Understanding the Adsorption of Quinoxaline Derivatives as Corrosion Inhibitors for Mild Steel in Acidic Medium: Experimental, Theoretical and Molecular Dynamic Simulation Studies

Lgaz H1,2, Salghi R2, Jodeh S3 , Ramli Y4, Larouj M1, Toumiat K5, Quraishi MA6*, Oudda H1 and Jodeh W7 1Faculty of Science, University Ibn Tofail, Morocco 2Laboratory of Applied Chemistry and Environment, Ibn Zohr University, Morocco 3Department of Chemistry, An-Najah National University, Nablus, State of Palestine 4Medical and Pharmaceutical College, University Mohammed V, Morocco 5Department of Materials Sciences, Laghouat University, Algeria 6Department of Chemistry, Indian Institute of Technology, Uttar Pradesh, India 7Department of Human Medicine, An-Najah National University, Palestine


Introduction
Mild steel is an iron-containing alloy, considered as one of important constructional materials extensively used in different applications. Generally, acid solution (especially hydrochloric acid) plays a significant role in many fields of industry such as pickling, descaling and oil well acidification, its price is generally low and more consistent [1,2]. In the few last decades the use of chemical compounds as corrosion inhibitors is considered as one of the efficient and practical methods to protect the metals surfaces against aggressive mediums such as acidic solutions [3][4][5]. The effectiveness of these molecules is mainly from their ability to adhere to metal surfaces [6]. The use of synthetic inhibitors also appears to be economically viable and promising because of their simplicity in application, and they're relatively cheaper. Meanwhile, the adsorption of these inhibitors produces a protective insoluble film on the MS surface, which reduces contact with the corrosive mediums and consequently the degree of metal attack [7][8][9]. The presence of N, O, S atoms and conjugates aromatic nucleus are responsible for their essential characteristics [10]. The quinoxaline is one of the important heterocyclic compounds; they have applications in many fields such as electroluminescent materials [11,12] and in the pharmacological industry [13,14] as well as in metallic industries [15,16], this indicates that the use of the quinoxaline derivatives as inhibitors is very interesting [17,18]. The high efficiency of these compounds against corrosion can be in their rich molecular structure, which explains the high capability of these molecules to overcome corrosion. Recently, in addition to experimental investigations, the evaluation of inhibition performance is also conducted theoretically by DFT calculation and molecular dynamic simulation studies for the understanding of some experimentally unknown properties, exploring and establishing relationships between inhibitor molecules and the metal surface [19,20]. N.A. Al-Mobarak et al. [21] have studied the corrosion inhibition of copper in 3.5% NaCl using new pyrimidine derivatives, namely, 2-mercapto-4-(p-methoxyphenyl)-6-oxo-1,6dihydropyrimidine-5-carbonitrile (MPD) by Monte Carlo simulation and theoretical calculation, and all quantum analysis correlated well with electrochemical investigation. In addition, Youguo Yan et al. [22] have applied the DFT method using the GGA/PW91 functional with the double numerical plus d-functions basis set to investigate the adsorption behavior of three purine compounds, A, B and C on the Fe (0 0 1) surface. The theoretical results, including global molecular reactivity descriptors and active sites by Fukui functions analysis well support the order of the IE%. They also applied molecular dynamic simulation to predict the inhibitive performance of purines studied, the tested molecules adsorbed parallel onto Fe (0 0 1) surface, and the order of interaction energy support the experimental IE%. Using combined quantum chemical and molecular dynamic simulation studies, S. Kr. Saha et al. [23] also studied the adsorption characteristics of two aminobenzonitrile derivatives, (2-AB) and (3-AB) to understand the inhibition mechanism of steel corrosion in acidic medium (HCl).
The quantum chemical parameters QCPs reveals that the electron donation and electron acceptance capability of 2-AB and 3-AB are in well accordance with experimental IE%. While, the MD simulation reveals that the distance between active sites and Fe (1 0 0) atoms are lying within a range of 3.5 Å, indicating that a chemical bonds are formed during the interaction of the inhibitors on the Fe (1 1 0) surface. Recently, Z. Zhang et al. [24] applied the radial distribution function (RDF) to study the mechanism of adsorption processes and the synergistic inhibition effect between indigo carmine and three cationic molecules on CS, in an acidic solution. The researchers reported that the bonding length of all heteroatoms-Fe and carbons-Fe are less than 3.5 Å, suggesting that the adsorption of indigo carmine and their cationic molecules occur mainly by these atoms. In addition, Si-Wei Xie et al. [25] also introduced the RDF accompanying with DFT and experimental studies to investigate the inhibitive performance of 3,5-dibromo salicylaldehyde Schiff 's base. The results obtained revealed that C, N, O and S atoms of three studied inhibitors are the most reactive sites responsible of efficiency of the tested compound. This work aims to evaluate the inhibitory properties and adsorption characteristics of three synthetic quinoxaline derivatives of the MS in 1.0 M HCl, using the weight loss (WL), electrochemical techniques (EIS and PDP) and surface examination by SEM. Quantum chemical parameters (QCPs) by DFT method and Monte Carlo simulation accompanying with radial distribution function (RDF) of the (E)-3styrylquinoxalin-2(1H)-one (STQ), (E)-1-benzyl-3-(4-methoxystyryl) quinoxalin-2(1H)-one (BMQ) and (E)-3-(2-(furan-2-yl) vinyl) quinoxalin-2(1H)-one (FVQ) were calculated and discussed.

