Synthesis and Assessment of Two Malonyl Dihydrazide Derivatives as Corrosion Inhibitors for Carbon Steel in Acidic Media: Experimental and Theoretical Studies

Despite the extensive use of carbon steel in all industrial sectors, particularly in the petroleum industry, its low corrosion resistance is an ongoing problem for these industries. In the current work, two malonyl dihydrazide derivatives, namely 2,2’-malonylbis (N-phenylhydrazine-1-carbothiamide (MBC) and N’1, N’3-bis(-2-hydroxybenzylidene) malonohydrazide (HBM), were examined as inhibitors for the carbon steel corrosion in 1.0 M HCl. Both MBC and HBM were characterised using thin-layer chromatography, elemental analysis, infrared spectroscopy, and nuclear magnetic resonance techniques. The corrosion tests were performed using mass loss measurements, polarisation curves, and electrochemical impedance spectroscopy. It is obtained from the mass loss studies that the optimal concentration for both inhibitors is 2.0 × 10−5 mol/L, and the inhibition efficiencies reached up to 90.7% and 84.5% for MBC and HBM, respectively. Electrochemical impedance spectroscopy (EIS) and potentiodynamic polarisation (PDP) indicate an increased impedance in the presence of both MBC and HBM and mixed-type inhibitors, respectively. Both inhibitors can mitigate corrosion in the range of 298–328 K. Values of free energy changes obtained from the Langmuir model suggest that the inhibitors suppress the corrosion process principally by chemisorption. The computational investigations were conducted to identify the factors connected with the anti-corrosive properties of the examined inhibitors.


Introduction
Acids have various uses in the industrial sector, such as acidification of oil and gas wells, marinating and cleaning metallic products [1,2]. It is well-known that these acids cause severe damage to metals and alloys. Consequently, there is an increasing need for new techniques to suppress corrosion reactions. Chemical inhibitors are among the most robust, inexpensive methods for hindering corrosion reactions [3][4][5][6]. Different organic compounds, such as ionic liquids and pyrazoline derivatives, and most compounds containing heteroatoms are widely exploited as corrosion inhibitors in various industries. These heteroatoms, such as O, S, and N, help the organic compound to be adsorbed quickly and firmly on the metal and alloy surfaces, and hence block the active sites and make a thin layer on the surface, which hinder the path of corrosive media to the surface [7][8][9][10][11]. The adsorption of the organic compound on metals or alloys is controlled by many factors, such as the surface nature, type of the metal charge, and the inhibitor structure. Among organic compounds, hydrazine compounds showed high corrosion inhibition effectiveness [12][13][14][15][16][17][18]. Experimental methods are appropriate for clarifying the inhibition mechanisms and the

Characterisation of the Inhibitors
The synthesis of both the thiosemicarbazide derivative (MBC) and the hydrazone Schiff base derivative (HBM) from malonyl dihydrazide is shown in Scheme 1 according to the published procedures [22][23][24][25]. The purity of both compounds was checked by thin-layer chromatography (TLC) and melting point. inhibition effectiveness [12][13][14][15][16][17][18]. Experimental methods are appropriate for clarifying the inhibition mechanisms and the corrosion behaviour of metals and alloys, but they are time-consuming and expensive. Rapid development in theoretical chemistry and computer software and hardware provides very effective computing and graphical tools for researchers. During the past decade, several corrosive works containing quantum chemical calculations have been published. Such calculations are typically used to explore several properties, such as the electronic properties of the inhibitors, the effect of the energies of the highest and the lowest occupied molecular orbitals (HOMO and LUMO, respectively), and the gap between them [19][20][21]. Theoretical studies including both density functional theory (DFT) calculations and molecular dynamic (MD) simulations on the inhibition action of some hydrazine derivatives have been reported recently [20]. This work aims to explore the corrosion behaviour of C-steel in the presence of two malonyl dihydrazide derivatives, namely, 2,2'-malonylbis(N-phenylhydrazine-1-carbothiamide), abbreviated as MBC, and N'1, N'3-bis(-2-hydroxybenzylidene)malonohydrazide, abbreviated as HBM. It is well-known that the derivatives of Schiff bases are considered as eco-friendly materials [19,20]. In addition, malonic acid is usually used as a green material for various applications [21]. This work also aims to investigate the inhibition effect of these two derivatives and to explain the nature of the inhibition process using the potentiodynamic polarisation curves (PDP), electrochemical impedance spectroscopy (EIS), and scanning electron microscopy (SEM). Additionally, to evaluate the adsorption affinity of the inhibitors under study on the surface of the carbon steel, comprehensive theoretical studies were performed using MD and DFT.

