Enhancing the anticorrosion performance of mild steel in sulfuric acid using synthetic non-ionic surfactants: practical and theoretical studies

ABSTRACT The anticorrosion potency of Sabic mild steel (MS) in 0.5 M H2SO4 solution was enhanced by three synthetic non-ionic surfactants (NI Surf.) containing pyridine and pyrimidine derivatives. These compounds are safe, environmentally friendly, and harmless to human health. Chemical and electrochemical measurements were used to compute the corrosion parameters. The anticorrosion efficacy increases with increasing the concentration of NI Surf. and with lowering temperature, surface and interfacial tension, and critical micelle concentration. The effectiveness of anticorrosion is interpreted due to the spontaneous horizontal adsorption on the surface of MS by the existence of some active centers that facilitate the adsorption. The adsorption process obeys Temkin isotherm. Potentiodynamic polarization elucidated that the synthetic NI Surf. acted as mixed-type inhibitors. Some surface properties were determined and confirm the anticorrosive effect of these molecules. Quantum chemical parameters as reactivity descriptors were carried out. It should be noted that the results obtained from computational calculations of the specifications are in full agreement with the experimental observations. There is good compatibility between the anticorrosion efficiency obtained from various techniques and surface properties and quantum chemical calculation. GRAPHICAL ABSTRACT


. Introduction
Sabic Mild steel (MS) is utilized in multiple industrial applications, but when exposed to sulfuric acid, it corrodes, causing countless economic losses. Therefore, scientists are trying to find ways to solve the risk of corrosion. The main one is the use of corrosion inhibitors.
In previous research, a lot of organic compounds have been used that contain a lot of active groups and oxygen, nitrogen, and sulfur atoms, which facilitate the adsorption process and consequently the corrosion rate reduces, Unfortunately, these compounds have bad effects on human health and the environment (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). There are several factors that influence the effectiveness of inhibition of organic compounds, such as the type of metal, the chemical composition of the additives, the active groups in the molecule, the temperature, and many other factors (15, 16 17).
Most of the organic compounds give high inhibition efficacy, but unfortunately these compounds are high in price and harmful to human health and the environment. And to create inhibitors that are safe, environmentally friendly for humans, and give high efficiency in preventing steel from corrosion attack. One of these inhibitors that solve these problems is the use of nonionic surfactants that are inexpensive, easy to dissolve in water, and have a high adsorption capacity on the steel surface (18)(19)(20)(21)(22). Some non-ionic surfactant molecules were utilized to protect some metals from the corrosion process in acidic solutions as the previous work by Abdallah et.al. (23)(24)(25)(26)(27)(28).
The strategic objective of this manuscript is to try to inhibit the corrosion of MS in 0.5 M H 2 SO 4 solution using nonionic surfactants (NI Surf.) containing pyridine and pyrimidine derivatives. The selected concentration (0.5 M HCl) is the suitable concentration for the pickling and chemical cleaning of MS. Weight reduction (WR), electrochemical impedance spectroscopy (EIS), and potentiodynamic polarization (PP) measurements were used in this study. Also, the impact of rising temperature on the dissolution of MS in devoid of and containing NI Surf. molecules were investigated. The relationship between the anticorrosion efficiency and the surface parameters with quantum chemical calculations is also explicated.

Chemical and electrochemical measurements
MS was applied in this study to conduct chemical and electrochemical experiments and its chemical composition as follows (weight %) carbon = 0.072, manganese = 0.610, phosphor = 0. 041, silicon = 0.041, vanadium = 0.020, and the rest iron.
For weight reduction experiments (WR) A mild steel coupon with dimensions of 2 × 3 × 0.1 cm was used and for potentiodynamic polarization (PDP) and electrochemical impedance (EIS), MS sample rod immersed in Araldite with the denuded surface area of 0.38 cm 2 , Before any experience the MS coupons or rod surface furbished with a diverse degree of emery papers (ranged from 200 to 1200). Finally, it is dried with a fine filter paper. The method of WR measurements is done as mentioned previously (29).