Inhibitors preparation
The tested inhibitors, namely (E)-3-styrylquinoxalin-2(1H)one (STQ), (E)-1-benzyl-3-(4-methoxystyryl)quinoxalin-2(1H)-one (BMQ) and (E)-3-(2-(furan-2-yl)vinyl)quinoxalin-2(1H)-one (FVQ) were synthesized according to this experimental procedure: The bibliography reports various methods to prepare styrylquinoxalines [26,27]. For our part, we suggested a different synthetic route which comprised reacting fusion 3-méthtylquinoxaline-2-one with aromatic aldehydes. This method was carried out in the absence of solvent. We had a possibility to isolate the desired compound in a yield of around 80% (Scheme 1). Indeed, 6.25 mmol of 3-méthylquinoxalin-2-one was fused with 12.5 mmol of the benzaldehyde for 2 hours, at the boiling temperature of the latter. At the end of the reaction, the solid compound is allowed to cool and then heated at 100°C for 10 minutes in 50 ml of ethanol. The product is filtered hot then washed with ethanol [5,28]  To a solution of (E)-3-(4-methoxystyryl)quinoxalin-2(1H)one in 20 ml of dimethyl formaldehyde was added (chloromethyl) benzene (0.85 ml), K2CO3 (1 g) and catalytic amount of tetrabutylammoniumbromide. The mixture was stirred at room temperature for 24 h. Then the solvent was remove under reduce pressure, the residue was crystallized in ethanol to afford the (E)-1allyl-3-(4-methoxystyryl) quinoxalin-2(1H)-one [29]. (Scheme 2). 6.25 mmol of 3-methylquinoxalin-2(1H)-one was merged with 12.5 mmol of the furan-2-carbaldehyde for 2 h, at the boiling temperature of the latter. At the end of the reaction, the solid was allowed to cool and then heated to 100°C for 10 min in 50 ml of ethanol. The product was filtered hot and washed with ethanol (Scheme 3).
Electrolytic solution and concentration range: Acid solutions (1.0 M HCl) were prepared by diluting a reagent of analytical grade HCl 37% (from Sigma-Aldrich) with double-distilled water. The concentration range of the quinoxaline derivatives used was 2 to 8 mM.

Weight loss tests, electrochemical measurements and surface observation:
In this study, the effects of quinoxaline derivatives (BMQ, FVQ and STQ) on the metal corrosion were performed by the electrochemical measurements (EIS and polarization curves), and weight loss (WL) tests (temperature range of 303 to 333 K). The detail of experiments referenced from the published article of Rachid Salghi et al. [4,30,31].