Characterisation of the Inhibitors
The synthesis of both the thiosemicarbazide derivative (MBC) and the hydrazone Schiff base derivative (HBM) from malonyl dihydrazide is shown in Scheme 1 according to the published procedures [22][23][24][25]. The purity of both compounds was checked by thin-layer chromatography (TLC) and melting point.  The number of NMR signals for the hydrazone Schiff base derivative (HBM) can only be explained by assuming at least three different tautomeric isomers, as shown in Scheme 2.
Twenty years ago, Zhang et al. [25] confirmed the three different tautomeric isomers by experimental and calculated spectra of NMR spectroscopy. The number of NMR signals for the hydrazone Schiff base derivative (HBM) can only be explained by assuming at least three different tautomeric isomers, as shown in Scheme 2. Twenty years ago, Zhang et al. [25] confirmed the three different tautomeric isomers by experimental and calculated spectra of NMR spectroscopy. Scheme 2. Keto-enol tautomeric isomers of the hydrazone Schiff base.

Weight Loss Measurements
A series of mass loss experiments were performed to determine the corrosion rate in the presence and absence of the two inhibitors under study. The corrosion rate of carbon steel and the MBC and HBM efficiencies as corrosion inhibitors were calculated by the weight loss method in 1.0 M HCl solutions containing various MBC and HBM concentrations at 298 K. The values of the inhibition efficiency, IEML%, were calculated using Equation (1) [26] and are displayed in Table 1.

Weight Loss Measurements
A series of mass loss experiments were performed to determine the corrosion rate in the presence and absence of the two inhibitors under study. The corrosion rate of carbon steel and the MBC and HBM efficiencies as corrosion inhibitors were calculated by the weight loss method in 1.0 M HCl solutions containing various MBC and HBM concentrations at 298 K. The values of the inhibition efficiency, IE ML %, were calculated using Equation (1) [26] and are displayed in Table 1.
where CR ML and CR o ML are corrosion rates of the carbon steel in the inhibited and uninhibited solutions. Obviously, from the data in Table 1, the inhibition efficiency values are directly proportional to the MBC and HBM concentrations. The highest corrosion rate and lowest inhibition efficiency are recorded at low concentrations of both inhibitors, MBC and HBM, and the hazards for the attack of the corrosive media are significantly increased. When the concentrations of MBC and HBM increase by a certain quantity, more protection is observed. The maximum inhibition efficiencies (IE ML %) were determined as 90.7% and 84.5% for MBC and HBM, respectively. The inhibitive performance of both MBC and HBM is most likely due to the inhibitors' adsorption on the carbon steel surface.

Temperature Effect
Numerous mass loss experiments were conducted at the range of 298-328 K in the presence and absence of 2.0 × 10 −5 mol/L of both inhibitors. Table 2 revealed that the corrosion rate increases for both the blank and the inhibited solutions as the temperature increases. The IE ML % drops from 90.7% to 79.4% and from 84.5% to 73.5% for MBC and HBM respectively, as the temperature increases. These results designate that both inhibitors could successfully suppress the corrosion reactions at relatively higher temperatures. Results showed in Table 2 confirm that the mass loss values increase as the temperature increases in both the blank and uninhibited solutions. Table 2 also revealed that IE% values of both inhibitors slightly decreased as the temperature increases. The mass loss values were adopted to determine the activation energy values, as shown in Equation (2). The entropy (∆S) and enthalpy (∆H) changes were calculated from the intercept and slope of Equation (3) and Figure 1, respectively.
where E a is the activation energy of the corrosion process, k B is the Boltzmann constant, T is the temperature in Kelvin, A is the frequency factor, and h is Planck's constant.
Molecules 2021, 26, x FOR PEER REVIEW 5 of 17 dition of the inhibitors. It is also clear that ΔS and ΔH are greater than those in the blank solution. The more significant negative sign of ΔH in the presence of the inhibitors indicates an exothermic nature of the corrosion process, suggesting that the ionisation of steel surface is slow [27] in the presence of both MBC and HBM. A significant and positive value of entropy (ΔS) means that during the rate-determining step, the activated complex is formed via an association rather than a dissociation step [28], confirming that an increase in the disorder takes place when going from reactants to the activated complex.

