Bridging density functional theory and degree-based topological indices for understanding tautomeric stability in azo-pyrazolone derivatives

The current research investigated the effect of electron-donating and electron-withdrawing substituents on the tautomeric equilibrium, intramolecular proton transfer, and intramolecular hydrogen-bonding (IMHB) strength of 5-methyl-2-phenyl-4-(2-phenylhydrazono)-2,4-dihydro-3 H-pyrazol-3-one (MPHP) derivatives. Density Functional Theory (DFT) using B3LYP/6-311G(d, p) level, with empirical dispersion=D3, was used to optimize all species in the gas phase and solvent media. Relative stabilities were evaluated using several hybrid functionals. Results revealed that the keto form was predicted to be energetically favored over the corresponding enol form for all investigated MPHP species derivatives. In addition, the results showed that the increase in the dielectric constant of the solvent further stabilizing the keto tautomer. Moreover, substituent effects on proton-transfer behavior were analyzed through calculated δ 1 H-NMR chemical shifts, vibrational frequencies, natural bond orbital (NBO) interactions, and frontier molecular orbital energies. Geometrical parameters, quantum theory of atoms in molecules (QTAIM), and reduced density gradient (RDG) analyses were used to examine the nature and strength of the IMHB. Results revealed moderate IMHB interactions, which strongly depends on the electronic nature of the substituent. Furthermore, we computed the degree-based topological indices and correlated them with molecular properties through QSPR models. The combined quantum-chemical and graph-theoretical approach offers a comprehensive understanding of structure–property relationships governing tautomerism and hydrogen bonding in azo–pyrazolone systems and offers useful guidelines for the rational design of functional dye molecules.