Molecular modeling and dynamic simulations:
All quantum chemical calculations of quinoxaline derivatives were performed at the DFT/B3LYP level of theory using 6-31G (d, p) basis set with Gassian03 program [32][33][34][35]. The adsorption configuration of BMQ, FVQ and STQ on iron surface were dynamically simulated by using the Adsorption Locator module of the Materials Studio 6.0 software from Accelrys Inc [36]. The Fe crystal was chosen to represent the MS surface. First the crystal was cleaved along the (1 1 0) plane, as it is the most stable surface as reported in the literature [37]. Then, the Fe (1 1 0) plane was subsequently enlarged into an appropriate supercell to provide a large surface for the interaction of the inhibitor. The interaction between BMQ, FVQ, STQ and Fe surface was assumed in a simulation box (29.78 × 29.78 × 60.13 Å) with periodic boundary conditions. After that, thickness of the vacuum slab was 50 Å. COMPASS force field was chosen to optimize the structures of all components of the system of interest. More detail of MC simulation is referenced from the published articles [37,38].

Results and Discussion
Weight loss measurement Effect of concentration and temperature: The inhibitive efficiency calculated by the Eq. (1) of BMQ, FVQ and STQ in the corrosive medium of the MS was carried out after immersion for 6 h at 303 to 333 K, in all studied concentrations by weight loss measurements. The results are presented in Table 1 and Figure 1 (Similar plots obtained for 313-333 K, but not presented in this article).
size of quinoxaline compounds. The high protection of our molecules is due to their adsorption on steel surface, which decreases the fatal effect of aggressive medium.

Activation parameters:
The inhibitive mechanism can be understood based on the thermodynamic and activation parameters. From Table 1, it can be observed that C R depends on temperature for all inhibitor concentrations. The C R is related to the temperature by the following Eqs. (2,3) [39]: where, a E is the activation energy,  Table 2. We can be find from Table 2 that the Ea (Inh) > Ea (Blank), which can be explained by the physical adsorption of quinoxaline molecules [40]. For three inhibitors, the value of the activation energy to take up higher maximum for the higher concentrations; and generally follows the order of Ea (BMQ) > Ea (FVQ) > Ea (STQ), this order is in good agreement with the order of inhibition efficiencies, that decreased with the increase of the temperature. In the same case, Saranya et al. [17] studied the inhibition effect of Acenaphtho [1,2-b] quinoxaline on the MS dissolution in acidic environment, the effect of temperature study reveals that the IE% decrease with the increase of the temperature and the E a value decrease remarkably than the value obtained in blank solution, which in good correlation with our investigation (Figure 4).
The positive sign of the enthalpy (Table 2) reflects the endothermic nature of the MS dissolution process. While the higher values of ΔSa in presence of investigated compounds compared to those calculated from the uninhibited solution might be the result of the adsorption of quinoxaline derivatives from the aggressive solution, which could be regarded as a quasi-substitution process between inhibitor molecules in the aqueous phase and water molecules on the MS surface [41,42].

Adsorption isotherm and thermodynamic parameters
On the basis of evaluation of the interaction between the inhibitors and steel surface, it is important to consider the adsorption isotherms to analyze the mechanism and nature of the adsorption processes of chemicals species on the MS surface [43]. For additional information about the compounds tested, several types of adsorption isotherms carried out such as Frumkin (Eq. 4), Temkin (Eq. 5), Freundlich (Eq. 6) and Langmuir (Eq. 7) among which the Langmuir isotherm showed the best fit with regression coefficient (R 2 ) values close to unity for all tested compounds. Considering a sufficient time for adsorption equilibrium, the fractional surface coverage (ɵ) can be easily calculated by η w (%)/100 from weight loss tests [44]: C R and C R(inh) are the corrosion rates in the absence and presence of BMQ, FVQ and STQ, respectively. Prominent decrease of the C R observed because of the addition of various concentrations of quinoxaline derivatives, while the IE% increases with increasing the concentration of tested inhibitors at the range of studied temperature. Over temperature increase the IE% of our molecules is reduced due to partial desorption of studied compounds. The IE% values of BMQ decreased slowly (95.07% to 88.19% in 8 mM) compared with those of FVQ and STQ (η w % reduced to 86.17% for FVQ and 82.99% for STQ) following the order: BMQ > FVQ > STQ. This can be attributed to the difference in molecular Temp.