Adsorption Isotherm Model
Both MBC and HBM are expected to be adsorbed on the carbon steel surface and, hence, protect the metallic surface from the aggressive acidic solution's attack. Consequently, it is essential to investigate which type of adsorption (physisorption or chemisorption) plays the controlling role during the adsorption process. Generally, inhibitors are adsorbed on metal/solution interface by the displacement of H2O molecules, as shown in Equation (4) [3]: The surface coverage values were found from the mass loss measurement and examined various adsorption models, namely, Langmuir, Temkin, and Freundlich. Results revealed that the Langmuir adsorption model fitted well ( Figure 2) with a correlation coefficient (R 2 ) of 0.991 and 0.990 for MBC and HBM, respectively. The Langmuir equation is shown in Equation (5) [28]: Values of ∆S, ∆H, and E a in the blank and inhibited solutions are presented in Table 3. The values of activation energies in the presence of both MBC and HBM are lower than that in the blank solution, proving that the corrosion process is more difficult after the addition of the inhibitors. It is also clear that ∆S and ∆H are greater than those in the blank solution. The more significant negative sign of ∆H in the presence of the inhibitors indicates an exothermic nature of the corrosion process, suggesting that the ionisation of steel surface is slow [27] in the presence of both MBC and HBM. A significant and positive value of entropy (∆S) means that during the rate-determining step, the activated complex is formed via an association rather than a dissociation step [28], confirming that an increase in the disorder takes place when going from reactants to the activated complex.

Adsorption Isotherm Model
Both MBC and HBM are expected to be adsorbed on the carbon steel surface and, hence, protect the metallic surface from the aggressive acidic solution's attack. Consequently, it is essential to investigate which type of adsorption (physisorption or chemisorption) plays the controlling role during the adsorption process. Generally, inhibitors are adsorbed on metal/solution interface by the displacement of H 2 O molecules, as shown in Equation (4) [3]: The surface coverage values were found from the mass loss measurement and examined various adsorption models, namely, Langmuir, Temkin, and Freundlich. Results revealed that the Langmuir adsorption model fitted well ( Figure 2) with a correlation coefficient (R 2 ) of 0.991 and 0.990 for MBC and HBM, respectively. The Langmuir equation is shown in Equation (5) [28]: where θ is the surface coverage, C inh is the concentration of the MBC and HBM, and K ads is the equilibrium constant of the adsorption. The plot of the Langmuir adsorption model ( Figure 3a) gives straight lines having high K ads values, indicating that both MBC and HBM molecules have strong interaction with the steel surface. K ads is directly related to the standard free energy change of adsorption (∆G o ads ) by Equation (6) [3]: where 55.5 is the molar concentration of water expressed in mol/L, R is the gas constant, and T is the temperature in Kelvin. The values of K ads and ∆G o are shown in Table 4.
where Ɵ is the surface coverage, Cinh is the concentration of the MBC and HBM, and Kads is the equilibrium constant of the adsorption. The plot of the Langmuir adsorption model ( Figure 3a) gives straight lines having high Kads values, indicating that both MBC and HBM molecules have strong interaction with the steel surface. Kads is directly related to the standard free energy change of adsorption (∆G ) by Equation (6) [3]: where 55.5 is the molar concentration of water expressed in mol/L, R is the gas constant, and T is the temperature in Kelvin. The values of Kads and ∆G o are shown in Table 4. The free energy changes' negative values designate that adsorption of MBC and HBM on the carbon steel surface is spontaneous. The values of ∆G o are more negative than 40 kJ mol/L, indicating a chemical nature of the adsorption process. The results shown in Table 4 demonstrate that MBC has a slightly higher negative value of ∆G o than that of the HBM inhibitor. This fact can be ascribed to the presence of sulphur atoms in the MBC structure. It actively boosts electron density over the whole molecular skeleton of the MBC inhibitor, and this is one of the potential reasons for the higher efficiency of MBC than that of HBM.