For PDP and EIS techniques, three-compartment cell containing MS as working electrode, Pt foil used as auxiliary electrode, and saturated calomel electrode (SCE) as reference electrode A PS remote Potentiostat with PS6 software was used to determine the corrosion parameters obtained from the PDP measurements. EIS measurements were accomplished at a frequency range from 10 kHz to 100 mHz and signal amplitude perturbation of 5 mV by using a computer-controlled potentiostate (Auto Lab 30, Metrohm). All the measurements were performed at a temperature of 30 ± 1°C by using ultra circulating thermostat.

Synthesis of pyridine and pyrimidine derivatives (I-III) as nonionic surface-active agents
This design was carried out by the following process: Process 1. Synthesis of pyridine 1 and pyrimidine derivatives 2, 3 Reaction of enaminonitrile derivative [prepared by stirring of malononitrile (0.01 mol) in dry ethanol for 2 h with palmitoyl chloride (0.01 mol) to give the malononitrile intermediate, followed by heating for 3 h with piperidine to yield the enaminonitrile derivative] in boiling DMF (20 mL) with the presence of base catalyst and malononitrile, phenyl isothiocyanate and/or formamide produced the pyridine 1 and/or pyrimidine derivatives 2,3, respectively (Scheme 1).
Process 2. Preparation of nonionic surfactants (I-III) from pyridine and pyrimidine (1)(2)(3) Addition of propylene oxide (10 moles) to the products (1-3) by fusion in presence of KOH, in each case gave surf (I-III), respectively (Scheme 2). The amount of propylene oxide, which reacted was determined by the gain in weight of the mixture after the addition.
The composition of all the products was established based on the spectra of IR with 1 HNMR.

Estimation of surface characteristics
Some of the surface characteristics of the three non-ionic surfactants were assigned as previously defined (30,31), the surface tension S. T (γ), interfacial tension (IFT) critical micelle concentration (CMC), the efficiency (π cmc ), the surface excess (Г max ), the surface area (A min ), the free energy of micellization (ΔG°m ic ) and adsorption (ΔG°a ds ) properties were measured at 25°C and depicted in Table 1.

Computational methods
All the calculations have been accomplished with the Gaussian 03 suite of programs. Geometry optimizations were carried out on 1-3 in vacuo with hybrid density functional theory (DFT) using Lee-Yang-Parr (B3LYP) exchange-correlation functional theory, together with the standard 6-31G (d) basis set. Frequency calculations were also carried out on the optimized geometries using the same level of theory.

. Results and discussion
3.1 WR measurements 3.1.1 . Impact of NI surf. concentration Figure 1 represents the relationship between the WR and time for MS coupons in free 0.5 M H 2 SO 4 solution and contains some concentrations (ranging from 50 to 250 ppm) of NI Surf. III molecule at 298 K. Like curves were acquired for the other two NI Surf. molecules but not shown and the corrosion data are recorded in Table 2. It is evident that with increasing the concentration of these molecules, the WR values decreased. This suggests that NI Surf exists retard the corrosion rate of MS in 0.5 M H 2 SO 4 solution or in another meaning, these molecules act as corrosion inhibitors. The linear relationship in Figure 1 due to insoluble surface films during corrosion (32).
The rate of corrosion R corr. (g.cm −2 .min −1 ) the surface coverage (θ) and the anticorrosion efficiency % AE were determined from the subsequent equation and listed in Table 1 (33).
where ΔW is the weight reduction (ΔW = W a -W b ), W a and W b are the weight of MS before and after exposure to the corrosive solution, S is the surface area and t is the inundation time, R free and R add are the corrosion rate in free 0.5 M H 2 SO 4 solution and including NI Surf., respectively. % AE increases with increasing concentration of NI Surf. by increased the adsorbed surfactant molecules at the MS surface and increase the amount of covering area.
