory (DFT).•Structural and spectroscopic analysis of TBH molecule were executed with DFT/B3LYP/6–311(d,p) calculations.•The tautomeric behavior, chemical reactivity, charge transfer and hyperconjugative properties of the molecule were explained theoretically using DFT. The spectral properties, including 1H–13C NMR, FTIR, and UV–Vis, of the newly synthesized compound, (E)-N'-(2-hydroxy-5-(thiophen-3-yl)benzylidene)benzohydrazide (TBH), were calculated using DFT/B3LYP/6–311G(d,p) and compared with experimental spectra. Experimental FTIR, UV–Vis, NMR and DFT calculations showed that the TBH was in the form of keto-amine/phenol-imine tautomer stabilized by intramolecular hydrogen bonding in solid state and solution. Theoretical calculations were also accomplished for the HOMO-LUMO energies, MEP surface, net atomic charges, and NBO analysis. The experimental and theoretical band gap (ΔE) values examined in different organic solvents for TBH were found to be in the range of 3.87–3.90 eV and 3.84–3.93 eV, respectively. The theoretical results revealed the molecule's high intramolecular charge transfer, realistic molecular stability, and high chemical reactivity. A good agreement was observed between the experimental data and the DFT-based calculations for the TBH molecule. Additionally, the DFT calculations were integrated with the fuzzy logic approach (FLA), and the Mamdani fuzzy logic system was used to pattern the potential energy of the molecule based on its two torsion angles. [Display omitted]