Potentiodynamic Polarisation
Potentiodynamic polarisation plots found for carbon steel corrosion in the presence and absence of MBC and HBM are shown in Figure 3a,b The kinetic parameters recorded in Table 5 were obtained from Tafel curves. The percentage of inhibition efficiency (EI%PDP) for each inhibitor concentration has been determined by Equation (7): where icorr and icorr[inh] are the blank and inhibited corrosion current densities, respectively. Table 5 exhibits that in the presence of MBC and HBM, the icorr[inh] is extremely reduced, which indicates the formation of a protective film on the surface of the carbon steel. Furthermore, the values of cathodic Tafel slope (bc) and anodic Tafel slope (ba) presented in Table 5 are almost constant because the hindrance of the corrosion process is principal as a result of the blocking of active positions on the steel surface, and hence, the dissolution mechanism does not change in the presence of inhibitors.  The free energy changes' negative values designate that adsorption of MBC and HBM on the carbon steel surface is spontaneous. The values of ∆G o are more negative than 40 kJ mol/L, indicating a chemical nature of the adsorption process. The results shown in Table 4 demonstrate that MBC has a slightly higher negative value of ∆G o than that of the HBM inhibitor. This fact can be ascribed to the presence of sulphur atoms in the MBC structure. It actively boosts electron density over the whole molecular skeleton of the MBC inhibitor, and this is one of the potential reasons for the higher efficiency of MBC than that of HBM.

Potentiodynamic Polarisation
Potentiodynamic polarisation plots found for carbon steel corrosion in the presence and absence of MBC and HBM are shown in Figure 3a,b The kinetic parameters recorded in Table 5 were obtained from Tafel curves. The percentage of inhibition efficiency (EI% PDP ) for each inhibitor concentration has been determined by Equation (7): where i corr and i corr [inh] are the blank and inhibited corrosion current densities, respectively. Table 5 exhibits that in the presence of MBC and HBM, the i corr[inh] is extremely reduced, which indicates the formation of a protective film on the surface of the carbon steel. Furthermore, the values of cathodic Tafel slope (b c ) and anodic Tafel slope (b a ) presented in Table 5 are almost constant because the hindrance of the corrosion process is principal as a result of the blocking of active positions on the steel surface, and hence, the dissolution mechanism does not change in the presence of inhibitors.
Inhibitors can be divided into three classes: cathodic, anodic, cathodic, or mixed type according to the displacement of the values of the corrosion potential in the presence and absence of the inhibitor. When the displacement of the corrosion potential's values is greater than 85 mV, the inhibitor is classified as anodic or cathodic type [3]. The displacement is less than 85 mV for both inhibitors, and thus MBC and HBM are classified as mixedtype inhibitors. Table 5 reveals that the icorr values decrease distinctly as the inhibitor concentration increases. This outcome confirms that both MBC and HBM can act as good corrosion inhibitors. The good inhibition efficiencies for both MBC and HBM are most likely ascribed to their molecular structures, amongst other factors. In Scheme 1, it is observed that both MBC and HBM contain benzene rings, delocalised p-electrons, N atoms, S atoms, and electron-donating groups in their structure, helping the MBC and HBM molecules to adhere firmly to the steel surface. Therefore, high inhibition efficiency is probable.

Electrochemical Impedance Spectroscopy EIS
EIS examined the capacity of MBC and HBM to inhibit the corrosion process. The Electrical Equivalent Circuit (EEC) formula usually used for adjustment is shown in Figure 4. Outcomes are shown in Figure 5a,b. It is clear that the addition of both inhibitors powerfully influenced the impedance response, and this effect is evident from the diameter of semi-circles, which increased clearly. HBM molecules to adhere firmly to the steel surface. Therefore, high inhibition efficiency is probable.