Obviously from Table 2, the R corr value was lowered and the % AE values increased, confirming the inhibiting strength of the NI Surf. molecules. % AE also increases with increased NI Surf. concentration. This is due to an is an activation-controlled chemical reaction, the R corr. greatly affected by temperature. Typically, R corr , increases significantly as temperature increases. Activation polarization is usually the controlling factor during corrosion of MS in strong acids. Certainly the rate determination step is not a chemical reaction because the corrosion in the present state and as clearly shown by the experimental results is simple absorption. In addition, the cathodic reaction in this study is the H 2 evolution. Therefore, the diffusion-controlled source is excluded. Activation thermodynamic parameters such as the activation energy (E a *), the enthalpy of activation ΔH* and the entropy of activation ΔS* for the dissolution of MS in 0.5 M H 2 SO 4 solutions of and containing 250 ppm of the examined NI Surf. molecules were computed using Arrhenius equation (34,35): where A is constant depends on the electrode and the electrolyte, R is the gas constant T is the temperature, h is the Plank's constant and N is the Avogadro's number. Figure     The presence of NI Surf. molecules increased the E a * values due to a significant lowering in the adsorption process of the NI Surf. molecules on the surface of MS with increasing temperature and increase in the reaction rate due to exposure of a large area of MS to H 2 SO 4 solution. In addition, tested NI Surf. molecules act as an inhibitor by increasing activation energy of MS corrosion by creating a barrier to mass and charge transfer by adsorption onto the surface of MS. Figure 3 represents a plot of log (R corr /T) vs1/T of uninhibited MS in 0.5 M H 2 SO 4 and inhibited by NI Surf. molecules. A straight line with a slope of (−ΔH*/ 2.303 R) and an intercept of [log (R/Nh) + ΔS*/2.303 R].
The values of ΔH* obtained from the slope of the straight line equal to and equal to 17.32 kJ mol −1 for the free 0.5 M H 2 SO 4 and equal to 30.18, 32.24, and 34.62 kJ mol −1 in the presence of the NI Surf. molecules I, II, and III, respectively. The positive sign of ΔH* reflects that the adsorption of the NI Surf. molecules on the MS surface are an endothermic process. The values of ΔS*obtained from the intercept of a straight line and to −196.24 J mol −1 K −1 for the free 0.5 M H 2 SO 4 and equal to −197. 23, 198.33, and 199.64 J mol −1 K −1 for the surfactants molecules I, II, and III respectively. The signs of ΔS* in the free and presence of NI Surf. molecules are negative. This demonstrates that the activation complex is a ratedetermining step that represents binding rather than secession indicates a reduction in perturbation on the transition from the reactants to the activated complex (36).   250 ppm) of NI Surf. III molecule with a sweep rate of 2 mV/s are represented in Figure 4. Similar curves for NI Surf. I and NI Surf. II molecules were obtained but were not shown and the corrosion data were registered in Table 4. By examining this Figure, it is apparent that the anodic and cathodic polarization curves were shifted to lower values of the current density upon adding any of the tested NI Surf. molecules. This result demonstrates the inhibitory activity of all molecules tested for MS corrosion in 0.5 M H 2 SO 4 solutions. The kinetic corrosion parameters e.g. corrosion potential (E corr ), corrosion current density (I corr ), anodic and cathodic Tafel slope (β c ) determined from the curves are inserted in Table 4. Some observations, due to the addition of the NI Surf. molecules examined, E corr values are not affected by adding tested NI Surf. molecules. The values of I corr lowered, and the % AE increase with increasing of the NI Surf. concentration. As the NI Surf. concentration increases in the bulk solution, The amount of particles adsorbed on the surface of MS increases, which leads to an increase in anticorrosion efficacy. Both β a and β c values are almost constant. This confirms that NI Surf. molecules acted as an inhibitor of the mixed type. This type of inhibitor works by adsorption of both anodic and cathodic sites on the MS surface and thus delays anodic and cathodic reactions. This behavior reduces the MS corrosion rate. This inhibitory action is due to the forming of an insoluble layer resulting from adsorption of the NI Surf. molecules on the MS surface. The % AE is reduced in the following sequence as NI Surf. III < NI Surf. II < NI Surf. I. This sequence is consistent with that obtained from the WR measurement.

