In the current research, quantum chemical calculations in terms of Density Functional Theory, DFT, were performed on 2-furaldehydesemicarbazone (FSC) and its derivatives, including 5MFSC, 5AFSC, 5DFSC, 5CFSC and 5NFSC, where M, A, D, C and N correspond, respectively, to -CH3, -NH2, N(CH3)2, -CN and -NO2 groups. The relative thermodynamic stabilities of the envisaged isomers (E and Z) and conformers (E1 and Z1) were calculated at the B3LYP/6-311 + + G(3df,2p)//6-311 + G(d, p) level of theory in the gas phase. Results revealed that the relative stability trend is E > Z > E1 > Z1. The rotation barrier of the E→Z isomerization process was calculated by performing the scan coordinate of the restricted C = N. Unexpectedly, the Z isomer of the FSC molecule is slightly more stable than the E isomer by 1.1 kcal/mol with a rotation barrier of ~ 97 kcal/mol. On the other hand, the E isomer of the other FSC derivatives, regardless of the nature of the substituents, is slightly more stable than the Z isomer, with a rotation barrier ranging from ~ 45–94 kcal/mol. Quantum theory of atoms in molecules (QTAIM) and the noncovalent interactions (NCIs) were used to confirm the stability of the E and Z isomers. The geometrical structure and the vibrational frequency analysis were also investigated and discussed. The global chemical reactivity descriptors, such as EHOMO, ELUMO, energy gap, hardness, electronegativity, and electrophilicity were also computed and discussed. The results revealed that the energy gap of the E isomer is lower than that of the Z isomer, reflecting its higher chemical reactivity and lower kinetic stability. To complement the quantum-chemical analysis, <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\:\varvec{M}-\)</EquationSource></InlineEquation>polynomial–derived topological indices were computed to quantify molecular connectivity and electronic symmetry. The E isomer shows the highest index values, the smoothest M-polynomial surface, the lowest Gibbs free energy, and the widest HOMO–LUMO gap, confirming its thermodynamic superiority. The stability trend <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(E> Z> E_{1} \approx Z_{1}\)</EquationSource></InlineEquation> aligns closely with DFT results. Overall, higher topological indices correspond to smoother <InlineEquation ID="IEq3"><EquationSource Format="TEX">\(\:\varvec{M}-\)</EquationSource></InlineEquation>polynomial surfaces, lower Gibbs energies, and greater stability, establishing the <InlineEquation ID="IEq4"><EquationSource Format="TEX">\(\:\varvec{M}-\)</EquationSource></InlineEquation>polynomial framework as a unified, predictive bridge between molecular topology and chemical reactivity.

Unveiling the electronic and thermodynamic properties of 2-furaldehyde semicarbazone derivatives: combined DFT and M-polynomial topological indices analysis

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2026年5月6日

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Suha Wazzan,
Zaki Safi,
Nuha Wazzan

摘要

In the current research, quantum chemical calculations in terms of Density Functional Theory, DFT, were performed on 2-furaldehydesemicarbazone (FSC) and its derivatives, including 5MFSC, 5AFSC, 5DFSC, 5CFSC and 5NFSC, where M, A, D, C and N correspond, respectively, to -CH₃, -NH₂, N(CH₃)₂, -CN and -NO₂ groups. The relative thermodynamic stabilities of the envisaged isomers (E and Z) and conformers (E1 and Z1) were calculated at the B3LYP/6-311 + + G(3df,2p)//6-311 + G(d, p) level of theory in the gas phase. Results revealed that the relative stability trend is E > Z > E1 > Z1. The rotation barrier of the E→Z isomerization process was calculated by performing the scan coordinate of the restricted C = N. Unexpectedly, the Z isomer of the FSC molecule is slightly more stable than the E isomer by 1.1 kcal/mol with a rotation barrier of ~ 97 kcal/mol. On the other hand, the E isomer of the other FSC derivatives, regardless of the nature of the substituents, is slightly more stable than the Z isomer, with a rotation barrier ranging from ~ 45–94 kcal/mol. Quantum theory of atoms in molecules (QTAIM) and the noncovalent interactions (NCIs) were used to confirm the stability of the E and Z isomers. The geometrical structure and the vibrational frequency analysis were also investigated and discussed. The global chemical reactivity descriptors, such as E_HOMO, E_LUMO, energy gap, hardness, electronegativity, and electrophilicity were also computed and discussed. The results revealed that the energy gap of the E isomer is lower than that of the Z isomer, reflecting its higher chemical reactivity and lower kinetic stability. To complement the quantum-chemical analysis, \(\:\varvec{M}-\)polynomial–derived topological indices were computed to quantify molecular connectivity and electronic symmetry. The E isomer shows the highest index values, the smoothest M-polynomial surface, the lowest Gibbs free energy, and the widest HOMO–LUMO gap, confirming its thermodynamic superiority. The stability trend \(E> Z> E_{1} \approx Z_{1}\) aligns closely with DFT results. Overall, higher topological indices correspond to smoother \(\:\varvec{M}-\)polynomial surfaces, lower Gibbs energies, and greater stability, establishing the \(\:\varvec{M}-\)polynomial framework as a unified, predictive bridge between molecular topology and chemical reactivity.