Electrochemical Impedance Spectroscopy EIS
EIS examined the capacity of MBC and HBM to inhibit the corrosion process. The Electrical Equivalent Circuit (EEC) formula usually used for adjustment is shown in Figure 4. Outcomes are shown in Figure 5a,b. It is clear that the addition of both inhibitors powerfully influenced the impedance response, and this effect is evident from the diameter of semi-circles, which increased clearly. The Nyquist spectra ( Figure 5) exhibit slightly depressed semi-circles at medium to high frequencies and an inductive feature at lower frequencies. The capacitive loop at a higher frequency range suggests that carbon steel's corrosion is mainly affected by a charge transfer process [29]. The increase of the diameter is more noticeable as the inhibitor concentration increases, which can be ascribed to the formation of a protective film on the steel surface [3]. The inductive loop is ascribed to the relaxation process caused by the adsorption of intermediate products in the presence of acid solutions and inhibitors [3,7].
It can be concluded from Table 6 that the Rct values are directly proportional to the inhibitor's concentrations, and in turn, the values of %IEEIS increase. Values of %IEEIS are obtained from the Rct values of charge transfer resistance data using Equation (8) [29]: where Rct and Rct(inh) are the charge-transfer resistance values without and with inhibitors, respectively. Rs is the solution resistance, Rct is charge-transfer resistance, Yο is the capacitance, and n is the phase shift that can be explained as the degree of the surface inhomogeneity [20].

Global Reactivity Descriptors
Quantum chemical calculation can support our findings with highlights on the relation between MBC and HBM molecular configuration and their performance as corrosion inhibitors through various vital data. We found no virtual frequency for the optimised MBC and HBM molecules by examining the calculated data. Figure 6 shows the most stable configuration of MBC and HBM molecules in their neutral conditions, besides the distribution of molecular orbital (LUMO and HOMO) maps. The calculations showed that it varies from 1.38 to 1.40 Å for the two aromatic ring moieties for the bond distance. For the substituted two hydroxyl groups on the aromatic rings in the HBM compound, the O-Ar bond distance was 1.345 Å. The two N-N bond distances were 1.356 Å for MBC and 1.329 Å for the HBM. The two azo methane groups N=C in the HBM compound showed a bond distance of 1.282 Å. The shortest bond distance was observed for the carbonyl groups C=O, with values of 1.229 Å in MBC and 1.207 Å in HBM.
On the other hand, the most extended bond length was observed for C=S groups in MBC (1.665 Å), facilitating its adsorption on the steel surface. The distribution of electron clouds belongs to the HOMO, and LUMO orbitals of the MBC and HBM molecules were located across the entire skeletons. The transfer of the electron is from MBC and HBM to the steel surface, and so protection is mainly a result of the interaction energy The Nyquist spectra ( Figure 5) exhibit slightly depressed semi-circles at medium to high frequencies and an inductive feature at lower frequencies. The capacitive loop at a higher frequency range suggests that carbon steel's corrosion is mainly affected by a charge transfer process [29]. The increase of the diameter is more noticeable as the inhibitor concentration increases, which can be ascribed to the formation of a protective film on the steel surface [3]. The inductive loop is ascribed to the relaxation process caused by the adsorption of intermediate products in the presence of acid solutions and inhibitors [3,7].
It can be concluded from Table 6 that the R ct values are directly proportional to the inhibitor's concentrations, and in turn, the values of %IE EIS increase. Values of %IE EIS are obtained from the R ct values of charge transfer resistance data using Equation (8) [29]: where R ct and R ct(inh) are the charge-transfer resistance values without and with inhibitors, respectively.