EIS measurements
EIS measurements were applied to examine the inhibition strength of NI Surf. molecules on MS including surface properties, electrode kinetics, and mechanistic information. The impedance spectra of different Nyquist plots were analyzed by relying on the experimental data to a simple equivalent circuit model as elucidate above (37). The Nyquist plots of MS in 0.5 M H 2 SO 4 solution free and contain diverse concentrations of NI Surf. III ranged from 50 to 250 ppm at 298°K ± 1 was represented in Figure 5. Like curves for the other two molecules NI Surf. I and NI Surf. II obtained not displayed.
Nyquist impedance does not show a perfect semicircle and is referred to the frequency dispersion due to roughness and heterogeneity of the steel surface. The impedance diagram shows the same direction (single capacitive loop), however, the diameter of this loop increases as the concentration of NI Surf. molecules increase. As a result, the corrosion rate reduces. The increase in the value of R ct due to the adsorption of NI Surf. on the MS surface (38,39). Corrosion inhibition was increased by increasing the NI Surf. concentration.  The capacity of double layer (C dl ) can be computed from the next equation: where f max . is the maximum frequency. The percentage anticorrosion efficiencies (% AE) of the tested NI Surf. molecules were determined from the following equations: where (R ct ) f and (R ct)in are the charge transfer resistance values in the free and existence of NI Surf. molecules. The corrosion parameters obtained from EIS measurements e.g. R ct , C dl , and % AE of the investigated NI Surf. are registered in Table 5.
From the data obtained in Table 5. Obviously, with rising the concentration of NI Surf. molecules, R ct values increase owing to the formation of a protective film at the MS/electrolyte interface while Cdl values decrease due to exchange of water molecules at the electrode interface by NI Surf. molecules of lower dielectric constant through adsorption. An increase in % AE values suggests that the NI Surf. molecules adsorb on the MS surface and cover several sites of the steel surface forming an adherent layer (40).
The anticorrosion efficacy sequence for the tested NI Surf. molecules are reduced as follows: NI Surf. III< NI Surf. II < NI Surf. I. This sequence corresponds to that obtained from the WR and PDP measurement. These results indicate the good compatibility between the different measurements and thus prove the sincerity of the results obtained. The % AE values of the investigated NI Surf. molecules are more efficient than other published works such as ethoxylated nonionic surfactants based on Schiff base (41). Nonionic surfactants based on propane tricarboxylic acid (42) and amino acids based-surfactant molecules, namely, sodium N-dodecyl asparagines (AS), sodium N-dodecylhistidine (HS) and sodium N-dodecyltryptophan (23, 24).

Adsorption isotherm
Adsorption of the synthesized NI Surf. molecules on the MS surface was accompanied by the removal of water molecules from the surface. The adsorption operation can be thought of as a replacement process in which the NI Surf. molecule in the aqueous phase NI Surf. (aq) replace the 'y' amount of adsorbed water molecules on MS surface according to the following equation (43).
where y is the amount of adsorbed water molecules substituted by a one NI Surf. compound. Several factors influence the adsorption process, for example, the types of surfactant molecules, the presence of heteroatoms in the chemical composition of surfactant molecules, the type of electrode used, concentration of aggressive acidic solutions, acidity of the solution, temperature, and other factors. The amount of (θ) for some concentrations of three NI Surf. were evaluated from the WR data. The values of θ of different concentrations of the synthesized NI Surf. were utilized to demonstrate the adsorption isotherm of these anticorrosive on the MS surface. Several adsorption isotherms have been applied to interpretation the adsorption behavior of NI Surf. molecules. Temkin isotherm has  been found to be the better description of adsorption behavior of the NI Surf. molecules on the MS surface, according to the subsequent equation (17). u = 2303/a(log K ads + log C) (8) where K ads is the equilibrium constant of the adsorption, C is the NI Surf. concentration, a is constant. Figure 6 represents the relationship of θ versus log C which gave a straight line confirming that the adsorption of NI Surf. on the surface of MS in a 0.5 M H 2 SO 4 solution at 25°C follows Temkin's adsorption isotherm. The applicability of Temkin's isotherm is achieved by assuming a monolayer adsorption on a homogeneous and uniform metallic surface with an interaction in the adsorption layer.