Concentration
(mM)  ( ) Where: C is the concentration of inhibitors in the electrolyte, K ads is the equilibrium constant for the adsorption-desorption process, θ is the surface coverage and f is the molecular interaction constant. The values of K ads can be calculated from the intercepts of the straight lines C inh / θ-axis. The K ads related to the standard free energy of adsorption ads G°∆ by following Eq.  Table 3. The values of K ads could take as an indication of the adsorption ability of BMQ, FVQ and STQ on the steel surface. On the other hand, the K ads values follow the order: K ads (BMQ) > K ads (FVQ) > K ads (STQ). This further confirms that n w (%) decreases with the increase in temperature and the better inhibitive performance of BMQ than the others compounds. The negative values of ads G°∆ imply that the adsorption was spontaneous and the stability of the adsorbed film on the MS surface [45]. All the ads G°∆ values are around -13 kJ/mol. normally; the physical adsorption is correlated with the absolute values of ΔG° around 20 kJ/mol or lower, and a value of ads G°∆ up to 40 kJ/mol or more negative is an indication of the chemical adsorption [46,47]. The ads G°∆ values in Table 3 indicate clearly the physical adsorption of tested compounds on the MS surface. In the literature, we can find in the investigation of Obot et al. [17] that the 2,3-Diphenylbenzoquinoxaline interact with the MS in the same way in sulphuric acid, the authors reported that the ads G°∆ is -11.4 kJ mol -1 , which explained by the electrostatic interaction with tested quinoxaline derivative and the MS surface. The ΔH ads and ΔS ads calculated by the following Eq.   The values of ΔH ads and ΔS ads are collected in Table 3 values of quinoxaline derivatives are negative, indicating the exothermic process of adsorption of studied inhibitors. The endothermic adsorption process 0 ads H°∆ > is correlated to chemical adsorption, while the exothermic adsorption process 0 ads H°∆ < is attributed to physical, chemical or mixture adsorption [48]. In an exothermic process, the physisorption process is correlated with the values of ads H°∆ lower than 40 kJ mol -1 . Whereas, chemical adsorption is for ads H°∆ values around 100 kJ mol -1 . In this investigation, ads H°∆ values of all quinoxalines derivatives are less than 40 kJ mol -1 , suggesting that the physical adsorption may occur during the interaction between the tested compounds and the MS surface. The negative values of ads S ∆ indicates that before the adsorption of inhibitor's molecules on the MS surface, inhibitor molecules might freely move in the bulk solution, but with the progress in the adsorption of BMQ, FVQ and STQ, inhibitors molecules were orderly adsorbed on the MS surface, as a result a decrease in entropy is observed [49]. Based on the thermodynamic principles, it can be noted that since the adsorption is an exothermic process, it must be accompanied by a decrease of entropy [50].

Potentiodynamic polarization study
The polarization experiments were undertaken to distinguish the behavior of the corrosion of the MS with and without studied concentrations of BMQ, FVQ and STQ at 303 K. The Tafel plots and the derived parameters are presented in Figures 5a-5c and Table 4, respectively. The IE% is calculated using the following Eq. It can be observed from Figures 5a-5c, that the addition of quinoxaline derivatives caused a decrease in the anodic and cathodic current densities with slight shifting of the corrosion potential ( corr E ), indicating that the quinoxaline derivatives investigated are mixed type inhibitors [53,54]. The small change of the constant cathodic Tafel slope, βc, suggests that the mechanism of proton discharge reaction does not modify by addition of quinoxaline derivatives [55,56]. From Table 4, it can be found that the increase of the concentration of our molecules result in a considerable decrease of the corr I values. In the same trend, a remarkable increase of the IE% is observed when increasing the inhibitors concentration reaching a maximum value at 8 mM in the three quinoxaline derivatives studied. It is also evident that BMQ presents the better performance than other inhibitors, which can be correlated to the difference of the structure of the three inhibitors molecules ( Figure 6).