Global Reactivity Descriptors
Quantum chemical calculation can support our findings with highlights on the relation between MBC and HBM molecular configuration and their performance as corrosion inhibitors through various vital data. We found no virtual frequency for the optimised MBC and HBM molecules by examining the calculated data. Figure 6 shows the most stable configuration of MBC and HBM molecules in their neutral conditions, besides the distribution of molecular orbital (LUMO and HOMO) maps. The calculations showed that it varies from 1.38 to 1.40 Å for the two aromatic ring moieties for the bond distance. For the substituted two hydroxyl groups on the aromatic rings in the HBM compound, the O-Ar bond distance was 1.345 Å. The two N-N bond distances were 1.356 Å for MBC and 1.329 Å for the HBM. The two azo methane groups N=C in the HBM compound showed a bond distance of 1.282 Å. The shortest bond distance was observed for the carbonyl groups C=O, with values of 1.229 Å in MBC and 1.207 Å in HBM. The different quantum chemical parameters obtained for MBC and HBM are summarised in Table 7. The increase in EHOMO values shows the high electron-donating ability of the molecule to vacant metal orbitals.
On the contrary, the decrease in ELUMO values indicates the high tendency of the On the other hand, the most extended bond length was observed for C=S groups in MBC (1.665 Å), facilitating its adsorption on the steel surface. The distribution of electron clouds belongs to the HOMO, and LUMO orbitals of the MBC and HBM molecules were located across the entire skeletons. The transfer of the electron is from MBC and HBM to the steel surface, and so protection is mainly a result of the interaction energy between the HOMO-inhibitor and the LUMO-steel, and vice versa. HOMO and LUMO are functions that determine molecules' capacity for electron-donating and accepting, respectively [30][31][32]. Therefore, we can infer that MBC and HBM can adsorb on the steel surface by multiple active sites, providing significant surface coverage and enhanced protection.
The different quantum chemical parameters obtained for MBC and HBM are summarised in Table 7. The increase in E HOMO values shows the high electron-donating ability of the molecule to vacant metal orbitals. On the contrary, the decrease in E LUMO values indicates the high tendency of the molecule to obtain electrons from steel [30][31][32]. The difference between E LUMO and E HOMO is related to the reactivity of the molecule. As the smaller is the value of ∆E, the higher is the molecule's reactivity [30][31][32]. Regarding our results in Table 7, we can find that MBC possesses more electron-donating tendency (E HOMO ) than HBM in all forms (neutral and protonated) and phases (gas and aqueous). This tendency to donate electrons supports the order results from the experimental studies. The MBC molecule also possesses the lowest values of E LUMO , indicating its high ability to accept electrons from steel (back donation) and therefore strong binding to the steel surface. The E HOMO values of the two molecules increased upon protonation, so the protonated form can be readily adsorbed by donating more electrons. Concerning the energy gap (∆E), the MBC molecule overcomes HBM in reactivity as it obtains the lowest values.
The presence of two S atoms and more conjugation in the MBC molecule increases its adsorption ability on the steel surface. The electron back donation from steel to inhibitor molecules was confirmed by negative values of ∆E Back-donation (∆E Back-donation = − η 4 ) [33]. We found that MBC possesses higher total negative charge (−6.755-neutral form-gas phase) than HBM (−5.634) for the electrostatic attraction between the inhibitors and steel surface. This high negative charge on the MBC molecule supports its high inhibition efficiency. Based on the fraction of electrons transferred (∆N) quantum parameter, positive values of ∆N prove that electrons can follow from inhibitor molecules to the metal surface [34]. ∆N of MBC is higher than HBM, suggest that the tendency of MBC molecules to share their electrons with steel surface is more prominent than HBM molecules.

Local Reactivity: Fukui Functions
The best way to describe the local sites for electrophilic/nucleophilic reactivity through the atomic charges is the local Fukui indices [35]. It enables us to identify the atomic sites for donating or accepting electrons. Fukui functions are the derivative of chemical potential and can be calculated for nucleophilic and electrophilic attacks by approximation method through the following mathematical relations [36].
where q k = atomic charge in different states (neutral (N), anionic (N + 1) or cationic (N − 1)). Fukui indices f + k and f − k represent either the nucleophilic or the electrophilic sites of the atoms. The large values of f − k are the most suitable sites to interact with electron-deficient species. On the other hand, the large values of f + k are the most suitable sites to interact with electron-rich species [37]. Table 8 collects the Fukui indices for the MBC and HBM molecules calculated from Hirshfeld atomic charges obtained from the DMol 3 calculations. As listed in Table 8   The identification of the active site is also confirmed by calculating the dual descriptor, by Equation (12) [38]: Positive values of ∆f are related to nucleophilic attack but negative values of ∆f are related to electrophilic attack. For ∆f > 0, the sites highly ready for nucleophilic attack are MBC: C8, C19, S10, and S21, and HBM: N8, N9, C10, and C11. On the contrary, for ∆f < 0, the sites highly ready for electrophilic attack are MBC: N6, N7, N17, and N18, and HBM: N6, N7, O24, and O25.