Surface characteristics
An eco-friendly non-ionic surfactant (I-III) was successfully synthesized by an environmentally benign process to the establishment of green chemistry. The surface characteristics such as γ, IFT, CMC, π cmc , Г max , A min , ΔG°m ic , and ΔG°a ds, were recorded in Table 1 and showed that the NI Surf. III have has higher efficacy than other NI Surf. (I, II) due to reducing the values of γ and IFT. In general, the synthesized products have the capability to diminish the γ, indicating that a great tendency for the output NI Surf. towards the adsorption at the air/water interface. Where the lower IFT values of the tested NI Surf. III indicated the increase of the strength of cohesion between the MS and NI Surf. molecules. The CMC feature can be identified as the efficacy of NI Surf. molecules, which detects the required amount of NI Surf. to cause maximum reduction of γ. Where, the low value of CMC has excellent emulsification, solubility, and cleaning properties. When the NI Surf. concentration increases, the values of γ decrease steadily and at critical concentrations there is no significant decrease in the γ. This indicates the achievement of saturation in the surface adsorbed layer and the initiation of micelle formation in the bulk. From the outcomes in Table 1, the NI Surf. showed that a sharp decrease of the γ was observed from NI Surf. molecules I to III. The increase in the gained CMC value can be referred to as an increase in the solubility of the NI Surf molecules. The maximum reduction in γ induced by the dissolution of a NI Surf. molecule was determined by the π cmc activity, which became a measure of the activity of the molecule to reduce the γ of water. The results showed that the tested compounds had ability to reduce γ in the aqueous system. The π cmc values of NI Surf. III in Table  1 are higher than NI Surf I and II in parallel with increasing of % AE and decreasing of γ and IFT the tested molecules (26).
The Г max activity is very useful in measuring the adsorption efficacy of NI Surf. at the water-air interface. Thus, a material that reduces γ is redundant at or near the surface, that is, when the γ decreases with an increasing surfactant activity, Г max is positive. Pumping surfactant particles onto boundary surfaces between phases to form an adsorbent layer. The higher values of Г max and the lower values of A min of NI Surf. III which has more inhibiting efficiency than the other two NI.Surf. molecule demonstrated the vigor aggregation capability at the air-water interface (30).
The computed values of (ΔG°m ic ) and (ΔG°a ds ) are a negative sign suggest that the two processes are spontaneous. A comparison of the two values showed a slight increase in (ΔG°m ic ) than (ΔG°a ds ). The more negative (ΔG°a ds ) values indicate the NI Surf. emigrate to the interface or aggregate in micelles to minimize the repulsion process and thus the free energy of the system is minimized (31).

Anticorrosion mechanism
The anticorrosive strength of the investigated nonionic surfactants originated from the formation of a protective layer that is adsorbed onto the MS surface. The adsorption process can be attributed to several different factors such as the electron donor hetero atoms, the ring size, and the electron-withdrawn groups in the structure. In addition, the existence of free lone pairs electron in the N, S atoms and π electron on double bond facilitates the adsorption of the NI Surf. molecules on the MS surface. NI Surf. long chain of hydrocarbons adsorbs it to the MS surface through water-loving (hydrophilic) parts which contain hetero atoms (N, O, and S). Moreover, hydrocarbon chains tend to be warped in water to reduce the contact area between them and the water molecule (44).