AC impedance study
Nyquist plots of the MS in acidic solutions with and without various concentrations of STQ, FVQ and BMQ at 303 K after 30min of immersion are given in Figures 7a-7c. Which a single capacitive loop is clearly observed over the frequency range studied [57,58]. Also appearing are depressed Nyquist plots into the real axis and imperfect semicircles, what can explained by the non-homogeneity and roughness of the MS surface [59]. As previously reported for steel/ acid interface, the EIS data obtained was fitted using the Rs(CPE/ Rct) equivalent circuit (Figures 8 and 9) [60], where Rs is the solution resistance, R ct denotes that the charge-transfer resistance and CPE is "constant phase element". The introduction of CPE was necessitated to compensate deviations from ideal capacitor due to distributed surface heterogeneity. The impedance of this element is frequency-dependent and can be calculated using the Eq. (11)

( j )
Where Q is the CPE constant (in Ω -1 S n cm -2 ), ω is the angular frequency (in rad s -1 ), j 2 = -1 is the imaginary number and n is a CPE exponent which can be used as a gauge for the heterogeneity or roughness of the surface [63]. The electrochemical parameters derived from the fitting of impedance spectra are collected in Table 5. The IE% was calculated by the Eq. (12): Where: R°c t and R ct are the charge transfer resistances without and with various concentrations of inhibitors respectively. According to the values of R ct displayed in Table 5, the R ct value increase considerably with rising in inhibitors concentration (from 231.1 to 847.1Ω for BMQ) resulting in a slower corrosion of steel due to the adsorption of quinoxaline derivatives on metal surface [64,65]. Regarding, the double layer capacitances, C dl is associated with a CPE by the following Eq.(13) [66]: The C dl values were decreased, so that the C dl values reached 15.09 μFcm -2 for BMQ, 18.48 μF cm -2 for FVQ and 21.07 μF cm -2 for STQ considering 85.89 μF cm -2 for the uninhibited solution. On the other side, the values of the proportional factor Q of CPE increase when decreasing the concentration of the quinoxaline derivatives. These results are probably correlated with the adsorption of the three inhibitors on steel surface [66,67]. Accordingly, the values of n lies between 0.89 and 0.92 for inhibited solutions, the addition of quinoxaline derivatives increased n values, indicating the increase in in-homogeneity of the MS surface, due to the adsorption of the our inhibitors [68,69].
The inhibition efficiency values in the absence and presence of BMQ, FVQ and STQ yielded 96.53%, 94.98% and 93.73% in the highest concentrations, respectively with the following order: BMQ > FVQ > STQ. This order can be explained by the presence of a phenyl and (-OCH 3 ) in BMQ, which raised their reactivity.

SEM analysis
SEM photomicrographs of the surface of MS were immersed for 6 h in a corrosive medium with and without 8 mM of STQ, BMQ and FVQ. Results are displayed in Figures 10a-10e. In acidic environment, obvious dissolution can be observed without the presence of any inhibitors. In presence of BMQ, FVQ and STQ, it can be seen (Figures  10a-10c) that the surface of the MS was improved, smooth, and that less pits and less damage was observed, This demonstrates the formation of insoluble film, resulting from the adsorption of BMQ, FVQ and STQ on the MS surface. These observations support the high inhibition performance of the quinoxaline derivatives.