Monte Carlo Simulations
It is imperative to study the interaction between MBC, HBM molecules, and steel surface with Monte Carlo simulations. It was used to determine the different forms of adsorption energy and total energy for MBC and HBM molecules, as presented in Table 9. The adsorption energy's negative values for both MBC and HBM molecules either in neutral or protonated states prove that their adsorption occurred spontaneously [39]. MBC molecules possess higher negative values of adsorption energy (−7285.79 kcal mol −1neutral, −7245.47 kcal mol −1 -protonated) than HBM molecules (−6473.38 kcal mol −1neutral, −6416.35 kcal mol −1 -protonated), which suggested the more vital adsorption ability and extra corrosion inhibition of MBC on the Fe (110). The high negative adsorption energy of the protonated forms suggested that MBC and HBM molecules are still highly effective inhibitors even after protonation. Figure 7 shows the equilibrium configuration of MBC and HBM/Fe (110) in the presence of H 2 O, H 3 O + , and Cl − . It is clear from Figure 7 that simulations of both molecules happened through parallel orientation adsorption on Fe (110) via heteroatoms (O, N, and S), conjugated systems of aromatic moieties, and π electrons. The side-by-side orientation adsorption will provide a higher blocking area and effective interactions between all active sites in MBC and HBM molecules and Fe (110) atoms and stimulate the inhibition effect. The large size of the MBC molecules associated with more adsorption centres, such as the sulphur atoms, resulted in more area than the HBM molecules. from Figure 7 that simulations of both molecules happened through parallel orientation adsorption on Fe (110) via heteroatoms (O, N, and S), conjugated systems of aromatic moieties, and π electrons. The side-by-side orientation adsorption will provide a higher blocking area and effective interactions between all active sites in MBC and HBM molecules and Fe (110) atoms and stimulate the inhibition effect. The large size of the MBC molecules associated with more adsorption centres, such as the sulphur atoms, resulted in more area than the HBM molecules.

Materials
The composition of the C-steel used throughout all experiments was (wt%) 0.20 C, 0.045 P, 0.

Materials
The composition of the C-steel used throughout all experiments was (wt%) 0.20 C, 0.045 P, 0.30 Si, 0.53 Mn, 0.055 S, Fe balance. The corrosive solution (1.0 M HCl) was prepared by direct dilution with double-distilled water.
Malonic diethyl ester, salicylaldehyde, phenyl isocyanate, and hydrazine hydrate (80%) were purchased commercially from Sigma Aldrich, St. Louis MO, USA, and used without any further purification. Absolute ethanol, DMSO, diethyl ether, and all used solvents were purchased from Merck, Mumbai, India. The melting points were reported on a heated stage Gallen Kamp melting point equipment (Gemini Lab, Apeldoom, Netherlands). Elemental C, H, N, and S analyses were carried out on a Fison EA 1108 analyser (Shimadzu, Kyoto, Japan). The infrared (FTIR) spectra were recorded by employing a FTIR.8300 Shimadzu Spectrophotometer (Shimadzu, Kyoto, Japan) by using KBr disc in the frequency range of 4000-400 cm −1 . The 1 H NMR spectra were recorded on an Ultra-Shield™ 500 MHz NMR Spectrometer (Shimadzu, Kyoto, Japan) using deuterated DMSO-d 6 s the solvent and tetramethylsilane (TMS) as the internal standard.