The anticorrosive mechanism can be elucidated as follows: the long hydrocarbon chain of NI surf. molecules are absorbed on the MS surface by the hydrophilic fractions, which contain oxygen, nitrogen, or sulfur atoms. On the other hand, the hydrocarbon chains tend to wrap in water to reduce the contact area between them and the water molecule. The NI Surf. molecules have a distinct structure composing of a structural group, and they have little attraction to the solvent, known as a hydrophobic group with a group of strong solvent attractiveness (Like water) is called a waterloving group. When the surf. molecules soluble in water, the existence of a hydrophobic group inside the solvent causes the structure of the solvent liquid to be distorted, which increases the system's free energy (44). In the aqueous solution, the hydrogen bonding between the water molecules is disfigured by the occurrence of non-polar materials. Thus, water attempted to completely dislodge the nonpolar substances as a separate phase. However, this is not as possible as the hydrophobic group set from NI Surf. hydrated and its expulsion would require blocking the adsorption of the NI Surf. molecules to the surface of MS.
It is apparent that the values of % AE acquired from the various techniques demonstrate the sensible anticorrosion efficiency of the NI Surf. for the corrosion of MS in 0.5 M H 2 SO 4 solution. This can be discussed according to the bonding strength between the hydrophilic group and the MS is more powerful than that power between expelling a hydrophobic group and the aqueous solution. In these circumstances, a diffusion barrier to chemical and/or electrochemical attack of the solution on MS surface was established and therefore, the % AE increases.
Moreover, the high molecular size of these compounds resulted in horizontal adsorption at the surface of MS due to the occurrence of some active center. Furthermore, the presence of electron-withdrawn groups as C=O, C=S, or C≡N resulted in an increase in electron motion leading to a high inhibiting effect on the MS surface.
On the other hand, the structures of NI Surf. molecules have heterogeneous rings like the pyridine ring with the existence of C=O and CN groups in NI Surf. I. and the presence of pyrimidine ring in surf. (II &  III). Obviously, the % AE computed from all various techniques increases in the following sequence NI Surf. III > NI Surf. II > NI Surf. I This can be explained as follows: Presence of a pyrimidine ring in the chemical composition of NI Surf. (II and III) make them more efficacious than NI Surf. I. The surf. III is more efficacious than surf. II due to the presence of more electron donor atoms such (C=O) and (C=S) in its chemical structure. This leads to an increase in the electron density in the adsorption center which leads to an improvement in the adsorption process and an increase of % AE. NI Surf. II is highly efficient than NI Surf. I due to the existence of electron donor atoms and the C=S group in the addition of the presence of pyrimidine ring, which promoted the adsorption process.

Quantum chemical calculations
The use of Density functional theory (DFT) finds increasing in the last four decades and affords various indices to rationalize and understand chemical structure. The concepts that emerge from this theory have also been widely used to generate a general approach to the description of chemical reactivity (45)(46)(47)(48)(49)(50). Moreover, quantum chemical methods mark a decisive breakthrough in these efforts and have proven very useful in anti-corrosion studies. In order to predict the reactivity of inhibitor molecules, the quantum chemical properties, such as E HOMO , E LUMO , HOMO-LUMO energy gap (ΔE) were performed and the results are collected in Table 6. It has been shown that the frontier molecular orbital (HOMO and LUMO) has significant importance on the mechanism of adsorption of molecules through electro-donation or electro-acceptation character onto the metallic surface.
It is known that the inhibitor with a higher E HOMO value is joined with more capability of the inhibitor molecule to electron sharing. It has been found that in our case the largest E HOMO corresponds to pyrimidine derivative (3) (−8.803) in line with the aforementioned experiments. Thus, we can consider that the pyrimidine derivative (3) would reveal a more suitable affinity to the adsorption onto the MS surface through the lone pair electrons located on N and S atom to the vacant iron d-orbital. On the other hand, some authors (38,(51)(52)(53)(54)(55) have reported a relationship between hardness (η) parameter and stability of the complex formed in which a weak value of the hardness corresponds to more stability of the surface-anticorrosive complex formed. In the same context, smaller values of E LUMO signifies a better ability of the anticorrosive to accept electrons. As can be seen in Table 6, the corresponding results for the E LUMO and hardness values follow the same trend in which the pyrimidine derivative (3) presents the smaller values of E LUMO and hardness among the anticorrosive studied in this work and consequently indicates a better inhibition efficiency. Furthermore, the greater value of the chemical (σ) softness is also envisageable value, generate the adsorptive tendency of the pyrimidine derivative (3) anticorrosive for the MS surface.