Quantum chemical calculations
Global molecular reactivity: We attempted to interpret the main factors responsible for the reactivity of the investigated quinoxaline derivatives and to analyse the capability of our molecules to donate and accept electrons to/and from the MS surface. The optimized structures of the quinoxaline derivatives molecules were calculated and presented in Figure 11. The QCPs such as E HOMO , E LUMO , ΔE = (E LUMO -E HOMO ), total energy (TE), softness (σ), the fraction of electrons transferred (ΔN) and dipole moment (μ) were collected in Table 6. The IE% of BMQ, FVQ and STQ according to our experimental studies is:

BMQ > FVQ > STQ
In Figure 11, The HOMO and LUMO orbitals are distributed over the entire quinoxaline molecules, resulting in the highest interaction of quinoxaline derivatives studied on the MS surface. This observation also suggests that the heteroatoms and the cycle rings containing π-bonds are the probable reactive sites for adsorption of inhibitors on the metal surface. Normally, E HOMO is often indicated the ability of a molecule to donate electrons; this ability becomes more considerable with a high value of E HOMO . While, the lowering of E LUMO is often associated with the capability of an inhibitor to accept electrons [70,71]. The ΔE = (E LUMO -E HOMO ) was reported as a main chemical reactivity factor of an inhibitor from theoretical point of view [71]. According to these literature findings and the results from Table 6, it can be observed that our compounds have higher interactions with the steel surface. The reactivity of BMQ, FVQ and      • The theoretical values of χ Fe (4.06 eV mol -1 ) and of η Fe (0 eV mol -1 ) are used to calculate ∆N [75,76]. The results from Table 6, show that the order of electron transfer is such that BMQ > FVQ > STQ which also confirms that BMQ has the highest tendency to donate electrons and therefore the highest tendency to bind onto the metal surface [76,77].
The hard-soft-acid-base (HSAB) theory introduced by Pearson [78] can be used in correlation with the FMO theory to understanding the tendencies of the inhibitors to bonding towards the MS atoms [79]. According to HSAB theory, hard acids prefer to co-ordinate to hard bases to give ionic complexes and soft acids prefer binding to soft bases to give covalent complexes. On the other hand, metal atoms are definite as soft acids. Hard molecules have a high value of ∆E HOMO-LUMO . In contrast, soft molecules have a small ∆E HOMO-LUMO [80]. Thus soft base compounds are the most capable to bind with metal atoms. So, the BMQ compound which has the lowest ∆E HOMO-LUMO and the highest softness has mostly been confirmed by calculating the softness, σ, to measures the reactivity of a molecule: σ = 1/ η, (Table 6). It was observed that BMQ compounds have the highest σ value and the order at which softness increases, so that the reactivity will be: Figure 12 shows the relationship between the FMO of quinoxaline compounds studied and their energy gap ∆Eg. BMQ, FVQ and STQ have low energy gap, which facilitate their adsorption. The order of the reactivity of tested molecules is clearly observed from this figure by considering a small difference between the energy of HOMO and LUMO [81,82].

Actives sites:
To investigate reactive sites in the tested inhibitors, molecular electrostatic potential (MESP) provides a visual method to understand the region of the electrophilic attack, nucleophilic attack and the electrostatic potential zero regions [83]. The total electron density surface mapped with molecular electrostatic potential (MEP) and contour representation of electrostatic potential of BMQ, FVQ and STQ are collected in Figures 13a-13b, respectively. In these maps, different values of the MESP were demonstrated with the help of different colors, which are red, yellow, green, light blue and blue. The red and yellow colors suitable for the negative parts of the MEP are linked to electrophilic reactivity, blue colors suitable for the positive parts to the nucleophilic reactivity and the green color represents the ESP zero region. In Figures 13a-13c, the red and yellow sites are mainly observed over the benzene ring, the heteroatoms (N13, N14, and Oxygen atoms) and the conjugated double bonds, the blue and light blue sites are mainly localized around the second atom of nitrogen and benzene ring. The green regions stand for the zero electrostatic potential.
These remarks confirmed by the Mulliken charges of the inhibitor atoms as can be seen in Figure 13c [84]. As noticed that the MS acting as an electrophilic, and the nucleophilic centers are heteroatoms with free electron pairs and π-systems in the conjugated double bonds. The inhibitors can promote formation of a chelate on the MS surface by transferring electrons from tested molecules to Fe-atoms (d-orbital) and forming a coordinate covalent bond through the adsorption process [85].
In order to analyze the active sites of BMQ, FVQ and STQ, Fukui indices was used to measure the local reactivity of the inhibitors molecules and indicate their chemical reactivity for nucleophilic and electrophilic nature. The condensed Fukui functions can be computed unambiguously using a scheme of finite difference approximations such as [86]: where ( )