Synthesis of Malonyl Dihydrazide
Malonic diethyl ester (38 mL, 40.05 g, 250.06 mmol) in 100 mL absolute ethanol was added slowly dropwise to a stirred excess hot solution of 61 mL of hydrazine hydrate (80%) (1002 mmol) in 100 mL absolute ethanol for 2 h. The reaction mixture was then refluxed in a water bath for 10 h then cooled in an ice-water bath. The white solid was filtrated, rinsed with ethanol and diethyl ether, and then dried in a desiccator over anhydrous CaCl 2 . Yield was 91% (30,227

Synthesis of 2,2'-Malonylbis(N-phenylhydrazine-1-carbothioamide) (MBC)
Phenyl isothiocyanate (2 mL, 2.26 g, 16.75 mmol) in 25 mL absolute ethanol was added slowly dropwise to a stirred hot suspension of malonyl dihydrazide (1.10 g, 8.33 mmol) in 25 mL absolute ethanol. The reaction mixture was then refluxed in a water bath for 8 h then cooled in an ice-water bath. The white solid was assembled and rinsed with ethanol prior to drying in an electric oven at 70 • C. Yield was 92.5%

Electrochemical Measurements
Electrochemical tests were performed using a three-electrode thermo-stated cell assembly using a Gamry potentiostat/galvanostat/ZRA (model Interface 1000, Gamry, Warminster, PA, USA). A saturated calomel electrode (SCE) and platinum were used as reference and counter electrodes, respectively. The working electrode was manufactured from carbon steel. The electrodes were abraded with various emery papers, degreased with acetone, rinsed with double-distilled water, and dried. All experiments were performed at 25 ± 0.1 • C. The potentiodynamic curves were recorded from −300 to +300 mV at a scan rate of 1 mV S −1 . The open-circuit potential (OCP) was obtained after 45 min. The electrochemical impedance spectroscopy (EIS) test was carried out using the same instrument. Gamry framework software (version 6.0, Gamry, Warminster, Pennsylvania, USA) was used for conducting the experiments. Echem Analyst Software (Gamry, Warminster, Pennsylvania, USA) was used for plotting and fitting data. EIS measurements were carried out in a frequency range of 10 MHz to 100 kHz with an amplitude of 5 mV peak-to-peak using A.C. signals at relevant corrosion potential.

Computational Study
Supporting the experimental results with the computational calculations is quite helpful to relate the inhibitory effect of the investigated compounds with their geometrical and chemical structures. With the aids of quantum calculations, we can investigate the active sites responsible for the corrosion inhibition mechanism. We reported a complete geometry optimisation for MBC and HBM compounds through the ADF2020.101 and the DMol3 module as a part of the Materials Studio software version of 2017 (Dassault Systems Materials studio, San Diego, CA, USA). The initial optimisation and vibrational frequencies were calculated using the ADF software (Software for Chemistry & Materials, Amsterdam, Netherlands). Further investigations were carried out using the DMol3.
The parameters of the DMol3 module during calculation were set as Task = Geometry Optimisation, Functional = LDA and PWC, Basis = DND (4.4), and COSMO control for solvent considerations. For the neutral and protonated form of MBC and HBM compounds, E HOMO and E LUMO as basic potent descriptors as well as some other parameters derived from them were excluded according to the following mathematical relations: Ionization potential, I = −E HOMO electron affinity, A = −E LUMO (13) electro negativity, X = − chemical potential (µ) = (I + A ) 2 (14) absolute hardness, η = ( I − A) 2 separation energy, ∆E = E LUMO − E HOMO (15) electrophilicity index, ω = µ 2 2η nucleophilicity index, ε = 1 ω After the optimisation process, the adsorption of MBC and HBM molecules on the Fe (110) surface was simulated using the adsorption locator module. The initial step is constructing a 10 × 10 × 10 3D Fe (110) model. MBC and HBM molecules were allowed to simulate on Fe (110)

Conclusions
This work aimed to assess two malonyl dihydrazide derivatives' efficiency as corrosion inhibitors for carbon steel in acidic media. The two inhibitors were studied experimentally and theoretically for carbon steel corrosion. It is conceivable to conclude the following facts:

Conflicts of Interest:
The authors declare no conflict of interest.