On the other hand, in accordance with the frontier molecular orbital theory of chemical reactivity, the separation (ΔE) energy with ΔE = E LUMO -E HOMO , represent a significant parameter as a function of reactivity behavioral inhibition of the anticorrosive molecule towards their adsorption on the MS surface. It is apparent that, as ΔE values decrease, this generates an increase in the reactivity of the anticorrosive molecule and consequently leads to an increase in their inhibition efficiency. The calculated (ΔE) values listed in Table 6 indicate that the pyrimidine derivative (3) display the weaker value of ΔE = 8.145, meaning that the inhibitor (3) molecule represent the highest reactivity, compared to the other anticorrosive ΔE = 8.527 for (1) and ΔE = 8.969 for (2) and, consequently, the better inhibition efficiency in accordance with the experimental observations (Figure 7).
It has been revealed also that, the dipole moment parameter depicts another informative quantity that informs us on molecule polarizability with the metal surface. Moreover, it is usually recognized that the anticorrosive efficiency is supposed to be highest for anticorrosive molecules with a greater dipole moment quantity. As expected, and once again in good agreement with the experimentally determined corrosion inhibition efficiency, the dipole moment for pyrimidine derivative (3) is 5.224 Debye, proves much greater than for (1) and (2), in which the values are 2.561 and 1.440 Debye, respectively.
The electroaccepting and electrodonating powers, ω + and ωare defined as (56,57) v in which ω + and ωrepresents respectively, the measure of the propensity of a given system to accept and to donate charge. It should be noted that a greater value of ω + reflects a better capacity of system to accepting charges, while a weaker value of ω + corresponds to a favorable electron donor character. Both quantities are determined by employing the vertical ionization energy I and electron affinity A and registered in Table 6.  Note that according to these definitions and as mentioned in Table 6 the pyrimidine derivative (3) is the molecule with the more capability to donate charge with ω -= 5.622.
The fraction of electrons transferred (ΔN) from the anticorrosive molecule to the metallic atom, can be also calculated by using the equation below (58-61) where χ Fe and χ inh , η Fe and η inh denotes the absolute electronegativity and hardness of iron and anticorrosive molecule, respectively. The theoretical reported value of χ Fe = 7 eV and η Fe = 0 (38,(54)(55)(56), owing to the features of the neutral metallic atoms. It is well known that the difference in electronegativity drives the electron transfer. Indeed, electrons displace from the anticorrosive molecules presenting the lower electronegativity value toward metal surface with a greater value of electronegativity, until the chemical potential equilibrium is achieved.
The theoretical values of the fractions transferred are presented in Table 6. It has been found that a great value of ΔN is associated with a high anticorrosive efficiency. Even more, our results indicate a similar previous behavior, since the greater value obtained of ΔN corresponds to pyrimidine derivative (3) with ΔN = 0.581, showing thus the more effective anticorrosive behavior.
In the literature (57), it has been reported that an electronic back-donation process may control the anticorrosive molecule-metallic surface interaction. According to this concept, in the case where the two processes namely charge transfer to the molecule and backdonation from the molecule occurs simultaneously, the change of energy show a direct proportionality to the hardness of the molecule, as defined in the following formula (62): If η > 0 and ΔE Back-donation < 0, this implies that backdonation from the molecule to metal is energetically favored. The results reported in Table 6 denote that ΔE Back-donation < 0 for our anticorrosive molecules (1-3), thus the charge transfer to an anticorrosive molecule followed by back-donation from the anticorrosive molecule is energetically favorable. This allows us to make a comparison within inhibiting molecules in relation to their stabilization, knowing that the inhibition efficiency increase in association with better adsorption of the molecule on the metallic surface, and consequently the anticorrosive efficiency ought to increase when the stabilization energy increases resulting from anticorrosive molecule-metallic surface interaction. In consistency with the experimental results and as expected, the calculated ΔE Back-donation values display the tendency: (3) > (1), (2).