Monte Carlo (Molecular dynamic) simulation
Molecular dynamics (MD) simulation provides considerable information about the physical movements of atoms and molecules, which gives a view of the motion of the atoms after interaction at a certain time. Figure 14 represents the top and side views of the most suitable configuration for adsorption of quinoxaline derivatives on Fe (1 1 0) substrates obtained by Monte Carlo simulation. The total energy, average total energy, van der Waals energy, electrostatic energy and intramolecular energy for BMQ/Fe (1 1 0) surface were calculated by optimizing the whole system; the curves are presented in Figure 15. The outputs and descriptors calculated by the Monte Carlo simulation are presented in Table 10. It is clearly observed from Figure 14 that the three quinoxaline derivatives adsorbed very nearly and in parallel to the Fe (1 1 0) surface in so as to maximize surface contact. This adsorption process occurs mainly through the formation of the insoluble film on the Fe (1 1 0) surface. It is generally noted that the adsorption process is the primary mechanism of corrosion inhibitor interaction with the MS. According to Table 10, the adsorption energies of BMQ, FVQ and STQ on the Fe (1 1 0) surface increased in the order BMQ > FVQ > STQ. The high negative values of adsorption energy of quinoxaline derivatives resulted in the strong interactions between mild steel and inhibitors molecules [87,88]. Which is in good accordance with the order of the IE% obtained by experimental and theoretical studies.

Radial distribution function (pair correlation function)
Pair correlation function was done in order to characterize the bond length and understand the interactions of the liquid and solid materials. The pair correlation function analysis can be calculated from the trajectory output of Monte Carlo simulation, and the basic information of molecule-molecule interaction can be obtained by the calculation of bonding length. Approximately, the bond lengths of van der Waals interaction are around 5 Å ~ 10 Å, while, bond lengths around 2 Å ~ 3 Å exist for metal complexation, and H bond lengths Energy (Kcal/mok) Step Figure 15: A typical energy profile for the adsorption progress of BMQ on Fe (110) surface using the Monte Carlo sampling procedure.
exist at around 2 Å ~ 3.5 Å. The pair correlation function, g(r), of C, N, and O of quinoxaline derivatives atoms and surface atoms was depicted in Figure 16. Generally, the chemical bonds can be formatted in correlation with the peak within 3.5 Å, while the Van der Waals force or Coulomb force interactions are correlated with the peak outside of 3.5 Å. We will consider the distribution of heteroatoms according to their importance on the adsorption process of chemical compounds on the metal surface, while, the carbons atoms reactivity can be obtained from π-system. For STQ, the highest peaks of the pair correlation function curve of O, C and N atoms appear at 3.43 Å, and the interactive force of these atoms on the Fe (1 1 0)

Conclusion
The synthesized quinoxaline derivatives act as good corrosion inhibitors for the MS in 1.0 M HCl solution and the inhibiting performance of BMQ is better than FVQ and STQ. Polarization results    showed that all tested inhibitors are of mixed type in nature. In the presence of all inhibitors, charge transfer resistance increases and double layer capacitance decreases due to adsorption of the inhibitors' molecules on the MS surface. The experimental results showed that the quinoxaline derivatives adsorb spontaneously on the MS surface and conform to the Langmuir adsorption isotherm. The adsorption process involves physical adsorption. DFT calculations, Monte Carlo simulation and RDF were performed to identify the reactivity of these molecules towards corrosion inhibition, and the results are in good agreement with the experimental investigations. Both experimental and quantum chemical results showed that the order of inhibition efficiency, for the studied compounds is as follows: BMQ > FVQ > STQ.