′-((2-methoxy-naphthalene-1-yl)methylene) pyrimidine-5-carbohydrazide (H5) and

3.7 Quantum chemical calculations

Theoretical chemistry has been used frequently to interpret the corrosion inhibition mechanism; quantum chemical calculations are the most common approach. This approach has been clarified as a very excellent system for researching the interaction mechanism. To assess their efficiency as corrosion inhibitors for carbon steel in HCl solution, quantum chemical calculations based on the density-functional theory (DFT) technique were conducted on the three investigated heterocyclic compounds. Matter of fact, an inhibitor's efficiency depends on its molecular structure. Frontier orbital theory is used to predict the adsorption centers of the inhibitor molecules which interact with Fe atoms. As reported, effective corrosion inhibitors are those which donates electrons to an empty orbital of the metal and at the same time receive electrons from the metal surface.⁴⁶ Frontier orbital theory stated that, any chemical reaction mainly happened between HOMO (highest occupied molecular orbital) of one reactant and LUMO (lowest unoccupied molecular orbital) of the other reactant, the interaction between these orbitals constitutes the adsorption mechanism. Hence, it is essential to assess the presence of HOMO and LUMO orbitals of the investigated compounds to interpret the inhibition mechanism. Inhibitors with a high energy level of HOMO can give electrons to the unoccupied orbitals of acceptor. E_HOMO corresponds to the molecule's capacity to donate electrons, and E_LUMO corresponds to the molecule's capacity to accept electrons. Table 11 illustrates the geometrical structure of three inhibitors with specific distribution sites for HOMO and LUMO. A molecule of the inhibitor was spread around the surface of carbon metal. This method of distribution guarantees the adsorption of the inhibitor on the metal surface in two ways: one is that the inhibitor molecules send electrons to unoccupied (d) orbitals of Fe atom to form a coordinate bond, the other is that Fe atom electrons are received by the inhibitor molecule, which forms a back-bond between the metal surface and the inhibitor. It was previously known that low values of ΔE give excellent inhibition efficiency; because the energy needed for separating an electron from the highest occupied molecular orbital (HOMO) is low. Table 11 shows the values of ΔE that was increased in the following order: (H5 > H4 > H6), which means that the adsorption efficiency can be arranged in the following order H6 > H4 > H5. The findings of quantum chemical calculations in this study were in harmony with the experimental results. The investigated compounds were different in adsorption ability that could be explained according to Gece and Bilgiç,⁴⁷ they stated that when the sites of N, O atoms was changed in their sites in the compound structure, the corrosion inhibition efficiency is consequently changed, which explains the difference in the obtained efficiencies between the three inhibitors. The electron configuration of Fe is [Ar]4s²3d⁶; the 3d orbitals are not fully occupied with electrons. N atom with electron configuration [He]2s²2p³ and O atom with electron configuration, [He]2s²2p⁴, has lonely electron pairs that are highly needed by Fe for completing unfilled 3d orbitals so, it adsorbed inhibitor molecules on the metal surface.⁴⁸ As shown in Fig. 15, the electron density concentrated on N atoms. The sites of highest electron density are in fact the sites which electrophiles attacked. Hence, N and O atoms are the active center, which has the best ability of binding with the Fe surface. Many reactivity parameters were evaluated to assure the effectiveness of hydrazide derivatives as corrosion inhibitors. These include softness σ(S), electronegativity (v), chemical hardness (η), ΔN, and Δw. All quantum parameters were shown in Table 11. And the optimized geometries HOMO and LUMO distribution of (H4 & H5 & H6) in their non-protonated form are shown in Fig. 15, the reference of orbitals colors that shown in Fig. 15 was illustrated in Table 12.